************** MAGMA *****************
Host ip074081.uvm.edu. (132.198.74.81)
Time: Thu Jun 17 15:52:13 2004

Input: 2+2

Output: Magma V2.10-22    Thu Jun 17 2004 15:52:11 on modular  [Seed = 1354884646]
   -------------------------------------

4

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Thu Jun 17 20:49:07 2004

Input:  RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;


Output: Magma V2.10-22    Thu Jun 17 2004 20:49:04 on modular  [Seed = 2923221632]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO103.gate.nec.co.jp. (210.143.35.13)
Time: Thu Jun 17 20:49:37 2004

Input:  RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;
RnadomHEC_3_2();


Output: Magma V2.10-22    Thu Jun 17 2004 20:49:34 on modular  [Seed = 2788481687]
   -------------------------------------


>> RnadomHEC_3_2();
   ^
User error: Identifier 'RnadomHEC_3_2' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Thu Jun 17 20:49:52 2004

Input:  RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;
RandomHEC_3_2();


Output: Magma V2.10-22    Thu Jun 17 2004 20:49:49 on modular  [Seed = 3190604477]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x + 1)*y = x^7 + x^5 + x^4 + x over 
GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO102.gate.nec.co.jp. (210.143.35.12)
Time: Thu Jun 17 20:50:14 2004

Input:  RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;
RandomHEC_3_2();


Output: Magma V2.10-22    Thu Jun 17 2004 20:50:11 on modular  [Seed = 2401104866]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x^3 + x + 1)*y = x^7 + x^6 + x^5 + 
    x^3 + x^2 over GF(2)

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO111.gate.nec.co.jp. (202.32.8.233)
Time: Thu Jun 17 20:50:40 2004

Input:  RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;
RandomHEC_3_2();
h; f;

Output: Magma V2.10-22    Thu Jun 17 2004 20:50:37 on modular  [Seed = 2266364916]
   -------------------------------------

false

>> h; f;;
   ^
User error: Identifier 'h' has not been declared or assigned

>> h; f;;
      ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 20:51:01 2004

Input:  RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 20:50:58 on modular  [Seed = 2618220736]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO102.gate.nec.co.jp. (210.143.35.12)
Time: Thu Jun 17 21:00:26 2004

Input: 
 // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
// TEST1
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 21:00:23 on modular  [Seed = 3394810947]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + x*y = x^7 + x^6 + x^4 + 1 over GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Thu Jun 17 21:30:11 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(1); v1:=P!(0);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 21:30:08 on modular  [Seed = 211683715]
   -------------------------------------

1
0

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 21:53:28 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 21:53:25 on modular  [Seed = 1710714463]
   -------------------------------------

x
1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Thu Jun 17 21:53:43 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x); v2:=P!(1);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 21:53:40 on modular  [Seed = 2112845430]
   -------------------------------------

1
0

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO103.gate.nec.co.jp. (210.143.35.13)
Time: Thu Jun 17 21:54:30 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x); v2:=P!(1);
C:=HyperellitpicCurve([f,h]);
C;


Output: Magma V2.10-22    Thu Jun 17 2004 21:54:27 on modular  [Seed = 1978105353]
   -------------------------------------


>> C:=HyperellitpicCurve([f,h]);
      ^
User error: Identifier 'HyperellitpicCurve' has not been declared or assigned

>> C;
   ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Thu Jun 17 21:54:48 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x); v2:=P!(1);
C:=HyperellipticCurve([f,h]);
C;


Output: Magma V2.10-22    Thu Jun 17 2004 21:54:45 on modular  [Seed = 1306478087]
   -------------------------------------

Hyperelliptic Curve defined by y^2 + x*y = x^7 + x^6 + x^4 + 1 over GF(2)

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Thu Jun 17 21:55:14 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x); v2:=P!(1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);


Output: Magma V2.10-22    Thu Jun 17 2004 21:55:12 on modular  [Seed = 1171738346]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 21:55:28 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x); v2:=P!(1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;

Output: Magma V2.10-22    Thu Jun 17 2004 21:55:25 on modular  [Seed = 1573869311]
   -------------------------------------

24

Total time: 2.509 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Thu Jun 17 21:56:14 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 21:56:11 on modular  [Seed = 1439129281]
   -------------------------------------

false

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Thu Jun 17 21:56:21 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 21:56:18 on modular  [Seed = 2906629696]
   -------------------------------------

false

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO102.gate.nec.co.jp. (210.143.35.12)
Time: Thu Jun 17 21:56:27 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 21:56:24 on modular  [Seed = 2771889730]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Thu Jun 17 21:56:42 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 21:56:39 on modular  [Seed = 3174020677]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 21:56:55 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1


Output: Magma V2.10-22    Thu Jun 17 2004 21:56:52 on modular  [Seed = 3039280766]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Thu Jun 17 21:57:06 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
RandomHEC_3_2();

Output: Magma V2.10-22    Thu Jun 17 2004 21:57:03 on modular  [Seed = 2367653453]
   -------------------------------------

false

Total time: 2.479 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Thu Jun 17 21:57:21 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// TEST1
RandomHEC_3_2();
//

Output: Magma V2.10-22    Thu Jun 17 2004 21:57:18 on modular  [Seed = 2232913492]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x^3 + x + 1)*y = x^7 + x^2 + 1 over 
GF(2)

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Thu Jun 17 21:59:47 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// 2
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x+1);
f:=P!(x^7 + x^2 + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#C;

Output: Magma V2.10-22    Thu Jun 17 2004 21:59:45 on modular  [Seed = 2601096997]
   -------------------------------------

1

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO111.gate.nec.co.jp. (202.32.8.233)
Time: Thu Jun 17 22:04:12 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// &#65299;
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
u1:=P!(1); v1:=P!(0);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 22:04:09 on modular  [Seed = 4285395529]
   -------------------------------------

1
0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 22:04:59 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// &#65299;
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x+1);
f:=P!(x^7+x^2+ 1);
u1:=P!(1); v1:=P!(0);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 22:04:57 on modular  [Seed = 4150655505]
   -------------------------------------

1
0

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 22:05:23 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// &#65299;
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x+1);
f:=P!(x^7+x^2+ 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 22:05:21 on modular  [Seed = 3479028225]
   -------------------------------------

x
1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Thu Jun 17 22:05:35 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// &#65299;
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x+1);
f:=P!(x^7+x^2+ 1);
u1:=P!(x); v1:=P!(0);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 22:05:32 on modular  [Seed = 3344288260]
   -------------------------------------

x
0

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Thu Jun 17 22:05:50 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// &#65299;
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x+1);
f:=P!(x^7+x^2+ 1);
u1:=P!(x); v1:=P!(0);
u2:=P!(x^2); v2:=P!(x);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 22:05:47 on modular  [Seed = 3746419211]
   -------------------------------------

x
0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Thu Jun 17 22:06:15 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
////////////////////////////////////
////////////////////////////////////
// &#65299;
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x+1);
f:=P!(x^7+x^2+ 1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x); v2:=P!(1);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Thu Jun 17 2004 22:06:12 on modular  [Seed = 3611679212]
   -------------------------------------

1
0

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.12.74.6)
Time: Thu Jun 17 23:16:00 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Thu Jun 17 2004 23:15:49 on modular  [Seed = 3039276000]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.12.74.6)
Time: Thu Jun 17 23:17:05 2004

Input: mersenne composite


Output: Magma V2.10-22    Thu Jun 17 2004 23:17:02 on modular  [Seed = 3207438625]
   -------------------------------------


>> mersenne composite
            ^
User error: bad syntax

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 00:46:08 2004

Input: 7+8;

Output: Magma V2.10-22    Fri Jun 18 2004 00:46:05 on modular  [Seed = 2028620740]
   -------------------------------------

15

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Fri Jun 18 00:46:20 2004

Input: 8+9;

Output: Magma V2.10-22    Fri Jun 18 2004 00:46:17 on modular  [Seed = 1626493896]
   -------------------------------------

17

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 00:46:36 2004

Input: 1+1+9+7+67898;

Output: Magma V2.10-22    Fri Jun 18 2004 00:46:33 on modular  [Seed = 1761238000]
   -------------------------------------

67916

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO104.gate.nec.co.jp. (210.143.35.14)
Time: Fri Jun 18 00:47:23 2004

Input: 1+1+9+7+67898;

Output: Magma V2.10-22    Fri Jun 18 2004 00:47:20 on modular  [Seed = 1539926194]
   -------------------------------------

67916

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 00:48:16 2004

Input: 6+7;

Output: Magma V2.10-22    Fri Jun 18 2004 00:48:13 on modular  [Seed = 1171747193]
   -------------------------------------

13

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 00:48:28 2004

Input: 67+78

Output: Magma V2.10-22    Fri Jun 18 2004 00:48:26 on modular  [Seed = 1306491238]
   -------------------------------------

145

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 01:20:19 2004

Input: (0,1) ne (1,1);

Output: Magma V2.10-22    Fri Jun 18 2004 01:20:16 on modular  [Seed = 3445618284]
   -------------------------------------


>> (0,1) ne (1,1);;
   ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO102.gate.nec.co.jp. (210.143.35.12)
Time: Fri Jun 18 01:20:34 2004

Input: [0,1] ne [1,1];

Output: Magma V2.10-22    Fri Jun 18 2004 01:20:32 on modular  [Seed = 916721060]
   -------------------------------------

true

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 01:20:53 2004

Input: [0,1] eq [1,1];

Output: Magma V2.10-22    Fri Jun 18 2004 01:20:50 on modular  [Seed = 1051461054]
   -------------------------------------

false

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 01:28:21 2004

Input: 
 // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve&#36229;&#26965;&#20870;&#26354;&#32218;&#12398;&#29983;&#25104;
// 2nd Step. Computation of the Order of Jacobian
// 3rd Step. Random Generation of the Two Elements of Jacobian
// 4th Step. Computation of Cantor Algorithm
// 5th Step. Scalar Multiplication of the Elements of Jacobian
//  &#65288;&#65297;&#65296;&#65296;&#65296;&#65311;&#20493;&#12375;&#12390;&#12418;&#12476;&#12525;&#12395;&#12394;&#12425;&#12394;&#12356;&#12424;&#12358;&#12394;&#12425;&#12289;&#35336;&#31639;&#12434;&#12473;&#12488;&#12483;&#12503;&#12377;&#12427;&#12290;&#65289;

// 1st Step
RandomHEC_3_2();


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Fri Jun 18 01:28:42 2004

Input: 
 // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve&#36229;&#26965;&#20870;&#26354;&#32218;&#12398;&#29983;&#25104;
// 2nd Step. Computation of the Order of Jacobian
// 3rd Step. Random Generation of the Two Elements of Jacobian
// 4th Step. Computation of Cantor Algorithm
// 5th Step. Scalar Multiplication of the Elements of Jacobian
//  &#65288;&#65297;&#65296;&#65296;&#65296;&#65311;&#20493;&#12375;&#12390;&#12418;&#12476;&#12525;&#12395;&#12394;&#12425;&#12394;&#12356;&#12424;&#12358;&#12394;&#12425;&#12289;&#35336;&#31639;&#12434;&#12473;&#12488;&#12483;&#12503;&#12377;&#12427;&#12290;&#65289;

// 1st Step
RandomHEC_3_2();


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host TYO104.gate.nec.co.jp. (210.143.35.14)
Time: Fri Jun 18 01:29:22 2004

Input: 
 // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve&#36229;&#26965;&#20870;&#26354;&#32218;&#12398;&#29983;&#25104;
// 2nd Step. Computation of the Order of Jacobian
// 3rd Step. Random Generation of the Two Elements of Jacobian
// 4th Step. Computation of Cantor Algorithm
// 5th Step. Scalar Multiplication of the Elements of Jacobian
//  &#65288;&#65297;&#65296;&#65296;&#65296;&#65311;&#20493;&#12375;&#12390;&#12418;&#12476;&#12525;&#12395;&#12394;&#12425;&#12394;&#12356;&#12424;&#12358;&#12394;&#12425;&#12289;&#35336;&#31639;&#12434;&#12473;&#12488;&#12483;&#12503;&#12377;&#12427;&#12290;&#65289;

// 1st Step
RandomHEC_3_2();


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host TYO102.gate.nec.co.jp. (210.143.35.12)
Time: Fri Jun 18 01:29:56 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

Output: Magma V2.10-22    Fri Jun 18 2004 01:29:54 on modular  [Seed = 1961249172]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Fri Jun 18 01:30:21 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;


Output: Magma V2.10-22    Fri Jun 18 2004 01:30:19 on modular  [Seed = 2095989157]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO103.gate.nec.co.jp. (210.143.35.13)
Time: Fri Jun 18 01:30:52 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////



Output: Magma V2.10-22    Fri Jun 18 2004 01:30:49 on modular  [Seed = 1693866591]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 01:31:09 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve&#36229;&#26965;&#20870;&#26354;&#32218;&#12398;&#29983;&#25104;
// 2nd Step. Computation of the Order of Jacobian
// 3rd Step. Random Generation of the Two Elements of Jacobian
// 4th Step. Computation of Cantor Algorithm
// 5th Step. Scalar Multiplication of the Elements of Jacobian
//  &#65288;&#65297;&#65296;&#65296;&#65296;&#65311;&#20493;&#12375;&#12390;&#12418;&#12476;&#12525;&#12395;&#12394;&#12425;&#12394;&#12356;&#12424;&#12358;&#12394;&#12425;&#12289;&#35336;&#31639;&#12434;&#12473;&#12488;&#12483;&#12503;&#12377;&#12427;&#12290;&#65289;


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 01:31:35 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();


Output: Magma V2.10-22    Fri Jun 18 2004 01:31:33 on modular  [Seed = 1472555344]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Fri Jun 18 01:31:44 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();


Output: Magma V2.10-22    Fri Jun 18 2004 01:31:42 on modular  [Seed = 1607295315]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 01:31:51 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();


Output: Magma V2.10-22    Fri Jun 18 2004 01:31:48 on modular  [Seed = 1205172529]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x^3)*y = x^7 + x^6 + x^5 + x^3 + x^2 
    + x + 1 over GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Fri Jun 18 01:33:43 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7 + x^6 + x^5 + x^3 + x^2 + x + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;


Output: Magma V2.10-22    Fri Jun 18 2004 01:33:41 on modular  [Seed = 3190587449]
   -------------------------------------

6

Total time: 2.539 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 01:35:03 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7 + x^6 + x^5 + x^3 + x^2 + x + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P1; P2; P3;

Output: Magma V2.10-22    Fri Jun 18 2004 01:35:01 on modular  [Seed = 2416095143]
   -------------------------------------

6
(1, 0, 0)
(x^2 + x + 1, x, 2)

>> P1; P2; P3;;
           ^
User error: Identifier 'P3' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Fri Jun 18 01:35:51 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7 + x^6 + x^5 + x^3 + x^2 + x + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;

Output: Magma V2.10-22    Fri Jun 18 2004 01:35:48 on modular  [Seed = 2550835102]
   -------------------------------------

6
(x, 1, 1)
(x^3 + x^2 + x, x^2 + 1, 3)
(x^2 + x + 1, x, 2)

Total time: 2.519 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO104.gate.nec.co.jp. (210.143.35.14)
Time: Fri Jun 18 01:41:07 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve&#36229;&#26965;&#20870;&#26354;&#32218;&#12398;&#29983;&#25104;
// 2nd Step. Computation of the Order of Jacobian
//           and Random Generation of the Two Elements of Jacobian
// 3rd Step. Computation of Cantor Algorithm
// 4th Step. Scalar Multiplication of the Elements of Jacobian
// (Calculation is stopped if it seems that it does not become zero 
// even if it doubles 1000.)

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host TYO111.gate.nec.co.jp. (202.32.8.233)
Time: Fri Jun 18 01:41:38 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]

Output: Magma V2.10-22    Fri Jun 18 2004 01:41:35 on modular  [Seed = 3260023423]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO102.gate.nec.co.jp. (210.143.35.12)
Time: Fri Jun 18 01:42:01 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of Jacobian
//           and Random Generation of the Two Elements of Jacobian
// 3rd Step. Computation of Cantor Algorithm
// 4th Step. Scalar Multiplication of the Elements of Jacobian
// (Calculation is stopped if it seems that it does not become zero 
// even if it doubles 1000.)


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 01:42:15 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve


Output: Magma V2.10-22    Fri Jun 18 2004 01:42:12 on modular  [Seed = 866251700]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 01:42:43 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of Jacobian
//           and Random Generation of the Two Elements of Jacobian
// 3rd Step. Computation of Cantor Algorithm

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO111.gate.nec.co.jp. (202.32.8.233)
Time: Fri Jun 18 01:43:02 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of Jacobian
//           and Random Generation of the Two Elements of Jacobian


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 01:43:12 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of Jacobian
// and Random Generation of the Two Elements of Jacobian


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 01:43:34 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of Jacobian
// and Random Generation of the Two Elements of `Jacobian'


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 01:43:44 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of Jacobian
// and Random Generation of the Two Elements of jacobian


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 01:43:51 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the Order of jacobian
// and Random Generation of the Two Elements of jacobian


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Fri Jun 18 01:44:02 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve
// 2nd Step. Computation of the order of jacobian
// and Random Generation of the Two Elements of jacobian


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 01:44:22 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// Test Code [1]
// 1st Step. Genration of Hyperelliptic Curve


Output: Magma V2.10-22    Fri Jun 18 2004 01:44:20 on modular  [Seed = 1659937637]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 01:46:24 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 3rd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7+x^6+x^5+x^3+x^2+x+1);
u1:=P!(x); v1:=P!(1);
u2:=P!(x^3+x^2+x); v2:=P!(x^2+1);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Fri Jun 18 2004 01:46:21 on modular  [Seed = 1104380127]
   -------------------------------------

x^2 + x + 1
1

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 01:48:45 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7+x^6+x^5+x^3+x^2+x+1);
u1:=P!(x); v1:=P!(1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u1,v1] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;


Output: Magma V2.10-22    Fri Jun 18 2004 01:48:42 on modular  [Seed = 3106634673]
   -------------------------------------

1
0
1001

Total time: 2.699 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO111.gate.nec.co.jp. (202.32.8.233)
Time: Fri Jun 18 01:49:35 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7+x^6+x^5+x^3+x^2+x+1);
u1:=P!(x); v1:=P!(1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;


Output: Magma V2.10-22    Fri Jun 18 2004 01:49:33 on modular  [Seed = 2704499711]
   -------------------------------------

1
0
2

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 01:51:48 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();


Output: Magma V2.10-22    Fri Jun 18 2004 01:51:46 on modular  [Seed = 2500286292]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Fri Jun 18 01:51:54 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();


Output: Magma V2.10-22    Fri Jun 18 2004 01:51:52 on modular  [Seed = 2635030358]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + x + 1)*y = x^7 + x^5 + x 
    + 1 over GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO103.gate.nec.co.jp. (210.143.35.13)
Time: Fri Jun 18 01:53:13 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x+1);
f:=P!(x^7 + x^5 + x + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;

Output: Magma V2.10-22    Fri Jun 18 2004 01:53:11 on modular  [Seed = 2333690111]
   -------------------------------------

6
(1, 0, 0)
(x^3 + x^2 + 1, x^2 + 1, 3)
(x^3 + x^2 + 1, x^2 + 1, 3)

Total time: 2.509 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Fri Jun 18 01:53:24 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x+1);
f:=P!(x^7 + x^5 + x + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;

Output: Magma V2.10-22    Fri Jun 18 2004 01:53:22 on modular  [Seed = 4285349022]
   -------------------------------------

6
(x + 1, 0, 1)
(x^3 + x^2 + 1, x^2 + x + 1, 3)
(x^3 + x + 1, x^2 + 1, 3)

Total time: 2.519 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Fri Jun 18 01:56:16 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 3rd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+1);
f:=P!(x^7+x^5+x+1);
u1:=P!(x+1); v1:=P!(0);
u2:=P!(x^3+x^2+1); v2:=P!(x^2+x+1);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Fri Jun 18 2004 01:56:14 on modular  [Seed = 3967692577]
   -------------------------------------

x^3 + x + 1
x + 1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Fri Jun 18 02:00:24 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 3rd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+1);
f:=P!(x^7+x^5+x+1);
u1:=P!(x+1); v1:=P!(0);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:00:21 on modular  [Seed = 900198900]
   -------------------------------------

1
0
2

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:02:32 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 4.1.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+1);
f:=P!(x^7+x^5+x+1);
u1:=P!(x^3+x^2+1); v1:=P!(x^2+x+1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:02:29 on modular  [Seed = 1034942588]
   -------------------------------------

1
0
2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 02:02:48 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 4.2.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+1);
f:=P!(x^7+x^5+x+1);
u1:=P!(x^3+x^2+1); v1:=P!(x^2+x+1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:02:45 on modular  [Seed = 632807572]
   -------------------------------------

1
0
2

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:04:10 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 4.1.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7+x^6+x^5+x^3+x^2+x+1);
u1:=P!(x); v1:=P!(1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:04:07 on modular  [Seed = 784133069]
   -------------------------------------

1
0
2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Fri Jun 18 02:05:05 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 4.2.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3);
f:=P!(x^7+x^6+x^5+x^3+x^2+x+1);
u1:=P!(x^3+x^2+x); v1:=P!(x^2+1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:05:02 on modular  [Seed = 377802796]
   -------------------------------------

1
0
2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Fri Jun 18 02:06:52 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();

Output: Magma V2.10-22    Fri Jun 18 2004 02:06:49 on modular  [Seed = 512546899]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Fri Jun 18 02:07:00 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 1st Step
RandomHEC_3_2();

Output: Magma V2.10-22    Fri Jun 18 2004 02:06:57 on modular  [Seed = 110411955]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + x)*y = x^7 + x^6 + x^5 + 
    x^4 + x^2 + x over GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO106.gate.nec.co.jp. (210.143.35.16)
Time: Fri Jun 18 02:08:04 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7 + x^6 + x^4 + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;


Output: Magma V2.10-22    Fri Jun 18 2004 02:08:01 on modular  [Seed = 2112863112]
   -------------------------------------

24
(x^3 + x, x + 1, 3)
(x, 1, 1)
(x^2 + 1, x + 1, 2)

Total time: 2.529 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:11:27 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x);
f:=P!(x^7 + x^6 + x^5 + x^4 + x^2 + x);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;


Output: Magma V2.10-22    Fri Jun 18 2004 02:11:24 on modular  [Seed = 1557044196]
   -------------------------------------

16
(1, 0, 0)
(x^3 + x^2 + x + 1, x + 1, 3)
(x^3 + x^2 + x + 1, x + 1, 3)

Total time: 2.549 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 02:11:34 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 2nd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x);
f:=P!(x^7 + x^6 + x^5 + x^4 + x^2 + x);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;


Output: Magma V2.10-22    Fri Jun 18 2004 02:11:31 on modular  [Seed = 1154909155]
   -------------------------------------

16
(x + 1, 1, 1)
(x, 0, 1)
(x^2 + x, x, 2)

Total time: 2.519 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Fri Jun 18 02:16:12 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////


// 3rd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x);
f:=P!(x^7 + x^6 + x^5 + x^4 + x^2 + x);
u1:=P!(x+1); v1:=P!(1);
u2:=P!(x); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);


Output: Magma V2.10-22    Fri Jun 18 2004 02:16:09 on modular  [Seed = 1255703255]
   -------------------------------------

x^2 + x
0

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Fri Jun 18 02:18:43 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////
// 4.1.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x);
f:=P!(x^7 + x^6 + x^5 + x^4 + x^2 + x);
u1:=P!(x+1); v1:=P!(1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;




Output: Magma V2.10-22    Fri Jun 18 2004 02:18:41 on modular  [Seed = 2704500948]
   -------------------------------------

1
0
2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:19:59 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4.1.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^3+x^2+x);
f:=P!(x^7 + x^6 + x^5 + x^4 + x^2 + x);
u1:=P!(x); v1:=P!(0);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:19:57 on modular  [Seed = 2668451366]
   -------------------------------------

1
0
2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 02:24:16 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 3rd Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7+x^6+x^4+ 1);
u1:=P!(x^3+x); v1:=P!(x+1);
u2:=P!(x); v2:=P!(1);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Fri Jun 18 2004 02:24:14 on modular  [Seed = 4001113172]
   -------------------------------------

x^2 + 1
0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO115.gate.nec.co.jp. (202.32.8.237)
Time: Fri Jun 18 02:25:57 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4.1.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7+x^6+x^4+ 1);
u1:=P!(x^3+x); v1:=P!(x+1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:25:55 on modular  [Seed = 3594787857]
   -------------------------------------

1
0
2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Fri Jun 18 02:27:25 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4.2.th Step
K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x);
f:=P!(x^7+x^6+x^4+ 1);
u1:=P!(x); v1:=P!(1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:27:22 on modular  [Seed = 3729528224]
   -------------------------------------

1
0
2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO111.gate.nec.co.jp. (202.32.8.233)
Time: Fri Jun 18 02:37:02 2004

Input: 
 // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

Output: Magma V2.10-22    Fri Jun 18 2004 02:36:59 on modular  [Seed = 598863517]
   -------------------------------------


Total time: 2.629 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 02:37:26 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 1st Step
RandomHEC_3_3();

Output: Magma V2.10-22    Fri Jun 18 2004 02:37:24 on modular  [Seed = 277011841]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (2*x^3 + 2*x^2 + 2*x)*y = x^7 + x^4 + 
    2*x + 1 over GF(3)

Total time: 2.499 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host TYO109.gate.nec.co.jp. (210.143.35.19)
Time: Fri Jun 18 02:38:59 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 2*x);
f:=P!(x^7 + x^4 + 2*x + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;

Output: Magma V2.10-22    Fri Jun 18 2004 02:38:56 on modular  [Seed = 43043895]
   -------------------------------------

28
(x^2 + x, x + 2, 2)
(x^2 + x, x + 2, 2)
(x^2, x + 2, 2)

Total time: 2.520 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO112.gate.nec.co.jp. (202.32.8.234)
Time: Fri Jun 18 02:40:22 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 3rd Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 2*x);
f:=P!(x^7 + x^4 + 2*x + 1);
u1:=P!(x^2+x); v1:=P!(x+2);
u2:=P!(1); v2:=P!(0);
Cantor(f,h,u1,u2,v1,v2);


Output: Magma V2.10-22    Fri Jun 18 2004 02:40:20 on modular  [Seed = 1744152838]
   -------------------------------------

x^2 + x
x + 2

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO105.gate.nec.co.jp. (210.143.35.15)
Time: Fri Jun 18 02:42:22 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 3rd Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 2*x);
f:=P!(x^7 + x^4 + 2*x + 1);
u1:=P!(x^2+x); v1:=P!(x+2);
u2:=P!(x^2+x); v2:=P!(x+2);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Fri Jun 18 2004 02:42:19 on modular  [Seed = 1878892950]
   -------------------------------------

x^3 + x^2 + 2
2*x + 1

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:44:01 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4.1.th Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 2*x);
f:=P!(x^7 + x^4 + 2*x + 1);
u1:=P!(x^2+x); v1:=P!(x+2);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Fri Jun 18 2004 02:43:58 on modular  [Seed = 1405197384]
   -------------------------------------

x^3 + x^2 + 2
2*x + 1
1001

Total time: 2.779 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Fri Jun 18 02:45:20 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 1st Step
RandomHEC_3_3();

Output: Magma V2.10-22    Fri Jun 18 2004 02:45:17 on modular  [Seed = 1523094802]
   -------------------------------------

false

Total time: 2.509 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host TYO104.gate.nec.co.jp. (210.143.35.14)
Time: Fri Jun 18 02:45:26 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 1st Step
RandomHEC_3_3();

Output: Magma V2.10-22    Fri Jun 18 2004 02:45:23 on modular  [Seed = 1120964084]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (2*x^3 + 2*x^2 + 1)*y = x^7 + x^6 + 
    2*x^4 + 2*x^3 + 2*x^2 + 1 over GF(3)

Total time: 2.499 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host TYO107.gate.nec.co.jp. (210.143.35.17)
Time: Fri Jun 18 02:46:46 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 2nd Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 1);
f:=P!(x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 1);
C:=HyperellipticCurve([f,h]);
J:=Jacobian(C);
#J;
P1:=Random(J); P2:=Random(J);
P3:=P1+P2;
P1; P2; P3;


Output: Magma V2.10-22    Fri Jun 18 2004 02:46:44 on modular  [Seed = 1255703979]
   -------------------------------------

52
(x^2 + 2*x + 2, x, 2)
(x^2 + 2*x + 2, 2*x + 1, 2)
(1, 0, 0)

Total time: 2.529 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:48:30 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 3rd Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 1);
f:=P!(x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 1);
u1:=P!(x^2+2*x+2); v1:=P!(x);
u2:=P!(x^2+2*x+2); v2:=P!(2*x+1);
Cantor(f,h,u1,u2,v1,v2);

Output: Magma V2.10-22    Fri Jun 18 2004 02:48:28 on modular  [Seed = 3106630064]
   -------------------------------------

x^3 + 2*x
2*x

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Fri Jun 18 02:49:51 2004

Input:  // HEC (Genus 3, Characteristic 3) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_3:=procedure();
 K:=GF(3);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

// 4.1.th Step
K:=GF(3);
P<x>:=PolynomialRing(K);
h:=P!(2*x^3 + 2*x^2 + 1);
f:=P!(x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 1);
u1:=P!(x^2+2*x+2); v1:=P!(x);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;


Output: Magma V2.10-22    Fri Jun 18 2004 02:49:48 on modular  [Seed = 2704503064]
   -------------------------------------

x^3 + x^2 + 2*x + 2
2*x^2 + 2*x + 2
1001

Total time: 2.779 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:23:26 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=672 
    for i:= 2 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:23:22 on modular  [Seed = 4117195639]
   -------------------------------------


>>     for i:= 2 to m-1 do
       ^
User error: bad syntax

>>          Q<z>:=z^m + z^i +1;
                    ^
User error: Identifier 'm' has not been declared or assigned

>>          if IsPrimitive(Q)
                           ^
User error: Identifier 'Q' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:23:48 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=672 ;
    for i:= 2 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:23:44 on modular  [Seed = 3782442761]
   -------------------------------------


Total time: 3.349 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:24:45 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=673 ;
    for i:= 2 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:24:23 on modular  [Seed = 3645589270]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:31:08 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=674 ;
    for i:= 2 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:31:05 on modular  [Seed = 3544281954]
   -------------------------------------


Total time: 3.029 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:36:43 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=674 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:36:40 on modular  [Seed = 3428740396]
   -------------------------------------


Total time: 3.039 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:36:57 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=675 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:36:54 on modular  [Seed = 3293996314]
   -------------------------------------


Total time: 3.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:37:08 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=676 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:37:04 on modular  [Seed = 1034919156]
   -------------------------------------

z^676 + z^241 + 1
z^676 + z^277 + 1
z^676 + z^399 + 1
z^676 + z^435 + 1

Total time: 4.489 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:38:35 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=1000 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:38:31 on modular  [Seed = 716736596]
   -------------------------------------


Total time: 4.119 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:39:00 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=999;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:38:45 on modular  [Seed = 581992526]
   -------------------------------------

z^999 + z^59 + 1
z^999 + z^940 + 1

Total time: 14.339 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:40:04 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=998;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:39:56 on modular  [Seed = 479116985]
   -------------------------------------

z^998 + z^101 + 1
z^998 + z^897 + 1

Total time: 8.049 seconds, Total memory usage: 3.27MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:41:24 2004

Input: P<z>:=PolynomialRing(GF(2));
 for m:=980 to 997 do 
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for; 
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:41:01 on modular  [Seed = 2045500317]
   -------------------------------------

z^982 + z^277 + 1
z^982 + z^705 + 1
z^983 + z^230 + 1
z^983 + z^342 + 1
z^983 + z^641 + 1
z^983 + z^753 + 1


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:42:19 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=801
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:42:17 on modular  [Seed = 1910755937]
   -------------------------------------


>>     for i:= 1 to m-1 do
       ^
User error: bad syntax

>>          Q<z>:=z^m + z^i +1;
                    ^
User error: Identifier 'm' has not been declared or assigned

>>          if IsPrimitive(Q)
                           ^
User error: Identifier 'Q' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:42:31 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=801;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:42:25 on modular  [Seed = 1778109025]
   -------------------------------------

z^801 + z^217 + 1
z^801 + z^325 + 1
z^801 + z^476 + 1
z^801 + z^584 + 1

Total time: 5.139 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:43:06 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=801;
    for i:= 585 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:43:03 on modular  [Seed = 1643364879]
   -------------------------------------


Total time: 2.799 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:43:21 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=802;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:43:17 on modular  [Seed = 1354953484]
   -------------------------------------


Total time: 3.109 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:44:36 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=980;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:44:32 on modular  [Seed = 1222306753]
   -------------------------------------


Total time: 4.039 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:44:50 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=983;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:44:45 on modular  [Seed = 1087562692]
   -------------------------------------

z^983 + z^230 + 1
z^983 + z^342 + 1
z^983 + z^641 + 1
z^983 + z^753 + 1

Total time: 4.329 seconds, Total memory usage: 2.46MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:45:09 2004

Input: P<z>:=PolynomialRing(GF(2));
 m:=983;
    for i:= 754 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:45:07 on modular  [Seed = 3089767250]
   -------------------------------------


Total time: 2.709 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:46:05 2004

Input: P<z>:=PolynomialRing(GF(2));
 for m:=984 to 990 do 
    for i:= 754 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:45:42 on modular  [Seed = 2955023231]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:46:55 2004

Input: P<z>:=PolynomialRing(GF(2));
 for m:=984 to 990 do 
    for i:= 754 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:46:32 on modular  [Seed = 2872643514]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:47:59 2004

Input: P<z>:=PolynomialRing(GF(2));
 for m:=990 to 997 do 
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:47:37 on modular  [Seed = 2721056498]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:49:49 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=997
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:49:47 on modular  [Seed = 2483433542]
   -------------------------------------


>>     for i:= 1 to m-1 do
       ^
User error: bad syntax

>>          Q<z>:=z^m + z^i +1;
                    ^
User error: Identifier 'm' has not been declared or assigned

>>          if IsPrimitive(Q)
                           ^
User error: Identifier 'Q' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:50:00 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=997;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:49:56 on modular  [Seed = 2350786625]
   -------------------------------------


Total time: 3.869 seconds, Total memory usage: 2.50MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:50:24 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=996;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:50:19 on modular  [Seed = 2216042929]
   -------------------------------------


Total time: 4.839 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:50:35 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=995;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:50:31 on modular  [Seed = 4235090386]
   -------------------------------------


Total time: 4.409 seconds, Total memory usage: 2.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:50:48 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=994;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:50:43 on modular  [Seed = 4100346350]
   -------------------------------------

z^994 + z^223 + 1
z^994 + z^771 + 1

Total time: 4.919 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:51:27 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=994;
    for i:= 772 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:51:24 on modular  [Seed = 3967699353]
   -------------------------------------


Total time: 2.969 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:51:52 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=993;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:51:37 on modular  [Seed = 3832955268]
   -------------------------------------

z^993 + z^62 + 1
z^993 + z^931 + 1

Total time: 15.239 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:52:24 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=992;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:52:20 on modular  [Seed = 3746396770]
   -------------------------------------


Total time: 4.329 seconds, Total memory usage: 2.56MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:52:53 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=991;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:52:30 on modular  [Seed = 3611652704]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:53:38 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=991;
    for i:= 500 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:53:15 on modular  [Seed = 3226625346]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:54:17 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=991;
    for i:= 1 to 500 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:53:54 on modular  [Seed = 1000972003]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:55:54 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=990;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:55:48 on modular  [Seed = 866227549]
   -------------------------------------


Total time: 5.849 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:56:08 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=989;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:56:04 on modular  [Seed = 733580661]
   -------------------------------------


Total time: 3.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:56:20 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=988;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:56:14 on modular  [Seed = 598836599]
   -------------------------------------

z^988 + z^121 + 1
z^988 + z^867 + 1

Total time: 5.769 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:57:42 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=987;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:57:37 on modular  [Seed = 411746019]
   -------------------------------------


Total time: 4.749 seconds, Total memory usage: 2.56MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:58:03 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=986;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:57:48 on modular  [Seed = 277001958]
   -------------------------------------


Total time: 14.929 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:58:25 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:58:03 on modular  [Seed = 394637814]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:58:44 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:58:21 on modular  [Seed = 211725019]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:58:53 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:58:50 on modular  [Seed = 2129451342]
   -------------------------------------


Total time: 2.789 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 08:59:28 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 200 to 500 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:59:05 on modular  [Seed = 1994707286]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:00:08 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 200 to 400 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 08:59:45 on modular  [Seed = 1862060309]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:00:24 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 400 to 600 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:00:21 on modular  [Seed = 1439166986]
   -------------------------------------


Total time: 2.699 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:00:59 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=985;
    for i:= 600 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:00:37 on modular  [Seed = 1306520066]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:01:18 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=984;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:01:14 on modular  [Seed = 1171776229]
   -------------------------------------


Total time: 3.729 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:01:30 2004

Input: P<z>:=PolynomialRing(GF(2));
  m:=983;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:01:25 on modular  [Seed = 3173980706]
   -------------------------------------

z^983 + z^230 + 1
z^983 + z^342 + 1
z^983 + z^641 + 1
z^983 + z^753 + 1

Total time: 4.319 seconds, Total memory usage: 2.46MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:02:45 2004

Input: P<z>:=PolynomialRing(GF(2));
  for m:=970 to 979 do 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:02:23 on modular  [Seed = 3039236688]
   -------------------------------------

z^972 + z^115 + 1
z^972 + z^155 + 1
z^972 + z^817 + 1
z^972 + z^857 + 1
z^975 + z^19 + 1
z^975 + z^956 + 1


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:04:12 2004

Input: P<z>:=PolynomialRing(GF(2));
  for m:=976 to 979 do 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:03:50 on modular  [Seed = 2721057454]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:04:51 2004

Input: P<z>:=PolynomialRing(GF(2));
  for m:=977 to 979 do 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:04:28 on modular  [Seed = 2584228604]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:05:22 2004

Input: P<z>:=PolynomialRing(GF(2));
  for m:=979 to 979 do 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:04:59 on modular  [Seed = 2449488595]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:06:08 2004

Input: P<z>:=PolynomialRing(GF(2));
  for m:=979 to 979 do 
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:05:45 on modular  [Seed = 2316837401]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:06:53 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=976 ; 
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:06:50 on modular  [Seed = 2198940499]
   -------------------------------------


Total time: 2.679 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:07:06 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=976 ; 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:07:02 on modular  [Seed = 4217983799]
   -------------------------------------


Total time: 3.419 seconds, Total memory usage: 2.46MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:07:33 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=977 ; 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:07:11 on modular  [Seed = 4083243830]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:09:11 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=977 ; 
    for i:=201 to 500 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:08:49 on modular  [Seed = 4017964724]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:09:54 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=978 ; 
    for i:=201 to 500 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:09:51 on modular  [Seed = 3849800768]
   -------------------------------------


Total time: 2.799 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:09:59 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=979 ;
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:09:36 on modular  [Seed = 3883224653]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:10:39 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=960 ;
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:10:36 on modular  [Seed = 3611655713]
   -------------------------------------


Total time: 2.779 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:11:06 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=961 ;
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:10:44 on modular  [Seed = 3479004705]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:11:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   for m:=965 to 969 do  
    for i:=201 to 500 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:11:22 on modular  [Seed = 3344264711]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:11:49 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=960 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:11:45 on modular  [Seed = 1018074646]
   -------------------------------------


Total time: 3.949 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:11:55 2004

Input: P<z>:=PolynomialRing(GF(2));
   for m:=965 to 969 do  
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:11:32 on modular  [Seed = 3310841851]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:12:31 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=961 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:12:08 on modular  [Seed = 784106557]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:13:07 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=961 ;
    for i:=1 to 400 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:12:45 on modular  [Seed = 649366608]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:13:24 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=962 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:13:20 on modular  [Seed = 495957846]
   -------------------------------------


Total time: 3.729 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:13:35 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=963 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:13:30 on modular  [Seed = 361217876]
   -------------------------------------


Total time: 4.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:13:46 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=964 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:13:40 on modular  [Seed = 228566962]
   -------------------------------------

z^964 + z^103 + 1
z^964 + z^441 + 1
z^964 + z^523 + 1
z^964 + z^861 + 1

Total time: 5.929 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:14:18 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=965 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:14:15 on modular  [Seed = 76983960]
   -------------------------------------


Total time: 3.639 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:14:29 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=966 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:14:24 on modular  [Seed = 1927338233]
   -------------------------------------


Total time: 5.629 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:15:14 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=967 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:14:51 on modular  [Seed = 1794687130]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:15:52 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=968 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:15:49 on modular  [Seed = 1659947356]
   -------------------------------------


Total time: 3.479 seconds, Total memory usage: 2.56MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:16:29 2004

Input: P<z>:=PolynomialRing(GF(2));
   for m:=965 to 969 do  
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:16:06 on modular  [Seed = 1523118455]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:19:52 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=969 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:19:46 on modular  [Seed = 1439170204]
   -------------------------------------

z^969 + z^74 + 1
z^969 + z^308 + 1
z^969 + z^446 + 1
z^969 + z^523 + 1
z^969 + z^661 + 1
z^969 + z^895 + 1

Total time: 6.049 seconds, Total memory usage: 2.56MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:22:47 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=959 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:22:24 on modular  [Seed = 2988449305]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:22:57 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=958 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:22:53 on modular  [Seed = 2855798332]
   -------------------------------------


Total time: 3.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:23:10 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=957 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:23:06 on modular  [Seed = 2687634465]
   -------------------------------------


Total time: 3.619 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:23:31 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=956 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:23:24 on modular  [Seed = 2668442472]
   -------------------------------------

z^956 + z^305 + 1
z^956 + z^347 + 1
z^956 + z^609 + 1
z^956 + z^651 + 1

Total time: 6.139 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:26:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=955 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:26:40 on modular  [Seed = 2533702204]
   -------------------------------------


Total time: 3.669 seconds, Total memory usage: 2.45MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:31:24 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=954 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:31:15 on modular  [Seed = 2198940955]
   -------------------------------------


Total time: 8.339 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:32:11 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=953 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:31:49 on modular  [Seed = 4217984261]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:33:17 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=953 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:32:54 on modular  [Seed = 4083244238]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:39:54 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=952 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:39:50 on modular  [Seed = 3984547184]
   -------------------------------------


Total time: 4.189 seconds, Total memory usage: 2.55MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:42:10 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=951 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:42:05 on modular  [Seed = 3378215135]
   -------------------------------------

z^951 + z^260 + 1
z^951 + z^290 + 1
z^951 + z^391 + 1
z^951 + z^560 + 1
z^951 + z^661 + 1
z^951 + z^691 + 1

Total time: 4.529 seconds, Total memory usage: 2.55MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:45:06 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=950 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:45:03 on modular  [Seed = 3226628388]
   -------------------------------------


Total time: 3.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:45:18 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=949 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:45:14 on modular  [Seed = 1068338921]
   -------------------------------------


Total time: 3.829 seconds, Total memory usage: 2.45MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:45:48 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=948 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:45:43 on modular  [Seed = 933594380]
   -------------------------------------


Total time: 5.289 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:46:03 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=947;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:45:59 on modular  [Seed = 800955652]
   -------------------------------------


Total time: 3.699 seconds, Total memory usage: 2.55MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:46:15 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=946;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:46:12 on modular  [Seed = 666211647]
   -------------------------------------


Total time: 3.309 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:46:30 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=945;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:46:22 on modular  [Seed = 529378573]
   -------------------------------------

z^945 + z^79 + 1
z^945 + z^94 + 1
z^945 + z^191 + 1
z^945 + z^229 + 1
z^945 + z^716 + 1
z^945 + z^754 + 1
z^945 + z^851 + 1
z^945 + z^866 + 1

Total time: 8.089 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:46:57 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=946;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:46:53 on modular  [Seed = 394634598]
   -------------------------------------


Total time: 3.329 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:47:05 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=944;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:47:01 on modular  [Seed = 261995878]
   -------------------------------------


Total time: 3.549 seconds, Total memory usage: 2.55MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:47:34 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=943;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:47:11 on modular  [Seed = 127251812]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:48:05 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=943;
    for i:=1 to 500 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:47:43 on modular  [Seed = 2028653115]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:48:34 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=943;
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:48:12 on modular  [Seed = 1910752209]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:50:40 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=943;
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:50:18 on modular  [Seed = 1626526534]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:51:05 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=943;
    for i:=1 to 200 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:50:43 on modular  [Seed = 1506536022]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:51:34 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=943;
    for i:=1 to 50 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:51:11 on modular  [Seed = 1371791906]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:57:16 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=942;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:57:11 on modular  [Seed = 1154937039]
   -------------------------------------


Total time: 4.969 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:57:28 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=941;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:57:24 on modular  [Seed = 3190557254]
   -------------------------------------


Total time: 3.679 seconds, Total memory usage: 2.55MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:57:43 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=940;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:57:39 on modular  [Seed = 2955019359]
   -------------------------------------


Total time: 3.699 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:58:00 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=939;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:57:56 on modular  [Seed = 2822380656]
   -------------------------------------


Total time: 3.729 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:58:22 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=938;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:58:17 on modular  [Seed = 2704479588]
   -------------------------------------

z^938 + z^207 + 1
z^938 + z^731 + 1

Total time: 5.089 seconds, Total memory usage: 2.55MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:59:36 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=937;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:59:14 on modular  [Seed = 2567646359]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 09:59:55 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=936;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 09:59:51 on modular  [Seed = 2432902394]
   -------------------------------------


Total time: 4.149 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:00:23 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=935;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:00:01 on modular  [Seed = 2300263636]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:00:35 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=934;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:00:31 on modular  [Seed = 3967703471]
   -------------------------------------


Total time: 3.359 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:00:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=933;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:00:40 on modular  [Seed = 3832959312]
   -------------------------------------


Total time: 4.109 seconds, Total memory usage: 2.45MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:00:57 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=932;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:00:50 on modular  [Seed = 3696126322]
   -------------------------------------

z^932 + z^275 + 1
z^932 + z^387 + 1
z^932 + z^455 + 1
z^932 + z^477 + 1
z^932 + z^545 + 1
z^932 + z^657 + 1

Total time: 6.219 seconds, Total memory usage: 3.25MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:01:23 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=931;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:01:19 on modular  [Seed = 3561382215]
   -------------------------------------


Total time: 4.089 seconds, Total memory usage: 2.45MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:01:37 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=930;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:01:30 on modular  [Seed = 3428743498]
   -------------------------------------


Total time: 6.739 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:01:46 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=929;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:01:43 on modular  [Seed = 3293999423]
   -------------------------------------


Total time: 3.379 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:01:57 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=928;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:01:54 on modular  [Seed = 1034914002]
   -------------------------------------


Total time: 3.259 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:02:09 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=927;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:02:02 on modular  [Seed = 900169938]
   -------------------------------------

z^927 + z^403 + 1
z^927 + z^455 + 1
z^927 + z^472 + 1
z^927 + z^524 + 1

Total time: 7.099 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:02:37 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=926;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:02:32 on modular  [Seed = 767531240]
   -------------------------------------

z^926 + z^365 + 1
z^926 + z^561 + 1

Total time: 4.139 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:03:02 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=925;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:02:59 on modular  [Seed = 632787723]
   -------------------------------------


Total time: 3.399 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:03:16 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=924;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:03:10 on modular  [Seed = 495954750]
   -------------------------------------


Total time: 6.109 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:03:27 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=923;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:03:23 on modular  [Seed = 344367618]
   -------------------------------------


Total time: 3.659 seconds, Total memory usage: 2.64MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:07:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=922;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:07:40 on modular  [Seed = 261994526]
   -------------------------------------


Total time: 3.459 seconds, Total memory usage: 2.54MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:08:49 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=921;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:08:26 on modular  [Seed = 9615207]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:09:32 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=920;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:09:28 on modular  [Seed = 2062077407]
   -------------------------------------


Total time: 3.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:10:01 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=919;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:09:38 on modular  [Seed = 1927333357]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:10:09 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=920;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:10:05 on modular  [Seed = 1744163047]
   -------------------------------------


Total time: 3.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:11:29 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=919;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:11:06 on modular  [Seed = 1607329944]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:11:41 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=918;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:11:36 on modular  [Seed = 1472589682]
   -------------------------------------

z^918 + z^77 + 1
z^918 + z^841 + 1

Total time: 4.669 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:12:09 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=917;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:12:05 on modular  [Seed = 1339946823]
   -------------------------------------


Total time: 3.949 seconds, Total memory usage: 2.44MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:12:21 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=916;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:12:15 on modular  [Seed = 1205206853]
   -------------------------------------


Total time: 5.849 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:12:32 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=915;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:12:28 on modular  [Seed = 3106603464]
   -------------------------------------


Total time: 4.049 seconds, Total memory usage: 2.34MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:13:01 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=914;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:12:57 on modular  [Seed = 2971863525]
   -------------------------------------


Total time: 3.579 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:13:34 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=913;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:13:12 on modular  [Seed = 2822377709]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:13:58 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=912;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:13:54 on modular  [Seed = 2687637567]
   -------------------------------------


Total time: 3.389 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:15:16 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=911;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:14:54 on modular  [Seed = 2601067384]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:15:47 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=910;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:15:43 on modular  [Seed = 2466327201]
   -------------------------------------


Total time: 3.839 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:15:59 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=909;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:15:54 on modular  [Seed = 2333684396]
   -------------------------------------


Total time: 4.189 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:16:14 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=908;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:16:08 on modular  [Seed = 2198944406]
   -------------------------------------

z^908 + z^143 + 1
z^908 + z^765 + 1

Total time: 5.919 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:16:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=907;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:16:40 on modular  [Seed = 4217979534]
   -------------------------------------


Total time: 3.409 seconds, Total memory usage: 2.54MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:16:53 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=906;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:16:48 on modular  [Seed = 4083239582]
   -------------------------------------

z^906 + z^187 + 1
z^906 + z^719 + 1

Total time: 4.939 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:17:42 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=905;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:17:19 on modular  [Seed = 3849804983]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:17:55 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=904;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:17:52 on modular  [Seed = 3696125297]
   -------------------------------------


Total time: 3.249 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:18:35 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=700;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:18:31 on modular  [Seed = 3611651677]
   -------------------------------------


Total time: 3.749 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:18:47 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=699;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:18:44 on modular  [Seed = 3479008822]
   -------------------------------------


Total time: 3.189 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:19:13 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=698;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:19:05 on modular  [Seed = 3344268835]
   -------------------------------------

z^698 + z^215 + 1
z^698 + z^311 + 1
z^698 + z^387 + 1
z^698 + z^483 + 1

Total time: 7.899 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:20:07 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=697;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:19:44 on modular  [Seed = 1018070530]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:20:56 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=695;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:20:53 on modular  [Seed = 598841688]
   -------------------------------------

z^695 + z^212 + 1
z^695 + z^483 + 1

Total time: 3.339 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:21:14 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=694;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:21:11 on modular  [Seed = 462004594]
   -------------------------------------


Total time: 3.169 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:21:58 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=692;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:21:54 on modular  [Seed = 327264687]
   -------------------------------------

z^692 + z^299 + 1
z^692 + z^393 + 1

Total time: 3.399 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:22:17 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=690;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:22:14 on modular  [Seed = 194621859]
   -------------------------------------


Total time: 3.549 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:22:48 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=689;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:22:44 on modular  [Seed = 59881865]
   -------------------------------------

z^689 + z^14 + 1
z^689 + z^87 + 1
z^689 + z^179 + 1
z^689 + z^207 + 1
z^689 + z^336 + 1
z^689 + z^353 + 1
z^689 + z^482 + 1
z^689 + z^510 + 1
z^689 + z^602 + 1
z^689 + z^675 + 1

Total time: 3.829 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:23:54 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=687;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:23:50 on modular  [Seed = 1994706110]
   -------------------------------------

z^687 + z^13 + 1
z^687 + z^133 + 1
z^687 + z^554 + 1
z^687 + z^674 + 1

Total time: 3.899 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:24:49 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=686;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:24:45 on modular  [Seed = 1862063485]
   -------------------------------------

z^686 + z^197 + 1
z^686 + z^489 + 1

Total time: 3.879 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:25:45 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=684;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:25:41 on modular  [Seed = 1727323453]
   -------------------------------------


Total time: 3.869 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:25:54 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=682;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:25:50 on modular  [Seed = 1590486286]
   -------------------------------------


Total time: 3.929 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:26:18 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=679;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:26:08 on modular  [Seed = 1455746536]
   -------------------------------------

z^679 + z^66 + 1
z^679 + z^216 + 1
z^679 + z^463 + 1
z^679 + z^613 + 1

Total time: 9.089 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:28:06 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=713;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:27:43 on modular  [Seed = 1339946158]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:28:22 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=714;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:28:17 on modular  [Seed = 1154939003]
   -------------------------------------

z^714 + z^23 + 1
z^714 + z^151 + 1
z^714 + z^563 + 1
z^714 + z^691 + 1

Total time: 4.979 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:28:40 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=716;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:28:36 on modular  [Seed = 3157131414]
   -------------------------------------

z^716 + z^183 + 1
z^716 + z^275 + 1
z^716 + z^441 + 1
z^716 + z^533 + 1

Total time: 3.649 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:29:35 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=718;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:29:32 on modular  [Seed = 3022391494]
   -------------------------------------


Total time: 3.489 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:30:03 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=719;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:29:41 on modular  [Seed = 2889748679]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:30:24 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=721;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:30:20 on modular  [Seed = 2755008742]
   -------------------------------------

z^721 + z^9 + 1
z^721 + z^159 + 1
z^721 + z^256 + 1
z^721 + z^270 + 1
z^721 + z^283 + 1
z^721 + z^328 + 1
z^721 + z^393 + 1
z^721 + z^438 + 1
z^721 + z^451 + 1
z^721 + z^465 + 1
z^721 + z^562 + 1
z^721 + z^712 + 1

Total time: 4.349 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:30:51 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=722;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:30:48 on modular  [Seed = 2618171450]
   -------------------------------------

z^722 + z^231 + 1
z^722 + z^491 + 1

Total time: 3.159 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:31:13 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=724;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:31:09 on modular  [Seed = 2483431431]
   -------------------------------------


Total time: 3.949 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:31:24 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=726;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:31:19 on modular  [Seed = 2350788613]
   -------------------------------------

z^726 + z^5 + 1
z^726 + z^241 + 1
z^726 + z^485 + 1
z^726 + z^721 + 1

Total time: 4.329 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:31:50 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=727;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:31:47 on modular  [Seed = 2216048745]
   -------------------------------------

z^727 + z^180 + 1
z^727 + z^217 + 1
z^727 + z^357 + 1
z^727 + z^370 + 1
z^727 + z^510 + 1
z^727 + z^547 + 1

Total time: 3.319 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:32:15 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=729;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:32:10 on modular  [Seed = 4235083816]
   -------------------------------------

z^729 + z^58 + 1
z^729 + z^253 + 1
z^729 + z^476 + 1
z^729 + z^671 + 1

Total time: 4.779 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:32:36 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=730;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:32:31 on modular  [Seed = 4100343861]
   -------------------------------------

z^730 + z^147 + 1
z^730 + z^583 + 1

Total time: 4.439 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:33:27 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=732;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:33:24 on modular  [Seed = 3984543975]
   -------------------------------------


Total time: 3.519 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:33:39 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=735;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:33:33 on modular  [Seed = 3849804006]
   -------------------------------------

z^735 + z^44 + 1
z^735 + z^89 + 1
z^735 + z^262 + 1
z^735 + z^473 + 1
z^735 + z^646 + 1
z^735 + z^691 + 1

Total time: 5.899 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:33:59 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=737;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:33:56 on modular  [Seed = 3712966839]
   -------------------------------------

z^737 + z^5 + 1
z^737 + z^303 + 1
z^737 + z^434 + 1
z^737 + z^732 + 1

Total time: 3.779 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:34:28 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=738;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:34:24 on modular  [Seed = 3578226843]
   -------------------------------------

z^738 + z^347 + 1
z^738 + z^391 + 1

Total time: 3.859 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:34:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=740;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:34:39 on modular  [Seed = 3445584012]
   -------------------------------------

z^740 + z^153 + 1
z^740 + z^317 + 1
z^740 + z^423 + 1
z^740 + z^587 + 1

Total time: 4.759 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:35:11 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=742;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:35:07 on modular  [Seed = 3310844000]
   -------------------------------------


Total time: 3.729 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:35:52 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=743;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:35:29 on modular  [Seed = 1018069426]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:36:02 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=745;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:35:59 on modular  [Seed = 883329476]
   -------------------------------------

z^745 + z^258 + 1
z^745 + z^336 + 1
z^745 + z^342 + 1
z^745 + z^403 + 1
z^745 + z^409 + 1
z^745 + z^487 + 1

Total time: 3.799 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:36:38 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=746;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:36:32 on modular  [Seed = 750686691]
   -------------------------------------

z^746 + z^351 + 1
z^746 + z^395 + 1

Total time: 5.689 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:37:07 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=748;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:37:02 on modular  [Seed = 615946773]
   -------------------------------------


Total time: 4.419 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:37:38 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=750;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:37:34 on modular  [Seed = 462005514]
   -------------------------------------


Total time: 3.579 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:37:49 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=751;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:37:46 on modular  [Seed = 327265558]
   -------------------------------------

z^751 + z^18 + 1
z^751 + z^187 + 1
z^751 + z^310 + 1
z^751 + z^441 + 1
z^751 + z^564 + 1
z^751 + z^733 + 1

Total time: 3.369 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:39:00 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=753;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:38:41 on modular  [Seed = 144356933]
   -------------------------------------

z^753 + z^158 + 1
z^753 + z^595 + 1

Total time: 18.729 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:39:24 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=754;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:39:13 on modular  [Seed = 9617070]
   -------------------------------------

z^754 + z^19 + 1
z^754 + z^147 + 1
z^754 + z^607 + 1
z^754 + z^735 + 1

Total time: 11.009 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:39:49 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=756;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:39:43 on modular  [Seed = 2028652264]
   -------------------------------------

z^756 + z^349 + 1
z^756 + z^407 + 1

Total time: 5.269 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:40:09 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=758;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:40:06 on modular  [Seed = 1573905316]
   -------------------------------------


Total time: 3.339 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:40:52 2004

Input: P<z>:=PolynomialRing(GF(2));
 for   m:=759 to 770 do 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end if ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:40:49 on modular  [Seed = 1439165339]
   -------------------------------------


>>   end if ;
         ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:41:23 2004

Input: P<z>:=PolynomialRing(GF(2));
 for   m:=759 to 770 do 
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  end for ;
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:41:00 on modular  [Seed = 1289679503]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:42:02 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=759 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:41:40 on modular  [Seed = 1154939743]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:42:46 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=761 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:42:23 on modular  [Seed = 3157132236]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:43:07 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=762 ;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:43:02 on modular  [Seed = 3022392317]
   -------------------------------------

z^762 + z^83 + 1
z^762 + z^679 + 1

Total time: 4.529 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:43:47 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=767;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:43:42 on modular  [Seed = 2872644619]
   -------------------------------------

z^767 + z^168 + 1
z^767 + z^254 + 1
z^767 + z^513 + 1
z^767 + z^599 + 1

Total time: 4.539 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:44:01 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=769;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:43:58 on modular  [Seed = 2737904690]
   -------------------------------------

z^769 + z^120 + 1
z^769 + z^216 + 1
z^769 + z^322 + 1
z^769 + z^447 + 1
z^769 + z^553 + 1
z^769 + z^649 + 1

Total time: 3.769 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:44:40 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=772;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:44:36 on modular  [Seed = 2601067632]
   -------------------------------------

z^772 + z^7 + 1
z^772 + z^121 + 1
z^772 + z^651 + 1
z^772 + z^765 + 1

Total time: 4.069 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:44:59 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=774;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:44:55 on modular  [Seed = 2466327627]
   -------------------------------------

z^774 + z^185 + 1
z^774 + z^589 + 1

Total time: 4.369 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:45:34 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=775;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:45:11 on modular  [Seed = 2316842306]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:45:44 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=777;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:45:39 on modular  [Seed = 2148778156]
   -------------------------------------

z^777 + z^29 + 1
z^777 + z^302 + 1
z^777 + z^475 + 1
z^777 + z^748 + 1

Total time: 4.939 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:46:01 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=778;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:45:56 on modular  [Seed = 4167809251]
   -------------------------------------

z^778 + z^375 + 1
z^778 + z^403 + 1

Total time: 5.059 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:46:32 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=780;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:46:27 on modular  [Seed = 4033065100]
   -------------------------------------


Total time: 4.829 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:46:47 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=782;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:46:43 on modular  [Seed = 3900418180]
   -------------------------------------

z^782 + z^329 + 1
z^782 + z^453 + 1

Total time: 4.709 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:47:10 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=783;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:47:06 on modular  [Seed = 3765674165]
   -------------------------------------

z^783 + z^68 + 1
z^783 + z^71 + 1
z^783 + z^103 + 1
z^783 + z^680 + 1
z^783 + z^712 + 1
z^783 + z^715 + 1

Total time: 4.189 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:47:32 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=785;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:47:28 on modular  [Seed = 3611596648]
   -------------------------------------

z^785 + z^92 + 1
z^785 + z^191 + 1
z^785 + z^212 + 1
z^785 + z^219 + 1
z^785 + z^566 + 1
z^785 + z^573 + 1
z^785 + z^594 + 1
z^785 + z^693 + 1

Total time: 4.419 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:48:43 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=791;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:48:20 on modular  [Seed = 3428813894]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:49:16 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=793;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:48:53 on modular  [Seed = 3294069806]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:49:29 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=794;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:49:22 on modular  [Seed = 1862086365]
   -------------------------------------

z^794 + z^143 + 1
z^794 + z^651 + 1

Total time: 6.949 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:50:02 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=798;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:49:57 on modular  [Seed = 1994733346]
   -------------------------------------


Total time: 4.599 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:50:36 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=799;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:50:13 on modular  [Seed = 2129477402]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:51:59 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=899;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:51:55 on modular  [Seed = 110446540]
   -------------------------------------


Total time: 3.789 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:52:17 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=898;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:52:12 on modular  [Seed = 245190611]
   -------------------------------------

z^898 + z^207 + 1
z^898 + z^691 + 1

Total time: 4.819 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:53:02 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=897;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:52:58 on modular  [Seed = 377837469]
   -------------------------------------

z^897 + z^113 + 1
z^897 + z^382 + 1
z^897 + z^515 + 1
z^897 + z^784 + 1

Total time: 4.189 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:53:15 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=895;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:53:11 on modular  [Seed = 548626870]
   -------------------------------------

z^895 + z^12 + 1
z^895 + z^883 + 1

Total time: 4.529 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:54:35 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=894;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:54:31 on modular  [Seed = 716793932]
   -------------------------------------

z^894 + z^173 + 1
z^894 + z^721 + 1

Total time: 4.249 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:54:56 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=892;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:54:50 on modular  [Seed = 849440840]
   -------------------------------------

z^892 + z^31 + 1
z^892 + z^861 + 1

Total time: 5.049 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:55:27 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=890;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:55:24 on modular  [Seed = 1034845984]
   -------------------------------------


Total time: 3.759 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:56:25 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=807;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:56:02 on modular  [Seed = 3310782214]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:56:53 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=809;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:56:30 on modular  [Seed = 3445526290]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:57:08 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=810
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:57:05 on modular  [Seed = 3594884182]
   -------------------------------------


>>     for i:=1 to m-1 do
       ^
User error: bad syntax

>>          Q<z>:=z^m + z^i +1;
                    ^
User error: Identifier 'm' has not been declared or assigned

>>          if IsPrimitive(Q)
                           ^
User error: Identifier 'Q' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Fri Jun 18 10:57:19 2004

Input: P<z>:=PolynomialRing(GF(2));
   m:=810;
    for i:=1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
  
end for;


Output: Magma V2.10-22    Fri Jun 18 2004 10:57:14 on modular  [Seed = 3729628245]
   -------------------------------------

z^810 + z^299 + 1
z^810 + z^511 + 1

Total time: 4.999 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host 3(NXDOMAIN) (164.81.181.245)
Time: Fri Jun 18 11:09:49 2004

Input: 3+3;

Output: Magma V2.10-22    Fri Jun 18 2004 11:09:46 on modular  [Seed = 2148779387]
   -------------------------------------

6

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (164.81.181.245)
Time: Fri Jun 18 11:10:11 2004

Input: 30!;

Output: Magma V2.10-22    Fri Jun 18 2004 11:10:08 on modular  [Seed = 2283523353]
   -------------------------------------


>> 30!;;
      ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (164.81.181.245)
Time: Fri Jun 18 11:10:26 2004

Input: 30 !;

Output: Magma V2.10-22    Fri Jun 18 2004 11:10:24 on modular  [Seed = 2466305586]
   -------------------------------------


>> 30 !;;
       ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (164.81.181.245)
Time: Fri Jun 18 11:10:49 2004

Input: factorial(30);

Output: Magma V2.10-22    Fri Jun 18 2004 11:10:47 on modular  [Seed = 2601049645]
   -------------------------------------


>> factorial(30);;
   ^
User error: Identifier 'factorial' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:29:33 2004

Input: E:=EllipticCurve([1,0,0,-134,-1942]);
Factorization(Numerator(Discriminant(E)));
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));
for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);
B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(1558,2,+1)))));
for i in [1..#B] do CongruenceGroupAnemic(Parent(Newform(E)),B[i]);


Output: Magma V2.10-22    Sat Jun 19 2004 16:29:29 on modular  [Seed = 2499901416]
   -------------------------------------

[ <2, 1>, <19, 1>, <41, 2>, <151, 2> ]

User error: syntax error at end of input

Total time: 2.869 seconds, Total memory usage: 2.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:30:27 2004

Input: E:=EllipticCurve([1,0,0,-134,-1942]);
Factorization(Numerator(Discriminant(E)));
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));
for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);end for;
B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(1558,2,+1)))));
for i in [1..#B] do CongruenceGroupAnemic(Parent(Newform(E)),B[i]);end for;


Output: Magma V2.10-22    Sat Jun 19 2004 16:30:04 on modular  [Seed = 2634645381]
   -------------------------------------

[ <2, 1>, <19, 1>, <41, 2>, <151, 2> ]

>> for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);end for;
                                            ^
Runtime error in 'CongruenceGroupAnemic': Bad argument types
Argument types given: ModFrm, ModSym


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:34:22 2004

Input: E:=EllipticCurve([1,0,0,-134,-1942]);
Factorization(Numerator(Discriminant(E)));
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));#A;
for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);end for;
B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(1558,2,+1)))));
for i in [1..#B] do CongruenceGroupAnemic(Parent(Newform(E)),B[i]);end for;


Output: Magma V2.10-22    Sat Jun 19 2004 16:33:59 on modular  [Seed = 2182504929]
   -------------------------------------

[ <2, 1>, <19, 1>, <41, 2>, <151, 2> ]
2

>> for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);end for;
                                            ^
Runtime error in 'CongruenceGroupAnemic': Bad argument types
Argument types given: ModFrm, ModSym


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:35:32 2004

Input: E:=EllipticCurve([1,0,0,-134,-1942]);
Factorization(Numerator(Discriminant(E)));
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));A[1];A[2];
for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);end for;
B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(1558,2,+1)))));
for i in [1..#B] do CongruenceGroupAnemic(Parent(Newform(E)),B[i]);end for;


Output: Magma V2.10-22    Sat Jun 19 2004 16:35:09 on modular  [Seed = 2334091426]
   -------------------------------------

[ <2, 1>, <19, 1>, <41, 2>, <151, 2> ]
Modular symbols space for Gamma_0(38) of weight 2 and dimension 1 over Rational 
Field
Modular symbols space for Gamma_0(38) of weight 2 and dimension 1 over Rational 
Field

>> for i in [1..#A] do CongruenceGroupAnemic(Parent(Newform(E)),A[i]);end for;
                                            ^
Runtime error in 'CongruenceGroupAnemic': Bad argument types
Argument types given: ModFrm, ModSym


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:37:14 2004

Input: E:=EllipticCurve([1,0,0,-134,-1942]);
Factorization(Numerator(Discriminant(E)));
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));A[1];A[2];
for i in [1..#A] do CongruenceGroupAnemic(Newform(E),A[i]);end for;
B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(1558,2,+1)))));
for i in [1..#B] do CongruenceGroupAnemic(Parent(Newform(E)),B[i]);end for;


Output: Magma V2.10-22    Sat Jun 19 2004 16:36:51 on modular  [Seed = 3089914639]
   -------------------------------------

[ <2, 1>, <19, 1>, <41, 2>, <151, 2> ]
Modular symbols space for Gamma_0(38) of weight 2 and dimension 1 over Rational 
Field
Modular symbols space for Gamma_0(38) of weight 2 and dimension 1 over Rational 
Field

>> for i in [1..#A] do CongruenceGroupAnemic(Newform(E),A[i]);end for;
                                            ^
Runtime error in 'CongruenceGroupAnemic': Bad argument types
Argument types given: ModFrmElt, ModSym


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:55:37 2004

Input: a:=x^2;
Evaluate(a,2);

Output: Magma V2.10-22    Sat Jun 19 2004 16:55:34 on modular  [Seed = 1744015220]
   -------------------------------------


>> a:=x^2;
      ^
User error: Identifier 'x' has not been declared or assigned

>> Evaluate(a,2);;
            ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:55:58 2004

Input: 
Evaluate(x^2,2);

Output: Magma V2.10-22    Sat Jun 19 2004 16:55:56 on modular  [Seed = 1878755174]
   -------------------------------------


>> Evaluate(x^2,2);;
            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:57:24 2004

Input: x:=PolynomialRing(Integer);
Evaluate(x^2,2);

Output: Magma V2.10-22    Sat Jun 19 2004 16:57:21 on modular  [Seed = 377683698]
   -------------------------------------


>> x:=PolynomialRing(Integer);
                     ^
User error: Identifier 'Integer' has not been declared or assigned

>> Evaluate(x^2,2);;
            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:57:37 2004

Input: x:=PolynomialRing(Integer());
Evaluate(x^2,2);

Output: Magma V2.10-22    Sat Jun 19 2004 16:57:34 on modular  [Seed = 76606703]
   -------------------------------------


>> x:=PolynomialRing(Integer());
                     ^
User error: Identifier 'Integer' has not been declared or assigned

>> Evaluate(x^2,2);;
            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.869 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:57:54 2004

Input: x:=PolynomialRing(Integral());
Evaluate(x^2,2);

Output: Magma V2.10-22    Sat Jun 19 2004 16:57:52 on modular  [Seed = 144498829]
   -------------------------------------


>> x:=PolynomialRing(Integral());
                             ^
Runtime error in 'Integral': Bad argument types
Argument types given:

>> Evaluate(x^2,2);;
            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 16:58:16 2004

Input: x:=PolynomialRing(Rational());
Evaluate(x^2,2);

Output: Magma V2.10-22    Sat Jun 19 2004 16:58:13 on modular  [Seed = 866638723]
   -------------------------------------


>> x:=PolynomialRing(Rational());
                     ^
User error: Identifier 'Rational' has not been declared or assigned

>> Evaluate(x^2,2);;
            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:01:37 2004

Input: 1 + 4 - 25 - 109 + 241 + 1190 - 1135 - 6733 + 2767 + 21461 - 3614 - 39433 + 3260 + 40825 - 3413 - 21643 + 2596 + 4400 - 557 - 83 - 2;

Output: Magma V2.10-22    Sat Jun 19 2004 17:01:34 on modular  [Seed = 3510974506]
   -------------------------------------

-2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:04:34 2004

Input: 1 + 19 + 115 - 19 - 3080 - 10778 + 10489 + 137847 + 210359 - 447875 - 1721189 - 969835 + 3223988 + 5765754 + 2211273 - 2276177 - 2308540 - 588808 - 9592 + 7344 + 448;

Output: Magma V2.10-22    Sat Jun 19 2004 17:04:31 on modular  [Seed = 3310432207]
   -------------------------------------

3231744

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:06:36 2004

Input: 1 + 20 + 92 - 655 - 6846 - 5329 + 131218 + 392658 - 804539 - 4815430 - 956784 + 23094326 + 23024741 - 47879610 - 67958140 + 43508464 + 71378619 - 20571245 - 24696236 + 5194189 - 130994;

Output: Magma V2.10-22    Sat Jun 19 2004 17:06:33 on modular  [Seed = 3478857027]
   -------------------------------------

-1101480

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:08:43 2004

Input: 1 + 16 - 63 - 2440 - 7789 + 115762 + 839554 - 985379 - 26167599 - 59644441 + 257356203 + 1408879306 + 897128040 - 8008409328 - 20356239189 - 7841226433 + 32086771726 + 42607668486 + 5343112275 - 18185702065 - 8258811291;

Output: Magma V2.10-22    Sat Jun 19 2004 17:08:40 on modular  [Seed = 4251522800]
   -------------------------------------

19864675352

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:10:51 2004

Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));#A;
CongruenceGroupAnemic(A[1],A[2]);

Output: Magma V2.10-22    Sat Jun 19 2004 17:10:48 on modular  [Seed = 3967289185]
   -------------------------------------

2

>> CongruenceGroupAnemic(A[1],A[2]);;
                        ^
Runtime error in 'CongruenceGroupAnemic': Bad argument types
Argument types given: ModSym, ModSym

Total time: 2.889 seconds, Total memory usage: 2.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:11:32 2004

Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1)))));#A;
CongruenceGroup(A[1],A[2]);

Output: Magma V2.10-22    Sat Jun 19 2004 17:11:29 on modular  [Seed = 2483058880]
   -------------------------------------

2

>> CongruenceGroup(A[1],A[2]);;
                  ^
Runtime error in 'CongruenceGroup': Bad argument types
Argument types given: ModSym, ModSym

Total time: 2.909 seconds, Total memory usage: 2.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:14:48 2004

Input: 1 + 6 + 6 - 14 - 15 - 1 + 1;

Output: Magma V2.10-22    Sat Jun 19 2004 17:14:45 on modular  [Seed = 2550952968]
   -------------------------------------

-16

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:15:47 2004

Input: 1 + 5 - 3 - 49 - 64 + 23 + 53;

Output: Magma V2.10-22    Sat Jun 19 2004 17:15:44 on modular  [Seed = 2182508503]
   -------------------------------------

-34

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:16:50 2004

Input: 1 + 1 - 50 - 11 + 261 - 209 + 41;

Output: Magma V2.10-22    Sat Jun 19 2004 17:16:47 on modular  [Seed = 3038861535]
   -------------------------------------

34

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.53.95.63)
Time: Sat Jun 19 17:17:50 2004

Input:  1 + 17 + 99 + 220 + 62 - 342 - 293;

Output: Magma V2.10-22    Sat Jun 19 2004 17:17:48 on modular  [Seed = 3106755728]
   -------------------------------------

-236

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:00:29 2004

Input: print 4+4


Output: Magma V2.10-22    Sat Jun 19 2004 21:00:26 on modular  [Seed = 950835658]
   -------------------------------------

8

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:00:47 2004

Input: ?print


Output: Magma V2.10-22    Sat Jun 19 2004 21:00:45 on modular  [Seed = 816091605]
   -------------------------------------

29 matches:
     1   O   /language/statement/print
     2   S   /language/IO/print
     3   S   /language/IO/print/auto-print
     4   S   /language/IO/print/print
     5   S   /magma/combinatorial-geometrical-incidence/network/\
             network-constr/network-print
     6   S   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access
     7   S   /magma/ring-field-algebra/distributive-multivariate-polynomial/\
             rings/print
     8   I   /language/IO/print/print/print
     9   I   /language/IO/print/printing-file/PrintFile
    10   I   /language/IO/print/printing-file/PrintFile
    11   I   /language/IO/print/printing-file/PrintFileMagma
    12   I   /magma/geometry/grd-rng/introduction/K3Print
    13   I   /magma/geometry/grd-rng/introduction/K3Print
    14   I   /magma/geometry/grd-rng/introduction/K3PrintDatabase
    15   I   /magma/geometry/grd-rng/introduction/K3PrintDatabase
    16   I   /magma/group/braid/braid-groups-construction/GetElementPrintFormat
    17   I   /magma/group/braid/braid-groups-construction/SetElementPrintFormat
    18   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintCollector
    19   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintExtensions
    20   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintModules
    21   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintPrimes
    22   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintProcess
    23   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintProcess
    24   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintQuotient
    25   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintRelat
    26   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintSeries
    27   I   /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree
    28   I   /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision
    29   I   /system/environment-options/Set-Get/SetPrintLevel
To view an entry, type ? followed by the number next to it

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:02:12 2004

Input: ?print
?29


Output: Magma V2.10-22    Sat Jun 19 2004 21:02:10 on modular  [Seed = 717129824]
   -------------------------------------

29 matches:
     1   O   /language/statement/print
     2   S   /language/IO/print
     3   S   /language/IO/print/auto-print
     4   S   /language/IO/print/print
     5   S   /magma/combinatorial-geometrical-incidence/network/\
             network-constr/network-print
     6   S   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access
     7   S   /magma/ring-field-algebra/distributive-multivariate-polynomial/\
             rings/print
     8   I   /language/IO/print/print/print
     9   I   /language/IO/print/printing-file/PrintFile
    10   I   /language/IO/print/printing-file/PrintFile
    11   I   /language/IO/print/printing-file/PrintFileMagma
    12   I   /magma/geometry/grd-rng/introduction/K3Print
    13   I   /magma/geometry/grd-rng/introduction/K3Print
    14   I   /magma/geometry/grd-rng/introduction/K3PrintDatabase
    15   I   /magma/geometry/grd-rng/introduction/K3PrintDatabase
    16   I   /magma/group/braid/braid-groups-construction/GetElementPrintFormat
    17   I   /magma/group/braid/braid-groups-construction/SetElementPrintFormat
    18   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintCollector
    19   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintExtensions
    20   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintModules
    21   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintPrimes
    22   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintProcess
    23   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintProcess
    24   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintQuotient
    25   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintRelat
    26   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/print-access/PrintSeries
    27   I   /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree
    28   I   /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision
    29   I   /system/environment-options/Set-Get/SetPrintLevel
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /system/environment-options/Set-Get/SetPrintLevel
KIND: Intrinsic
===============================================================================
SetPrintLevel(l) : MonStgElt ->
GetPrintLevel() : -> MonStgElt

    Controls the global printing level, which is one of "Minimal",
    "Magma", "Maximal", "Default".  Default is SetPrintLevel("Default").
===============================================================================

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:02:57 2004

Input: ?setup


Output: Magma V2.10-22    Sat Jun 19 2004 21:02:54 on modular  [Seed = 3679418813]
   -------------------------------------

No references for word "setup"

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:04:13 2004

Input: ?config



Output: Magma V2.10-22    Sat Jun 19 2004 21:04:10 on modular  [Seed = 3577837319]
   -------------------------------------

No references for word "config"

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:04:56 2004

Input: Help


Output: Magma V2.10-22    Sat Jun 19 2004 21:04:54 on modular  [Seed = 3462032416]
   -------------------------------------


>> Help
   ^
User error: Identifier 'Help' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 100.pittsburgh-08rh16rt.pa.dial-access.att.net. (12.76.123.100)
Time: Sat Jun 19 21:05:12 2004

Input: HELP

Output: Magma V2.10-22    Sat Jun 19 2004 21:05:10 on modular  [Seed = 3327288408]
   -------------------------------------


>> HELP;
   ^
User error: Identifier 'HELP' has not been declared or assigned

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:51:56 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x);
D := Curve(A, x - 2);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:51:51 on modular  [Seed = 615634645]
   -------------------------------------

0

Total time: 2.829 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:52:10 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x);
D := Curve(A, y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:52:07 on modular  [Seed = 899729403]
   -------------------------------------

1

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:52:26 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:52:23 on modular  [Seed = 228130771]
   -------------------------------------

2

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:52:43 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, y^2+x^3);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:52:40 on modular  [Seed = 93386660]
   -------------------------------------

4

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:53:12 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, y^2+x^2);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:53:10 on modular  [Seed = 529198480]
   -------------------------------------

Infinity

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:54:16 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, (y+3)^2+x^2);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:54:13 on modular  [Seed = 377742682]
   -------------------------------------

0

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:54:39 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, x^2+x^2+1);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:54:37 on modular  [Seed = 4001045946]
   -------------------------------------

0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:55:08 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, x^2+y^2+1);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:55:06 on modular  [Seed = 3866301909]
   -------------------------------------

0

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:55:21 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, x^2);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:55:19 on modular  [Seed = 4268428784]
   -------------------------------------

4

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:56:15 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x);
D := Curve(A, x+1);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:56:12 on modular  [Seed = 4133684483]
   -------------------------------------

0

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:57:03 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x);
D := Curve(A, x);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:57:01 on modular  [Seed = 3462085994]
   -------------------------------------

Infinity

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:58:08 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, (x-1)^2+(y-1)^2);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:58:05 on modular  [Seed = 3712494010]
   -------------------------------------

0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:58:58 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A, (x^2 - y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:58:55 on modular  [Seed = 3561037954]
   -------------------------------------


>> D := Curve(A, (x^2 - y);
                          ^
User error: bad syntax

>> IntersectionNumber(C,D,p);;
                        ^
User error: Identifier 'D' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 11:59:10 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x^2+y^2);
D := Curve(A,x^2 - y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 11:59:07 on modular  [Seed = 2889439374]
   -------------------------------------

2

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:00:04 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A, x-y);
D := Curve(A,x);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:00:01 on modular  [Seed = 2754695244]
   -------------------------------------

1

Total time: 2.539 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:02:56 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x-y);
D := Curve(A,x+1-y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:02:53 on modular  [Seed = 2148890052]
   -------------------------------------

0

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:03:10 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x-y);
D := Curve(A,x+y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:03:08 on modular  [Seed = 2551016909]
   -------------------------------------

1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:04:17 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^2-y^2);
D := Curve(A,x^2-y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:04:14 on modular  [Seed = 2466670212]
   -------------------------------------

2

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:05:05 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^3-y);
D := Curve(A,x^2-y);
p := Origin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:05:03 on modular  [Seed = 1761451437]
   -------------------------------------

2

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:05:54 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^3-y);
D := Curve(A,x^2-y);
p := (1,1);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:05:51 on modular  [Seed = 1710264528]
   -------------------------------------


>> p := (1,1);
        ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

>> IntersectionNumber(C,D,p);;
                          ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:06:34 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^3-y);
D := Curve(A,x^2-y);
p := Orgin(A);
IntersectionNumber(C,D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:06:32 on modular  [Seed = 2112391967]
   -------------------------------------


>> p := Orgin(A);
        ^
User error: Identifier 'Orgin' has not been declared or assigned

>> IntersectionNumber(C,D,p);;
                          ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:07:16 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^3-y);
D := Curve(A,x^2-y);
p := Origin(A);
IntersectionNumber(C,D,p);
Multiplicity(C,p) * Multiplicity(D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:07:13 on modular  [Seed = 1289337367]
   -------------------------------------

2
1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:10:26 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,(x^2+y^2)^2+3*x^2*y-y^3);
D := Curve(A,(x^2+y^2)^3+4*x^2*y^2);
p := Origin(A);
IntersectionNumber(C,D,p);
Multiplicity(C,p) * Multiplicity(D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:10:23 on modular  [Seed = 1607117274]
   -------------------------------------

14
12

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:11:41 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,(x^2+y^2)^2+3*x^2*y-y^3);
D := Curve(A,(x^2+y^2)^3+4*x^2*y^2);
p := Origin(A);
GCD(C,D);
IntersectionNumber(C,D,p);
Multiplicity(C,p) * Multiplicity(D,p);

Output: Magma V2.10-22    Sun Jun 20 2004 12:11:39 on modular  [Seed = 1472372742]
   -------------------------------------


>> GCD(C,D);
      ^
Runtime error in 'GCD': Bad argument types
Argument types given: Crv, Crv
14
12

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:14:09 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,(x^2+y^2)^2+3*x^2*y-y^3);
D := Curve(A,(x^2+y^2)^3+4*x^2*y^2);
p := Origin(A);
GCD((x^2+y^2)^2+3*x^2*y-y^3,(x^2+y^2)^3+4*x^2*y^2);


Output: Magma V2.10-22    Sun Jun 20 2004 12:14:06 on modular  [Seed = 750377864]
   -------------------------------------

1

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E17BAE.dip.t-dialin.net. (217.225.123.174)
Time: Sun Jun 20 12:14:30 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,(x^2+y^2)^2+3*x^2*y-y^3);
D := Curve(A,(x^2+y^2)^3+4*x^2*y^2);
p := Origin(A);
GCD((x^2+y^2)^2+3*x^2*y-y^3,(x^2+y^2));


Output: Magma V2.10-22    Sun Jun 20 2004 12:14:27 on modular  [Seed = 615633837]
   -------------------------------------

1

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host duvar.bilten.metu.edu.tr. (193.140.92.250)
Time: Mon Jun 21 03:06:53 2004

Input: 363

Output: Magma V2.10-22    Mon Jun 21 2004 03:06:47 on modular  [Seed = 1472306724]
   -------------------------------------

363

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.186.125.210)
Time: Mon Jun 21 05:11:05 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Mon Jun 21 2004 05:11:03 on modular  [Seed = 1455468551]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host d213-101-198-69.cust.tele2.fr. (213.101.198.69)
Time: Mon Jun 21 08:42:25 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Mon Jun 21 2004 08:42:19 on modular  [Seed = 178036187]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.690 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host d213-102-161-186.cust.tele2.fr. (213.102.161.186)
Time: Mon Jun 21 08:42:26 2004

Input: u=7


Output: Magma V2.10-22    Mon Jun 21 2004 08:42:23 on modular  [Seed = 144613341]
   -------------------------------------


>> u=7
   ^
User error: Identifier 'u' has not been declared or assigned

Total time: 3.179 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host d213-102-161-186.cust.tele2.fr. (213.102.161.186)
Time: Mon Jun 21 08:42:27 2004

Input: u=7


Output: Magma V2.10-22    Mon Jun 21 2004 08:42:24 on modular  [Seed = 244881860]
   -------------------------------------


>> u=7
   ^
User error: Identifier 'u' has not been declared or assigned

Total time: 3.079 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host d213-101-198-69.cust.tele2.fr. (213.101.198.69)
Time: Mon Jun 21 08:42:50 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"




mm

Output: Magma V2.10-22    Mon Jun 21 2004 08:42:48 on modular  [Seed = 4066665792]
   -------------------------------------


>> mm;
   ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host badiane.ens.fr. (129.199.98.43)
Time: Mon Jun 21 09:45:52 2004

Input: 3+4;


Output: Magma V2.10-22    Mon Jun 21 2004 09:45:49 on modular  [Seed = 833066951]
   -------------------------------------

7

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:05:02 2004

Input: Q<s,t,u>, h := Group< a, b | a^3, b^4, ab = ba^2 >;


Output: Magma V2.10-22    Mon Jun 21 2004 11:04:59 on modular  [Seed = 1339684392]
   -------------------------------------


>> Q<s,t,u>, h := Group< a, b | a^3, b^4, ab = ba^2 >;
                                               ^
User error: Identifier 'ba' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:05:15 2004

Input: Q<s,t,u> := Group< a, b | a^3, b^4, a*b = b*a^2 >;


Output: Magma V2.10-22    Mon Jun 21 2004 11:05:12 on modular  [Seed = 1204944403]
   -------------------------------------


>> Q<s,t,u> := Group< a, b | a^3, b^4, a*b = b*a^2 >;
    ^
Runtime error in 'AssignNames': Too many names given for this object

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:05:25 2004

Input: G<a, b> := Group< a, b | a^3, b^4, a*b = b*a^2 >;


Output: Magma V2.10-22    Mon Jun 21 2004 11:05:22 on modular  [Seed = 1068074609]
   -------------------------------------


Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:06:30 2004

Input: G<a, b> := Group< a, b | a^3, b^4, a*b = b*a^2 >;
Order(G);


Output: Magma V2.10-22    Mon Jun 21 2004 11:06:27 on modular  [Seed = 816220479]
   -------------------------------------

12

Total time: 2.699 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:08:11 2004

Input: G<a, b> := Group< a, b | a^3, b^4, a*b = b*a^2 >;
Order(G);
ConjugacyClasses(G);


Output: Magma V2.10-22    Mon Jun 21 2004 11:08:09 on modular  [Seed = 649109379]
   -------------------------------------

12

>> ConjugacyClasses(G);
                   ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: GrpFP

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:14:10 2004

Input: G<a, b> := Group< a, b | a^3, b^4, a*b = b*a^2 >;
Order(G);
CharacterTable(G);


Output: Magma V2.10-22    Mon Jun 21 2004 11:14:07 on modular  [Seed = 194883656]
   -------------------------------------

12

>> CharacterTable(G);
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.659 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:18:50 2004

Input: G<a,b> := PolycyclicGroup< a, b | a^3, b^4, a^b = a^2 >;


Output: Magma V2.10-22    Mon Jun 21 2004 11:18:48 on modular  [Seed = 4218243039]
   -------------------------------------


>> G<a,b> := PolycyclicGroup< a, b | a^3, b^4, a^b = a^2 >;
                            ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : 
$.2^$.1 = $.1^2

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:19:23 2004

Input: G<a,b> := PolycyclicGroup< a, b | b^4, a^3, a^b = a^2 >;


Output: Magma V2.10-22    Mon Jun 21 2004 11:19:20 on modular  [Seed = 3967439080]
   -------------------------------------


>> G<a,b> := PolycyclicGroup< a, b | b^4, a^3, a^b = a^2 >;
                            ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : 
$.2^$.1 = $.1^2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:19:51 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;


Output: Magma V2.10-22    Mon Jun 21 2004 11:19:48 on modular  [Seed = 3816120075]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:19:59 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;
G;


Output: Magma V2.10-22    Mon Jun 21 2004 11:19:57 on modular  [Seed = 3679283002]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:20:14 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;
G;
a*b;


Output: Magma V2.10-22    Mon Jun 21 2004 11:20:12 on modular  [Seed = 3190293102]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b * a^2

Total time: 2.479 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:20:32 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;
G;
CharacterTable(G);

Output: Magma V2.10-22    Mon Jun 21 2004 11:20:30 on modular  [Seed = 3072396149]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2

>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:20:49 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;
G;
ConjugacyClasses(G);

Output: Magma V2.10-22    Mon Jun 21 2004 11:20:46 on modular  [Seed = 2939753245]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2

>> ConjugacyClasses(G);;
                   ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: GrpGPC

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:22:58 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;
G;
NumberOfClasses(G);
ConjugacyClasses(G);

Output: Magma V2.10-22    Mon Jun 21 2004 11:22:55 on modular  [Seed = 2317105081]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2

>> NumberOfClasses(G);
                  ^
Runtime error in 'NumberOfClasses': Bad argument types
Argument types given: GrpGPC

>> ConjugacyClasses(G);;
                   ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: GrpGPC

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pcp03773043pcs.chrstn01.pa.comcast.net. (68.34.178.134)
Time: Mon Jun 21 11:23:29 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a^b = a^2 >;
G;
Classes(G);

Output: Magma V2.10-22    Mon Jun 21 2004 11:23:27 on modular  [Seed = 1927597920]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2

>> Classes(G);;
          ^
Runtime error in 'Classes': Bad argument types
Argument types given: GrpGPC

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:25:12 2004

Input: E:=EllipticCurve([0,1,0,4,0]);
E;

Output: Magma V2.10-22    Mon Jun 21 2004 11:25:09 on modular  [Seed = 1272837859]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x^2 + 4*x over Rational Field

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:29:00 2004

Input: E:=EllipticCurve([0,1,0,4,0]);
E;
G,m:=MordellWeilGroup(E);
G;

Output: Magma V2.10-22    Mon Jun 21 2004 11:28:57 on modular  [Seed = 582261990]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x^2 + 4*x over Rational Field
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*G.1 = 0

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:29:43 2004

Input: E:=EllipticCurve([0,17,0,16,0]);
E;
G,m:=MordellWeilGroup(E);
G;

Output: Magma V2.10-22    Mon Jun 21 2004 11:29:39 on modular  [Seed = 43302044]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 17*x^2 + 16*x over Rational Field
Abelian Group isomorphic to Z/2 + Z/4
Defined on 2 generators
Relations:
    2*G.1 = 0
    4*G.2 = 0

Total time: 3.139 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:30:38 2004

Input: E:=EllipticCurve([0,10,0,16,0]);
E;
G,m:=MordellWeilGroup(E);
G;

Output: Magma V2.10-22    Mon Jun 21 2004 11:30:36 on modular  [Seed = 4133505431]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 10*x^2 + 16*x over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:32:14 2004

Input: E:=EllipticCurve([0,10,0,16,0]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:32:11 on modular  [Seed = 3900594158]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 10*x^2 + 16*x over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(0 : 0 : 1)
(-2 : 0 : 1)
[ 2, 3 ]

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:33:19 2004

Input: E:=EllipticCurve([0,10,0,16,0]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:33:17 on modular  [Seed = 3799276834]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 10*x^2 + 16*x over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(0 : 0 : 1)
(-2 : 0 : 1)
147456

>> Factorization(Discriminant(E));
                ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldRatElt
[ 2, 3 ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:34:08 2004

Input: E:=EllipticCurve([0,10,0,16,0]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:34:05 on modular  [Seed = 3577965125]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 10*x^2 + 16*x over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(0 : 0 : 1)
(-2 : 0 : 1)
147456
[ <2, 14>, <3, 2> ]
[ 2, 3 ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache00.erlm.siemens.de. (217.194.34.120)
Time: Mon Jun 21 11:39:47 2004

Input: factor(99999999999999999)

Output: Magma V2.10-22    Mon Jun 21 2004 11:39:44 on modular  [Seed = 3106863236]
   -------------------------------------


>> factor(99999999999999999);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache00.erlm.siemens.de. (217.194.34.120)
Time: Mon Jun 21 11:40:32 2004

Input: ifactor(99999999999999999)

Output: Magma V2.10-22    Mon Jun 21 2004 11:40:30 on modular  [Seed = 2721440689]
   -------------------------------------


>> ifactor(99999999999999999);
   ^
User error: Identifier 'ifactor' has not been declared or assigned

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:41:42 2004

Input: E:=EllipticCurve([0,9,0,23,15]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:41:40 on modular  [Seed = 2199175754]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 9*x^2 + 23*x + 15 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(-5 : 0 : 1)
(-3 : 0 : 1)
4096
[ <2, 12> ]
[ 2 ]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:43:18 2004

Input: E:=EllipticCurve([0,-9,0,23,-15]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:43:16 on modular  [Seed = 1743791373]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 9*x^2 + 23*x - 15 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(1 : 0 : 1)
(3 : 0 : 1)
4096
[ <2, 12> ]
[ 2 ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:45:20 2004

Input: E:=EllipticCurve([0,11,0,31,-21]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:45:17 on modular  [Seed = 1540102568]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11*x^2 + 31*x - 21 over Rational Field
Abelian Group isomorphic to Z
Defined on 1 generator (free)
(310/49 : -10109/343 : 1)

>> g[2];
    ^
Runtime error in '[]': Sequence element 2 not defined
-510144
[ <2, 6>, <3, 1>, <2657, 1> ]
[ 2, 3, 2657 ]

Total time: 2.679 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:45:59 2004

Input: E:=EllipticCurve([0,11,0,31,21]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:45:56 on modular  [Seed = 1355223706]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11*x^2 + 31*x + 21 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2 + Z
Defined on 3 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(-7 : 0 : 1)
(-3 : 0 : 1)
36864
[ <2, 12>, <3, 2> ]
[ 2, 3 ]

Total time: 2.679 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:47:57 2004

Input: E:=EllipticCurve([0,10,0,31,30]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:47:55 on modular  [Seed = 1188103443]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 10*x^2 + 31*x + 30 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(-5 : 0 : 1)
(-3 : 0 : 1)
576
[ <2, 6>, <3, 2> ]
[ 2, 3 ]

Total time: 2.579 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:48:37 2004

Input: E:=EllipticCurve([0,-10,0,31,-30]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:48:35 on modular  [Seed = 1017872145]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 10*x^2 + 31*x - 30 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(2 : 0 : 1)
(3 : 0 : 1)
576
[ <2, 6>, <3, 2> ]
[ 2, 3 ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:50:41 2004

Input: E:=EllipticCurve([0,12,0,41,42]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:50:39 on modular  [Seed = 783904159]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 12*x^2 + 41*x + 42 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(-7 : 0 : 1)
(-3 : 0 : 1)
6400
[ <2, 8>, <5, 2> ]
[ 2, 5 ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.248.72.37)
Time: Mon Jun 21 11:51:29 2004

Input: E:=EllipticCurve([0,-12,0,41,-42]);
E;
G,m:=MordellWeilGroup(E);
G;
g:=Generators(E);
g[1];
g[2];
Discriminant(E);
Factorization(Integers()!Discriminant(E));
BadPrimes(E);


Output: Magma V2.10-22    Mon Jun 21 2004 11:51:27 on modular  [Seed = 665871526]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 12*x^2 + 41*x - 42 over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*G.1 = 0
    2*G.2 = 0
(3 : 0 : 1)
(7 : 0 : 1)
6400
[ <2, 8>, <5, 2> ]
[ 2, 5 ]

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host host40.200-117-219.telecom.net.ar. (200.117.219.40)
Time: Mon Jun 21 13:56:18 2004

Input: 1+1

Output: Magma V2.10-22    Mon Jun 21 2004 13:56:15 on modular  [Seed = 3243679873]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host host40.200-117-219.telecom.net.ar. (200.117.219.40)
Time: Mon Jun 21 13:57:32 2004

Input: (a+1)*(a+1)-a

Output: Magma V2.10-22    Mon Jun 21 2004 13:57:29 on modular  [Seed = 3090143566]
   -------------------------------------


>> (a+1)*(a+1)-a;
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:47:42 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >;

Output: Magma V2.10-22    Mon Jun 21 2004 21:47:39 on modular  [Seed = 377608633]
   -------------------------------------


Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:47:49 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >;
Order(G);

Output: Magma V2.10-22    Mon Jun 21 2004 21:47:46 on modular  [Seed = 512348616]
   -------------------------------------

12

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:48:07 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
a*b^-1;

Output: Magma V2.10-22    Mon Jun 21 2004 21:48:04 on modular  [Seed = 110217670]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b^3 * a^2

Total time: 2.549 seconds, Total memory usage: 2.35MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:48:30 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
a*b^(-1);

Output: Magma V2.10-22    Mon Jun 21 2004 21:48:28 on modular  [Seed = 261669111]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b^3 * a^2

Total time: 2.540 seconds, Total memory usage: 2.35MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:49:23 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
a*b^(-1);
ConjugacyClasses(G);

Output: Magma V2.10-22    Mon Jun 21 2004 21:49:20 on modular  [Seed = 816308228]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b^3 * a^2

>> ConjugacyClasses(G);;
                   ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: GrpGPC

Total time: 2.539 seconds, Total memory usage: 2.35MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:50:40 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(b)^(-1)*a*(b);
(b*a)^(-1)*a*(b*a);
(b*a^2)^(-1)*a*(b*a^2);
(b^2)^(-1)*a*(b^2);
(b^2*a)^(-1)*a*(b^2*a);
(b^2*a^2)^(-1)*a*(b^2*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:50:37 on modular  [Seed = 967764288]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
a^2
a^2
a^2
a
a
a

Total time: 2.609 seconds, Total memory usage: 3.38MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:54:06 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(b)^(-1)*a*(b);
(b*a)^(-1)*a*(b*a);
(b*a^2)^(-1)*a*(b*a^2);
(b^3)^(-1)*a*(b^3);
(b^3*a)^(-1)*a*(b^3*a);
(b^3*a^2)^(-1)*a*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:54:03 on modular  [Seed = 683669767]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
a^2
a^2
a^2
a^2
a^2
a^2

Total time: 2.619 seconds, Total memory usage: 3.38MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:54:36 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(b)^(-1)*b*(b);
(b*a)^(-1)*b*(b*a);
(b*a^2)^(-1)*b*(b*a^2);
(b^2)^(-1)*b*(b^2);
(b^2*a)^(-1)*b*(b^2*a);
(b^2*a^2)^(-1)*ab*(b^2*a^2);
(b^3)^(-1)*b*(b^3);
(b^3*a)^(-1)*b*(b^3*a);
(b^3*a^2)^(-1)*ab*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:54:34 on modular  [Seed = 1355251998]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b
b * a^2
b * a
b
b * a^2

>> (b^2*a^2)^(-1)*ab*(b^2*a^2);
                  ^
User error: Identifier 'ab' has not been declared or assigned
b
b * a^2

>> (b^3*a^2)^(-1)*ab*(b^3*a^2);
                  ^
User error: Identifier 'ab' has not been declared or assigned

Total time: 2.619 seconds, Total memory usage: 3.38MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:54:46 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(b)^(-1)*b*(b);
(b*a)^(-1)*b*(b*a);
(b*a^2)^(-1)*b*(b*a^2);
(b^2)^(-1)*b*(b^2);
(b^2*a)^(-1)*b*(b^2*a);
(b^2*a^2)^(-1)*ab*(b^2*a^2);
(b^3)^(-1)*b*(b^3);
(b^3*a)^(-1)*b*(b^3*a);
(b^3*a^2)^(-1)*b*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:54:44 on modular  [Seed = 1489996072]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b
b * a^2
b * a
b
b * a^2

>> (b^2*a^2)^(-1)*ab*(b^2*a^2);
                  ^
User error: Identifier 'ab' has not been declared or assigned
b
b * a^2
b * a

Total time: 2.639 seconds, Total memory usage: 3.38MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:54:56 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(b)^(-1)*b*(b);
(b*a)^(-1)*b*(b*a);
(b*a^2)^(-1)*b*(b*a^2);
(b^2)^(-1)*b*(b^2);
(b^2*a)^(-1)*b*(b^2*a);
(b^2*a^2)^(-1)*b*(b^2*a^2);
(b^3)^(-1)*b*(b^3);
(b^3*a)^(-1)*b*(b^3*a);
(b^3*a^2)^(-1)*b*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:54:53 on modular  [Seed = 1104580664]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b
b * a^2
b * a
b
b * a^2
b * a
b
b * a^2
b * a

Total time: 2.669 seconds, Total memory usage: 3.38MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:55:36 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(a)^(-1)*b*(a);
(a^2)^(-1)*b*(a^2);
(b)^(-1)*b*(b);
(b*a)^(-1)*b*(b*a);
(b*a^2)^(-1)*b*(b*a^2);
(b^2)^(-1)*b*(b^2);
(b^2*a)^(-1)*b*(b^2*a);
(b^2*a^2)^(-1)*b*(b^2*a^2);
(b^3)^(-1)*b*(b^3);
(b^3*a)^(-1)*b*(b^3*a);
(b^3*a^2)^(-1)*b*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:55:33 on modular  [Seed = 1239324872]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b * a^2
b * a
b
b * a^2
b * a
b
b * a^2
b * a
b
b * a^2
b * a

Total time: 2.749 seconds, Total memory usage: 3.38MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 21:56:09 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
(a)^(-1)*b^2*(a);
(a^2)^(-1)*b^2*(a^2);
(b)^(-1)*b^2*(b);
(b*a)^(-1)*b^2*(b*a);
(b*a^2)^(-1)*b^2*(b*a^2);
(b^2)^(-1)*b^2*(b^2);
(b^2*a)^(-1)*b^2*(b^2*a);
(b^2*a^2)^(-1)*b^2*(b^2*a^2);
(b^3)^(-1)*b^2*(b^3);
(b^3*a)^(-1)*b^2*(b^3*a);
(b^3*a^2)^(-1)*b^2*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 21:56:06 on modular  [Seed = 1927652304]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b^2
b^2
b^2
b^2
b^2
b^2
b^2
b^2
b^2
b^2
b^2

Total time: 2.719 seconds, Total memory usage: 3.72MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 22:00:27 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
c := b^2*a;
(a)^(-1)*c*(a);
(a^2)^(-1)*c*(a^2);
(b)^(-1)*c*(b);
(b*a)^(-1)*c*(b*a);
(b*a^2)^(-1)*c*(b*a^2);
(b^2)^(-1)*c*(b^2);
(b^2*a)^(-1)*c*(b^2*a);
(b^2*a^2)^(-1)*c*(b^2*a^2);
(b^3)^(-1)*c*(b^3);
(b^3*a)^(-1)*c*(b^3*a);
(b^3*a^2)^(-1)*c*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 22:00:25 on modular  [Seed = 2584561719]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b^2 * a
b^2 * a
b^2 * a^2
b^2 * a^2
b^2 * a^2
b^2 * a
b^2 * a
b^2 * a
b^2 * a^2
b^2 * a^2
b^2 * a^2

Total time: 2.689 seconds, Total memory usage: 3.72MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Mon Jun 21 22:00:47 2004

Input: G< b, a > := PolycyclicGroup< b, a | b^4, a^3, a^b=a^2 >; G;
c := b^3;
(a)^(-1)*c*(a);
(a^2)^(-1)*c*(a^2);
(b)^(-1)*c*(b);
(b*a)^(-1)*c*(b*a);
(b*a^2)^(-1)*c*(b*a^2);
(b^2)^(-1)*c*(b^2);
(b^2*a)^(-1)*c*(b^2*a);
(b^2*a^2)^(-1)*c*(b^2*a^2);
(b^3)^(-1)*c*(b^3);
(b^3*a)^(-1)*c*(b^3*a);
(b^3*a^2)^(-1)*c*(b^3*a^2);



Output: Magma V2.10-22    Mon Jun 21 2004 22:00:44 on modular  [Seed = 2182434906]
   -------------------------------------

GrpGPC : G of order 12 = 2^2 * 3 on 2 PC-generators
PC-Relations:
    b^4 = Id(G), 
    a^3 = Id(G), 
    a^b = a^2
b^3 * a^2
b^3 * a
b^3
b^3 * a^2
b^3 * a
b^3
b^3 * a^2
b^3 * a
b^3
b^3 * a^2
b^3 * a

Total time: 2.689 seconds, Total memory usage: 3.72MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:15:31 2004

Input: 1 + 2;

Output: Magma V2.10-22    Tue Jun 22 2004 13:15:26 on modular  [Seed = 850008923]
   -------------------------------------

3

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:30:17 2004

Input: list := SmallGroups(27, func<x|not IsAbelian(x)> );

Output: Magma V2.10-22    Tue Jun 22 2004 13:30:14 on modular  [Seed = 3294423077]
   -------------------------------------


Total time: 2.569 seconds, Total memory usage: 22.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:30:26 2004

Input: list := SmallGroups(27, func<x|not IsAbelian(x)> );
list;

Output: Magma V2.10-22    Tue Jun 22 2004 13:30:24 on modular  [Seed = 3729191465]
   -------------------------------------

[*
GrpPC of order 27 = 3^3
PC-Relations:
    $.2^$.1 = $.2 * $.3,

GrpPC of order 27 = 3^3
PC-Relations:
    $.1^3 = $.3, 
    $.2^$.1 = $.2 * $.3
*]

Total time: 2.549 seconds, Total memory usage: 22.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:30:34 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
list;

Output: Magma V2.10-22    Tue Jun 22 2004 13:30:31 on modular  [Seed = 3850225941]
   -------------------------------------

[*
GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^2 = $.2, 
    $.2^2 = Id($), 
    $.3^3 = Id($), 
    $.3^$.1 = $.3^2,

GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^3 = Id($), 
    $.2^2 = Id($), 
    $.3^2 = Id($), 
    $.2^$.1 = $.3, 
    $.3^$.1 = $.2 * $.3,

GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^2 = Id($), 
    $.2^2 = Id($), 
    $.3^3 = Id($), 
    $.3^$.1 = $.3^2
*]

Total time: 2.509 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:31:40 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
list;
G := list[1];

Output: Magma V2.10-22    Tue Jun 22 2004 13:31:37 on modular  [Seed = 2400690993]
   -------------------------------------

[*
GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^2 = $.2, 
    $.2^2 = Id($), 
    $.3^3 = Id($), 
    $.3^$.1 = $.3^2,

GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^3 = Id($), 
    $.2^2 = Id($), 
    $.3^2 = Id($), 
    $.2^$.1 = $.3, 
    $.3^$.1 = $.2 * $.3,

GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^2 = Id($), 
    $.2^2 = Id($), 
    $.3^3 = Id($), 
    $.3^$.1 = $.3^2
*]

Total time: 2.549 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:31:48 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
list;
G := list[1]; G;

Output: Magma V2.10-22    Tue Jun 22 2004 13:31:46 on modular  [Seed = 2789116899]
   -------------------------------------

[*
GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^2 = $.2, 
    $.2^2 = Id($), 
    $.3^3 = Id($), 
    $.3^$.1 = $.3^2,

GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^3 = Id($), 
    $.2^2 = Id($), 
    $.3^2 = Id($), 
    $.2^$.1 = $.3, 
    $.3^$.1 = $.2 * $.3,

GrpPC of order 12 = 2^2 * 3
PC-Relations:
    $.1^2 = Id($), 
    $.2^2 = Id($), 
    $.3^3 = Id($), 
    $.3^$.1 = $.3^2
*]
GrpPC : G of order 12 = 2^2 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.3^G.1 = G.3^2

Total time: 2.489 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:32:02 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1]; G;

Output: Magma V2.10-22    Tue Jun 22 2004 13:32:00 on modular  [Seed = 2922808313]
   -------------------------------------

GrpPC : G of order 12 = 2^2 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.3^G.1 = G.3^2

Total time: 2.489 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:32:24 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1]; G;
ConjugacyClasses(G);

Output: Magma V2.10-22    Tue Jun 22 2004 13:32:21 on modular  [Seed = 1272145446]
   -------------------------------------

GrpPC : G of order 12 = 2^2 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.3^G.1 = G.3^2
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1      
        Rep G.2

[3]     Order 3       Length 2      
        Rep G.3

[4]     Order 4       Length 3      
        Rep G.1

[5]     Order 4       Length 3      
        Rep G.1 * G.2

[6]     Order 6       Length 2      
        Rep G.2 * G.3



Total time: 2.529 seconds, Total memory usage: 2.11MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:32:53 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1]; G;
ConjugacyClasses(G);
CharacterTable(G);

Output: Magma V2.10-22    Tue Jun 22 2004 13:32:50 on modular  [Seed = 1539536465]
   -------------------------------------

GrpPC : G of order 12 = 2^2 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.3^G.1 = G.3^2
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1      
        Rep G.2

[3]     Order 3       Length 2      
        Rep G.3

[4]     Order 4       Length 3      
        Rep G.1

[5]     Order 4       Length 3      
        Rep G.1 * G.2

[6]     Order 6       Length 2      
        Rep G.2 * G.3




Character Table of Group G
--------------------------


-----------------------
Class |   1 2 3  4  5 6
Size  |   1 1 2  3  3 2
Order |   1 2 3  4  4 6
-----------------------
p  =  2   1 1 3  2  2 3
p  =  3   1 2 1  5  4 2
-----------------------
X.1   +   1 1 1  1  1 1
X.2   0   1-1 1  I -I-1
X.3   +   1 1 1 -1 -1 1
X.4   0   1-1 1 -I  I-1
X.5   +   2 2-1  0  0-1
X.6   -   2-2-1  0  0 1


Explanation of Symbols:
-----------------------

I = RootOfUnity(4)



Total time: 2.549 seconds, Total memory usage: 22.06MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:44:11 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1];

a := G.3;
b := G.1;
c := a;
d := b;
c*d*c^(-1)*d^(-1);

Output: Magma V2.10-22    Tue Jun 22 2004 13:44:09 on modular  [Seed = 4251308637]
   -------------------------------------

G.3^2

Total time: 2.509 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:44:38 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1];

a := G.3;
b := G.1;
c := a^2;
d := b;
c*d*c^(-1)*d^(-1);

Output: Magma V2.10-22    Tue Jun 22 2004 13:44:35 on modular  [Seed = 4100768958]
   -------------------------------------

G.3

Total time: 2.499 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:44:45 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1];

a := G.3;
b := G.1;
c := a^2;
d := b*a;
c*d*c^(-1)*d^(-1);

Output: Magma V2.10-22    Tue Jun 22 2004 13:44:43 on modular  [Seed = 2350169294]
   -------------------------------------

G.3

Total time: 2.509 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:45:00 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1];
Commutator(G);
a := G.3;
b := G.1;
c := a^2;
d := b*a;
c*d*c^(-1)*d^(-1);

Output: Magma V2.10-22    Tue Jun 22 2004 13:44:58 on modular  [Seed = 2216473815]
   -------------------------------------


>> Commutator(G);
             ^
Runtime error in 'Commutator': Bad argument types
Argument types given: GrpPC
G.3

Total time: 2.499 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 13:45:59 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1];
CommutatorSubgroup(G, G, G);
a := G.3;
b := G.1;
c := a^2;
d := b*a;
c*d*c^(-1)*d^(-1);

Output: Magma V2.10-22    Tue Jun 22 2004 13:45:57 on modular  [Seed = 2668081027]
   -------------------------------------

GrpPC of order 3
PC-Relations:
    $.1^3 = Id($)
G.3

Total time: 2.509 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host 4n33.math.upenn.edu. (130.91.49.169)
Time: Tue Jun 22 14:13:06 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1];
CharacterTable(G);

Output: Magma V2.10-22    Tue Jun 22 2004 14:13:03 on modular  [Seed = 1188982946]
   -------------------------------------



Character Table of Group G
--------------------------


-----------------------
Class |   1 2 3  4  5 6
Size  |   1 1 2  3  3 2
Order |   1 2 3  4  4 6
-----------------------
p  =  2   1 1 3  2  2 3
p  =  3   1 2 1  5  4 2
-----------------------
X.1   +   1 1 1  1  1 1
X.2   0   1-1 1  I -I-1
X.3   +   1 1 1 -1 -1 1
X.4   0   1-1 1 -I  I-1
X.5   +   2 2-1  0  0-1
X.6   -   2-2-1  0  0 1


Explanation of Symbols:
-----------------------

I = RootOfUnity(4)



Total time: 2.579 seconds, Total memory usage: 22.06MB


************** MAGMA *****************
Host p508E4980.dip0.t-ipconnect.de. (80.142.73.128)
Time: Tue Jun 22 15:58:02 2004

Input: (a+b)*(a+b)


Output: Magma V2.10-22    Tue Jun 22 2004 15:57:59 on modular  [Seed = 2550159246]
   -------------------------------------


>> (a+b)*(a+b)
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host roam243-171.fas.harvard.edu. (140.247.243.171)
Time: Tue Jun 22 17:49:40 2004

Input: 2+2

Output: Magma V2.10-22    Tue Jun 22 2004 17:49:37 on modular  [Seed = 3022806449]
   -------------------------------------

4

Total time: 2.470 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Wed Jun 23 06:42:58 2004

Input: K:=GF(2);


Output: Magma V2.10-22    Wed Jun 23 2004 06:42:54 on modular  [Seed = 77404861]
   -------------------------------------


Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Wed Jun 23 06:49:36 2004

Input: K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^2+x);
f:=P!(x^7+x^5+x^4+x^3+x^2+x+1);
IsHyperellipticCurve([f,h]);

Output: Magma V2.10-22    Wed Jun 23 2004 06:49:33 on modular  [Seed = 883758110]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host TYO113.gate.nec.co.jp. (202.32.8.235)
Time: Wed Jun 23 06:52:42 2004

Input: K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^2+x);
f:=P!(x^7+x^5+ x^4 + x^3 + x^2 + x + 1);
u1:=P!(x^3); v1:=P!(x^2+1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Wed Jun 23 2004 06:52:40 on modular  [Seed = 666765256]
   -------------------------------------


>>  u2,v2:=Cantor(f,h,u1,u1,v1,v1);
           ^
User error: Identifier 'Cantor' has not been declared or assigned
x^3
x^2 + 1
1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host TYO108.gate.nec.co.jp. (210.143.35.18)
Time: Wed Jun 23 06:53:20 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
///////////////////////////////////////////////////
//////////  END  //////////////////////////////////
//////////////////////////////////////////////////

K:=GF(2);
P<x>:=PolynomialRing(K);
h:=P!(x^2+x);
f:=P!(x^7+x^5+ x^4 + x^3 + x^2 + x + 1);
u1:=P!(x^3); v1:=P!(x^2+1);
u2:=u1; v2:=v1; 
c:=1; 
while (([u2,v2] ne [1,0]) and (c le 1000)) do
 u2,v2:=Cantor(f,h,u1,u1,v1,v1);
 c:=c+1;
end while;
u2; v2; c;

Output: Magma V2.10-22    Wed Jun 23 2004 06:53:17 on modular  [Seed = 750062886]
   -------------------------------------

1
0
2

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-222-52-66.msy.bellsouth.net. (68.222.52.66)
Time: Wed Jun 23 20:08:39 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jun 23 2004 20:08:34 on modular  [Seed = 866740372]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.650 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-222-52-66.msy.bellsouth.net. (68.222.52.66)
Time: Wed Jun 23 20:09:03 2004

Input: integrate(x/(x^3+1),x);

Output: Magma V2.10-22    Wed Jun 23 2004 20:09:00 on modular  [Seed = 77488060]
   -------------------------------------


>> integrate(x/(x^3+1),x);;
             ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-222-52-66.msy.bellsouth.net. (68.222.52.66)
Time: Wed Jun 23 20:09:14 2004

Input: integrate(x/(x^3+1),x)

Output: Magma V2.10-22    Wed Jun 23 2004 20:09:12 on modular  [Seed = 211179392]
   -------------------------------------


>> integrate(x/(x^3+1),x);
             ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-222-52-66.msy.bellsouth.net. (68.222.52.66)
Time: Wed Jun 23 20:09:52 2004

Input: int(x/(x^3+1),x)

Output: Magma V2.10-22    Wed Jun 23 2004 20:09:50 on modular  [Seed = 361713407]
   -------------------------------------


>> int(x/(x^3+1),x);
       ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ip68-1-108-75.pn.at.cox.net. (68.1.108.75)
Time: Thu Jun 24 01:44:23 2004

Input: int(x,x)

Output: Magma V2.10-22    Thu Jun 24 2004 01:44:20 on modular  [Seed = 127741211]
   -------------------------------------


>> int(x,x);
       ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ip68-1-108-75.pn.at.cox.net. (68.1.108.75)
Time: Thu Jun 24 01:44:45 2004

Input: int(12)

Output: Magma V2.10-22    Thu Jun 24 2004 01:44:42 on modular  [Seed = 1643858691]
   -------------------------------------


>> int(12);
   ^
User error: Identifier 'int' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jun 24 04:42:15 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Thu Jun 24 2004 04:42:05 on modular  [Seed = 261479678]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:16:30 2004

Input: P<z>:=PolynomialRing(GF(2));
for m:=850 to 8600 do 
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
    end for;
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:16:05 on modular  [Seed = 228058310]
   -------------------------------------

z^850 + z^111 + 1
z^850 + z^139 + 1
z^850 + z^711 + 1
z^850 + z^739 + 1
z^855 + z^29 + 1
z^855 + z^142 + 1
z^855 + z^146 + 1
z^855 + z^151 + 1
z^855 + z^254 + 1
z^855 + z^379 + 1
z^855 + z^476 + 1
z^855 + z^601 + 1
z^855 + z^704 + 1
z^855 + z^709 + 1
z^855 + z^713 + 1
z^855 + z^826 + 1


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:18:39 2004

Input: P<z>:=PolynomialRing(GF(2));
for m:=856 to 860 do 
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
    end for;
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:18:16 on modular  [Seed = 495449944]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:22:37 2004

Input: P<z>:=PolynomialRing(GF(2));
for m:=857 to 860 do 
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
    end for;
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:22:15 on modular  [Seed = 2145752069]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:24:35 2004

Input: P<z>:=PolynomialRing(GF(2));
for m:=885 to 890 do 
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
    end for;
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:24:13 on modular  [Seed = 1944688787]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:27:05 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=885 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:27:00 on modular  [Seed = 1388887563]
   -------------------------------------


Total time: 4.089 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:27:15 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=886 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:27:12 on modular  [Seed = 2855290375]
   -------------------------------------


Total time: 3.309 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:27:45 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=887 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:27:22 on modular  [Seed = 2721598981]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:27:54 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=888 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:27:51 on modular  [Seed = 3039779135]
   -------------------------------------


Total time: 3.429 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:28:16 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=889 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:28:11 on modular  [Seed = 2367119643]
   -------------------------------------

z^889 + z^169 + 1
z^889 + z^310 + 1
z^889 + z^312 + 1
z^889 + z^577 + 1
z^889 + z^579 + 1
z^889 + z^720 + 1

Total time: 4.879 seconds, Total memory usage: 2.43MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:28:35 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=890 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:28:31 on modular  [Seed = 2233428327]
   -------------------------------------


Total time: 3.719 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:29:00 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=891 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:28:56 on modular  [Seed = 2617667673]
   -------------------------------------


Total time: 4.099 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:29:39 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=884 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:29:35 on modular  [Seed = 2483976630]
   -------------------------------------

z^884 + z^173 + 1
z^884 + z^711 + 1

Total time: 3.819 seconds, Total memory usage: 2.53MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:30:03 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=883 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:29:59 on modular  [Seed = 4000580580]
   -------------------------------------


Total time: 3.619 seconds, Total memory usage: 2.43MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:30:23 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=882 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:30:17 on modular  [Seed = 3866889202]
   -------------------------------------


Total time: 6.099 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:30:58 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=881 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:30:36 on modular  [Seed = 4267971487]
   -------------------------------------



************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:31:10 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=880 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:31:06 on modular  [Seed = 4050328758]
   -------------------------------------


Total time: 3.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:31:26 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=879 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:31:17 on modular  [Seed = 3377669265]
   -------------------------------------

z^879 + z^11 + 1
z^879 + z^80 + 1
z^879 + z^91 + 1
z^879 + z^121 + 1
z^879 + z^190 + 1
z^879 + z^689 + 1
z^879 + z^758 + 1
z^879 + z^788 + 1
z^879 + z^799 + 1
z^879 + z^868 + 1

Total time: 9.059 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:32:28 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=878 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:32:24 on modular  [Seed = 3227135317]
   -------------------------------------


Total time: 3.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:32:38 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=877 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:32:35 on modular  [Seed = 3628217654]
   -------------------------------------


Total time: 3.369 seconds, Total memory usage: 2.43MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:34:53 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=876 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:34:48 on modular  [Seed = 2350277354]
   -------------------------------------


Total time: 4.119 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host public.eurecom.fr. (193.55.113.196)
Time: Thu Jun 24 06:40:02 2004

Input: P<z>:=PolynomialRing(GF(2));
m:=875 ;
    for i:= 1 to m-1 do
         Q<z>:=z^m + z^i +1;
         if IsPrimitive(Q)
             then z^m + z^i + 1;
         end if;
   
end for;


Output: Magma V2.10-22    Thu Jun 24 2004 06:39:58 on modular  [Seed = 2617668556]
   -------------------------------------


Total time: 3.729 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host delta.ams.ubc.ca. (137.82.188.68)
Time: Thu Jun 24 11:59:03 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,1,-11628462570762,15262701995165573655]))));

Output: Magma V2.10-22    Thu Jun 24 2004 11:59:00 on modular  [Seed = 666738000]
   -------------------------------------

[ <2, 27>, <3, 18>, <31, 8>, <127, 1> ]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 14:46:30 2004

Input: F<a,b>:=FreeGroup(2);
G<x,y>,phi:=quo< F | a*b*a = b*a*b, a^4=1, b^4=1 >;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 14:46:27 on modular  [Seed = 94266547]
   -------------------------------------

96

Total time: 2.639 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 14:47:05 2004

Input: F<a,b>:=FreeGroup(2);
G<x,y>,phi:=quo< F | a*b*a = b*a*b, a^12=1, b^12=1 >;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 14:47:01 on modular  [Seed = 244674462]
   -------------------------------------

0

Total time: 3.859 seconds, Total memory usage: 19.02MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 14:50:38 2004

Input: F<a,b>:=FreeGroup(2);
G<x,y>,phi:=quo< F | a*b*a = b*a*b, a^12=1, b^12=1 >;
IsFinite(G);

Output: Magma V2.10-22    Thu Jun 24 2004 14:50:35 on modular  [Seed = 2078284085]
   -------------------------------------


>> IsFinite(G);;
           ^
Runtime error in 'IsFinite': Bad argument types
Argument types given: GrpFP

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 14:56:19 2004

Input: F<a,b>:=FreeGroup(2);
G<x,y>,phi:=quo< F | a*b*a = b*a*b, a^12=1, b^12=1 >;
G;

Output: Magma V2.10-22    Thu Jun 24 2004 14:56:16 on modular  [Seed = 1794181519]
   -------------------------------------

Finitely presented group G on 2 generators
Relations
    x * y * x = y * x * y
    x^12 = Id(G)
    y^12 = Id(G)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:12:55 2004

Input: F<a,b>:=FreeGroup(2);
G<x,y>,phi:=quo< F | a*b*a = b*a*b, a^12=1, b^12=1 >;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:12:52 on modular  [Seed = 2855390507]
   -------------------------------------

Infinity

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:14:12 2004

Input: F<a,b>,phi:=group<a,b|a*b*a=b*a*b,a^4=1>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:14:09 on modular  [Seed = 2617767080]
   -------------------------------------


>> F<a,b>,phi:=group<a,b|a*b*a=b*a*b,a^4=1>;
                    ^
User error: bad syntax

>> Order(F);;
         ^
User error: Identifier 'F' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:15:00 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4=1>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:14:57 on modular  [Seed = 2266820483]
   -------------------------------------

96

Total time: 2.639 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:15:19 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:15:13 on modular  [Seed = 2383800058]
   -------------------------------------

0

Total time: 5.559 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:19:31 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1>;
FactoredOrder(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:19:26 on modular  [Seed = 4234647031]
   -------------------------------------


>> FactoredOrder(F);;
                ^
Runtime error in 'FactoredOrder': Could not construct a closed coset table

Total time: 5.559 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:22:23 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1>;
FactoredOrder(F,CosetLimit:=1200000,Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:22:20 on modular  [Seed = 3729110791]
   -------------------------------------


>> FactoredOrder(F,CosetLimit:=1200000,Strategy:="Hard");;
                             ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:23:09 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1>;
FactoredOrder(F : CosetLimit:=1200000,Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:23:03 on modular  [Seed = 3277367777]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=1200000,Strategy:="Hard");;
                ^
Runtime error in 'FactoredOrder': Could not construct a closed coset table

Total time: 5.799 seconds, Total memory usage: 41.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:23:26 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1>;
FactoredOrder(F : CosetLimit:=12000000,Strategy:="Hard");

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Thu Jun 24 2004 15:23:22 on modular  [Seed = 3394347221]
   -------------------------------------


Current total memory usage: 93.2MB, failed memory request: 45.8MB
System Error: User memory limit has been reached

Total time: 3.399 seconds, Total memory usage: 97.68MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:24:09 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=1200000,Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:24:03 on modular  [Seed = 833248084]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=1200000,Strategy:="Hard");;
                ^
Runtime error in 'FactoredOrder': Could not construct a closed coset table

Total time: 5.469 seconds, Total memory usage: 41.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:24:27 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=1200000);

Output: Magma V2.10-22    Thu Jun 24 2004 15:24:21 on modular  [Seed = 966939498]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=1200000);;
                ^
Runtime error in 'FactoredOrder': Could not construct a closed coset table

Total time: 6.369 seconds, Total memory usage: 21.45MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:27:01 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=1000000,Strategy="Hard",Lookahead=2);

Output: Magma V2.10-22    Thu Jun 24 2004 15:26:59 on modular  [Seed = 766920216]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=1000000,Strategy="Hard",Lookahead=2);;
                                                 ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:27:26 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=1000000, Strategy="Hard", Lookahead=2);

Output: Magma V2.10-22    Thu Jun 24 2004 15:27:23 on modular  [Seed = 361659960]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=1000000, Strategy="Hard", Lookahead=2);;
                                                  ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:27:44 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=1000000, Strategy:="Hard", Lookahead:=2);

Output: Magma V2.10-22    Thu Jun 24 2004 15:27:38 on modular  [Seed = 444690694]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=1000000, Strategy:="Hard", Lookahead:=2);;
                ^
Runtime error in 'FactoredOrder': Could not construct a closed coset table

Total time: 5.169 seconds, Total memory usage: 41.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:28:07 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=5000000, Strategy:="Hard", Lookahead:=2);

Output: Magma V2.10-22    Thu Jun 24 2004 15:27:55 on modular  [Seed = 43608335]
   -------------------------------------


>> FactoredOrder(F : CosetLimit:=5000000, Strategy:="Hard", Lookahead:=2);;
                ^
Runtime error in 'FactoredOrder': Could not construct a closed coset table

Total time: 12.079 seconds, Total memory usage: 81.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:28:26 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
FactoredOrder(F : CosetLimit:=9000000, Strategy:="Hard", Lookahead:=2);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Thu Jun 24 2004 15:28:23 on modular  [Seed = 177299819]
   -------------------------------------


Current total memory usage: 70.3MB, failed memory request: 34.3MB
System Error: User memory limit has been reached

Total time: 3.129 seconds, Total memory usage: 73.67MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:29:01 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
Order(F : CosetLimit:=5000000, Strategy:="Hard", Lookahead:=2);

Output: Magma V2.10-22    Thu Jun 24 2004 15:28:49 on modular  [Seed = 1944590388]
   -------------------------------------

0

Total time: 12.059 seconds, Total memory usage: 81.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:29:20 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6=1,b^6=1>;
Order(F : CosetLimit:=7000000, Strategy:="Hard", Lookahead:=2);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Thu Jun 24 2004 15:29:17 on modular  [Seed = 2078281920]
   -------------------------------------


Current total memory usage: 81.7MB, failed memory request: 26.7MB
System Error: User memory limit has been reached

Total time: 3.269 seconds, Total memory usage: 85.67MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:32:58 2004

Input: F:=BraidGroup(2);
F;

Output: Magma V2.10-22    Thu Jun 24 2004 15:32:56 on modular  [Seed = 1844838707]
   -------------------------------------

GrpBrd : F on 2 strings

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:33:14 2004

Input: F<a,b>:=BraidGroup(2);
F;

Output: Magma V2.10-22    Thu Jun 24 2004 15:33:12 on modular  [Seed = 1439578395]
   -------------------------------------


>> F<a,b>:=BraidGroup(2);
    ^
Runtime error in 'AssignNames': Too many names given for this object
GrpBrd : F on 2 strings

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:34:03 2004

Input: F<a,b>:=BraidGroup(3);
F;

Output: Magma V2.10-22    Thu Jun 24 2004 15:34:00 on modular  [Seed = 1522611908]
   -------------------------------------

GrpBrd : F on 3 strings

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:35:10 2004

Input: F<a,b>:=BraidGroup(3);
G=quo<F|a^4=0>;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:35:07 on modular  [Seed = 1088105629]
   -------------------------------------


>> G=quo<F|a^4=0>;
   ^
User error: Identifier 'G' has not been declared or assigned

>> Order(G);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:35:29 2004

Input: F<a,b>:=BraidGroup(3);
G:=quo<F|a^4=0>;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:35:26 on modular  [Seed = 1221796992]
   -------------------------------------


>> G:=quo<F|a^4=0>;
               ^
Runtime error in elt< ... >: LHS and RHS of relation constructor are not 
compatible

>> Order(G);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:35:45 2004

Input: F<a,b>:=BraidGroup(3);
G:=quo<F|a^4>;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:35:42 on modular  [Seed = 2972376201]
   -------------------------------------


>> G:=quo<F|a^4>;
         ^
Runtime error: No constructor provided for this type of object

>> Order(G);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:36:49 2004

Input: F<a,b>:=BraidGroup(3);
G<x,y>,phi:=quo<F|a^4>;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:36:47 on modular  [Seed = 2789067743]
   -------------------------------------


>> G<x,y>,phi:=quo<F|a^4>;
                  ^
Runtime error: No constructor provided for this type of object

>> Order(G);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:37:27 2004

Input: F<a,b>:=BraidGroup(3);
G<x,y>,phi := quo< F | a^4>;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:37:25 on modular  [Seed = 2922759149]
   -------------------------------------


>> G<x,y>,phi := quo< F | a^4>;
                    ^
Runtime error: No constructor provided for this type of object

>> Order(G);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:38:42 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:38:39 on modular  [Seed = 2500786204]
   -------------------------------------

96

Total time: 2.639 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:39:22 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:39:15 on modular  [Seed = 2583820111]
   -------------------------------------

0

Total time: 7.089 seconds, Total memory usage: 19.02MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:39:35 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^2>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:39:32 on modular  [Seed = 2182737728]
   -------------------------------------

24

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:40:03 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^3>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:40:00 on modular  [Seed = 2299717551]
   -------------------------------------

648

Total time: 2.680 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:40:24 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 15:40:17 on modular  [Seed = 3967255291]
   -------------------------------------

0

Total time: 7.109 seconds, Total memory usage: 19.02MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:41:46 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F : CosetLimit:=100000);

Output: Magma V2.10-22    Thu Jun 24 2004 15:41:43 on modular  [Seed = 3528047763]
   -------------------------------------

0

Total time: 3.099 seconds, Total memory usage: 4.39MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:42:02 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.10-22    Thu Jun 24 2004 15:41:53 on modular  [Seed = 3678451052]
   -------------------------------------

0

Total time: 9.699 seconds, Total memory usage: 28.04MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:42:34 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.10-22    Thu Jun 24 2004 15:42:24 on modular  [Seed = 3277368661]
   -------------------------------------

0

Total time: 10.529 seconds, Total memory usage: 28.04MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:42:50 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=5000000);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Thu Jun 24 2004 15:42:47 on modular  [Seed = 3360925257]
   -------------------------------------


Current total memory usage: 77.9MB, failed memory request: 19.1MB
System Error: User memory limit has been reached

Total time: 3.209 seconds, Total memory usage: 81.68MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:43:22 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=2000000);

Output: Magma V2.10-22    Thu Jun 24 2004 15:43:03 on modular  [Seed = 1051021518]
   -------------------------------------

0

Total time: 19.639 seconds, Total memory usage: 55.12MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:45:08 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=2000000, Strategy="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:45:06 on modular  [Seed = 599280726]
   -------------------------------------


>> Order(F : CosetLimit:=2000000, Strategy="Hard");;
                                          ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:45:29 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=2000000, Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:45:16 on modular  [Seed = 732972112]
   -------------------------------------

0

Total time: 12.919 seconds, Total memory usage: 49.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:52:10 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
RandomSchreier(G);
Order(F : CosetLimit:=2000000, Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:51:57 on modular  [Seed = 461401073]
   -------------------------------------


>> RandomSchreier(G);
                  ^
User error: Identifier 'G' has not been declared or assigned
0

Total time: 12.979 seconds, Total memory usage: 49.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:52:34 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
RandomSchreier(F);
Order(F : CosetLimit:=2000000, Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:52:21 on modular  [Seed = 43610816]
   -------------------------------------


>> RandomSchreier(F);
                 ^
Runtime error in 'RandomSchreier': Bad argument types
Argument types given: GrpFP
0

Total time: 12.969 seconds, Total memory usage: 49.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:56:39 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
G:=Simplify(F);
Order(G : CosetLimit:=2000000, Strategy:="Hard");

Output: Magma V2.10-22    Thu Jun 24 2004 15:56:17 on modular  [Seed = 1894449574]
   -------------------------------------



************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:56:58 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
G:=Simplify(F);
G;

Output: Magma V2.10-22    Thu Jun 24 2004 15:56:55 on modular  [Seed = 1744573783]
   -------------------------------------

Finitely presented group G on 3 generators
Generators as words in group F
    G.1 = a
    G.2 = b
    G.3 = F.3
Relations
    (G.1^-1, G.3^-1) = Id(G)
    G.1^4 = Id(G)
    G.2^4 = Id(G)
    G.3^4 = Id(G)
    G.1 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 = Id(G)
    G.2 * G.3 * G.2 * G.3^-1 * G.2^-1 * G.3^-1 = Id(G)

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:57:41 2004

Input: F<a,b>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
G:=Simplify(F);
G;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:57:25 on modular  [Seed = 1861557372]
   -------------------------------------

Finitely presented group G on 3 generators
Generators as words in group F
    G.1 = a
    G.2 = b
    G.3 = F.3
Relations
    (G.1^-1, G.3^-1) = Id(G)
    G.1^4 = Id(G)
    G.2^4 = Id(G)
    G.3^4 = Id(G)
    G.1 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 = Id(G)
    G.2 * G.3 * G.2 * G.3^-1 * G.2^-1 * G.3^-1 = Id(G)
0

Total time: 15.329 seconds, Total memory usage: 19.12MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:58:29 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4,b^4>;
G:=Simplify(F);
G;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:58:27 on modular  [Seed = 1355489796]
   -------------------------------------

Finitely presented group G on 2 generators
Generators as words in group F
    G.1 = a
    G.2 = b
Relations
    G.1^4 = Id(G)
    G.2^4 = Id(G)
    G.1 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 = Id(G)
96

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 15:59:03 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
G:=Simplify(F);
G;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 15:59:01 on modular  [Seed = 1489185514]
   -------------------------------------

Finitely presented group G on 2 generators
Generators as words in group F
    G.1 = a
    G.2 = b
Relations
    G.1^4 = Id(G)
    G.1 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 = Id(G)
96

Total time: 2.649 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:02:28 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4,b^4>;
G:=Simplify(F);
G;
Order(G);

Output: Magma V2.10-22    Thu Jun 24 2004 16:02:25 on modular  [Seed = 2755647426]
   -------------------------------------

Finitely presented group G on 2 generators
Generators as words in group F
    G.1 = a
    G.2 = b
Relations
    G.1^4 = Id(G)
    G.2^4 = Id(G)
    G.1 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 = Id(G)
96

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:02:54 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^5>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:02:51 on modular  [Seed = 2484070344]
   -------------------------------------

600

Total time: 2.649 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:03:43 2004

Input: F<a,b,c>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^3>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:03:41 on modular  [Seed = 2600527921]
   -------------------------------------

648

Total time: 2.659 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:05:06 2004

Input: F<a,b,c>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^3>;
IsFinite(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:05:04 on modular  [Seed = 2166026822]
   -------------------------------------


>> IsFinite(F);;
           ^
Runtime error in 'IsFinite': Bad argument types
Argument types given: GrpFP

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:06:31 2004

Input: F<a,b,c>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:06:24 on modular  [Seed = 4117660034]
   -------------------------------------

0

Total time: 7.119 seconds, Total memory usage: 19.02MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:07:21 2004

Input: F<a,b,c>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:07:11 on modular  [Seed = 4234643620]
   -------------------------------------

0

Total time: 10.539 seconds, Total memory usage: 28.05MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:08:40 2004

Input: F<a,b,c>,phi:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4,b^4,c^4>;
Order(F : CosetLimit:=2000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:08:20 on modular  [Seed = 3782907234]
   -------------------------------------

0

Total time: 19.839 seconds, Total memory usage: 55.12MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:09:47 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);
(a*b)^12

Output: Magma V2.10-22    Thu Jun 24 2004 16:09:45 on modular  [Seed = 3612123881]
   -------------------------------------

96
(a * b)^12

Total time: 2.639 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:10:02 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);
(a*b)^12==1;

Output: Magma V2.10-22    Thu Jun 24 2004 16:09:59 on modular  [Seed = 3729107966]
   -------------------------------------

96

>> (a*b)^12==1;;
            ^
User error: bad syntax

Total time: 2.649 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:17:28 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : Strategy:="Easy");

Output: Magma V2.10-22    Thu Jun 24 2004 16:17:26 on modular  [Seed = 3360931369]
   -------------------------------------

0

Total time: 2.739 seconds, Total memory usage: 5.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:17:47 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : Strategy:="Easy", CosetLimit=1000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:17:44 on modular  [Seed = 1067731439]
   -------------------------------------


>> Order(F : Strategy:="Easy", CosetLimit=1000000);;
                                         ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:21:49 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : Strategy:="Easy", CosetLimit:=1000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:21:46 on modular  [Seed = 528771325]
   -------------------------------------

0

Total time: 3.409 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:22:07 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : Strategy:="Easy", CosetLimit:=5000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:21:59 on modular  [Seed = 143884247]
   -------------------------------------

0

Total time: 7.409 seconds, Total memory usage: 81.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:28:48 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : CosetLimit:=5000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:28:28 on modular  [Seed = 2061566766]
   -------------------------------------

0

Total time: 20.059 seconds, Total memory usage: 82.00MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:29:43 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
phi;
Order(F : CosetLimit:=5000000);

Output: Magma V2.10-22    Thu Jun 24 2004 16:29:23 on modular  [Seed = 1944586984]
   -------------------------------------

Mapping from: GrpFP to GrpFP: F
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP: F
0

Total time: 20.199 seconds, Total memory usage: 82.00MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:30:23 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:30:20 on modular  [Seed = 1844843657]
   -------------------------------------

96

Total time: 2.629 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:41:04 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
#a

Output: Magma V2.10-22    Thu Jun 24 2004 16:41:02 on modular  [Seed = 3190145752]
   -------------------------------------

1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:41:27 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
a;

Output: Magma V2.10-22    Thu Jun 24 2004 16:41:25 on modular  [Seed = 3056454395]
   -------------------------------------

a

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:42:40 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(a);

Output: Magma V2.10-22    Thu Jun 24 2004 16:42:38 on modular  [Seed = 2704989479]
   -------------------------------------


>> Order(a);;
        ^
Runtime error in 'Order': Bad argument types
Argument types given: GrpFPElt

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:43:56 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
a eq 1;

Output: Magma V2.10-22    Thu Jun 24 2004 16:43:54 on modular  [Seed = 2583816104]
   -------------------------------------


>> a eq 1;;
     ^
Runtime error in 'eq': Bad argument types
Argument types given: GrpFPElt, RngIntElt

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:44:15 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
a eq Id(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:44:13 on modular  [Seed = 2450124727]
   -------------------------------------

false

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:44:24 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
a^4 eq Id(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:44:22 on modular  [Seed = 2316433300]
   -------------------------------------

false

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:48:52 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a>;
Index(F,G);

Output: Magma V2.10-22    Thu Jun 24 2004 16:48:49 on modular  [Seed = 4167272177]
   -------------------------------------

24

Total time: 2.629 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:49:18 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a>;
Index(F,G);

Output: Magma V2.10-22    Thu Jun 24 2004 16:49:12 on modular  [Seed = 4033580672]
   -------------------------------------

0

Total time: 6.569 seconds, Total memory usage: 29.76MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:49:49 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a,b>;
Index(F,G);

Output: Magma V2.10-22    Thu Jun 24 2004 16:49:47 on modular  [Seed = 3916601274]
   -------------------------------------

1

Total time: 2.639 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:50:07 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a,b^2>;
Index(F,G);

Output: Magma V2.10-22    Thu Jun 24 2004 16:50:04 on modular  [Seed = 3799620774]
   -------------------------------------

3

Total time: 2.639 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:51:25 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:51:12 on modular  [Seed = 3678446883]
   -------------------------------------

0
0

Total time: 13.079 seconds, Total memory usage: 29.76MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:51:38 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^5>;
G<x>:=sub<F|a>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:51:35 on modular  [Seed = 3544755516]
   -------------------------------------

120
600

Total time: 2.799 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:52:31 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^5>;
G<x>:=sub<F|a,b^2>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:52:28 on modular  [Seed = 3428299768]
   -------------------------------------

1
600

Total time: 2.779 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:53:32 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:53:29 on modular  [Seed = 966936137]
   -------------------------------------

48
96

Total time: 2.779 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:56:48 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:56:45 on modular  [Seed = 900609281]
   -------------------------------------

8
96

Total time: 2.809 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:57:54 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b*a>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Thu Jun 24 2004 16:57:51 on modular  [Seed = 750201946]
   -------------------------------------

12
96

Total time: 2.789 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host c160203.adsl.hansenet.de. (213.39.160.203)
Time: Thu Jun 24 16:58:33 2004

Input: F<a,b>,phi:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b*a>;
Index(F,G);
Order(F);
x;

Output: Magma V2.10-22    Thu Jun 24 2004 16:58:30 on modular  [Seed = 666642281]
   -------------------------------------

12
96
x

Total time: 2.799 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:39:00 2004

Input: 3+3

Output: Magma V2.10-22    Thu Jun 24 2004 17:38:57 on modular  [Seed = 2367063109]
   -------------------------------------

6

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:39:28 2004

Input: 3^234 mod 17

Output: Magma V2.10-22    Thu Jun 24 2004 17:39:26 on modular  [Seed = 2216660659]
   -------------------------------------

8

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:39:49 2004

Input: 3^21934 mod 176

Output: Magma V2.10-22    Thu Jun 24 2004 17:39:47 on modular  [Seed = 4234671846]
   -------------------------------------

169

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:46:49 2004

Input: P<x> := PolynomialRing(IntegerRing());
P;
Factorization(x^8 - 1);

Output: Magma V2.10-22    Thu Jun 24 2004 17:46:46 on modular  [Seed = 3478438960]
   -------------------------------------

Univariate Polynomial Ring in x over Integer Ring
[
    <x - 1, 1>,
    <x + 1, 1>,
    <x^2 + 1, 1>,
    <x^4 + 1, 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:48:46 2004

Input: P<x> := PolynomialRing(IntegerRing());
P;
Factorization(x^254 + 1);

Output: Magma V2.10-22    Thu Jun 24 2004 17:48:43 on modular  [Seed = 983643707]
   -------------------------------------

Univariate Polynomial Ring in x over Integer Ring
[
    <x^2 + 1, 1>,
    <x^252 - x^250 + x^248 - x^246 + x^244 - x^242 + x^240 - x^238 + x^236 - 
        x^234 + x^232 - x^230 + x^228 - x^226 + x^224 - x^222 + x^220 - x^218 + 
        x^216 - x^214 + x^212 - x^210 + x^208 - x^206 + x^204 - x^202 + x^200 - 
        x^198 + x^196 - x^194 + x^192 - x^190 + x^188 - x^186 + x^184 - x^182 + 
        x^180 - x^178 + x^176 - x^174 + x^172 - x^170 + x^168 - x^166 + x^164 - 
        x^162 + x^160 - x^158 + x^156 - x^154 + x^152 - x^150 + x^148 - x^146 + 
        x^144 - x^142 + x^140 - x^138 + x^136 - x^134 + x^132 - x^130 + x^128 - 
        x^126 + x^124 - x^122 + x^120 - x^118 + x^116 - x^114 + x^112 - x^110 + 
        x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90
        + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + 
        x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + 
        x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + 
        x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + 
        x^8 - x^6 + x^4 - x^2 + 1, 1>
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:51:36 2004

Input: P<x> := PolynomialRing(IntegerRing());

Factorization(x^254 + 1);

Output: Magma V2.10-22    Thu Jun 24 2004 17:51:34 on modular  [Seed = 649931514]
   -------------------------------------

[
    <x^2 + 1, 1>,
    <x^252 - x^250 + x^248 - x^246 + x^244 - x^242 + x^240 - x^238 + x^236 - 
        x^234 + x^232 - x^230 + x^228 - x^226 + x^224 - x^222 + x^220 - x^218 + 
        x^216 - x^214 + x^212 - x^210 + x^208 - x^206 + x^204 - x^202 + x^200 - 
        x^198 + x^196 - x^194 + x^192 - x^190 + x^188 - x^186 + x^184 - x^182 + 
        x^180 - x^178 + x^176 - x^174 + x^172 - x^170 + x^168 - x^166 + x^164 - 
        x^162 + x^160 - x^158 + x^156 - x^154 + x^152 - x^150 + x^148 - x^146 + 
        x^144 - x^142 + x^140 - x^138 + x^136 - x^134 + x^132 - x^130 + x^128 - 
        x^126 + x^124 - x^122 + x^120 - x^118 + x^116 - x^114 + x^112 - x^110 + 
        x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90
        + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + 
        x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + 
        x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + 
        x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + 
        x^8 - x^6 + x^4 - x^2 + 1, 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:51:47 2004

Input: P<x> := PolynomialRing(IntegerRing());
P;


Factorization(x^254 + 1);

Output: Magma V2.10-22    Thu Jun 24 2004 17:51:44 on modular  [Seed = 512037588]
   -------------------------------------

Univariate Polynomial Ring in x over Integer Ring
[
    <x^2 + 1, 1>,
    <x^252 - x^250 + x^248 - x^246 + x^244 - x^242 + x^240 - x^238 + x^236 - 
        x^234 + x^232 - x^230 + x^228 - x^226 + x^224 - x^222 + x^220 - x^218 + 
        x^216 - x^214 + x^212 - x^210 + x^208 - x^206 + x^204 - x^202 + x^200 - 
        x^198 + x^196 - x^194 + x^192 - x^190 + x^188 - x^186 + x^184 - x^182 + 
        x^180 - x^178 + x^176 - x^174 + x^172 - x^170 + x^168 - x^166 + x^164 - 
        x^162 + x^160 - x^158 + x^156 - x^154 + x^152 - x^150 + x^148 - x^146 + 
        x^144 - x^142 + x^140 - x^138 + x^136 - x^134 + x^132 - x^130 + x^128 - 
        x^126 + x^124 - x^122 + x^120 - x^118 + x^116 - x^114 + x^112 - x^110 + 
        x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90
        + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + 
        x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + 
        x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + 
        x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + 
        x^8 - x^6 + x^4 - x^2 + 1, 1>
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 17:53:20 2004

Input: P<x> := PolynomialRing(IntegerRing());
P;


Factorization(x^254 + 1);

Output: Magma V2.10-22    Thu Jun 24 2004 17:53:17 on modular  [Seed = 60296820]
   -------------------------------------

Univariate Polynomial Ring in x over Integer Ring
[
    <x^2 + 1, 1>,
    <x^252 - x^250 + x^248 - x^246 + x^244 - x^242 + x^240 - x^238 + x^236 - 
        x^234 + x^232 - x^230 + x^228 - x^226 + x^224 - x^222 + x^220 - x^218 + 
        x^216 - x^214 + x^212 - x^210 + x^208 - x^206 + x^204 - x^202 + x^200 - 
        x^198 + x^196 - x^194 + x^192 - x^190 + x^188 - x^186 + x^184 - x^182 + 
        x^180 - x^178 + x^176 - x^174 + x^172 - x^170 + x^168 - x^166 + x^164 - 
        x^162 + x^160 - x^158 + x^156 - x^154 + x^152 - x^150 + x^148 - x^146 + 
        x^144 - x^142 + x^140 - x^138 + x^136 - x^134 + x^132 - x^130 + x^128 - 
        x^126 + x^124 - x^122 + x^120 - x^118 + x^116 - x^114 + x^112 - x^110 + 
        x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90
        + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + 
        x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + 
        x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + 
        x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + 
        x^8 - x^6 + x^4 - x^2 + 1, 1>
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FF35A8.dip.t-dialin.net. (217.255.53.168)
Time: Thu Jun 24 18:10:24 2004

Input: ?

Output: Magma V2.10-22    Thu Jun 24 2004 18:10:21 on modular  [Seed = 2821962207]
   -------------------------------------

===============================================================================
PATH: /language/statement
KIND: Overview
===============================================================================

A statement is a complete command to Magma.
Every statement must end with a semicolon ( ; ).

If you press the <return> key before typing ; then Magma
may give you a special prompt symbol such as

print>

or

if>

to remind you that the statement is not yet finished.

EXAMPLE:
> print 5+8;

> DivBy3 := func< n | IsZero(n mod 3) >;
===============================================================================

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cronos.ugr.es. (150.214.190.144)
Time: Fri Jun 25 04:43:13 2004

Input: /*
 *  An implementation of a search for a non-skewed NFS polynomial, based
 *  on Brian Murphy's thesis.
 *
 *  By Contini - May, 2000.
 *
 *  Please report bugs, improvements, and suggestions to
 *  contini@maths.usyd.edu.au
 */



/*
 *  A polynomial for  n  can be reconstructed from its degree  d  and its
 *  value of  m1  (assuming  m2 = 1).    This function does that.
 */
function m1ToPoly( n, m1, d )

    rem := n;
    coeffs := [];
    for i := d to 0 by -1 do
        temp := m1^i;
        coeff := rem div temp;
        Append (~coeffs, coeff);
        rem -:= coeff*temp;
    end for;
 
    m1div2 := m1 div 2;
    /* adjust the coefficients to be between  -m1div2  and  m1div2  */
    for i := d+1 to 2 by -1 do
        if coeffs[i] gt m1div2 then
            coeffs[i] -:= m1;
            coeffs[i-1] +:= 1;
        end if;
    end for;
 
    P<X, Y> := PolynomialRing(Integers(), 2);
    F := P!0;
    for i in [0..d] do
        F +:= coeffs[i+1]*X^(d-i)*Y^i;
    end for;

    return F;
end function;



/*
 *  Compute  cont_p  (defined in section 3.2.1 of Murphy's thesis) of
 *  homogeneous polynomial  F  corresponding to univariate polynomial  f
 *  for the prime  p .  The following input values are required:
 *      - disc  should be the discriminant of  f .
 *      - bound is the size of the sample space to look through in
 *      order to estimate  cont_p  for the case of  p  dividing  disc .
 *      For example,  bound=10000  may be a good choice.
 */
function ComputeCont_p( p, disc, bound, F, f );
    if disc mod p eq 0 then
        /* estimate using some small sample space */
        cont_p := 0;
        upper_limit := bound^2;
        for i in [1..bound] do
            repeat
                a := Random( upper_limit );
                b := Random( upper_limit );
            until Gcd( a, b ) eq 1;
            value := Evaluate( F, [a, b] );
            while value mod p eq 0 do
                value div:= p;
                cont_p +:= 1;
            end while;
        end for;
        cont_p := cont_p / (0.0 + bound);
    else
        K := GF(p);
        roots_mod_p := Roots( f, K );
        q_p := #roots_mod_p;
        /* add in the contribution of the projective roots
         */
        d := Degree( f );
	if Coefficient(f, d) mod p eq 0 then
	    q_p +:= 1;
	end if;
            
        cont_p := q_p * p / (p * p - 1.0);
    end if;

    return cont_p;
end function;



/*
 *  Compute the  alpha  value corresponding to polynomial  F .  For
 *  primes  p  that divide the discriminant, do a random sampling of
 *  bound  elements to estimate  cont_p  (the expected exponent of
 *  prime  p  on the set of  F  values).  Include an early abort strategy:
 *  if by the time we reach  abort_p , the estimated  alpha  value is >
 *  abort_alpha  then stop the computation and return (the estimated)  alpha .
 *  If the early abort will not be used, then just set  abort_p  and
 *  abort_alpha  to 0.
 *  Function uses primes up to  max_p .
 */
function ComputeAlpha( F, bound, abort_p, abort_alpha, max_p );
 
    Q<X> := PolynomialRing(Integers());
    f := Q!Evaluate( F, [X, 1] );
 
    disc := Discriminant( f );
    a_d := Coefficient(f, Degree(f));
    primes := [p : p in [1..max_p] | IsPrime(p)];
 
    alpha := 0.0;
 
    for p in primes do
        cont_p := ComputeCont_p( p, disc, bound, F, f );
 
        alpha +:= (1.0/(p-1) - cont_p)*Log(p);
 
        /* early-abort strategy */
        if p eq abort_p and alpha gt abort_alpha then
            break;
        end if;
    end for;
 
    return alpha;
 
end function;


/*
 *  Compute  rho( x )  where  rho  is the Dickman rho function.
 *  This can be optimized by precomputing the coefficients of
 *  the polynomials and storing those coefficients for future calls.
 */
function DickmanRho( x );

    if x le 1.0 then
	return 1.0;
    end if;
    k := Ceiling( x );
    zeta := k - x;
 
 
    c := [];
    c[1] :=  1.0 - Log( 2.0 );
    for i in [1..54] do
	c[i+1] := 1.0 /(i * 2^i);
    end for;

    prev_c := [];
    l := 2;
    while l lt k do
	for i in [0..54] do
	    prev_c[i+1] := c[i+1];
	end for;

	for i in [1..54] do
	    sum := 0.0;

	    for j in [0..i-1] do
		sum := sum + prev_c[j+1]/(i * (l + 1.0)^(i-j) );
	    end for;

	    c[i+1] := sum;
	end for;

	sum := 0.0;
	for j in [1..54] do
	    sum +:= c[j+1]/( j + 1.0 );
	end for;
	c[1] := sum/l;

	l +:= 1;
    end while;
 
    rho_k := 0.0;
    for i in [0..54] do
	rho_k +:= c[i+1] * zeta^i;
    end for;

    return rho_k;

end function;


/*
 *  Quickly compute an approximation to the Dickman rho function.
 */
function ApproxDickmanRho( u );

    if u le 1.0 then
	return 1.0;
    end if;
    return u^-u;

end function;


/*
 *  Rate the polynomial pair  F1  and  F2 , where  F1  has degree  d
 *  and corresponding  alpha  value and  F2  is linear.  B1  and  B2
 *  represent upperbounds for the primes in the algebraic and rational
 *  factor bases, respectively.  High ratings tend to mean better
 *  polynomials.
 *
 *  Actually, we modify his rating method in 2 ways.
 *  First, we divide through by  K  (the number of intervals) so that
 *  the rating is not proportional to the number of intervals we choose.
 *  Second, we add in a  log B1^d  to the numerator of  u1  (which is
 *  equivalent to adding  d  to the whole quantity of  u1 ) so that the
 *  rho values are more typical of what will happen in practice.  A
 *  similar modification is done to the  u2  computation.
 */
function RatePolynomials( F1, F2, alpha, B1, B2, d )

    pi := Pi(RealField());
    K := 1000;

    rating := 0.0;
    logB1 := Log( B1 );
    logB2 := Log( B2 );
    for i in [1..K] do
	theta := pi/K*(i - 0.5);
	tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) );
	u1 := ( Log( tmp ) + alpha ) / logB1 + d;
	tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) );
	u2 := Log( tmp ) / logB2 + 1.0;
	rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 );
    end for;

    return rating/K;

end function;



/*
 *  Let  X  be a sequence, where  X[i]  represents the ranking
 *  of the  i'th  best polynomial under some ranking scheme.  This
 *  function computes the correlation coefficient of the ranking scheme
 *  (i.e. it gives us an idea of how good the ranking scheme is).
 *
 *  for example, to compute the correlation coefficient of the E-rank
 *  in table 6.4 of Murphy's thesis, you would send in  X :=
 *  [ 1, 3, 6, 7, 2, 8, 4, 10, 5, 9, 15, 11, 18, 13, 12, 14, 17, 16 ] .
 *
 *  Remark: there seem to be small differences between Murphy's and my
 *  calculations.
 */
function CorrelationCoeff( X )
    /*  compute  eXY  =  expected value of  X * Y  where Y is identity
        perumtation */
    eXY := &+[X[i]*i: i in [1..#X]]/(#X + 0.0);
    eX := (#X+1.0)/2.0;
    eX2 := &+[X[i]*X[i]: i in [1..#X]]/(#X + 0.0);
    sigma := Sqrt( eX2 - eX*eX );
    return (eXY - eX*eX)/sigma^2;

end function;


/*
 *  Choose a leading coefficient for our polynomial.  We want this leading
 *  coefficient to have lots of small prime factors, and to be close to
 *  high_a_d .  This procedure uses randomness, so that we should get a
 *  new leading coefficient every time it is called (assuming it is not
 *  called too many times).
 */
function ChooseLeadingCoeff( high_a_d );

    /*  Start with some value for the leading coefficient  c  that has
     *  many small prime factors.  However, don't let this start value
     *  get too close to  high_a_d , since this can severely limit the
     *  number of unique leading coefficients we can get.
     */
    c := 32 * 27 * 25 * 49 ;
    c_limit := high_a_d div 300;
    if 10*c gt c_limit then
	c := 2 * 3 * 5 * 7;
	if 10*c gt c_limit then
	    c := 2 * 3;
	    if 10*c gt c_limit then
		c := 2;
	    end if;
	end if;
    end if;

    if high_a_d lt 1000 then
	primes := [2, 3, 5, 7, 11];
    else
	primes := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29];
    end if;
    num_primes := #primes;

    min := high_a_d div 2;
    while c lt min do
	p := primes[ Random( 1, num_primes ) ];
	if c*p le high_a_d then
	    c := c * p;
	end if;
    end while;

    return c;

end function;


/*
 *  Let  n  be the number we want to factor.  This algorithm works
 *  something like Murphy's procedure 5.1.4 to find a good NFS polynomial.
 *  (though I've modified it to fit my own understanding, so there are
 *  definitely some differences from procedure 5.1.4).  Remark: this
 *  function alone randomly chooses one leading coefficient  a_d  for
 *  the polynomials being searched.  The user should try calling this
 *  several times so several leading coefficients are tried.
 *
 *  Returns a sequence of tuples which contain candidate polynomials and
 *  information about those candidates.  More precisely, the tuple has
 *  the following items (in this order):
 *	- the polynomial  F  ( F  is homogeneous).
 *	- a rating for the polynomial  F  (see 5.7 in Murphy's thesis).
 *      - the alpha value (see section 3.2.3 of Murphy's thesis) of candidate
 *	polynomial  F .
 *	- the  m1  value corresponding to polynomial  F (i.e  F(m1, m2) = n ).
 *	- the  m2  value corresponding to polynomial  F .  This function
 *	always has  m2=1 .
 *
 *  Description of input variables:
 *	n		the number we want to factor.
 *
 *	chi		only consider polynomials that have all their
 *			leading coefficients  <=  m1 * chi
 *
 *	max_k		for each choice of the leading coefficient, only
 *			consider polynomials whose  m1  lies within this
 *			range: [best_m1-max_k..best_m1+max_k] , where
 *			"best_m1" indicates the  m1  which minimizes the
 *			coefficient  a_{d-1}  of polynomial  F  (where  d
 *			is the degree of  F ).  This is used to limit the
 *			amount of time spent on a single leading coefficient.
 *			Also the number of  m1  considered may be even
 *			smaller than the range indicated above since some of
 *			these  m1  may correspond to a different leading
 *			coefficient.
 *
 *	max_alpha	The maximum value of  alpha  to allow for a polynomial
 *			to be a candidate.  Generally you want this to be
 *			a negative number, say -1.0 or smaller.  Values less
 *			than -3.0 are considered very good.
 *
 *	max_cands	maximum number of candidate polynomials to allow.
 *			(this is used to limit the amount of time spent
 *			on a single choice for the leading coefficient).
 *
 */
function PolySearch1( n, chi, max_k, max_alpha, max_cands );

    /* The set of return polynomials */
    candidates := [];

    /* select a degree according to the asymptotic formula */
    d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) );
print "degree ", d;
 
    /* Compute  B  - an upper bound for the factor base primes.  This
       will be used in Murphy's rating scheme for the candidate
       polynomials */
    dlogd := d*Log(d);
    temp := 1.0/d * Log( n );
    e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) );
    B := Round( Exp( 0.5*e ) );

    P<X, Y> := PolynomialRing(Integers(), 2);
 
    m2 := 1;
    /*  Need to choose  m1  between  n^[1/(d+1)]  and  n^[1/d] .
	Murphy's procedure 5.1.4 actually requests that  m1  is
	significantly larger than  n^[1/(d+1)].  (This is implied
	by the request that  a_d  is significantly smaller than its
	corresponding  m1 ).  We allow the lowest  m1  to be the
	geometric mean of these two values.  The use of the geomretic
	mean just seems to work well - it can be changed.
     */
    low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 );
    high_m1 := Iroot( n, d );
    low_a_d := n div high_m1^d;
    high_a_d := n div low_m1^d;
 
    c := ChooseLeadingCoeff( high_a_d );
print "using leading coeff ", c;
    a_d := c;
    if a_d lt low_a_d then
	a_d := ((low_a_d div c) + 1) * c;
    end if;

    /* The value of  m1  that causes  a_{d-1} to be minimized */
    best_m1 := Iroot( n div a_d, d );
    /* Determine  a_{d-1}  for this value of  best_m1 */
    a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1);
    coeff_bound := Round( best_m1 * chi );
    /* we try values between values [best_m1-k...best_m1+k] */
    k := (coeff_bound - a_dminus1) div (a_d * d);

    if k gt max_k then
	k := max_k;
    end if;
print "k=",k;

    for m1 in [best_m1-k..best_m1+k] do

	rem := n;
	coeffs := [];
	for i := d to 0 by -1 do
	    temp := m1^i;
	    coeff := rem div temp;
	    Append (~coeffs, coeff);
	    rem -:= coeff*temp;
	end for;

	m1div2 := m1 div 2;
	/* adjust the coefficients to be between  -m1div2  and  m1div2  */
	for i := d+1 to 2 by -1 do
	    if coeffs[i] gt m1div2 then
		coeffs[i] -:= m1;
		coeffs[i-1] +:= 1;
	    end if;
	end for;
     
	/* check that the coefficients are sufficiently small */
	small_coeffs := true;
	for i in [1..#coeffs] do
	    if Abs( coeffs[i] ) gt coeff_bound then
		small_coeffs := false;
		break;
	    end if;
	end for;

	if small_coeffs eq false then
	    continue;
	end if;

	F := P!0;
	for i in [0..d] do
	    F +:= coeffs[i+1]*X^(d-i)*Y^i;
	end for;

	/* obtain a quick estimate for  alpha  */
	alpha := ComputeAlpha( F, 2500, 11, max_alpha+0.5, 100 );
print m1, alpha;

	if alpha le max_alpha then
	    /*  get a more accurate value for  alpha  */
	    alpha := ComputeAlpha( F, 10000, 0, 0, 2000 );
print "recomputed alpha: ", alpha;
	    if alpha gt max_alpha then
		continue;
	    end if;
	    /* create the linear polynomial */
	    F2 := X*m2 - Y*m1;
	    rating := RatePolynomials( F, F2, alpha, B, B, d );
	    Append( ~candidates, <F, rating, alpha, m1, m2> );
	    if #candidates eq max_cands then
		break;
	    end if;
print F;
print "";
	end if;

    end for;
    return candidates;
end function;





/*
 *  Let  n  be the number we want to factor.  This algorithm calls a
 *  function named PolySearch1() which is similar to Murphy's procedure 5.1.4
 *  to find a good NFS polynomial.  Each call to PolySearch1() uses a
 *  (hopefully) new leading coefficient, that is somewhat randomly chosen.
 *  Up to  max_leading_coeffs  will be tried.
 *
 *  Returns a sequence of tuples which contain candidate polynomials and
 *  information about those candidates.  More precisely, the tuple has
 *  the following items (in this order):
 *	- the polynomial  F  ( F  is homogeneous).
 *	- a rating for the polynomial  F  (see 5.7 in Murphy's thesis).
 *      - the alpha value (see section 3.2.3 of Murphy's thesis) of candidate
 *	polynomial  F .
 *	- the  m1  value corresponding to polynomial  F (i.e  F(m1, m2) = n ).
 *	- the  m2  value corresponding to polynomial  F .  This function
 *	always has  m2=1 .
 *
 *  Description of input variables:
 *	n		the number we want to factor.
 *
 *	chi		only consider polynomials that have all their
 *			leading coefficients  <=  m1 * chi
 *
 *	max_k		for each choice of the leading coefficient, only
 *			consider polynomials whose  m1  lies within this
 *			range: [best_m1-max_k..best_m1+max_k] , where
 *			"best_m1" indicates the  m1  which minimizes the
 *			coefficient  a_{d-1}  of polynomial  F  (where  d
 *			is the degree of  F ).  This is used to limit the
 *			amount of time spent on a single leading coefficient.
 *			Also the number of  m1  considered may be even
 *			smaller than the range indicated above since some of
 *			these  m1  may correspond to a different leading
 *			coefficient.
 *
 *	max_alpha	The maximum value of  alpha  to allow for a polynomial
 *			to be a candidate.  Generally you want this to be
 *			a negative number, say -1.0 or smaller.  Values less
 *			than -3.0 are considered very good.
 *
 *	max_cands	maximum number of candidate polynomials to allow.
 *			(this is used to limit the amount of time spent
 *			on a single choice for the leading coefficient).
 *
 */
function MurphyPolynomial1( n, chi, max_k, max_alpha, max_cands,
  max_leading_coeffs );

    candidates := [];
    for i in [1..max_leading_coeffs] do
	new_cands := PolySearch1( n, chi, max_k, max_alpha, max_cands );
	for j in [1..#new_cands] do
	    Append( ~candidates, new_cands[j] );
	end for;
	max_cands -:= #new_cands;
	if max_cands eq 0 then
	    break;
	end if;
    end for;

    return candidates;

end function;

PolySearch1( 2397849861273491874265873455, 1, 5, -1, 1 );

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Fri Jun 25 05:01:24 2004

Input: SizeScreen( [ 72, ] );

W := CoxeterGroup( "A", 4 );;
w := Braid( W )( 1, 2, 3, 4 );
w ^ 3;
w ^ 4;
w ^ -1;

CheviePrintOption("Garside","GAP");
w;
w ^ 3;
w ^ -1;

CheviePrintOption("Garside","");
w ^ -1;

CheviePrintOption("Garside","Greedy");
W := CoxeterGroup( "A", 3 );;
B := Braid( W );
B( W.generators[1] );
B( 2, 1, 2, 1, 1 );
B( [ 2, 1, 2, 1, 1 ], -1 );

W := CoxeterGroup( "A", 2 );;
a := Braid( W )( [1] );
b := Braid( W )( [2] );
a * b;

( a * b ) ^ 4;
( a * b ) ^ -1;

a ^ b;

a / b;

CoxeterGroup( a );

CheviePrintOption("Garside","GAP");;
( a * b ) ^ -1;
CheviePrintOption("Garside","");;
( a * b ) ^ -1;
CheviePrintOption("Garside","Greedy");;
( a * b ) ^ -1;

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
p := EltBraid( b );
CoxeterWord( W, p );

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
WordBraid( b );

W := CoxeterGroup( "F", 4 );;
w:=[ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ];;
GoodCoxeterWord( W, w );
OrderPerm( EltWord( W, w ) );
Braid( W )( w ) ^ 6;
GoodCoxeterWord( W, [ 3, 2, 3, 4, 3, 2, 1, 3, 4, 2 ] );


W := CoxeterGroup( [ [ 1, -1, 0 ], [ 0, 1, -1 ] ],
                      [ [ 1, -1, 0 ], [ 0, 1, -1 ] ] );;
gu3 := CoxeterCoset( W, -IdentityMat( 3 ) );
F4 := CoxeterGroup( "F", 4 );;
D4 := ReflectionSubgroup( F4, [ 1, 2, 16, 48 ] );
PrintDiagram( D4 );
3D4 := CoxeterCoset( D4, (2,9,16) );

#CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), [ 1 ] );
f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
w := RepresentativeOperation( Group( f4coset ),
                     [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;
3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
PrintDiagram( 3d4again );

WF := CoxeterCoset( CoxeterGroup( "A", 4 ), (1,4)(2,3) );
Display( InductionTable( CoxeterSubCoset( WF, [ 2, 3 ] ), WF ) );

HF := CoxeterSubCoset( WF, [1, 2], LongestCoxeterElement( Group( WF ) ) );;
Display( InductionTable( HF, WF ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3)(2,4) );
Display( InductionTable( CoxeterSubCoset( W, [ 1, 3 ] ), W ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "G", 2, "A", 2 ), (1,5,2,6) );
ReflectionName( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
PrintDiagram( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
ReflectionType( W );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );

W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
Display( CharTable( W ) );

W := CoxeterGroup( "E", 6 );; WF := CoxeterCoset( W );
phi := EltWord( W, [ 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ] );;
HF := CoxeterSubCoset( WF, [ 2..5 ], phi );;
PrintDiagram( HF );
PhiFactors( HF );
ReflectionDegrees( Group( HF ) );


W := CoxeterGroup( "A", 3 );;
Display( CharTable( W ));

W := CoxeterGroup( "G", 2);;
ct := CharTable( W );
ct.classtext;
ct.classnames;
ct.irredinfo;

W := CoxeterGroup( "A", 3 );
List( Elements( W ), x -> ReflectionCharValue( W, x ) );

W := CoxeterGroup( "H", 4 );
ReflectionDegrees( W );
Size( W );

q := X( Rationals );; q.name := "q";;
FakeDegrees( CoxeterGroup( "A", 2 ), q );

q := X( Rationals );; q.name := "q";;
FakeDegree( CoxeterGroup( "A", 2 ), [ [ 2, 1 ] ], q );

LowestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

LowestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

 ChevieCharInfo( CoxeterGroup( "G", 2 ) );

W := CoxeterGroup( "E", 6 );;
ChevieCharInfo( W ).frame;


G := ComplexReflectionGroup( 4 );
ReflectionDegrees( G );
Size( G );
q := X( Cyclotomics );; q.name := "q";;
FakeDegrees( G, q );

G := ComplexReflectionGroup( 4, 2, 3 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );

G := ComplexReflectionGroup( 4 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );
Display( CharTable( CH ) );


W := CoxeterGroup( "D", 4 );
PrintArray( W.cartan );

W := CoxeterGroup( "A", 2, "B", 2 );; PrintArray( W.cartan );

W := CoxeterGroup( [ [ -1, 1, 0], [ 0, -1, 1 ] ],
                      [ [ -1, 1, 0], [ 0, -1, 1 ] ] );
MatXPerm( W, W.generators[1] );

C := CartanMat( "F", 4 );;
PrintArray( C );

CartanMat( "I", 2, 5 );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionType( C );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionName( ReflectionType( C ) );
ReflectionName( ReflectionType( CartanMat( "I", 2, 7 ) ) );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
t := ReflectionType( C );
PrintDiagram( t );
PrintDiagram( ReflectionType( CartanMat( "E", 8) ) );

W := CoxeterGroup( "A", 4 );;
PrintArray( W.cartan );
W.matgens;
W.roots;

W := CoxeterGroup( "D", 4 );;
p := EltWord( W, [ 1, 3, 2, 1, 3 ] );
CoxeterWord( W, p );

LongestCoxeterWord( W );
w0 := LongestCoxeterElement( W );
CoxeterLength( W, w0 );

List( Reflections( W ), i -> CoxeterWord( W, i ) );
l := List( [1 .. W.N+1], x -> CoxeterElements( W, x-1 ) );;
List( l, Length );

W := CoxeterGroup( "G", 2 );;
EltWord( W, [1,2,1] );

W := CoxeterGroup( "A", 3 );;
w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);;
w in W;
CHEVIE.BrieskornNormalForm := true;;
CoxeterWord( W, w );
CHEVIE.BrieskornNormalForm := false;;
CoxeterWord( W, w );

W := CoxeterGroup( "F", 4 );;
p := EltWord( W, [ 1, 2, 3, 4, 2 ] );
CoxeterLength( W, p );
CoxeterWord( W, p );

W := CoxeterGroup( "E", 6 );;
ReducedCoxeterWord( W, [ 1, 1, 1, 1, 1, 2, 2, 2, 3 ] );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
LeftDescentSet( W, w );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
RightDescentSet( W, w );

W := CoxeterGroup( "B", 2 );; W.roots;
Reflections( W );

LongestCoxeterElement( CoxeterGroup( "A", 4 ) );

LongestCoxeterWord( CoxeterGroup( "A", 4 ) );

W := CoxeterGroup( "G", 2 );;  W.roots;
HighestShortRoot( W );
#W1 := CoxeterGroup( "A", 1, "B", 3 );;
#HighestShortRoot( W1 );

W := CoxeterGroup( "G", 2 );;
e := CoxeterElements( W, 6 );
e[1] = LongestCoxeterElement( W );

CoxeterWords( CoxeterGroup( "G", 2 ) );

CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( W );

W := CoxeterGroup( "H", 3 );;
w := EltWord( W, [ 1, 2, 1, 3 ] );;
b := Filtered( Elements( W ), i -> Bruhat( W, i, w,
                                CoxeterLength( W, i ), 4 ) );;
List( b, x -> CoxeterWord( W, x ) );

W := CoxeterGroup(
[ [ 2, 0,-1, 0, 0, 0, 1 ], [ 0, 2, 0,-1, 0, 0, 0 ],
  [-1, 0, 2,-1, 0, 0,-1 ], [ 0,-1,-1, 2,-1, 0, 0 ],
  [ 0, 0, 0,-1, 2,-1, 0 ], [ 0, 0, 0, 0,-1, 2, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] );;
w0 := LongestCoxeterElement( W );;
mx := MatXPerm( W, w0 );

my := MatYPerm( W, w0 );

PermMatX( W, mx ) = w0;

PermMatY( W, my ) = w0;


W := CoxeterGroup( "A", 2 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );

W := CoxeterGroup( "A", 2, "A", 3 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );


W := CoxeterGroup( "A", 2 );

H := Hecke( W, 0 );

T := Basis( H, "T" );
el := CoxeterWords( W );

mat := []; for i in [1..6] do mat[i]:=[]; for j in [1..6] do
Add( mat[i], T( el[i]) * T( el[j] ) ); od; od;
PrintArray(mat);

W := CoxeterGroup( "B", 3 );
u := X( Rationals );; u.name := "u";;

H := Hecke( W, u );
H := Hecke( W, u^2, u );
H := Hecke( W, [ u^6, u^4, u^4 ], [ u^3, -u^2, -u^2 ] );

H := Hecke( W, 9, 3 );
#H := Hecke( W, [ u^6, u^4, u^8] );

u := X( Rationals );; u.name := "u";;
H := Hecke( CoxeterGroup( "B", 2 ), u );
HeckeSubAlgebra( H, [ 1, 4 ] );
#HeckeSubAlgebra( H, [ 1, 7 ] );

T := Basis( H, "T" );

W := CoxeterGroup( "B", 3 );;
u := X( Rationals );; u.name := "u";;
H := Hecke( W, u );;
T := Basis( H, "T" );
T( 1, 2 ) = T( [ 1, 2 ] );
T( 1, 2 ) = T( EltWord( W, [ 1, 2 ] ) );
l := [ [], [ 1, 2, 3 ], [ 1 ], [ 2 ], [ 3 ] ];;
pl := List( l, i -> EltWord( W, i ) );;
h := T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
h.elm;
h.coeff;

CHEVIE.PrintHecke := "GAP";
T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
CHEVIE.PrintHecke := "";

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "A", 2 ), q );
T := Basis( H, "T" );
( T() + T( 1 ) ) * ( T() + T( 2 ) );
T( 1 ) * T( 1 );
T( 1, 1 );

( q * T( 1, 2 ) ) ^ -1;
#( T( 1 ) + T( 2 ) ) ^ -1;
( T( 1 ) + T( 2 ) ) ^ 2;

T( 1 ) + T();
T( 1 ) - T( 1 );

h := T( [ EltWord( Group( H ), [ 1 ] ),() ],[ 0, q^100 ] );
Normalize( h );
h;

AlphaInvolution( T( 1, 2 ) );

CreateHeckeBasis( "t", rec(
T := h->Basis( Hecke(h), "T" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^CoxeterLength(
             Group( Hecke(h) ), h.elm[i] ) *  h.coeff[i] ) ),
t := h->Basis( Hecke(h), "t" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^-CoxeterLength(
              Group( Hecke(h) ), h.elm[i] ) * h.coeff[i] ) ),
BetaInvolution := h->Basis( Hecke( h ),"t")(
                    HeckeAlgebraOps.T.BetaInvolution(
                            Basis( Hecke( h ), "T" )( h ) ) ) ), AbsHeckeOps );
Inherit(HeckeAlgebraOps,AbsHeckeOps);
v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "A", 3 ), v ^ 2, v );;
h := Basis( H, "t" )( 3, 1, 2 );
h1 := Basis( H, "T")( h );
h2 := Basis( H, "t" )( h1 );
BetaInvolution( h2 );


v:= X( Rationals );;  v.name := "v";;
H := Hecke(CoxeterGroup( "B", 2) , v^2, v);
ref:= HeckeReflectionRepresentation( H );

H := Hecke( CoxeterGroup( "H", 3 ));;
HeckeReflectionRepresentation( H );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := HeckeReflectionRepresentation( H );;
CheckHeckeDefiningRelations( H, r );

W := CoxeterGroup( "G", 2 );;
u := X( Rationals );;  u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
u := u * v^0;;
H := Hecke( W, [ u^2, v^2 ], [ u, v ] );
Display( CharTable( H ) );

H1 := Hecke( W, [ E(6)^2, E(6)^4 ],[ E(6), E(6)^2 ] );
ct := CharTable( H1 );
Display( ct );
RankMat( ct.irreducibles );

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "B", 2 ), q ^ 2, q );;
HeckeCharValues( Basis( H, "C'" )( 1, 2, 1 ) );

u := X( Rationals );; u.name := "u";;
W := CoxeterGroup( "A", 3 );
H := Hecke( W, u );;
h := Basis( H, "T" )( LongestCoxeterElement( W ) );
cp := HeckeClassPolynomials( h );
CharTable( H ).irreducibles * cp;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "G", 2 );; H := Hecke( W, q );
PoincarePolynomial( H );

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
schur := SchurElements( Hecke( CoxeterGroup( "G", 2 ),
                                   [ u ^ 2, v ^ 2 ], [ u, v ] ) );

schur[1];

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
H := Hecke( CoxeterGroup( "G", 2 ), [ u ^ 2, v ^ 2 ], [ u, v ] );
SchurElement( H, [ [ 1, 3, "'" ] ] );

v := X( Cyclotomics );; v.name := "v";;
H := Hecke( CoxeterGroup( "H", 3 ), v ^ 2, v );;
HeckeCentralMonomials( H );

HeckeCharValuesGood( H, [ 1, 2, 3 ] );

klpol := function(W,x,y)return 
  KazhdanLusztigPolynomial(W,EltWord(W,x),EltWord(W,y),Length(x),Length(y));
end;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "B", 3 );;
el := CoxeterWords( W );
List( el, w -> klpol( W, [], w ) );

W.klpol;

W := CoxeterGroup( "F", 4 );
w := LongestCoxeterElement( W ) * W.generators[1];;
CoxeterLength( W, w );
y := EltWord( W, [ 1, 2, 3, 4 ] );;
cr := CriticalPair( W, y, w);;
CoxeterWord( W, cr[1] );
cr[3];
KazhdanLusztigPolynomial( W, y, w, 4, 23 );
KazhdanLusztigPolynomial( W, cr[1], cr[2], 16, 23 );

W := CoxeterGroup( "B", 4 );;
y := [ 1, 2, 3, 4, 3, 2, 1 ];;
py := EltWord( W, y );
x := [ 1 ];;
px := EltWord( W, x );
Bruhat( W, px, py );
List([0..3],i->KazhdanLusztigCoefficient( W, px, py, 1, 7, i ) );

W := CoxeterGroup( "G", 2 );;
LeftCells(W);

v := X( Cyclotomics ) ;; v.name := "v";;
W := Hecke(CoxeterGroup( "H", 3), v^2, v );
c := LeftCells( Group( W ) );;
List( c, i -> Length( i[ 1 ] ) );
LeftCellRepresentation(W,c[3]);

W := CoxeterGroup( "B", 3 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
C := Basis( H, "C" );
T( C( 1 ) );
C( T( 1 ) );

ref := HeckeReflectionRepresentation( H );;
c := CharRepresentationWords( ref, CoxeterConjugacyClasses( W ) );
List( ChevieClassInfo( W ).classtext, i ->
                            HeckeCharValues( C( i ), c ) );

v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "B", 2 ), v ^ 2, v );;
h := Basis( H, "C'" )( 1 );
h2 := h * h;
Basis( H, "T" )( h2 );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
D := Basis( H, "D" );
D( T( 1 ) );
BetaInvolution( D( 1 ) );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
Dp := Basis( H, "D'" );
AltInvolution( Dp( 1 ) );
Dp( 1 )^3;


W := CoxeterGroup( "G", 2 );
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );
PrintDiagram( H );

H.rootInclusion;

CoxeterLength( W, H.generators[2] );
CoxeterLength( H, H.generators[2] );

el := CoxeterWords( H );

el1 := List( el, x -> H.rootRestriction{ x } );

el2 := List( el, x -> EltWord( H, x ) );

List( el2, x -> CoxeterWord( W, x ) );

W := CoxeterGroup( "G", 2 );;
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 11, 20 ] );
ReflectionName( H );
H.rootRestriction;
ReflectionSubgroup( H, [ 1, 2, 6 ] );

W := CoxeterGroup( "F", 4 );
H := ReflectionSubgroup( W, [ 10, 11, 12 ] );
PrintDiagram( H );
LongestCoxeterWord( H );

W := CoxeterGroup("F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 9, 16 ] );;
PrintDiagram( H );
w := EltWord( W, [ 3, 2, 3, 4, 3, 2 ] );;
f := ReducedInCoset( H, w );;
CoxeterWord( W, f );
H.rootInclusion{[ 1 ..4 ]};

OnTuples( H.rootInclusion{[ 1 .. 4 ]}, f );

W := CoxeterGroup( "B", 3 );;
H := ReflectionSubgroup(W, [ 2, 3 ]);;
List( ReducedRightCosetRepresentatives( W, H ),
                               x-> CoxeterWord( W, x ) );

W := CoxeterGroup( "F", 4 );;
PermCosetsSubgroup( W, ReflectionSubgroup( W, [ 1, 2, 3 ] ) );

W := CoxeterGroup( "D", 4);;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( jInductionTable( H, W ) );

W := CoxeterGroup( "D", 4 );;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( JInductionTable( H, W ) );


W := Group( [ (1,2), (2,3), (3,4) ], () );
H:=Subgroup( W, [ (1,2), (3,4) ] );
W.name := "W";; H.name := "H";;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "G", 2 );;
H := ReflectionSubgroup( W, [ 1, 4 ] );
ReflectionName( H );
Display(InductionTable( H, W ) );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := ChevieClassInfo( Group( H ) ).classtext;;
t := HeckeReflectionRepresentation( H );;
CharRepresentationWords( t, r );

G := Group( (1,2)(3,4), (1,2,3,4,5) );;
ConjugacyClasses( G );
 g := Random( G );
PositionClass( G, g );

G := Group( (1,7)(2,3)(5,6)(8,9)(11,12),
               (1,5)(2,8)(3,4)(7,11)(9,10) );;
PointsAndRepresentativesOrbits( G );

C1 := [ [   2,  -1,   0,   0 ],
           [  -1,   2,  -1,   0 ],
           [   0,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
C2 := [ [   2,   0,  -1,   0 ],
           [   0,   2,  -1,   0 ],
           [  -1,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
d := DirectSumMat( C1, C2 );;
PrintArray( d );

m := [ [  0,  0,  0,  1 ],
          [  0,  0,  1,  0 ],
          [  0,  1,  0,  0 ],
          [  1,  0,  0,  0 ] ];;
DecomposedMat( m );
PrintArray( m{[ 1, 4 ]}{[ 1, 4 ]});

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsDiagonalMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsLowerTriangularMat( a );
a[1][2] := 0;;
IsLowerTriangularMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
l := [ [ 1, 0 ], [ 0, 1 ], [ 1, 1 ], [ 0, 0 ] ];;
l * a;
IsNormalizing( l, a );

l := [ 1, , 2, , , 3 ];;
SublistUnbnd( l, [ 1..4 ] );

a := [ 1, 2, 3, 4 ];;
b := [ 2, 3, 1, 4 ];;
p := PermListList( a, b );
Permuted( b, p );
PermListList( a, [ 3, 2, 1, 5 ] );

IntListToString( [ 4, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ], "{}" );

d := PartitionTuples( 3, 2 );
for i in d do
     Print( PartitionTupleToString( i ),"   ");
od; Print("n");


Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Fri Jun 25 05:01:35 2004

Input: SizeScreen( [ 72, ] );

W := CoxeterGroup( "A", 4 );;
w := Braid( W )( 1, 2, 3, 4 );
w ^ 3;
w ^ 4;
w ^ -1;

CheviePrintOption("Garside","GAP");
w;
w ^ 3;
w ^ -1;

CheviePrintOption("Garside","");
w ^ -1;

CheviePrintOption("Garside","Greedy");
W := CoxeterGroup( "A", 3 );;
B := Braid( W );
B( W.generators[1] );
B( 2, 1, 2, 1, 1 );
B( [ 2, 1, 2, 1, 1 ], -1 );

W := CoxeterGroup( "A", 2 );;
a := Braid( W )( [1] );
b := Braid( W )( [2] );
a * b;

( a * b ) ^ 4;
( a * b ) ^ -1;

a ^ b;

a / b;

CoxeterGroup( a );

CheviePrintOption("Garside","GAP");;
( a * b ) ^ -1;
CheviePrintOption("Garside","");;
( a * b ) ^ -1;
CheviePrintOption("Garside","Greedy");;
( a * b ) ^ -1;

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
p := EltBraid( b );
CoxeterWord( W, p );

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
WordBraid( b );

W := CoxeterGroup( "F", 4 );;
w:=[ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ];;
GoodCoxeterWord( W, w );
OrderPerm( EltWord( W, w ) );
Braid( W )( w ) ^ 6;
GoodCoxeterWord( W, [ 3, 2, 3, 4, 3, 2, 1, 3, 4, 2 ] );


W := CoxeterGroup( [ [ 1, -1, 0 ], [ 0, 1, -1 ] ],
                      [ [ 1, -1, 0 ], [ 0, 1, -1 ] ] );;
gu3 := CoxeterCoset( W, -IdentityMat( 3 ) );
F4 := CoxeterGroup( "F", 4 );;
D4 := ReflectionSubgroup( F4, [ 1, 2, 16, 48 ] );
PrintDiagram( D4 );
3D4 := CoxeterCoset( D4, (2,9,16) );

#CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), [ 1 ] );
f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
w := RepresentativeOperation( Group( f4coset ),
                     [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;
3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
PrintDiagram( 3d4again );

WF := CoxeterCoset( CoxeterGroup( "A", 4 ), (1,4)(2,3) );
Display( InductionTable( CoxeterSubCoset( WF, [ 2, 3 ] ), WF ) );

HF := CoxeterSubCoset( WF, [1, 2], LongestCoxeterElement( Group( WF ) ) );;
Display( InductionTable( HF, WF ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3)(2,4) );
Display( InductionTable( CoxeterSubCoset( W, [ 1, 3 ] ), W ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "G", 2, "A", 2 ), (1,5,2,6) );
ReflectionName( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
PrintDiagram( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
ReflectionType( W );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );

W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
Display( CharTable( W ) );

W := CoxeterGroup( "E", 6 );; WF := CoxeterCoset( W );
phi := EltWord( W, [ 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ] );;
HF := CoxeterSubCoset( WF, [ 2..5 ], phi );;
PrintDiagram( HF );
PhiFactors( HF );
ReflectionDegrees( Group( HF ) );


W := CoxeterGroup( "A", 3 );;
Display( CharTable( W ));

W := CoxeterGroup( "G", 2);;
ct := CharTable( W );
ct.classtext;
ct.classnames;
ct.irredinfo;

W := CoxeterGroup( "A", 3 );
List( Elements( W ), x -> ReflectionCharValue( W, x ) );

W := CoxeterGroup( "H", 4 );
ReflectionDegrees( W );
Size( W );

q := X( Rationals );; q.name := "q";;
FakeDegrees( CoxeterGroup( "A", 2 ), q );

q := X( Rationals );; q.name := "q";;
FakeDegree( CoxeterGroup( "A", 2 ), [ [ 2, 1 ] ], q );

LowestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

LowestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

 ChevieCharInfo( CoxeterGroup( "G", 2 ) );

W := CoxeterGroup( "E", 6 );;
ChevieCharInfo( W ).frame;


G := ComplexReflectionGroup( 4 );
ReflectionDegrees( G );
Size( G );
q := X( Cyclotomics );; q.name := "q";;
FakeDegrees( G, q );

G := ComplexReflectionGroup( 4, 2, 3 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );

G := ComplexReflectionGroup( 4 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );
Display( CharTable( CH ) );


W := CoxeterGroup( "D", 4 );
PrintArray( W.cartan );

W := CoxeterGroup( "A", 2, "B", 2 );; PrintArray( W.cartan );

W := CoxeterGroup( [ [ -1, 1, 0], [ 0, -1, 1 ] ],
                      [ [ -1, 1, 0], [ 0, -1, 1 ] ] );
MatXPerm( W, W.generators[1] );

C := CartanMat( "F", 4 );;
PrintArray( C );

CartanMat( "I", 2, 5 );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionType( C );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionName( ReflectionType( C ) );
ReflectionName( ReflectionType( CartanMat( "I", 2, 7 ) ) );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
t := ReflectionType( C );
PrintDiagram( t );
PrintDiagram( ReflectionType( CartanMat( "E", 8) ) );

W := CoxeterGroup( "A", 4 );;
PrintArray( W.cartan );
W.matgens;
W.roots;

W := CoxeterGroup( "D", 4 );;
p := EltWord( W, [ 1, 3, 2, 1, 3 ] );
CoxeterWord( W, p );

LongestCoxeterWord( W );
w0 := LongestCoxeterElement( W );
CoxeterLength( W, w0 );

List( Reflections( W ), i -> CoxeterWord( W, i ) );
l := List( [1 .. W.N+1], x -> CoxeterElements( W, x-1 ) );;
List( l, Length );

W := CoxeterGroup( "G", 2 );;
EltWord( W, [1,2,1] );

W := CoxeterGroup( "A", 3 );;
w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);;
w in W;
CHEVIE.BrieskornNormalForm := true;;
CoxeterWord( W, w );
CHEVIE.BrieskornNormalForm := false;;
CoxeterWord( W, w );

W := CoxeterGroup( "F", 4 );;
p := EltWord( W, [ 1, 2, 3, 4, 2 ] );
CoxeterLength( W, p );
CoxeterWord( W, p );

W := CoxeterGroup( "E", 6 );;
ReducedCoxeterWord( W, [ 1, 1, 1, 1, 1, 2, 2, 2, 3 ] );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
LeftDescentSet( W, w );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
RightDescentSet( W, w );

W := CoxeterGroup( "B", 2 );; W.roots;
Reflections( W );

LongestCoxeterElement( CoxeterGroup( "A", 4 ) );

LongestCoxeterWord( CoxeterGroup( "A", 4 ) );

W := CoxeterGroup( "G", 2 );;  W.roots;
HighestShortRoot( W );
#W1 := CoxeterGroup( "A", 1, "B", 3 );;
#HighestShortRoot( W1 );

W := CoxeterGroup( "G", 2 );;
e := CoxeterElements( W, 6 );
e[1] = LongestCoxeterElement( W );

CoxeterWords( CoxeterGroup( "G", 2 ) );

CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( W );

W := CoxeterGroup( "H", 3 );;
w := EltWord( W, [ 1, 2, 1, 3 ] );;
b := Filtered( Elements( W ), i -> Bruhat( W, i, w,
                                CoxeterLength( W, i ), 4 ) );;
List( b, x -> CoxeterWord( W, x ) );

W := CoxeterGroup(
[ [ 2, 0,-1, 0, 0, 0, 1 ], [ 0, 2, 0,-1, 0, 0, 0 ],
  [-1, 0, 2,-1, 0, 0,-1 ], [ 0,-1,-1, 2,-1, 0, 0 ],
  [ 0, 0, 0,-1, 2,-1, 0 ], [ 0, 0, 0, 0,-1, 2, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] );;
w0 := LongestCoxeterElement( W );;
mx := MatXPerm( W, w0 );

my := MatYPerm( W, w0 );

PermMatX( W, mx ) = w0;

PermMatY( W, my ) = w0;


W := CoxeterGroup( "A", 2 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );

W := CoxeterGroup( "A", 2, "A", 3 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );


W := CoxeterGroup( "A", 2 );

H := Hecke( W, 0 );

T := Basis( H, "T" );
el := CoxeterWords( W );

mat := []; for i in [1..6] do mat[i]:=[]; for j in [1..6] do
Add( mat[i], T( el[i]) * T( el[j] ) ); od; od;
PrintArray(mat);

W := CoxeterGroup( "B", 3 );
u := X( Rationals );; u.name := "u";;

H := Hecke( W, u );
H := Hecke( W, u^2, u );
H := Hecke( W, [ u^6, u^4, u^4 ], [ u^3, -u^2, -u^2 ] );

H := Hecke( W, 9, 3 );
#H := Hecke( W, [ u^6, u^4, u^8] );

u := X( Rationals );; u.name := "u";;
H := Hecke( CoxeterGroup( "B", 2 ), u );
HeckeSubAlgebra( H, [ 1, 4 ] );
#HeckeSubAlgebra( H, [ 1, 7 ] );

T := Basis( H, "T" );

W := CoxeterGroup( "B", 3 );;
u := X( Rationals );; u.name := "u";;
H := Hecke( W, u );;
T := Basis( H, "T" );
T( 1, 2 ) = T( [ 1, 2 ] );
T( 1, 2 ) = T( EltWord( W, [ 1, 2 ] ) );
l := [ [], [ 1, 2, 3 ], [ 1 ], [ 2 ], [ 3 ] ];;
pl := List( l, i -> EltWord( W, i ) );;
h := T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
h.elm;
h.coeff;

CHEVIE.PrintHecke := "GAP";
T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
CHEVIE.PrintHecke := "";

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "A", 2 ), q );
T := Basis( H, "T" );
( T() + T( 1 ) ) * ( T() + T( 2 ) );
T( 1 ) * T( 1 );
T( 1, 1 );

( q * T( 1, 2 ) ) ^ -1;
#( T( 1 ) + T( 2 ) ) ^ -1;
( T( 1 ) + T( 2 ) ) ^ 2;

T( 1 ) + T();
T( 1 ) - T( 1 );

h := T( [ EltWord( Group( H ), [ 1 ] ),() ],[ 0, q^100 ] );
Normalize( h );
h;

AlphaInvolution( T( 1, 2 ) );

CreateHeckeBasis( "t", rec(
T := h->Basis( Hecke(h), "T" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^CoxeterLength(
             Group( Hecke(h) ), h.elm[i] ) *  h.coeff[i] ) ),
t := h->Basis( Hecke(h), "t" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^-CoxeterLength(
              Group( Hecke(h) ), h.elm[i] ) * h.coeff[i] ) ),
BetaInvolution := h->Basis( Hecke( h ),"t")(
                    HeckeAlgebraOps.T.BetaInvolution(
                            Basis( Hecke( h ), "T" )( h ) ) ) ), AbsHeckeOps );
Inherit(HeckeAlgebraOps,AbsHeckeOps);
v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "A", 3 ), v ^ 2, v );;
h := Basis( H, "t" )( 3, 1, 2 );
h1 := Basis( H, "T")( h );
h2 := Basis( H, "t" )( h1 );
BetaInvolution( h2 );


v:= X( Rationals );;  v.name := "v";;
H := Hecke(CoxeterGroup( "B", 2) , v^2, v);
ref:= HeckeReflectionRepresentation( H );

H := Hecke( CoxeterGroup( "H", 3 ));;
HeckeReflectionRepresentation( H );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := HeckeReflectionRepresentation( H );;
CheckHeckeDefiningRelations( H, r );

W := CoxeterGroup( "G", 2 );;
u := X( Rationals );;  u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
u := u * v^0;;
H := Hecke( W, [ u^2, v^2 ], [ u, v ] );
Display( CharTable( H ) );

H1 := Hecke( W, [ E(6)^2, E(6)^4 ],[ E(6), E(6)^2 ] );
ct := CharTable( H1 );
Display( ct );
RankMat( ct.irreducibles );

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "B", 2 ), q ^ 2, q );;
HeckeCharValues( Basis( H, "C'" )( 1, 2, 1 ) );

u := X( Rationals );; u.name := "u";;
W := CoxeterGroup( "A", 3 );
H := Hecke( W, u );;
h := Basis( H, "T" )( LongestCoxeterElement( W ) );
cp := HeckeClassPolynomials( h );
CharTable( H ).irreducibles * cp;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "G", 2 );; H := Hecke( W, q );
PoincarePolynomial( H );

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
schur := SchurElements( Hecke( CoxeterGroup( "G", 2 ),
                                   [ u ^ 2, v ^ 2 ], [ u, v ] ) );

schur[1];

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
H := Hecke( CoxeterGroup( "G", 2 ), [ u ^ 2, v ^ 2 ], [ u, v ] );
SchurElement( H, [ [ 1, 3, "'" ] ] );

v := X( Cyclotomics );; v.name := "v";;
H := Hecke( CoxeterGroup( "H", 3 ), v ^ 2, v );;
HeckeCentralMonomials( H );

HeckeCharValuesGood( H, [ 1, 2, 3 ] );

klpol := function(W,x,y)return 
  KazhdanLusztigPolynomial(W,EltWord(W,x),EltWord(W,y),Length(x),Length(y));
end;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "B", 3 );;
el := CoxeterWords( W );
List( el, w -> klpol( W, [], w ) );

W.klpol;

W := CoxeterGroup( "F", 4 );
w := LongestCoxeterElement( W ) * W.generators[1];;
CoxeterLength( W, w );
y := EltWord( W, [ 1, 2, 3, 4 ] );;
cr := CriticalPair( W, y, w);;
CoxeterWord( W, cr[1] );
cr[3];
KazhdanLusztigPolynomial( W, y, w, 4, 23 );
KazhdanLusztigPolynomial( W, cr[1], cr[2], 16, 23 );

W := CoxeterGroup( "B", 4 );;
y := [ 1, 2, 3, 4, 3, 2, 1 ];;
py := EltWord( W, y );
x := [ 1 ];;
px := EltWord( W, x );
Bruhat( W, px, py );
List([0..3],i->KazhdanLusztigCoefficient( W, px, py, 1, 7, i ) );

W := CoxeterGroup( "G", 2 );;
LeftCells(W);

v := X( Cyclotomics ) ;; v.name := "v";;
W := Hecke(CoxeterGroup( "H", 3), v^2, v );
c := LeftCells( Group( W ) );;
List( c, i -> Length( i[ 1 ] ) );
LeftCellRepresentation(W,c[3]);

W := CoxeterGroup( "B", 3 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
C := Basis( H, "C" );
T( C( 1 ) );
C( T( 1 ) );

ref := HeckeReflectionRepresentation( H );;
c := CharRepresentationWords( ref, CoxeterConjugacyClasses( W ) );
List( ChevieClassInfo( W ).classtext, i ->
                            HeckeCharValues( C( i ), c ) );

v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "B", 2 ), v ^ 2, v );;
h := Basis( H, "C'" )( 1 );
h2 := h * h;
Basis( H, "T" )( h2 );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
D := Basis( H, "D" );
D( T( 1 ) );
BetaInvolution( D( 1 ) );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
Dp := Basis( H, "D'" );
AltInvolution( Dp( 1 ) );
Dp( 1 )^3;


W := CoxeterGroup( "G", 2 );
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );
PrintDiagram( H );

H.rootInclusion;

CoxeterLength( W, H.generators[2] );
CoxeterLength( H, H.generators[2] );

el := CoxeterWords( H );

el1 := List( el, x -> H.rootRestriction{ x } );

el2 := List( el, x -> EltWord( H, x ) );

List( el2, x -> CoxeterWord( W, x ) );

W := CoxeterGroup( "G", 2 );;
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 11, 20 ] );
ReflectionName( H );
H.rootRestriction;
ReflectionSubgroup( H, [ 1, 2, 6 ] );

W := CoxeterGroup( "F", 4 );
H := ReflectionSubgroup( W, [ 10, 11, 12 ] );
PrintDiagram( H );
LongestCoxeterWord( H );

W := CoxeterGroup("F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 9, 16 ] );;
PrintDiagram( H );
w := EltWord( W, [ 3, 2, 3, 4, 3, 2 ] );;
f := ReducedInCoset( H, w );;
CoxeterWord( W, f );
H.rootInclusion{[ 1 ..4 ]};

OnTuples( H.rootInclusion{[ 1 .. 4 ]}, f );

W := CoxeterGroup( "B", 3 );;
H := ReflectionSubgroup(W, [ 2, 3 ]);;
List( ReducedRightCosetRepresen

Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Fri Jun 25 05:01:36 2004

Input: SizeScreen( [ 72, ] );

W := CoxeterGroup( "A", 4 );;
w := Braid( W )( 1, 2, 3, 4 );
w ^ 3;
w ^ 4;
w ^ -1;

CheviePrintOption("Garside","GAP");
w;
w ^ 3;
w ^ -1;

CheviePrintOption("Garside","");
w ^ -1;

CheviePrintOption("Garside","Greedy");
W := CoxeterGroup( "A", 3 );;
B := Braid( W );
B( W.generators[1] );
B( 2, 1, 2, 1, 1 );
B( [ 2, 1, 2, 1, 1 ], -1 );

W := CoxeterGroup( "A", 2 );;
a := Braid( W )( [1] );
b := Braid( W )( [2] );
a * b;

( a * b ) ^ 4;
( a * b ) ^ -1;

a ^ b;

a / b;

CoxeterGroup( a );

CheviePrintOption("Garside","GAP");;
( a * b ) ^ -1;
CheviePrintOption("Garside","");;
( a * b ) ^ -1;
CheviePrintOption("Garside","Greedy");;
( a * b ) ^ -1;

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
p := EltBraid( b );
CoxeterWord( W, p );

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
WordBraid( b );

W := CoxeterGroup( "F", 4 );;
w:=[ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ];;
GoodCoxeterWord( W, w );
OrderPerm( EltWord( W, w ) );
Braid( W )( w ) ^ 6;
GoodCoxeterWord( W, [ 3, 2, 3, 4, 3, 2, 1, 3, 4, 2 ] );


W := CoxeterGroup( [ [ 1, -1, 0 ], [ 0, 1, -1 ] ],
                      [ [ 1, -1, 0 ], [ 0, 1, -1 ] ] );;
gu3 := CoxeterCoset( W, -IdentityMat( 3 ) );
F4 := CoxeterGroup( "F", 4 );;
D4 := ReflectionSubgroup( F4, [ 1, 2, 16, 48 ] );
PrintDiagram( D4 );
3D4 := CoxeterCoset( D4, (2,9,16) );

#CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), [ 1 ] );
f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
w := RepresentativeOperation( Group( f4coset ),
                     [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;
3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
PrintDiagram( 3d4again );

WF := CoxeterCoset( CoxeterGroup( "A", 4 ), (1,4)(2,3) );
Display( InductionTable( CoxeterSubCoset( WF, [ 2, 3 ] ), WF ) );

HF := CoxeterSubCoset( WF, [1, 2], LongestCoxeterElement( Group( WF ) ) );;
Display( InductionTable( HF, WF ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3)(2,4) );
Display( InductionTable( CoxeterSubCoset( W, [ 1, 3 ] ), W ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "G", 2, "A", 2 ), (1,5,2,6) );
ReflectionName( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
PrintDiagram( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
ReflectionType( W );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );

W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
Display( CharTable( W ) );

W := CoxeterGroup( "E", 6 );; WF := CoxeterCoset( W );
phi := EltWord( W, [ 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ] );;
HF := CoxeterSubCoset( WF, [ 2..5 ], phi );;
PrintDiagram( HF );
PhiFactors( HF );
ReflectionDegrees( Group( HF ) );


W := CoxeterGroup( "A", 3 );;
Display( CharTable( W ));

W := CoxeterGroup( "G", 2);;
ct := CharTable( W );
ct.classtext;
ct.classnames;
ct.irredinfo;

W := CoxeterGroup( "A", 3 );
List( Elements( W ), x -> ReflectionCharValue( W, x ) );

W := CoxeterGroup( "H", 4 );
ReflectionDegrees( W );
Size( W );

q := X( Rationals );; q.name := "q";;
FakeDegrees( CoxeterGroup( "A", 2 ), q );

q := X( Rationals );; q.name := "q";;
FakeDegree( CoxeterGroup( "A", 2 ), [ [ 2, 1 ] ], q );

LowestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

LowestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

 ChevieCharInfo( CoxeterGroup( "G", 2 ) );

W := CoxeterGroup( "E", 6 );;
ChevieCharInfo( W ).frame;


G := ComplexReflectionGroup( 4 );
ReflectionDegrees( G );
Size( G );
q := X( Cyclotomics );; q.name := "q";;
FakeDegrees( G, q );

G := ComplexReflectionGroup( 4, 2, 3 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );

G := ComplexReflectionGroup( 4 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );
Display( CharTable( CH ) );


W := CoxeterGroup( "D", 4 );
PrintArray( W.cartan );

W := CoxeterGroup( "A", 2, "B", 2 );; PrintArray( W.cartan );

W := CoxeterGroup( [ [ -1, 1, 0], [ 0, -1, 1 ] ],
                      [ [ -1, 1, 0], [ 0, -1, 1 ] ] );
MatXPerm( W, W.generators[1] );

C := CartanMat( "F", 4 );;
PrintArray( C );

CartanMat( "I", 2, 5 );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionType( C );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionName( ReflectionType( C ) );
ReflectionName( ReflectionType( CartanMat( "I", 2, 7 ) ) );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
t := ReflectionType( C );
PrintDiagram( t );
PrintDiagram( ReflectionType( CartanMat( "E", 8) ) );

W := CoxeterGroup( "A", 4 );;
PrintArray( W.cartan );
W.matgens;
W.roots;

W := CoxeterGroup( "D", 4 );;
p := EltWord( W, [ 1, 3, 2, 1, 3 ] );
CoxeterWord( W, p );

LongestCoxeterWord( W );
w0 := LongestCoxeterElement( W );
CoxeterLength( W, w0 );

List( Reflections( W ), i -> CoxeterWord( W, i ) );
l := List( [1 .. W.N+1], x -> CoxeterElements( W, x-1 ) );;
List( l, Length );

W := CoxeterGroup( "G", 2 );;
EltWord( W, [1,2,1] );

W := CoxeterGroup( "A", 3 );;
w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);;
w in W;
CHEVIE.BrieskornNormalForm := true;;
CoxeterWord( W, w );
CHEVIE.BrieskornNormalForm := false;;
CoxeterWord( W, w );

W := CoxeterGroup( "F", 4 );;
p := EltWord( W, [ 1, 2, 3, 4, 2 ] );
CoxeterLength( W, p );
CoxeterWord( W, p );

W := CoxeterGroup( "E", 6 );;
ReducedCoxeterWord( W, [ 1, 1, 1, 1, 1, 2, 2, 2, 3 ] );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
LeftDescentSet( W, w );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
RightDescentSet( W, w );

W := CoxeterGroup( "B", 2 );; W.roots;
Reflections( W );

LongestCoxeterElement( CoxeterGroup( "A", 4 ) );

LongestCoxeterWord( CoxeterGroup( "A", 4 ) );

W := CoxeterGroup( "G", 2 );;  W.roots;
HighestShortRoot( W );
#W1 := CoxeterGroup( "A", 1, "B", 3 );;
#HighestShortRoot( W1 );

W := CoxeterGroup( "G", 2 );;
e := CoxeterElements( W, 6 );
e[1] = LongestCoxeterElement( W );

CoxeterWords( CoxeterGroup( "G", 2 ) );

CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( W );

W := CoxeterGroup( "H", 3 );;
w := EltWord( W, [ 1, 2, 1, 3 ] );;
b := Filtered( Elements( W ), i -> Bruhat( W, i, w,
                                CoxeterLength( W, i ), 4 ) );;
List( b, x -> CoxeterWord( W, x ) );

W := CoxeterGroup(
[ [ 2, 0,-1, 0, 0, 0, 1 ], [ 0, 2, 0,-1, 0, 0, 0 ],
  [-1, 0, 2,-1, 0, 0,-1 ], [ 0,-1,-1, 2,-1, 0, 0 ],
  [ 0, 0, 0,-1, 2,-1, 0 ], [ 0, 0, 0, 0,-1, 2, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] );;
w0 := LongestCoxeterElement( W );;
mx := MatXPerm( W, w0 );

my := MatYPerm( W, w0 );

PermMatX( W, mx ) = w0;

PermMatY( W, my ) = w0;


W := CoxeterGroup( "A", 2 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );

W := CoxeterGroup( "A", 2, "A", 3 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );


W := CoxeterGroup( "A", 2 );

H := Hecke( W, 0 );

T := Basis( H, "T" );
el := CoxeterWords( W );

mat := []; for i in [1..6] do mat[i]:=[]; for j in [1..6] do
Add( mat[i], T( el[i]) * T( el[j] ) ); od; od;
PrintArray(mat);

W := CoxeterGroup( "B", 3 );
u := X( Rationals );; u.name := "u";;

H := Hecke( W, u );
H := Hecke( W, u^2, u );
H := Hecke( W, [ u^6, u^4, u^4 ], [ u^3, -u^2, -u^2 ] );

H := Hecke( W, 9, 3 );
#H := Hecke( W, [ u^6, u^4, u^8] );

u := X( Rationals );; u.name := "u";;
H := Hecke( CoxeterGroup( "B", 2 ), u );
HeckeSubAlgebra( H, [ 1, 4 ] );
#HeckeSubAlgebra( H, [ 1, 7 ] );

T := Basis( H, "T" );

W := CoxeterGroup( "B", 3 );;
u := X( Rationals );; u.name := "u";;
H := Hecke( W, u );;
T := Basis( H, "T" );
T( 1, 2 ) = T( [ 1, 2 ] );
T( 1, 2 ) = T( EltWord( W, [ 1, 2 ] ) );
l := [ [], [ 1, 2, 3 ], [ 1 ], [ 2 ], [ 3 ] ];;
pl := List( l, i -> EltWord( W, i ) );;
h := T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
h.elm;
h.coeff;

CHEVIE.PrintHecke := "GAP";
T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
CHEVIE.PrintHecke := "";

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "A", 2 ), q );
T := Basis( H, "T" );
( T() + T( 1 ) ) * ( T() + T( 2 ) );
T( 1 ) * T( 1 );
T( 1, 1 );

( q * T( 1, 2 ) ) ^ -1;
#( T( 1 ) + T( 2 ) ) ^ -1;
( T( 1 ) + T( 2 ) ) ^ 2;

T( 1 ) + T();
T( 1 ) - T( 1 );

h := T( [ EltWord( Group( H ), [ 1 ] ),() ],[ 0, q^100 ] );
Normalize( h );
h;

AlphaInvolution( T( 1, 2 ) );

CreateHeckeBasis( "t", rec(
T := h->Basis( Hecke(h), "T" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^CoxeterLength(
             Group( Hecke(h) ), h.elm[i] ) *  h.coeff[i] ) ),
t := h->Basis( Hecke(h), "t" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^-CoxeterLength(
              Group( Hecke(h) ), h.elm[i] ) * h.coeff[i] ) ),
BetaInvolution := h->Basis( Hecke( h ),"t")(
                    HeckeAlgebraOps.T.BetaInvolution(
                            Basis( Hecke( h ), "T" )( h ) ) ) ), AbsHeckeOps );
Inherit(HeckeAlgebraOps,AbsHeckeOps);
v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "A", 3 ), v ^ 2, v );;
h := Basis( H, "t" )( 3, 1, 2 );
h1 := Basis( H, "T")( h );
h2 := Basis( H, "t" )( h1 );
BetaInvolution( h2 );


v:= X( Rationals );;  v.name := "v";;
H := Hecke(CoxeterGroup( "B", 2) , v^2, v);
ref:= HeckeReflectionRepresentation( H );

H := Hecke( CoxeterGroup( "H", 3 ));;
HeckeReflectionRepresentation( H );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := HeckeReflectionRepresentation( H );;
CheckHeckeDefiningRelations( H, r );

W := CoxeterGroup( "G", 2 );;
u := X( Rationals );;  u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
u := u * v^0;;
H := Hecke( W, [ u^2, v^2 ], [ u, v ] );
Display( CharTable( H ) );

H1 := Hecke( W, [ E(6)^2, E(6)^4 ],[ E(6), E(6)^2 ] );
ct := CharTable( H1 );
Display( ct );
RankMat( ct.irreducibles );

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "B", 2 ), q ^ 2, q );;
HeckeCharValues( Basis( H, "C'" )( 1, 2, 1 ) );

u := X( Rationals );; u.name := "u";;
W := CoxeterGroup( "A", 3 );
H := Hecke( W, u );;
h := Basis( H, "T" )( LongestCoxeterElement( W ) );
cp := HeckeClassPolynomials( h );
CharTable( H ).irreducibles * cp;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "G", 2 );; H := Hecke( W, q );
PoincarePolynomial( H );

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
schur := SchurElements( Hecke( CoxeterGroup( "G", 2 ),
                                   [ u ^ 2, v ^ 2 ], [ u, v ] ) );

schur[1];

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
H := Hecke( CoxeterGroup( "G", 2 ), [ u ^ 2, v ^ 2 ], [ u, v ] );
SchurElement( H, [ [ 1, 3, "'" ] ] );

v := X( Cyclotomics );; v.name := "v";;
H := Hecke( CoxeterGroup( "H", 3 ), v ^ 2, v );;
HeckeCentralMonomials( H );

HeckeCharValuesGood( H, [ 1, 2, 3 ] );

klpol := function(W,x,y)return 
  KazhdanLusztigPolynomial(W,EltWord(W,x),EltWord(W,y),Length(x),Length(y));
end;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "B", 3 );;
el := CoxeterWords( W );
List( el, w -> klpol( W, [], w ) );

W.klpol;

W := CoxeterGroup( "F", 4 );
w := LongestCoxeterElement( W ) * W.generators[1];;
CoxeterLength( W, w );
y := EltWord( W, [ 1, 2, 3, 4 ] );;
cr := CriticalPair( W, y, w);;
CoxeterWord( W, cr[1] );
cr[3];
KazhdanLusztigPolynomial( W, y, w, 4, 23 );
KazhdanLusztigPolynomial( W, cr[1], cr[2], 16, 23 );

W := CoxeterGroup( "B", 4 );;
y := [ 1, 2, 3, 4, 3, 2, 1 ];;
py := EltWord( W, y );
x := [ 1 ];;
px := EltWord( W, x );
Bruhat( W, px, py );
List([0..3],i->KazhdanLusztigCoefficient( W, px, py, 1, 7, i ) );

W := CoxeterGroup( "G", 2 );;
LeftCells(W);

v := X( Cyclotomics ) ;; v.name := "v";;
W := Hecke(CoxeterGroup( "H", 3), v^2, v );
c := LeftCells( Group( W ) );;
List( c, i -> Length( i[ 1 ] ) );
LeftCellRepresentation(W,c[3]);

W := CoxeterGroup( "B", 3 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
C := Basis( H, "C" );
T( C( 1 ) );
C( T( 1 ) );

ref := HeckeReflectionRepresentation( H );;
c := CharRepresentationWords( ref, CoxeterConjugacyClasses( W ) );
List( ChevieClassInfo( W ).classtext, i ->
                            HeckeCharValues( C( i ), c ) );

v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "B", 2 ), v ^ 2, v );;
h := Basis( H, "C'" )( 1 );
h2 := h * h;
Basis( H, "T" )( h2 );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
D := Basis( H, "D" );
D( T( 1 ) );
BetaInvolution( D( 1 ) );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
Dp := Basis( H, "D'" );
AltInvolution( Dp( 1 ) );
Dp( 1 )^3;


W := CoxeterGroup( "G", 2 );
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );
PrintDiagram( H );

H.rootInclusion;

CoxeterLength( W, H.generators[2] );
CoxeterLength( H, H.generators[2] );

el := CoxeterWords( H );

el1 := List( el, x -> H.rootRestriction{ x } );

el2 := List( el, x -> EltWord( H, x ) );

List( el2, x -> CoxeterWord( W, x ) );

W := CoxeterGroup( "G", 2 );;
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 11, 20 ] );
ReflectionName( H );
H.rootRestriction;
ReflectionSubgroup( H, [ 1, 2, 6 ] );

W := CoxeterGroup( "F", 4 );
H := ReflectionSubgroup( W, [ 10, 11, 12 ] );
PrintDiagram( H );
LongestCoxeterWord( H );

W := CoxeterGroup("F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 9, 16 ] );;
PrintDiagram( H );
w := EltWord( W, [ 3, 2, 3, 4, 3, 2 ] );;
f := ReducedInCoset( H, w );;
CoxeterWord( W, f );
H.rootInclusion{[ 1 ..4 ]};

OnTuples( H.rootInclusion{[ 1 .. 4 ]}, f );

W := CoxeterGroup( "B", 3 );;
H := ReflectionSubgroup(W, [ 2, 3 ]);;
List( ReducedRightCosetRepresentatives( W, H ),
                               x-> CoxeterWord( W, x ) );

W := CoxeterGroup( "F", 4 );;
PermCosetsSubgroup( W, ReflectionSubgroup( W, [ 1, 2, 3 ] ) );

W := CoxeterGroup( "D", 4);;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( jInductionTable( H, W ) );

W := CoxeterGroup( "D", 4 );;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( JInductionTable( H, W ) );


W := Group( [ (1,2), (2,3), (3,4) ], () );
H:=Subgroup( W, [ (1,2), (3,4) ] );
W.name := "W";; H.name := "H";;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "G", 2 );;
H := ReflectionSubgroup( W, [ 1, 4 ] );
ReflectionName( H );
Display(InductionTable( H, W ) );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := ChevieClassInfo( Group( H ) ).classtext;;
t := HeckeReflectionRepresentation( H );;
CharRepresentationWords( t, r );

G := Group( (1,2)(3,4), (1,2,3,4,5) );;
ConjugacyClasses( G );
 g := Random( G );
PositionClass( G, g );

G := Group( (1,7)(2,3)(5,6)(8,9)(11,12),
               (1,5)(2,8)(3,4)(7,11)(9,10) );;
PointsAndRepresentativesOrbits( G );

C1 := [ [   2,  -1,   0,   0 ],
           [  -1,   2,  -1,   0 ],
           [   0,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
C2 := [ [   2,   0,  -1,   0 ],
           [   0,   2,  -1,   0 ],
           [  -1,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
d := DirectSumMat( C1, C2 );;
PrintArray( d );

m := [ [  0,  0,  0,  1 ],
          [  0,  0,  1,  0 ],
          [  0,  1,  0,  0 ],
          [  1,  0,  0,  0 ] ];;
DecomposedMat( m );
PrintArray( m{[ 1, 4 ]}{[ 1, 4 ]});

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsDiagonalMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsLowerTriangularMat( a );
a[1][2] := 0;;
IsLowerTriangularMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
l := [ [ 1, 0 ], [ 0, 1 ], [ 1, 1 ], [ 0, 0 ] ];;
l * a;
IsNormalizing( l, a );

l := [ 1, , 2, , , 3 ];;
SublistUnbnd( l, [ 1..4 ] );

a := [ 1, 2, 3, 4 ];;
b := [ 2, 3, 1, 4 ];;
p := PermListList( a, b );
Permuted( b, p );
PermListList( a, [ 3, 2, 1, 5 ] );

IntListToString( [ 4, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ], "{}" );

d := PartitionTuples( 3, 2 );
for i in d do
     Print( PartitionTupleToString( i ),"   ");
od; Print("n");


Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Fri Jun 25 05:01:55 2004

Input: SizeScreen( [ 72, ] );

W := CoxeterGroup( "A", 4 );;
w := Braid( W )( 1, 2, 3, 4 );
w ^ 3;
w ^ 4;
w ^ -1;

CheviePrintOption("Garside","GAP");
w;
w ^ 3;
w ^ -1;

CheviePrintOption("Garside","");
w ^ -1;

CheviePrintOption("Garside","Greedy");
W := CoxeterGroup( "A", 3 );;
B := Braid( W );
B( W.generators[1] );
B( 2, 1, 2, 1, 1 );
B( [ 2, 1, 2, 1, 1 ], -1 );

W := CoxeterGroup( "A", 2 );;
a := Braid( W )( [1] );
b := Braid( W )( [2] );
a * b;

( a * b ) ^ 4;
( a * b ) ^ -1;

a ^ b;

a / b;

CoxeterGroup( a );

CheviePrintOption("Garside","GAP");;
( a * b ) ^ -1;
CheviePrintOption("Garside","");;
( a * b ) ^ -1;
CheviePrintOption("Garside","Greedy");;
( a * b ) ^ -1;

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
p := EltBraid( b );
CoxeterWord( W, p );

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
WordBraid( b );

W := CoxeterGroup( "F", 4 );;
w:=[ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ];;
GoodCoxeterWord( W, w );
OrderPerm( EltWord( W, w ) );
Braid( W )( w ) ^ 6;
GoodCoxeterWord( W, [ 3, 2, 3, 4, 3, 2, 1, 3, 4, 2 ] );


W := CoxeterGroup( [ [ 1, -1, 0 ], [ 0, 1, -1 ] ],
                      [ [ 1, -1, 0 ], [ 0, 1, -1 ] ] );;
gu3 := CoxeterCoset( W, -IdentityMat( 3 ) );
F4 := CoxeterGroup( "F", 4 );;
D4 := ReflectionSubgroup( F4, [ 1, 2, 16, 48 ] );
PrintDiagram( D4 );
3D4 := CoxeterCoset( D4, (2,9,16) );

#CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), [ 1 ] );
f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
w := RepresentativeOperation( Group( f4coset ),
                     [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;
3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
PrintDiagram( 3d4again );

WF := CoxeterCoset( CoxeterGroup( "A", 4 ), (1,4)(2,3) );
Display( InductionTable( CoxeterSubCoset( WF, [ 2, 3 ] ), WF ) );

HF := CoxeterSubCoset( WF, [1, 2], LongestCoxeterElement( Group( WF ) ) );;
Display( InductionTable( HF, WF ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3)(2,4) );
Display( InductionTable( CoxeterSubCoset( W, [ 1, 3 ] ), W ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "G", 2, "A", 2 ), (1,5,2,6) );
ReflectionName( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
PrintDiagram( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
ReflectionType( W );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );

W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
Display( CharTable( W ) );

W := CoxeterGroup( "E", 6 );; WF := CoxeterCoset( W );
phi := EltWord( W, [ 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ] );;
HF := CoxeterSubCoset( WF, [ 2..5 ], phi );;
PrintDiagram( HF );
PhiFactors( HF );
ReflectionDegrees( Group( HF ) );


W := CoxeterGroup( "A", 3 );;
Display( CharTable( W ));

W := CoxeterGroup( "G", 2);;
ct := CharTable( W );
ct.classtext;
ct.classnames;
ct.irredinfo;

W := CoxeterGroup( "A", 3 );
List( Elements( W ), x -> ReflectionCharValue( W, x ) );

W := CoxeterGroup( "H", 4 );
ReflectionDegrees( W );
Size( W );

q := X( Rationals );; q.name := "q";;
FakeDegrees( CoxeterGroup( "A", 2 ), q );

q := X( Rationals );; q.name := "q";;
FakeDegree( CoxeterGroup( "A", 2 ), [ [ 2, 1 ] ], q );

LowestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

LowestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

 ChevieCharInfo( CoxeterGroup( "G", 2 ) );

W := CoxeterGroup( "E", 6 );;
ChevieCharInfo( W ).frame;


G := ComplexReflectionGroup( 4 );
ReflectionDegrees( G );
Size( G );
q := X( Cyclotomics );; q.name := "q";;
FakeDegrees( G, q );

G := ComplexReflectionGroup( 4, 2, 3 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );

G := ComplexReflectionGroup( 4 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );
Display( CharTable( CH ) );


W := CoxeterGroup( "D", 4 );
PrintArray( W.cartan );

W := CoxeterGroup( "A", 2, "B", 2 );; PrintArray( W.cartan );

W := CoxeterGroup( [ [ -1, 1, 0], [ 0, -1, 1 ] ],
                      [ [ -1, 1, 0], [ 0, -1, 1 ] ] );
MatXPerm( W, W.generators[1] );

C := CartanMat( "F", 4 );;
PrintArray( C );

CartanMat( "I", 2, 5 );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionType( C );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionName( ReflectionType( C ) );
ReflectionName( ReflectionType( CartanMat( "I", 2, 7 ) ) );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
t := ReflectionType( C );
PrintDiagram( t );
PrintDiagram( ReflectionType( CartanMat( "E", 8) ) );

W := CoxeterGroup( "A", 4 );;
PrintArray( W.cartan );
W.matgens;
W.roots;

W := CoxeterGroup( "D", 4 );;
p := EltWord( W, [ 1, 3, 2, 1, 3 ] );
CoxeterWord( W, p );

LongestCoxeterWord( W );
w0 := LongestCoxeterElement( W );
CoxeterLength( W, w0 );

List( Reflections( W ), i -> CoxeterWord( W, i ) );
l := List( [1 .. W.N+1], x -> CoxeterElements( W, x-1 ) );;
List( l, Length );

W := CoxeterGroup( "G", 2 );;
EltWord( W, [1,2,1] );

W := CoxeterGroup( "A", 3 );;
w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);;
w in W;
CHEVIE.BrieskornNormalForm := true;;
CoxeterWord( W, w );
CHEVIE.BrieskornNormalForm := false;;
CoxeterWord( W, w );

W := CoxeterGroup( "F", 4 );;
p := EltWord( W, [ 1, 2, 3, 4, 2 ] );
CoxeterLength( W, p );
CoxeterWord( W, p );

W := CoxeterGroup( "E", 6 );;
ReducedCoxeterWord( W, [ 1, 1, 1, 1, 1, 2, 2, 2, 3 ] );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
LeftDescentSet( W, w );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
RightDescentSet( W, w );

W := CoxeterGroup( "B", 2 );; W.roots;
Reflections( W );

LongestCoxeterElement( CoxeterGroup( "A", 4 ) );

LongestCoxeterWord( CoxeterGroup( "A", 4 ) );

W := CoxeterGroup( "G", 2 );;  W.roots;
HighestShortRoot( W );
#W1 := CoxeterGroup( "A", 1, "B", 3 );;
#HighestShortRoot( W1 );

W := CoxeterGroup( "G", 2 );;
e := CoxeterElements( W, 6 );
e[1] = LongestCoxeterElement( W );

CoxeterWords( CoxeterGroup( "G", 2 ) );

CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( W );

W := CoxeterGroup( "H", 3 );;
w := EltWord( W, [ 1, 2, 1, 3 ] );;
b := Filtered( Elements( W ), i -> Bruhat( W, i, w,
                                CoxeterLength( W, i ), 4 ) );;
List( b, x -> CoxeterWord( W, x ) );

W := CoxeterGroup(
[ [ 2, 0,-1, 0, 0, 0, 1 ], [ 0, 2, 0,-1, 0, 0, 0 ],
  [-1, 0, 2,-1, 0, 0,-1 ], [ 0,-1,-1, 2,-1, 0, 0 ],
  [ 0, 0, 0,-1, 2,-1, 0 ], [ 0, 0, 0, 0,-1, 2, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] );;
w0 := LongestCoxeterElement( W );;
mx := MatXPerm( W, w0 );

my := MatYPerm( W, w0 );

PermMatX( W, mx ) = w0;

PermMatY( W, my ) = w0;


W := CoxeterGroup( "A", 2 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );

W := CoxeterGroup( "A", 2, "A", 3 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );


W := CoxeterGroup( "A", 2 );

H := Hecke( W, 0 );

T := Basis( H, "T" );
el := CoxeterWords( W );

mat := []; for i in [1..6] do mat[i]:=[]; for j in [1..6] do
Add( mat[i], T( el[i]) * T( el[j] ) ); od; od;
PrintArray(mat);

W := CoxeterGroup( "B", 3 );
u := X( Rationals );; u.name := "u";;

H := Hecke( W, u );
H := Hecke( W, u^2, u );
H := Hecke( W, [ u^6, u^4, u^4 ], [ u^3, -u^2, -u^2 ] );

H := Hecke( W, 9, 3 );
#H := Hecke( W, [ u^6, u^4, u^8] );

u := X( Rationals );; u.name := "u";;
H := Hecke( CoxeterGroup( "B", 2 ), u );
HeckeSubAlgebra( H, [ 1, 4 ] );
#HeckeSubAlgebra( H, [ 1, 7 ] );

T := Basis( H, "T" );

W := CoxeterGroup( "B", 3 );;
u := X( Rationals );; u.name := "u";;
H := Hecke( W, u );;
T := Basis( H, "T" );
T( 1, 2 ) = T( [ 1, 2 ] );
T( 1, 2 ) = T( EltWord( W, [ 1, 2 ] ) );
l := [ [], [ 1, 2, 3 ], [ 1 ], [ 2 ], [ 3 ] ];;
pl := List( l, i -> EltWord( W, i ) );;
h := T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
h.elm;
h.coeff;

CHEVIE.PrintHecke := "GAP";
T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
CHEVIE.PrintHecke := "";

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "A", 2 ), q );
T := Basis( H, "T" );
( T() + T( 1 ) ) * ( T() + T( 2 ) );
T( 1 ) * T( 1 );
T( 1, 1 );

( q * T( 1, 2 ) ) ^ -1;
#( T( 1 ) + T( 2 ) ) ^ -1;
( T( 1 ) + T( 2 ) ) ^ 2;

T( 1 ) + T();
T( 1 ) - T( 1 );

h := T( [ EltWord( Group( H ), [ 1 ] ),() ],[ 0, q^100 ] );
Normalize( h );
h;

AlphaInvolution( T( 1, 2 ) );

CreateHeckeBasis( "t", rec(
T := h->Basis( Hecke(h), "T" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^CoxeterLength(
             Group( Hecke(h) ), h.elm[i] ) *  h.coeff[i] ) ),
t := h->Basis( Hecke(h), "t" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^-CoxeterLength(
              Group( Hecke(h) ), h.elm[i] ) * h.coeff[i] ) ),
BetaInvolution := h->Basis( Hecke( h ),"t")(
                    HeckeAlgebraOps.T.BetaInvolution(
                            Basis( Hecke( h ), "T" )( h ) ) ) ), AbsHeckeOps );
Inherit(HeckeAlgebraOps,AbsHeckeOps);
v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "A", 3 ), v ^ 2, v 

Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Fri Jun 25 05:01:56 2004

Input: SizeScreen( [ 72, ] );

W := CoxeterGroup( "A", 4 );;
w := Braid( W )( 1, 2, 3, 4 );
w ^ 3;
w ^ 4;
w ^ -1;

CheviePrintOption("Garside","GAP");
w;
w ^ 3;
w ^ -1;

CheviePrintOption("Garside","");
w ^ -1;

CheviePrintOption("Garside","Greedy");
W := CoxeterGroup( "A", 3 );;
B := Braid( W );
B( W.generators[1] );
B( 2, 1, 2, 1, 1 );
B( [ 2, 1, 2, 1, 1 ], -1 );

W := CoxeterGroup( "A", 2 );;
a := Braid( W )( [1] );
b := Braid( W )( [2] );
a * b;

( a * b ) ^ 4;
( a * b ) ^ -1;

a ^ b;

a / b;

CoxeterGroup( a );

CheviePrintOption("Garside","GAP");;
( a * b ) ^ -1;
CheviePrintOption("Garside","");;
( a * b ) ^ -1;
CheviePrintOption("Garside","Greedy");;
( a * b ) ^ -1;

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
p := EltBraid( b );
CoxeterWord( W, p );

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
WordBraid( b );

W := CoxeterGroup( "F", 4 );;
w:=[ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ];;
GoodCoxeterWord( W, w );
OrderPerm( EltWord( W, w ) );
Braid( W )( w ) ^ 6;
GoodCoxeterWord( W, [ 3, 2, 3, 4, 3, 2, 1, 3, 4, 2 ] );


W := CoxeterGroup( [ [ 1, -1, 0 ], [ 0, 1, -1 ] ],
                      [ [ 1, -1, 0 ], [ 0, 1, -1 ] ] );;
gu3 := CoxeterCoset( W, -IdentityMat( 3 ) );
F4 := CoxeterGroup( "F", 4 );;
D4 := ReflectionSubgroup( F4, [ 1, 2, 16, 48 ] );
PrintDiagram( D4 );
3D4 := CoxeterCoset( D4, (2,9,16) );

#CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), [ 1 ] );
f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
w := RepresentativeOperation( Group( f4coset ),
                     [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;
3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
PrintDiagram( 3d4again );

WF := CoxeterCoset( CoxeterGroup( "A", 4 ), (1,4)(2,3) );
Display( InductionTable( CoxeterSubCoset( WF, [ 2, 3 ] ), WF ) );

HF := CoxeterSubCoset( WF, [1, 2], LongestCoxeterElement( Group( WF ) ) );;
Display( InductionTable( HF, WF ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3)(2,4) );
Display( InductionTable( CoxeterSubCoset( W, [ 1, 3 ] ), W ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "G", 2, "A", 2 ), (1,5,2,6) );
ReflectionName( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
PrintDiagram( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
ReflectionType( W );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );

W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
Display( CharTable( W ) );

W := CoxeterGroup( "E", 6 );; WF := CoxeterCoset( W );
phi := EltWord( W, [ 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ] );;
HF := CoxeterSubCoset( WF, [ 2..5 ], phi );;
PrintDiagram( HF );
PhiFactors( HF );
ReflectionDegrees( Group( HF ) );


W := CoxeterGroup( "A", 3 );;
Display( CharTable( W ));

W := CoxeterGroup( "G", 2);;
ct := CharTable( W );
ct.classtext;
ct.classnames;
ct.irredinfo;

W := CoxeterGroup( "A", 3 );
List( Elements( W ), x -> ReflectionCharValue( W, x ) );

W := CoxeterGroup( "H", 4 );
ReflectionDegrees( W );
Size( W );

q := X( Rationals );; q.name := "q";;
FakeDegrees( CoxeterGroup( "A", 2 ), q );

q := X( Rationals );; q.name := "q";;
FakeDegree( CoxeterGroup( "A", 2 ), [ [ 2, 1 ] ], q );

LowestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

LowestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

 ChevieCharInfo( CoxeterGroup( "G", 2 ) );

W := CoxeterGroup( "E", 6 );;
ChevieCharInfo( W ).frame;


G := ComplexReflectionGroup( 4 );
ReflectionDegrees( G );
Size( G );
q := X( Cyclotomics );; q.name := "q";;
FakeDegrees( G, q );

G := ComplexReflectionGroup( 4, 2, 3 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );

G := ComplexReflectionGroup( 4 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );
Display( CharTable( CH ) );


W := CoxeterGroup( "D", 4 );
PrintArray( W.cartan );

W := CoxeterGroup( "A", 2, "B", 2 );; PrintArray( W.cartan );

W := CoxeterGroup( [ [ -1, 1, 0], [ 0, -1, 1 ] ],
                      [ [ -1, 1, 0], [ 0, -1, 1 ] ] );
MatXPerm( W, W.generators[1] );

C := CartanMat( "F", 4 );;
PrintArray( C );

CartanMat( "I", 2, 5 );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionType( C );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionName( ReflectionType( C ) );
ReflectionName( ReflectionType( CartanMat( "I", 2, 7 ) ) );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
t := ReflectionType( C );
PrintDiagram( t );
PrintDiagram( ReflectionType( CartanMat( "E", 8) ) );

W := CoxeterGroup( "A", 4 );;
PrintArray( W.cartan );
W.matgens;
W.roots;

W := CoxeterGroup( "D", 4 );;
p := EltWord( W, [ 1, 3, 2, 1, 3 ] );
CoxeterWord( W, p );

LongestCoxeterWord( W );
w0 := LongestCoxeterElement( W );
CoxeterLength( W, w0 );

List( Reflections( W ), i -> CoxeterWord( W, i ) );
l := List( [1 .. W.N+1], x -> CoxeterElements( W, x-1 ) );;
List( l, Length );

W := CoxeterGroup( "G", 2 );;
EltWord( W, [1,2,1] );

W := CoxeterGroup( "A", 3 );;
w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);;
w in W;
CHEVIE.BrieskornNormalForm := true;;
CoxeterWord( W, w );
CHEVIE.BrieskornNormalForm := false;;
CoxeterWord( W, w );

W := CoxeterGroup( "F", 4 );;
p := EltWord( W, [ 1, 2, 3, 4, 2 ] );
CoxeterLength( W, p );
CoxeterWord( W, p );

W := CoxeterGroup( "E", 6 );;
ReducedCoxeterWord( W, [ 1, 1, 1, 1, 1, 2, 2, 2, 3 ] );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
LeftDescentSet( W, w );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
RightDescentSet( W, w );

W := CoxeterGroup( "B", 2 );; W.roots;
Reflections( W );

LongestCoxeterElement( CoxeterGroup( "A", 4 ) );

LongestCoxeterWord( CoxeterGroup( "A", 4 ) );

W := CoxeterGroup( "G", 2 );;  W.roots;
HighestShortRoot( W );
#W1 := CoxeterGroup( "A", 1, "B", 3 );;
#HighestShortRoot( W1 );

W := CoxeterGroup( "G", 2 );;
e := CoxeterElements( W, 6 );
e[1] = LongestCoxeterElement( W );

CoxeterWords( CoxeterGroup( "G", 2 ) );

CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( W );

W := CoxeterGroup( "H", 3 );;
w := EltWord( W, [ 1, 2, 1, 3 ] );;
b := Filtered( Elements( W ), i -> Bruhat( W, i, w,
                                CoxeterLength( W, i ), 4 ) );;
List( b, x -> CoxeterWord( W, x ) );

W := CoxeterGroup(
[ [ 2, 0,-1, 0, 0, 0, 1 ], [ 0, 2, 0,-1, 0, 0, 0 ],
  [-1, 0, 2,-1, 0, 0,-1 ], [ 0,-1,-1, 2,-1, 0, 0 ],
  [ 0, 0, 0,-1, 2,-1, 0 ], [ 0, 0, 0, 0,-1, 2, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] );;
w0 := LongestCoxeterElement( W );;
mx := MatXPerm( W, w0 );

my := MatYPerm( W, w0 );

PermMatX( W, mx ) = w0;

PermMatY( W, my ) = w0;


W := CoxeterGroup( "A", 2 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );

W := CoxeterGroup( "A", 2, "A", 3 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );


W := CoxeterGroup( "A", 2 );

H := Hecke( W, 0 );

T := Basis( H, "T" );
el := CoxeterWords( W );

mat := []; for i in [1..6] do mat[i]:=[]; for j in [1..6] do
Add( mat[i], T( el[i]) * T( el[j] ) ); od; od;
PrintArray(mat);

W := CoxeterGroup( "B", 3 );
u := X( Rationals );; u.name := "u";;

H := Hecke( W, u );
H := Hecke( W, u^2, u );
H := Hecke( W, [ u^6, u^4, u^4 ], [ u^3, -u^2, -u^2 ] );

H := Hecke( W, 9, 3 );
#H := Hecke( W, [ u^6, u^4, u^8] );

u := X( Rationals );; u.name := "u";;
H := Hecke( CoxeterGroup( "B", 2 ), u );
HeckeSubAlgebra( H, [ 1, 4 ] );
#HeckeSubAlgebra( H, [ 1, 7 ] );

T := Basis( H, "T" );

W := CoxeterGroup( "B", 3 );;
u := X( Rationals );; u.name := "u";;
H := Hecke( W, u );;
T := Basis( H, "T" );
T( 1, 2 ) = T( [ 1, 2 ] );
T( 1, 2 ) = T( EltWord( W, [ 1, 2 ] ) );
l := [ [], [ 1, 2, 3 ], [ 1 ], [ 2 ], [ 3 ] ];;
pl := List( l, i -> EltWord( W, i ) );;
h := T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
h.elm;
h.coeff;

CHEVIE.PrintHecke := "GAP";
T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
CHEVIE.PrintHecke := "";

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "A", 2 ), q );
T := Basis( H, "T" );
( T() + T( 1 ) ) * ( T() + T( 2 ) );
T( 1 ) * T( 1 );
T( 1, 1 );

( q * T( 1, 2 ) ) ^ -1;
#( T( 1 ) + T( 2 ) ) ^ -1;
( T( 1 ) + T( 2 ) ) ^ 2;

T( 1 ) + T();
T( 1 ) - T( 1 );

h := T( [ EltWord( Group( H ), [ 1 ] ),() ],[ 0, q^100 ] );
Normalize( h );
h;

AlphaInvolution( T( 1, 2 ) );

CreateHeckeBasis( "t", rec(
T := h->Basis( Hecke(h), "T" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^CoxeterLength(
             Group( Hecke(h) ), h.elm[i] ) *  h.coeff[i] ) ),
t := h->Basis( Hecke(h), "t" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^-CoxeterLength(
              Group( Hecke(h) ), h.elm[i] ) * h.coeff[i] ) ),
BetaInvolution := h->Basis( Hecke( h ),"t")(
                    HeckeAlgebraOps.T.BetaInvolution(
                            Basis( Hecke( h ), "T" )( h ) ) ) ), AbsHeckeOps );
Inherit(HeckeAlgebraOps,AbsHeckeOps);
v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "A", 3 ), v ^ 2, v );;
h := Basis( H, "t" )( 3, 1, 2 );
h1 := Basis( H, "T")( h );
h2 := Basis( H, "t" )( h1 );
BetaInvolution( h2 );


v:= X( Rationals );;  v.name := "v";;
H := Hecke(CoxeterGroup( "B", 2) , v^2, v);
ref:= HeckeReflectionRepresentation( H );

H := Hecke( CoxeterGroup( "H", 3 ));;
HeckeReflectionRepresentation( H );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := HeckeReflectionRepresentation( H );;
CheckHeckeDefiningRelations( H, r );

W := CoxeterGroup( "G", 2 );;
u := X( Rationals );;  u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
u := u * v^0;;
H := Hecke( W, [ u^2, v^2 ], [ u, v ] );
Display( CharTable( H ) );

H1 := Hecke( W, [ E(6)^2, E(6)^4 ],[ E(6), E(6)^2 ] );
ct := CharTable( H1 );
Display( ct );
RankMat( ct.irreducibles );

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "B", 2 ), q ^ 2, q );;
HeckeCharValues( Basis( H, "C'" )( 1, 2, 1 ) );

u := X( Rationals );; u.name := "u";;
W := CoxeterGroup( "A", 3 );
H := Hecke( W, u );;
h := Basis( H, "T" )( LongestCoxeterElement( W ) );
cp := HeckeClassPolynomials( h );
CharTable( H ).irreducibles * cp;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "G", 2 );; H := Hecke( W, q );
PoincarePolynomial( H );

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
schur := SchurElements( Hecke( CoxeterGroup( "G", 2 ),
                                   [ u ^ 2, v ^ 2 ], [ u, v ] ) );

schur[1];

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
H := Hecke( CoxeterGroup( "G", 2 ), [ u ^ 2, v ^ 2 ], [ u, v ] );
SchurElement( H, [ [ 1, 3, "'" ] ] );

v := X( Cyclotomics );; v.name := "v";;
H := Hecke( CoxeterGroup( "H", 3 ), v ^ 2, v );;
HeckeCentralMonomials( H );

HeckeCharValuesGood( H, [ 1, 2, 3 ] );

klpol := function(W,x,y)return 
  KazhdanLusztigPolynomial(W,EltWord(W,x),EltWord(W,y),Length(x),Length(y));
end;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "B", 3 );;
el := CoxeterWords( W );
List( el, w -> klpol( W, [], w ) );

W.klpol;

W := CoxeterGroup( "F", 4 );
w := LongestCoxeterElement( W ) * W.generators[1];;
CoxeterLength( W, w );
y := EltWord( W, [ 1, 2, 3, 4 ] );;
cr := CriticalPair( W, y, w);;
CoxeterWord( W, cr[1] );
cr[3];
KazhdanLusztigPolynomial( W, y, w, 4, 23 );
KazhdanLusztigPolynomial( W, cr[1], cr[2], 16, 23 );

W := CoxeterGroup( "B", 4 );;
y := [ 1, 2, 3, 4, 3, 2, 1 ];;
py := EltWord( W, y );
x := [ 1 ];;
px := EltWord( W, x );
Bruhat( W, px, py );
List([0..3],i->KazhdanLusztigCoefficient( W, px, py, 1, 7, i ) );

W := CoxeterGroup( "G", 2 );;
LeftCells(W);

v := X( Cyclotomics ) ;; v.name := "v";;
W := Hecke(CoxeterGroup( "H", 3), v^2, v );
c := LeftCells( Group( W ) );;
List( c, i -> Length( i[ 1 ] ) );
LeftCellRepresentation(W,c[3]);

W := CoxeterGroup( "B", 3 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
C := Basis( H, "C" );
T( C( 1 ) );
C( T( 1 ) );

ref := HeckeReflectionRepresentation( H );;
c := CharRepresentationWords( ref, CoxeterConjugacyClasses( W ) );
List( ChevieClassInfo( W ).classtext, i ->
                            HeckeCharValues( C( i ), c ) );

v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "B", 2 ), v ^ 2, v );;
h := Basis( H, "C'" )( 1 );
h2 := h * h;
Basis( H, "T" )( h2 );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
D := Basis( H, "D" );
D( T( 1 ) );
BetaInvolution( D( 1 ) );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
Dp := Basis( H, "D'" );
AltInvolution( Dp( 1 ) );
Dp( 1 )^3;


W := CoxeterGroup( "G", 2 );
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );
PrintDiagram( H );

H.rootInclusion;

CoxeterLength( W, H.generators[2] );
CoxeterLength( H, H.generators[2] );

el := CoxeterWords( H );

el1 := List( el, x -> H.rootRestriction{ x } );

el2 := List( el, x -> EltWord( H, x ) );

List( el2, x -> CoxeterWord( W, x ) );

W := CoxeterGroup( "G", 2 );;
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 11, 20 ] );
ReflectionName( H );
H.rootRestriction;
ReflectionSubgroup( H, [ 1, 2, 6 ] );

W := CoxeterGroup( "F", 4 );
H := ReflectionSubgroup( W, [ 10, 11, 12 ] );
PrintDiagram( H );
LongestCoxeterWord( H );

W := CoxeterGroup("F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 9, 16 ] );;
PrintDiagram( H );
w := EltWord( W, [ 3, 2, 3, 4, 3, 2 ] );;
f := ReducedInCoset( H, w );;
CoxeterWord( W, f );
H.rootInclusion{[ 1 ..4 ]};

OnTuples( H.rootInclusion{[ 1 .. 4 ]}, f );

W := CoxeterGroup( "B", 3 );;
H := ReflectionSubgroup(W, [ 2, 3 ]);;
List( ReducedRightCosetRepresentatives( W, H ),
                               x-> CoxeterWord( W, x ) );

W := CoxeterGroup( "F", 4 );;
PermCosetsSubgroup( W, ReflectionSubgroup( W, [ 1, 2, 3 ] ) );

W := CoxeterGroup( "D", 4);;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( jInductionTable( H, W ) );

W := CoxeterGroup( "D", 4 );;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( JInductionTable( H, W ) );


W := Group( [ (1,2), (2,3), (3,4) ], () );
H:=Subgroup( W, [ (1,2), (3,4) ] );
W.name := "W";; H.name := "H";;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "G", 2 );;
H := ReflectionSubgroup( W, [ 1, 4 ] );
ReflectionName( H );
Display(InductionTable( H, W ) );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := ChevieClassInfo( Group( H ) ).classtext;;
t := HeckeReflectionRepresentation( H );;
CharRepresentationWords( t, r );

G := Group( (1,2)(3,4), (1,2,3,4,5) );;
ConjugacyClasses( G );
 g := Random( G );
PositionClass( G, g );

G := Group( (1,7)(2,3)(5,6)(8,9)(11,12),
               (1,5)(2,8)(3,4)(7,11)(9,10) );;
PointsAndRepresentativesOrbits( G );

C1 := [ [   2,  -1,   0,   0 ],
           [  -1,   2,  -1,   0 ],
           [   0,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
C2 := [ [   2,   0,  -1,   0 ],
           [   0,   2,  -1,   0 ],
           [  -1,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
d := DirectSumMat( C1, C2 );;
PrintArray( d );

m := [ [  0,  0,  0,  1 ],
          [  0,  0,  1,  0 ],
          [  0,  1,  0,  0 ],
          [  1,  0,  0,  0 ] ];;
DecomposedMat( m );
PrintArray( m{[ 1, 4 ]}{[ 1, 4 ]});

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsDiagonalMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsLowerTriangularMat( a );
a[1][2] := 0;;
IsLowerTriangularMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
l := [ [ 1, 0 ], [ 0, 1 ], [ 1, 1 ], [ 0, 0 ] ];;
l * a;
IsNormalizing( l, a );

l := [ 1, , 2, , , 3 ];;
SublistUnbnd( l, [ 1..4 ] );

a := [ 1, 2, 3, 4 ];;
b := [ 2, 3, 1, 4 ];;
p := PermListList( a, b );
Permuted( b, p );
PermListList( a, [ 3, 2, 1, 5 ] );

IntListToString( [ 4, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ], "{}" );

d := PartitionTuples( 3, 2 );
for i in d do
     Print( PartitionTupleToString( i ),"   ");
od; Print("n");


Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Fri Jun 25 05:02:49 2004

Input: SizeScreen( [ 72, ] );

W := CoxeterGroup( "A", 4 );;
w := Braid( W )( 1, 2, 3, 4 );
w ^ 3;
w ^ 4;
w ^ -1;

CheviePrintOption("Garside","GAP");
w;
w ^ 3;
w ^ -1;

CheviePrintOption("Garside","");
w ^ -1;

CheviePrintOption("Garside","Greedy");
W := CoxeterGroup( "A", 3 );;
B := Braid( W );
B( W.generators[1] );
B( 2, 1, 2, 1, 1 );
B( [ 2, 1, 2, 1, 1 ], -1 );

W := CoxeterGroup( "A", 2 );;
a := Braid( W )( [1] );
b := Braid( W )( [2] );
a * b;

( a * b ) ^ 4;
( a * b ) ^ -1;

a ^ b;

a / b;

CoxeterGroup( a );

CheviePrintOption("Garside","GAP");;
( a * b ) ^ -1;
CheviePrintOption("Garside","");;
( a * b ) ^ -1;
CheviePrintOption("Garside","Greedy");;
( a * b ) ^ -1;

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
p := EltBraid( b );
CoxeterWord( W, p );

W := CoxeterGroup( "A", 3 );;
b := Braid( W )( [ 2, 1, 2, 1, 1 ] );
WordBraid( b );

W := CoxeterGroup( "F", 4 );;
w:=[ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ];;
GoodCoxeterWord( W, w );
OrderPerm( EltWord( W, w ) );
Braid( W )( w ) ^ 6;
GoodCoxeterWord( W, [ 3, 2, 3, 4, 3, 2, 1, 3, 4, 2 ] );


W := CoxeterGroup( [ [ 1, -1, 0 ], [ 0, 1, -1 ] ],
                      [ [ 1, -1, 0 ], [ 0, 1, -1 ] ] );;
gu3 := CoxeterCoset( W, -IdentityMat( 3 ) );
F4 := CoxeterGroup( "F", 4 );;
D4 := ReflectionSubgroup( F4, [ 1, 2, 16, 48 ] );
PrintDiagram( D4 );
3D4 := CoxeterCoset( D4, (2,9,16) );

#CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), [ 1 ] );
f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
w := RepresentativeOperation( Group( f4coset ),
                     [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;
3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
PrintDiagram( 3d4again );

WF := CoxeterCoset( CoxeterGroup( "A", 4 ), (1,4)(2,3) );
Display( InductionTable( CoxeterSubCoset( WF, [ 2, 3 ] ), WF ) );

HF := CoxeterSubCoset( WF, [1, 2], LongestCoxeterElement( Group( WF ) ) );;
Display( InductionTable( HF, WF ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3)(2,4) );
Display( InductionTable( CoxeterSubCoset( W, [ 1, 3 ] ), W ) );

W := CoxeterCoset( CoxeterGroup( "A", 2, "G", 2, "A", 2 ), (1,5,2,6) );
ReflectionName( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
PrintDiagram( W );

W := CoxeterCoset( CoxeterGroup( "A", 2, "A", 2 ), (1,3,2,4) );
ReflectionType( W );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );

W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
Display( CharTable( W ) );

W := CoxeterGroup( "E", 6 );; WF := CoxeterCoset( W );
phi := EltWord( W, [ 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ] );;
HF := CoxeterSubCoset( WF, [ 2..5 ], phi );;
PrintDiagram( HF );
PhiFactors( HF );
ReflectionDegrees( Group( HF ) );


W := CoxeterGroup( "A", 3 );;
Display( CharTable( W ));

W := CoxeterGroup( "G", 2);;
ct := CharTable( W );
ct.classtext;
ct.classnames;
ct.irredinfo;

W := CoxeterGroup( "A", 3 );
List( Elements( W ), x -> ReflectionCharValue( W, x ) );

W := CoxeterGroup( "H", 4 );
ReflectionDegrees( W );
Size( W );

q := X( Rationals );; q.name := "q";;
FakeDegrees( CoxeterGroup( "A", 2 ), q );

q := X( Rationals );; q.name := "q";;
FakeDegree( CoxeterGroup( "A", 2 ), [ [ 2, 1 ] ], q );

LowestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerFakeDegrees( CoxeterGroup( "D", 4 ) );

LowestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

HighestPowerGenericDegrees( CoxeterGroup( "D", 4 ) );

 ChevieCharInfo( CoxeterGroup( "G", 2 ) );

W := CoxeterGroup( "E", 6 );;
ChevieCharInfo( W ).frame;


G := ComplexReflectionGroup( 4 );
ReflectionDegrees( G );
Size( G );
q := X( Cyclotomics );; q.name := "q";;
FakeDegrees( G, q );

G := ComplexReflectionGroup( 4, 2, 3 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );

G := ComplexReflectionGroup( 4 );
v := X( Cyclotomics );; v.name := "v";;
CH := Hecke( G, v );
Display( CharTable( CH ) );


W := CoxeterGroup( "D", 4 );
PrintArray( W.cartan );

W := CoxeterGroup( "A", 2, "B", 2 );; PrintArray( W.cartan );

W := CoxeterGroup( [ [ -1, 1, 0], [ 0, -1, 1 ] ],
                      [ [ -1, 1, 0], [ 0, -1, 1 ] ] );
MatXPerm( W, W.generators[1] );

C := CartanMat( "F", 4 );;
PrintArray( C );

CartanMat( "I", 2, 5 );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionType( C );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
ReflectionName( ReflectionType( C ) );
ReflectionName( ReflectionType( CartanMat( "I", 2, 7 ) ) );

C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
t := ReflectionType( C );
PrintDiagram( t );
PrintDiagram( ReflectionType( CartanMat( "E", 8) ) );

W := CoxeterGroup( "A", 4 );;
PrintArray( W.cartan );
W.matgens;
W.roots;

W := CoxeterGroup( "D", 4 );;
p := EltWord( W, [ 1, 3, 2, 1, 3 ] );
CoxeterWord( W, p );

LongestCoxeterWord( W );
w0 := LongestCoxeterElement( W );
CoxeterLength( W, w0 );

List( Reflections( W ), i -> CoxeterWord( W, i ) );
l := List( [1 .. W.N+1], x -> CoxeterElements( W, x-1 ) );;
List( l, Length );

W := CoxeterGroup( "G", 2 );;
EltWord( W, [1,2,1] );

W := CoxeterGroup( "A", 3 );;
w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);;
w in W;
CHEVIE.BrieskornNormalForm := true;;
CoxeterWord( W, w );
CHEVIE.BrieskornNormalForm := false;;
CoxeterWord( W, w );

W := CoxeterGroup( "F", 4 );;
p := EltWord( W, [ 1, 2, 3, 4, 2 ] );
CoxeterLength( W, p );
CoxeterWord( W, p );

W := CoxeterGroup( "E", 6 );;
ReducedCoxeterWord( W, [ 1, 1, 1, 1, 1, 2, 2, 2, 3 ] );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
LeftDescentSet( W, w );

W := CoxeterGroup( "A", 2 );;
w := EltWord( W, [ 1, 2 ] );;
RightDescentSet( W, w );

W := CoxeterGroup( "B", 2 );; W.roots;
Reflections( W );

LongestCoxeterElement( CoxeterGroup( "A", 4 ) );

LongestCoxeterWord( CoxeterGroup( "A", 4 ) );

W := CoxeterGroup( "G", 2 );;  W.roots;
HighestShortRoot( W );
#W1 := CoxeterGroup( "A", 1, "B", 3 );;
#HighestShortRoot( W1 );

W := CoxeterGroup( "G", 2 );;
e := CoxeterElements( W, 6 );
e[1] = LongestCoxeterElement( W );

CoxeterWords( CoxeterGroup( "G", 2 ) );

CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) );

W := CoxeterGroup( "D", 4 );;
ChevieClassInfo( W );

W := CoxeterGroup( "H", 3 );;
w := EltWord( W, [ 1, 2, 1, 3 ] );;
b := Filtered( Elements( W ), i -> Bruhat( W, i, w,
                                CoxeterLength( W, i ), 4 ) );;
List( b, x -> CoxeterWord( W, x ) );

W := CoxeterGroup(
[ [ 2, 0,-1, 0, 0, 0, 1 ], [ 0, 2, 0,-1, 0, 0, 0 ],
  [-1, 0, 2,-1, 0, 0,-1 ], [ 0,-1,-1, 2,-1, 0, 0 ],
  [ 0, 0, 0,-1, 2,-1, 0 ], [ 0, 0, 0, 0,-1, 2, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] );;
w0 := LongestCoxeterElement( W );;
mx := MatXPerm( W, w0 );

my := MatYPerm( W, w0 );

PermMatX( W, mx ) = w0;

PermMatY( W, my ) = w0;


W := CoxeterGroup( "A", 2 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );

W := CoxeterGroup( "A", 2, "A", 3 );;
q := X( Rationals );; q.name := "q";;
HF := Hecke( CoxeterCoset( W, (1,2) ), q^2, q );
Display( CharTable( HF ) );


W := CoxeterGroup( "A", 2 );

H := Hecke( W, 0 );

T := Basis( H, "T" );
el := CoxeterWords( W );

mat := []; for i in [1..6] do mat[i]:=[]; for j in [1..6] do
Add( mat[i], T( el[i]) * T( el[j] ) ); od; od;
PrintArray(mat);

W := CoxeterGroup( "B", 3 );
u := X( Rationals );; u.name := "u";;

H := Hecke( W, u );
H := Hecke( W, u^2, u );
H := Hecke( W, [ u^6, u^4, u^4 ], [ u^3, -u^2, -u^2 ] );

H := Hecke( W, 9, 3 );
#H := Hecke( W, [ u^6, u^4, u^8] );

u := X( Rationals );; u.name := "u";;
H := Hecke( CoxeterGroup( "B", 2 ), u );
HeckeSubAlgebra( H, [ 1, 4 ] );
#HeckeSubAlgebra( H, [ 1, 7 ] );

T := Basis( H, "T" );

W := CoxeterGroup( "B", 3 );;
u := X( Rationals );; u.name := "u";;
H := Hecke( W, u );;
T := Basis( H, "T" );
T( 1, 2 ) = T( [ 1, 2 ] );
T( 1, 2 ) = T( EltWord( W, [ 1, 2 ] ) );
l := [ [], [ 1, 2, 3 ], [ 1 ], [ 2 ], [ 3 ] ];;
pl := List( l, i -> EltWord( W, i ) );;
h := T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
h.elm;
h.coeff;

CHEVIE.PrintHecke := "GAP";
T( pl, [ u^100, 1/u^20, 1, -5, 0 ] );
CHEVIE.PrintHecke := "";

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "A", 2 ), q );
T := Basis( H, "T" );
( T() + T( 1 ) ) * ( T() + T( 2 ) );
T( 1 ) * T( 1 );
T( 1, 1 );

( q * T( 1, 2 ) ) ^ -1;
#( T( 1 ) + T( 2 ) ) ^ -1;
( T( 1 ) + T( 2 ) ) ^ 2;

T( 1 ) + T();
T( 1 ) - T( 1 );

h := T( [ EltWord( Group( H ), [ 1 ] ),() ],[ 0, q^100 ] );
Normalize( h );
h;

AlphaInvolution( T( 1, 2 ) );

CreateHeckeBasis( "t", rec(
T := h->Basis( Hecke(h), "T" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^CoxeterLength(
             Group( Hecke(h) ), h.elm[i] ) *  h.coeff[i] ) ),
t := h->Basis( Hecke(h), "t" )( h.elm, List( [1 .. Length( h.elm )],
 i->Hecke(h).rootParameter[1]^-CoxeterLength(
              Group( Hecke(h) ), h.elm[i] ) * h.coeff[i] ) ),
BetaInvolution := h->Basis( Hecke( h ),"t")(
                    HeckeAlgebraOps.T.BetaInvolution(
                            Basis( Hecke( h ), "T" )( h ) ) ) ), AbsHeckeOps );
Inherit(HeckeAlgebraOps,AbsHeckeOps);
v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "A", 3 ), v ^ 2, v );;
h := Basis( H, "t" )( 3, 1, 2 );
h1 := Basis( H, "T")( h );
h2 := Basis( H, "t" )( h1 );
BetaInvolution( h2 );


v:= X( Rationals );;  v.name := "v";;
H := Hecke(CoxeterGroup( "B", 2) , v^2, v);
ref:= HeckeReflectionRepresentation( H );

H := Hecke( CoxeterGroup( "H", 3 ));;
HeckeReflectionRepresentation( H );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := HeckeReflectionRepresentation( H );;
CheckHeckeDefiningRelations( H, r );

W := CoxeterGroup( "G", 2 );;
u := X( Rationals );;  u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
u := u * v^0;;
H := Hecke( W, [ u^2, v^2 ], [ u, v ] );
Display( CharTable( H ) );

H1 := Hecke( W, [ E(6)^2, E(6)^4 ],[ E(6), E(6)^2 ] );
ct := CharTable( H1 );
Display( ct );
RankMat( ct.irreducibles );

q := X( Rationals );; q.name := "q";;
H := Hecke( CoxeterGroup( "B", 2 ), q ^ 2, q );;
HeckeCharValues( Basis( H, "C'" )( 1, 2, 1 ) );

u := X( Rationals );; u.name := "u";;
W := CoxeterGroup( "A", 3 );
H := Hecke( W, u );;
h := Basis( H, "T" )( LongestCoxeterElement( W ) );
cp := HeckeClassPolynomials( h );
CharTable( H ).irreducibles * cp;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "G", 2 );; H := Hecke( W, q );
PoincarePolynomial( H );

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
schur := SchurElements( Hecke( CoxeterGroup( "G", 2 ),
                                   [ u ^ 2, v ^ 2 ], [ u, v ] ) );

schur[1];

u := X( Rationals );; u.name := "u";;
v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
H := Hecke( CoxeterGroup( "G", 2 ), [ u ^ 2, v ^ 2 ], [ u, v ] );
SchurElement( H, [ [ 1, 3, "'" ] ] );

v := X( Cyclotomics );; v.name := "v";;
H := Hecke( CoxeterGroup( "H", 3 ), v ^ 2, v );;
HeckeCentralMonomials( H );

HeckeCharValuesGood( H, [ 1, 2, 3 ] );

klpol := function(W,x,y)return 
  KazhdanLusztigPolynomial(W,EltWord(W,x),EltWord(W,y),Length(x),Length(y));
end;

q := X( Rationals );; q.name := "q";;
W := CoxeterGroup( "B", 3 );;
el := CoxeterWords( W );
List( el, w -> klpol( W, [], w ) );

W.klpol;

W := CoxeterGroup( "F", 4 );
w := LongestCoxeterElement( W ) * W.generators[1];;
CoxeterLength( W, w );
y := EltWord( W, [ 1, 2, 3, 4 ] );;
cr := CriticalPair( W, y, w);;
CoxeterWord( W, cr[1] );
cr[3];
KazhdanLusztigPolynomial( W, y, w, 4, 23 );
KazhdanLusztigPolynomial( W, cr[1], cr[2], 16, 23 );

W := CoxeterGroup( "B", 4 );;
y := [ 1, 2, 3, 4, 3, 2, 1 ];;
py := EltWord( W, y );
x := [ 1 ];;
px := EltWord( W, x );
Bruhat( W, px, py );
List([0..3],i->KazhdanLusztigCoefficient( W, px, py, 1, 7, i ) );

W := CoxeterGroup( "G", 2 );;
LeftCells(W);

v := X( Cyclotomics ) ;; v.name := "v";;
W := Hecke(CoxeterGroup( "H", 3), v^2, v );
c := LeftCells( Group( W ) );;
List( c, i -> Length( i[ 1 ] ) );
LeftCellRepresentation(W,c[3]);

W := CoxeterGroup( "B", 3 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
C := Basis( H, "C" );
T( C( 1 ) );
C( T( 1 ) );

ref := HeckeReflectionRepresentation( H );;
c := CharRepresentationWords( ref, CoxeterConjugacyClasses( W ) );
List( ChevieClassInfo( W ).classtext, i ->
                            HeckeCharValues( C( i ), c ) );

v := X( Rationals );; v.name := "v";;
H := Hecke( CoxeterGroup( "B", 2 ), v ^ 2, v );;
h := Basis( H, "C'" )( 1 );
h2 := h * h;
Basis( H, "T" )( h2 );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
D := Basis( H, "D" );
D( T( 1 ) );
BetaInvolution( D( 1 ) );

W := CoxeterGroup( "B", 2 );;
v := X( Rationals );; v.name := "v";;
H := Hecke( W, v^2, v );
T := Basis( H, "T" );
Dp := Basis( H, "D'" );
AltInvolution( Dp( 1 ) );
Dp( 1 )^3;


W := CoxeterGroup( "G", 2 );
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );
PrintDiagram( H );

H.rootInclusion;

CoxeterLength( W, H.generators[2] );
CoxeterLength( H, H.generators[2] );

el := CoxeterWords( H );

el1 := List( el, x -> H.rootRestriction{ x } );

el2 := List( el, x -> EltWord( H, x ) );

List( el2, x -> CoxeterWord( W, x ) );

W := CoxeterGroup( "G", 2 );;
W.roots[4];
H := ReflectionSubgroup( W, [ 2, 4 ] );;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 11, 20 ] );
ReflectionName( H );
H.rootRestriction;
ReflectionSubgroup( H, [ 1, 2, 6 ] );

W := CoxeterGroup( "F", 4 );
H := ReflectionSubgroup( W, [ 10, 11, 12 ] );
PrintDiagram( H );
LongestCoxeterWord( H );

W := CoxeterGroup("F", 4 );;
H := ReflectionSubgroup( W, [ 1, 2, 9, 16 ] );;
PrintDiagram( H );
w := EltWord( W, [ 3, 2, 3, 4, 3, 2 ] );;
f := ReducedInCoset( H, w );;
CoxeterWord( W, f );
H.rootInclusion{[ 1 ..4 ]};

OnTuples( H.rootInclusion{[ 1 .. 4 ]}, f );

W := CoxeterGroup( "B", 3 );;
H := ReflectionSubgroup(W, [ 2, 3 ]);;
List( ReducedRightCosetRepresentatives( W, H ),
                               x-> CoxeterWord( W, x ) );

W := CoxeterGroup( "F", 4 );;
PermCosetsSubgroup( W, ReflectionSubgroup( W, [ 1, 2, 3 ] ) );

W := CoxeterGroup( "D", 4);;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( jInductionTable( H, W ) );

W := CoxeterGroup( "D", 4 );;
H := ReflectionSubgroup( W, [ 1, 3 ] );;
Display( JInductionTable( H, W ) );


W := Group( [ (1,2), (2,3), (3,4) ], () );
H:=Subgroup( W, [ (1,2), (3,4) ] );
W.name := "W";; H.name := "H";;
Display( InductionTable( H, W ) );

W := CoxeterGroup( "G", 2 );;
H := ReflectionSubgroup( W, [ 1, 4 ] );
ReflectionName( H );
Display(InductionTable( H, W ) );

H := Hecke(CoxeterGroup( "F", 4 ));;
r := ChevieClassInfo( Group( H ) ).classtext;;
t := HeckeReflectionRepresentation( H );;
CharRepresentationWords( t, r );

G := Group( (1,2)(3,4), (1,2,3,4,5) );;
ConjugacyClasses( G );
 g := Random( G );
PositionClass( G, g );

G := Group( (1,7)(2,3)(5,6)(8,9)(11,12),
               (1,5)(2,8)(3,4)(7,11)(9,10) );;
PointsAndRepresentativesOrbits( G );

C1 := [ [   2,  -1,   0,   0 ],
           [  -1,   2,  -1,   0 ],
           [   0,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
C2 := [ [   2,   0,  -1,   0 ],
           [   0,   2,  -1,   0 ],
           [  -1,  -1,   2,  -1 ],
           [   0,   0,  -1,   2 ] ];;
d := DirectSumMat( C1, C2 );;
PrintArray( d );

m := [ [  0,  0,  0,  1 ],
          [  0,  0,  1,  0 ],
          [  0,  1,  0,  0 ],
          [  1,  0,  0,  0 ] ];;
DecomposedMat( m );
PrintArray( m{[ 1, 4 ]}{[ 1, 4 ]});

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsDiagonalMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
IsLowerTriangularMat( a );
a[1][2] := 0;;
IsLowerTriangularMat( a );

a := [ [ 1, 2 ], [ 3, 1 ] ];;
l := [ [ 1, 0 ], [ 0, 1 ], [ 1, 1 ], [ 0, 0 ] ];;
l * a;
IsNormalizing( l, a );

l := [ 1, , 2, , , 3 ];;
SublistUnbnd( l, [ 1..4 ] );

a := [ 1, 2, 3, 4 ];;
b := [ 2, 3, 1, 4 ];;
p := PermListList( a, b );
Permuted( b, p );
PermListList( a, [ 3, 2, 1, 5 ] );

IntListToString( [ 4, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ] );
IntListToString( [ 14, 2, 2, 1, 1 ], "{}" );

d := PartitionTuples( 3, 2 );
for i in d do
     Print( PartitionTupleToString( i ),"   ");
od; Print("n");


Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host 3(NXDOMAIN) (202.84.100.17)
Time: Fri Jun 25 05:24:15 2004

Input: 1+1;

Output: Magma V2.10-22    Fri Jun 25 2004 05:24:12 on modular  [Seed = 599297111]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.84.100.17)
Time: Fri Jun 25 05:24:58 2004

Input: IsPrime(31567);

Output: Magma V2.10-22    Fri Jun 25 2004 05:24:56 on modular  [Seed = 833265169]
   -------------------------------------

true

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.84.100.17)
Time: Fri Jun 25 05:26:17 2004

Input: D:=HadamardDatabase();
NumberOfMatrices(D,32);

Output: Magma V2.10-22    Fri Jun 25 2004 05:26:15 on modular  [Seed = 3394331957]
   -------------------------------------


>> D:=HadamardDatabase();
                      ^
Runtime error in 'HadamardDatabase': The file GetLibraryRoot()/data/hadamard.dat
either does not exist or cannot be read.  If you do not have the file it can be 
acquired from magma@maths.usyd.edu.au; otherwise the library root must be set to
the right location.  This can be done by setting the environment variable 
MAGMA_LIBRARY_ROOT before invoking Magma, or by using the intrinsic 
SetLibraryRoot() during a session.

>> NumberOfMatrices(D,32);;
                    ^
User error: Identifier 'D' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.84.100.17)
Time: Fri Jun 25 05:28:10 2004

Input: R:=Matrix(1,1,-1,1);
IsHadamard(R);

Output: Magma V2.10-22    Fri Jun 25 2004 05:28:07 on modular  [Seed = 3294590123]
   -------------------------------------


>> R:=Matrix(1,1,-1,1);
            ^
Runtime error in 'Matrix': Bad argument types
Argument types given: RngIntElt, RngIntElt, RngIntElt, RngIntElt

>> IsHadamard(R);;
              ^
User error: Identifier 'R' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.84.100.17)
Time: Fri Jun 25 05:29:30 2004

Input: R:=MatrixRing(2);
H:=R![1,1,-1,1];
IsHadamard(H);

Output: Magma V2.10-22    Fri Jun 25 2004 05:29:28 on modular  [Seed = 3712380397]
   -------------------------------------


>> R:=MatrixRing(2);
                ^
Runtime error in 'MatrixRing': Bad argument types
Argument types given: RngIntElt

>> H:=R![1,1,-1,1];
      ^
User error: Identifier 'R' has not been declared or assigned

>> IsHadamard(H);;
              ^
User error: Identifier 'H' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host bom84.neoplus.adsl.tpnet.pl. (83.29.28.84)
Time: Fri Jun 25 05:42:27 2004

Input: factor(9501438237425119273)

Output: Magma V2.10-22    Fri Jun 25 2004 05:42:25 on modular  [Seed = 3173387892]
   -------------------------------------


>> factor(9501438237425119273);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host bom84.neoplus.adsl.tpnet.pl. (83.29.28.84)
Time: Fri Jun 25 05:47:11 2004

Input: factorial(12345)

Output: Magma V2.10-22    Fri Jun 25 2004 05:47:09 on modular  [Seed = 1894499492]
   -------------------------------------


>> factorial(12345);
   ^
User error: Identifier 'factorial' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:06:34 2004

Input: 
k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [31..32] do
for k in [17..23] do
for m in [14..17] do
for n in [8..13] do
        C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^11) + X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;


Output: Magma V2.10-22    Fri Jun 25 2004 09:06:23 on modular  [Seed = 2617311134]
   -------------------------------------

X^9 + X^4 + 1
13
16
22
31
9
16
23
31
12
16
21
32
12
16
23
32

Total time: 9.009 seconds, Total memory usage: 2.22MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:07:36 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [31..32] do
for k in [18..23] do
for m in [14..17] do
for n in [8..13] do
        C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^11) + X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;


Output: Magma V2.10-22    Fri Jun 25 2004 09:07:27 on modular  [Seed = 2534143061]
   -------------------------------------

X^9 + X^4 + 1
13
16
22
31
9
16
23
31
12
16
21
32
12
16
23
32

Total time: 8.269 seconds, Total memory usage: 2.22MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:09:32 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [31..32] do
for k in [18..23] do
for m in [14..17] do
for n in [8..13] do
        C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^11) + X^1279;
        if IsPrimitive(C) then 
           C;
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;


Output: Magma V2.10-22    Fri Jun 25 2004 09:09:24 on modular  [Seed = 2872561634]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1146 + X^1133 + X^1130 + X^1124 + X^1120 + X^1117 + X^1115 + X^1111 +
    X^1108 + X^1107 + X^1104 + X^1102 + X^1099 + X^1098 + X^1095 + X^1093 + 
    X^1091 + X^1089 + X^1086 + X^1085 + X^1084 + X^1082 + X^1080 + X^1077 + 
    X^1076 + X^1073 + X^1071 + X^1069 + X^1068 + X^1067 + X^1064 + X^1062 + 
    X^1060 + X^1055 + X^1054 + X^1053 + X^1051 + X^1049 + X^1046 + X^1040 + 
    X^1038 + X^1037 + X^1033 + X^1032 + X^1031 + X^1024 + X^1019 + X^1018 + 
    X^1016 + X^1015 + X^1010 + X^1003 + X^1002 + X^1001 + X^997 + X^996 + X^994 
    + X^988 + X^985 + X^983 + X^981 + X^980 + X^979 + X^974 + X^972 + X^967 + 
    X^966 + X^965 + X^963 + X^961 + X^958 + X^952 + X^950 + X^949 + X^945 + 
    X^944 + X^943 + X^938 + X^936 + X^931 + X^930 + X^928 + X^927 + X^925 + 
    X^916 + X^915 + X^914 + X^913 + X^912 + X^908 + X^907 + X^906 + X^903 + 
    X^899 + X^898 + X^897 + X^896 + X^895 + X^894 + X^893 + X^892 + X^887 + 
    X^886 + X^884 + X^883 + X^882 + X^881 + X^879 + X^877 + X^875 + X^873 + 
    X^870 + X^867 + X^865 + X^862 + X^861 + X^859 + X^857 + X^856 + X^850 + 
    X^840 + X^836 + X^835 + X^833 + X^829 + X^827 + X^825 + X^821 + X^820 + 
    X^819 + X^818 + X^817 + X^815 + X^814 + X^813 + X^812 + X^810 + X^809 + 
    X^807 + X^802 + X^801 + X^799 + X^798 + X^797 + X^796 + X^792 + X^791 + 
    X^790 + X^789 + X^788 + X^787 + X^786 + X^783 + X^780 + X^778 + X^776 + 
    X^774 + X^770 + X^769 + X^766 + X^765 + X^764 + X^759 + X^758 + X^757 + 
    X^756 + X^754 + X^751 + X^749 + X^748 + X^745 + X^744 + X^743 + X^742 + 
    X^741 + X^736 + X^734 + X^733 + X^731 + X^729 + X^727 + X^726 + X^722 + 
    X^720 + X^717 + X^716 + X^715 + X^714 + X^713 + X^712 + X^711 + X^709 + 
    X^706 + X^704 + X^700 + X^698 + X^697 + X^695 + X^694 + X^693 + X^692 + 
    X^690 + X^685 + X^684 + X^679 + X^678 + X^677 + X^676 + X^675 + X^674 + 
    X^672 + X^670 + X^668 + X^666 + X^664 + X^662 + X^657 + X^655 + X^654 + 
    X^653 + X^652 + X^650 + X^647 + X^646 + X^645 + X^644 + X^643 + X^641 + 
    X^633 + X^632 + X^631 + X^630 + X^626 + X^624 + X^623 + X^622 + X^621 + 
    X^620 + X^617 + X^616 + X^615 + X^613 + X^612 + X^610 + X^608 + X^607 + 
    X^599 + X^598 + X^593 + X^591 + X^590 + X^588 + X^587 + X^586 + X^581 + 
    X^580 + X^578 + X^577 + X^576 + X^575 + X^571 + X^570 + X^569 + X^568 + 
    X^566 + X^565 + X^560 + X^559 + X^558 + X^556 + X^555 + X^553 + X^548 + 
    X^547 + X^539 + X^538 + X^536 + X^534 + X^533 + X^531 + X^530 + X^529 + 
    X^526 + X^525 + X^524 + X^523 + X^522 + X^520 + X^516 + X^515 + X^514 + 
    X^513 + X^505 + X^503 + X^502 + X^501 + X^500 + X^499 + X^496 + X^494 + 
    X^493 + X^492 + X^491 + X^489 + X^484 + X^482 + X^480 + X^478 + X^476 + 
    X^474 + X^472 + X^471 + X^470 + X^469 + X^468 + X^467 + X^462 + X^461 + 
    X^456 + X^454 + X^453 + X^452 + X^451 + X^449 + X^448 + X^446 + X^442 + 
    X^440 + X^437 + X^435 + X^434 + X^433 + X^432 + X^431 + X^430 + X^429 + 
    X^426 + X^424 + X^420 + X^419 + X^417 + X^415 + X^413 + X^412 + X^410 + 
    X^405 + X^404 + X^403 + X^402 + X^401 + X^398 + X^397 + X^395 + X^392 + 
    X^390 + X^389 + X^388 + X^387 + X^382 + X^381 + X^380 + X^377 + X^376 + 
    X^372 + X^370 + X^368 + X^366 + X^363 + X^360 + X^359 + X^358 + X^357 + 
    X^356 + X^355 + X^354 + X^350 + X^349 + X^348 + X^347 + X^345 + X^344 + 
    X^339 + X^337 + X^336 + X^334 + X^333 + X^332 + X^331 + X^329 + X^328 + 
    X^327 + X^326 + X^325 + X^321 + X^319 + X^317 + X^313 + X^311 + X^310 + 
    X^306 + X^296 + X^290 + X^289 + X^287 + X^285 + X^284 + X^281 + X^279 + 
    X^276 + X^273 + X^271 + X^269 + X^267 + X^265 + X^264 + X^263 + X^262 + 
    X^260 + X^259 + X^254 + X^253 + X^252 + X^251 + X^250 + X^249 + X^248 + 
    X^247 + X^243 + X^240 + X^239 + X^238 + X^234 + X^233 + X^232 + X^231 + 
    X^230 + X^221 + X^219 + X^218 + X^216 + X^215 + X^210 + X^208 + X^203 + 
    X^202 + X^201 + X^197 + X^196 + X^194 + X^188 + X^185 + X^183 + X^181 + 
    X^180 + X^179 + X^174 + X^172 + X^167 + X^166 + X^165 + X^163 + X^161 + 
    X^158 + X^152 + X^150 + X^149 + X^145 + X^144 + X^143 + X^136 + X^131 + 
    X^130 + X^128 + X^127 + X^122 + X^115 + X^114 + X^113 + X^109 + X^108 + 
    X^106 + X^100 + X^97 + X^95 + X^93 + X^92 + X^91 + X^86 + X^84 + X^82 + X^79
    + X^78 + X^77 + X^75 + X^73 + X^70 + X^69 + X^66 + X^64 + X^62 + X^61 + X^60
    + X^57 + X^55 + X^53 + X^51 + X^48 + X^47 + X^44 + X^42 + X^39 + X^38 + X^35
    + X^31 + X^29 + X^26 + X^22 + X^16 + X^13 + 1
13
16
22
31
X^1279 + X^1083 + X^1074 + X^1067 + X^1065 + X^1060 + X^1058 + X^1056 + X^1052 +
    X^1051 + X^1049 + X^1044 + X^1043 + X^1042 + X^1040 + X^1036 + X^1035 + 
    X^1034 + X^1033 + X^1029 + X^1027 + X^1026 + X^1025 + X^1021 + X^1020 + 
    X^1018 + X^1017 + X^1013 + X^1012 + X^1011 + X^1009 + X^1005 + X^1004 + 
    X^1003 + X^1002 + X^998 + X^996 + X^995 + X^994 + X^991 + X^990 + X^989 + 
    X^987 + X^986 + X^981 + X^980 + X^978 + X^975 + X^974 + X^972 + X^971 + 
    X^968 + X^967 + X^966 + X^965 + X^963 + X^960 + X^959 + X^958 + X^957 + 
    X^956 + X^955 + X^952 + X^950 + X^949 + X^948 + X^947 + X^944 + X^943 + 
    X^941 + X^940 + X^939 + X^937 + X^935 + X^934 + X^930 + X^929 + X^928 + 
    X^926 + X^925 + X^924 + X^923 + X^920 + X^919 + X^917 + X^916 + X^914 + 
    X^913 + X^911 + X^910 + X^908 + X^907 + X^906 + X^905 + X^904 + X^903 + 
    X^902 + X^900 + X^897 + X^896 + X^895 + X^894 + X^892 + X^891 + X^890 + 
    X^888 + X^886 + X^885 + X^881 + X^880 + X^879 + X^877 + X^875 + X^871 + 
    X^869 + X^866 + X^864 + X^863 + X^861 + X^859 + X^857 + X^856 + X^855 + 
    X^854 + X^850 + X^849 + X^848 + X^847 + X^846 + X^835 + X^833 + X^832 + 
    X^831 + X^830 + X^829 + X^827 + X^826 + X^825 + X^824 + X^823 + X^822 + 
    X^820 + X^819 + X^817 + X^816 + X^815 + X^813 + X^812 + X^811 + X^809 + 
    X^807 + X^804 + X^803 + X^801 + X^799 + X^792 + X^788 + X^787 + X^784 + 
    X^783 + X^781 + X^779 + X^777 + X^774 + X^769 + X^767 + X^765 + X^764 + 
    X^758 + X^757 + X^756 + X^755 + X^753 + X^750 + X^749 + X^743 + X^739 + 
    X^738 + X^737 + X^735 + X^734 + X^733 + X^730 + X^728 + X^727 + X^725 + 
    X^724 + X^722 + X^721 + X^720 + X^718 + X^717 + X^712 + X^710 + X^707 + 
    X^706 + X^703 + X^702 + X^701 + X^699 + X^697 + X^696 + X^694 + X^693 + 
    X^692 + X^691 + X^690 + X^689 + X^688 + X^687 + X^686 + X^681 + X^675 + 
    X^668 + X^666 + X^665 + X^663 + X^658 + X^657 + X^656 + X^653 + X^652 + 
    X^651 + X^648 + X^647 + X^646 + X^644 + X^642 + X^641 + X^640 + X^638 + 
    X^636 + X^634 + X^633 + X^632 + X^629 + X^628 + X^625 + X^622 + X^621 + 
    X^620 + X^618 + X^615 + X^613 + X^612 + X^611 + X^610 + X^607 + X^605 + 
    X^603 + X^602 + X^601 + X^600 + X^598 + X^597 + X^596 + X^594 + X^590 + 
    X^589 + X^581 + X^579 + X^578 + X^576 + X^575 + X^574 + X^573 + X^572 + 
    X^570 + X^567 + X^565 + X^564 + X^563 + X^562 + X^560 + X^558 + X^557 + 
    X^553 + X^551 + X^545 + X^538 + X^532 + X^530 + X^526 + X^525 + X^523 + 
    X^521 + X^520 + X^519 + X^518 + X^516 + X^513 + X^511 + X^510 + X^509 + 
    X^508 + X^507 + X^505 + X^504 + X^502 + X^494 + X^493 + X^489 + X^487 + 
    X^486 + X^485 + X^483 + X^482 + X^481 + X^480 + X^478 + X^476 + X^473 + 
    X^472 + X^471 + X^470 + X^468 + X^465 + X^463 + X^462 + X^461 + X^458 + 
    X^455 + X^454 + X^451 + X^450 + X^449 + X^447 + X^445 + X^443 + X^442 + 
    X^441 + X^439 + X^437 + X^436 + X^435 + X^432 + X^431 + X^430 + X^427 + 
    X^426 + X^425 + X^420 + X^418 + X^417 + X^415 + X^408 + X^402 + X^397 + 
    X^396 + X^395 + X^394 + X^393 + X^392 + X^391 + X^390 + X^389 + X^387 + 
    X^386 + X^384 + X^382 + X^381 + X^380 + X^377 + X^376 + X^373 + X^371 + 
    X^366 + X^365 + X^363 + X^362 + X^361 + X^359 + X^358 + X^356 + X^355 + 
    X^353 + X^350 + X^349 + X^348 + X^346 + X^345 + X^344 + X^340 + X^334 + 
    X^333 + X^330 + X^328 + X^327 + X^326 + X^325 + X^319 + X^318 + X^316 + 
    X^314 + X^309 + X^306 + X^304 + X^302 + X^300 + X^299 + X^296 + X^295 + 
    X^291 + X^284 + X^282 + X^280 + X^279 + X^276 + X^274 + X^272 + X^271 + 
    X^270 + X^268 + X^267 + X^266 + X^264 + X^263 + X^261 + X^260 + X^259 + 
    X^258 + X^257 + X^256 + X^254 + X^253 + X^252 + X^251 + X^250 + X^248 + 
    X^237 + X^236 + X^235 + X^234 + X^233 + X^229 + X^228 + X^227 + X^226 + 
    X^224 + X^222 + X^220 + X^219 + X^217 + X^214 + X^212 + X^208 + X^206 + 
    X^204 + X^203 + X^202 + X^198 + X^197 + X^195 + X^193 + X^192 + X^191 + 
    X^189 + X^188 + X^187 + X^186 + X^183 + X^181 + X^180 + X^179 + X^178 + 
    X^177 + X^176 + X^175 + X^173 + X^172 + X^170 + X^169 + X^167 + X^166 + 
    X^164 + X^163 + X^160 + X^159 + X^158 + X^157 + X^155 + X^154 + X^153 + 
    X^149 + X^148 + X^146 + X^144 + X^143 + X^142 + X^140 + X^139 + X^136 + 
    X^135 + X^134 + X^133 + X^131 + X^128 + X^127 + X^126 + X^125 + X^124 + 
    X^123 + X^120 + X^118 + X^117 + X^116 + X^115 + X^112 + X^111 + X^109 + 
    X^108 + X^105 + X^103 + X^102 + X^97 + X^96 + X^94 + X^93 + X^92 + X^89 + 
    X^88 + X^87 + X^85 + X^81 + X^80 + X^79 + X^78 + X^74 + X^72 + X^71 + X^70 +
    X^66 + X^65 + X^63 + X^62 + X^58 + X^57 + X^56 + X^54 + X^50 + X^49 + X^48 +
    X^47 + X^43 + X^41 + X^40 + X^39 + X^34 + X^32 + X^31 + X^27 + X^25 + X^23 +
    X^18 + X^16 + X^9 + 1
9
16
23
31
X^1279 + X^1125 + X^1113 + X^1109 + X^1104 + X^1101 + X^1097 + X^1093 + X^1092 +
    X^1089 + X^1088 + X^1085 + X^1081 + X^1080 + X^1077 + X^1076 + X^1073 + 
    X^1072 + X^1069 + X^1068 + X^1065 + X^1064 + X^1061 + X^1060 + X^1057 + 
    X^1056 + X^1053 + X^1052 + X^1049 + X^1048 + X^1045 + X^1044 + X^1040 + 
    X^1037 + X^1036 + X^1033 + X^1032 + X^1028 + X^1024 + X^1021 + X^1016 + 
    X^1012 + X^1000 + X^997 + X^985 + X^981 + X^976 + X^973 + X^969 + X^965 + 
    X^964 + X^961 + X^960 + X^953 + X^952 + X^949 + X^948 + X^944 + X^940 + 
    X^937 + X^933 + X^932 + X^928 + X^921 + X^917 + X^916 + X^913 + X^912 + 
    X^909 + X^905 + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:15:01 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^21)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
  C;
end if;

C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
  C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 09:14:57 on modular  [Seed = 3139952295]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1125 + X^1113 + X^1109 + X^1104 + X^1101 + X^1097 + X^1093 + X^1092 +
    X^1089 + X^1088 + X^1085 + X^1081 + X^1080 + X^1077 + X^1076 + X^1073 + 
    X^1072 + X^1069 + X^1068 + X^1065 + X^1064 + X^1061 + X^1060 + X^1057 + 
    X^1056 + X^1053 + X^1052 + X^1049 + X^1048 + X^1045 + X^1044 + X^1040 + 
    X^1037 + X^1036 + X^1033 + X^1032 + X^1028 + X^1024 + X^1021 + X^1016 + 
    X^1012 + X^1000 + X^997 + X^985 + X^981 + X^976 + X^973 + X^969 + X^965 + 
    X^964 + X^961 + X^960 + X^953 + X^952 + X^949 + X^948 + X^944 + X^940 + 
    X^937 + X^933 + X^932 + X^928 + X^921 + X^917 + X^916 + X^913 + X^912 + 
    X^909 + X^905 + X^900 + X^896 + X^893 + X^892 + X^888 + X^884 + X^873 + 
    X^872 + X^861 + X^857 + X^852 + X^845 + X^841 + X^840 + X^836 + X^824 + 
    X^820 + X^817 + X^813 + X^801 + X^797 + X^796 + X^792 + X^785 + X^780 + 
    X^776 + X^765 + X^764 + X^753 + X^749 + X^745 + X^744 + X^741 + X^737 + 
    X^732 + X^728 + X^725 + X^724 + X^721 + X^720 + X^716 + X^709 + X^705 + 
    X^704 + X^700 + X^697 + X^693 + X^689 + X^688 + X^685 + X^684 + X^677 + 
    X^676 + X^673 + X^672 + X^668 + X^664 + X^661 + X^656 + X^652 + X^640 + 
    X^637 + X^625 + X^621 + X^616 + X^609 + X^605 + X^604 + X^600 + X^593 + 
    X^588 + X^584 + X^572 + X^553 + X^541 + X^537 + X^532 + X^525 + X^521 + 
    X^520 + X^516 + X^509 + X^504 + X^500 + X^488 + X^485 + X^473 + X^469 + 
    X^464 + X^461 + X^457 + X^453 + X^452 + X^449 + X^448 + X^441 + X^440 + 
    X^437 + X^436 + X^432 + X^428 + X^425 + X^421 + X^420 + X^416 + X^409 + 
    X^405 + X^404 + X^401 + X^400 + X^397 + X^393 + X^388 + X^384 + X^381 + 
    X^380 + X^376 + X^372 + X^361 + X^360 + X^349 + X^345 + X^340 + X^333 + 
    X^329 + X^328 + X^324 + X^312 + X^308 + X^305 + X^301 + X^289 + X^285 + 
    X^284 + X^280 + X^273 + X^268 + X^264 + X^253 + X^252 + X^241 + X^237 + 
    X^233 + X^232 + X^229 + X^225 + X^220 + X^216 + X^213 + X^212 + X^209 + 
    X^208 + X^204 + X^197 + X^193 + X^192 + X^188 + X^185 + X^181 + X^177 + 
    X^176 + X^173 + X^172 + X^165 + X^164 + X^161 + X^160 + X^156 + X^152 + 
    X^149 + X^144 + X^140 + X^128 + X^125 + X^113 + X^109 + X^104 + X^101 + X^97
    + X^93 + X^92 + X^89 + X^88 + X^85 + X^81 + X^80 + X^77 + X^76 + X^73 + X^72
    + X^69 + X^68 + X^65 + X^64 + X^61 + X^60 + X^57 + X^56 + X^53 + X^52 + X^49
    + X^48 + X^45 + X^44 + X^40 + X^37 + X^36 + X^33 + X^32 + X^28 + X^24 + X^21
    + X^16 + X^12 + 1
X^1279 + X^1151 + X^1139 + X^1135 + X^1128 + X^1127 + X^1123 + X^1119 + X^1116 +
    X^1115 + X^1112 + X^1111 + X^1107 + X^1104 + X^1103 + X^1100 + X^1099 + 
    X^1096 + X^1095 + X^1092 + X^1091 + X^1088 + X^1087 + X^1084 + X^1083 + 
    X^1080 + X^1079 + X^1076 + X^1075 + X^1072 + X^1071 + X^1068 + X^1067 + 
    X^1064 + X^1063 + X^1060 + X^1056 + X^1055 + X^1052 + X^1051 + X^1048 + 
    X^1044 + X^1040 + X^1039 + X^1032 + X^1028 + X^1023 + X^1016 + X^1011 + 
    X^1007 + X^1000 + X^999 + X^995 + X^991 + X^988 + X^987 + X^984 + X^983 + 
    X^979 + X^976 + X^975 + X^972 + X^971 + X^968 + X^964 + X^963 + X^960 + 
    X^956 + X^952 + X^948 + X^943 + X^940 + X^935 + X^927 + X^923 + X^920 + 
    X^912 + X^911 + X^904 + X^900 + X^888 + X^875 + X^867 + X^863 + X^859 + 
    X^855 + X^852 + X^847 + X^844 + X^840 + X^839 + X^836 + X^832 + X^831 + 
    X^827 + X^824 + X^823 + X^819 + X^816 + X^811 + X^808 + X^804 + X^800 + 
    X^796 + X^788 + X^775 + X^763 + X^759 + X^752 + X^751 + X^743 + X^740 + 
    X^736 + X^728 + X^723 + X^720 + X^715 + X^711 + X^707 + X^703 + X^700 + 
    X^699 + X^695 + X^692 + X^691 + X^688 + X^687 + X^684 + X^680 + X^679 + 
    X^676 + X^675 + X^672 + X^668 + X^664 + X^663 + X^656 + X^652 + X^647 + 
    X^640 + X^639 + X^635 + X^631 + X^627 + X^624 + X^619 + X^616 + X^612 + 
    X^608 + X^604 + X^596 + X^555 + X^547 + X^543 + X^539 + X^535 + X^532 + 
    X^527 + X^524 + X^520 + X^516 + X^512 + X^511 + X^504 + X^499 + X^495 + 
    X^488 + X^487 + X^483 + X^479 + X^476 + X^475 + X^472 + X^471 + X^467 + 
    X^464 + X^463 + X^460 + X^459 + X^456 + X^452 + X^451 + X^448 + X^444 + 
    X^440 + X^436 + X^431 + X^428 + X^423 + X^415 + X^411 + X^408 + X^400 + 
    X^399 + X^392 + X^388 + X^376 + X^363 + X^355 + X^351 + X^347 + X^343 + 
    X^340 + X^335 + X^332 + X^328 + X^327 + X^324 + X^320 + X^319 + X^315 + 
    X^312 + X^311 + X^307 + X^304 + X^299 + X^296 + X^292 + X^288 + X^284 + 
    X^276 + X^263 + X^251 + X^247 + X^240 + X^239 + X^231 + X^228 + X^224 + 
    X^216 + X^211 + X^208 + X^203 + X^199 + X^195 + X^191 + X^188 + X^187 + 
    X^183 + X^180 + X^179 + X^176 + X^175 + X^172 + X^168 + X^167 + X^164 + 
    X^163 + X^160 + X^156 + X^152 + X^151 + X^144 + X^140 + X^135 + X^128 + 
    X^123 + X^119 + X^112 + X^111 + X^107 + X^103 + X^100 + X^99 + X^96 + X^95 +
    X^91 + X^88 + X^87 + X^84 + X^83 + X^80 + X^79 + X^76 + X^75 + X^72 + X^71 +
    X^68 + X^67 + X^64 + X^63 + X^60 + X^59 + X^56 + X^55 + X^52 + X^51 + X^48 +
    X^47 + X^44 + X^40 + X^39 + X^36 + X^35 + X^32 + X^28 + X^24 + X^23 + X^16 +
    X^12 + 1

Total time: 3.939 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:18:06 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for t in [32..41] do
for j in [30..31] do
for k in [22..29] do
for m in [15..21] do
for n in [9..14] do
        C := ((1 + X^n)^8)*((1 + X^m)^16)*((1 + X^k)^16)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
           t;
        end if;
end for;
end for;
end for;
end for;
end for;


Output: Magma V2.10-22    Fri Jun 25 2004 09:17:43 on modular  [Seed = 1305553140]
   -------------------------------------

X^9 + X^4 + 1
9
17
24
30
32
10
17
25
30
33
14
15
25
31
33


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:21:17 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [30..31] do
for k in [22..29] do
for m in [15..21] do
for n in [9..14] do
        C := ((1 + X^n)^7)*((1 + X^m)^13)*((1 + X^k)^17)*((1 + X^j)^11)+ X^1279;
        if IsPrimitive(C) then 
           C;
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;


Output: Magma V2.10-22    Fri Jun 25 2004 09:21:03 on modular  [Seed = 1827670685]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1057 + X^1048 + X^1039 + X^1036 + X^1034 + X^1030 + X^1025 + X^1021 +
    X^1016 + X^1013 + X^1012 + X^1007 + X^1006 + X^1003 + X^998 + X^994 + X^989 
    + X^983 + X^980 + X^976 + X^973 + X^971 + X^955 + X^953 + X^952 + X^950 + 
    X^934 + X^932 + X^929 + X^922 + X^911 + X^904 + X^901 + X^899 + X^889 + 
    X^883 + X^881 + X^878 + X^871 + X^868 + X^866 + X^860 + X^850 + X^848 + 
    X^845 + X^838 + X^827 + X^820 + X^815 + X^808 + X^805 + X^797 + X^796 + 
    X^790 + X^787 + X^785 + X^784 + X^782 + X^781 + X^773 + X^772 + X^767 + 
    X^764 + X^763 + X^761 + X^758 + X^749 + X^740 + X^689 + X^685 + X^680 + 
    X^676 + X^671 + X^668 + X^667 + X^666 + X^664 + X^661 + X^658 + X^657 + 
    X^652 + X^648 + X^645 + X^643 + X^641 + X^640 + X^639 + X^630 + X^629 + 
    X^628 + X^626 + X^621 + X^620 + X^617 + X^615 + X^612 + X^610 + X^608 + 
    X^603 + X^598 + X^585 + X^584 + X^582 + X^580 + X^577 + X^575 + X^566 + 
    X^565 + X^564 + X^561 + X^559 + X^557 + X^547 + X^544 + X^543 + X^542 + 
    X^533 + X^531 + X^526 + X^524 + X^515 + X^514 + X^513 + X^510 + X^500 + 
    X^498 + X^496 + X^493 + X^492 + X^491 + X^482 + X^480 + X^477 + X^475 + 
    X^473 + X^472 + X^459 + X^454 + X^449 + X^447 + X^445 + X^442 + X^440 + 
    X^437 + X^436 + X^431 + X^429 + X^428 + X^427 + X^418 + X^417 + X^416 + 
    X^414 + X^412 + X^409 + X^405 + X^400 + X^399 + X^396 + X^393 + X^391 + 
    X^390 + X^389 + X^386 + X^381 + X^377 + X^372 + X^368 + X^317 + X^308 + 
    X^299 + X^296 + X^294 + X^293 + X^290 + X^285 + X^284 + X^276 + X^275 + 
    X^273 + X^272 + X^270 + X^267 + X^261 + X^260 + X^252 + X^249 + X^242 + 
    X^237 + X^230 + X^219 + X^212 + X^209 + X^207 + X^197 + X^191 + X^189 + 
    X^186 + X^179 + X^176 + X^174 + X^168 + X^158 + X^156 + X^153 + X^146 + 
    X^135 + X^128 + X^125 + X^123 + X^107 + X^105 + X^104 + X^102 + X^86 + X^84 
    + X^81 + X^77 + X^74 + X^68 + X^63 + X^59 + X^54 + X^51 + X^50 + X^45 + X^44
    + X^41 + X^36 + X^32 + X^27 + X^23 + X^21 + X^18 + X^9 + 1
9
21
23
30
X^1279 + X^1074 + X^1065 + X^1056 + X^1053 + X^1050 + X^1047 + X^1041 + X^1038 +
    X^1032 + X^1020 + X^1014 + X^1011 + X^1005 + X^999 + X^996 + X^993 + X^990 +
    X^987 + X^972 + X^966 + X^951 + X^948 + X^945 + X^939 + X^927 + X^921 + 
    X^918 + X^915 + X^906 + X^900 + X^897 + X^894 + X^888 + X^885 + X^882 + 
    X^876 + X^867 + X^864 + X^861 + X^855 + X^843 + X^837 + X^831 + X^825 + 
    X^822 + X^807 + X^804 + X^783 + X^777 + X^774 + X^765 + X^756 + X^702 + 
    X^693 + X^690 + X^684 + X^675 + X^672 + X^669 + X^666 + X^663 + X^657 + 
    X^651 + X^648 + X^633 + X^630 + X^612 + X^609 + X^606 + X^597 + X^594 + 
    X^591 + X^588 + X^576 + X^573 + X^570 + X^567 + X^558 + X^555 + X^552 + 
    X^540 + X^534 + X^522 + X^519 + X^516 + X^507 + X^504 + X^501 + X^498 + 
    X^486 + X^483 + X^480 + X^477 + X^468 + X^465 + X^462 + X^444 + X^441 + 
    X^426 + X^423 + X^417 + X^411 + X^408 + X^405 + X^402 + X^399 + X^390 + 
    X^384 + X^381 + X^372 + X^318 + X^309 + X^300 + X^297 + X^291 + X^270 + 
    X^267 + X^252 + X^249 + X^243 + X^237 + X^231 + X^219 + X^213 + X^210 + 
    X^207 + X^198 + X^192 + X^189 + X^186 + X^180 + X^177 + X^174 + X^168 + 
    X^159 + X^156 + X^153 + X^147 + X^135 + X^129 + X^126 + X^123 + X^108 + 
    X^102 + X^87 + X^84 + X^81 + X^78 + X^75 + X^69 + X^63 + X^60 + X^54 + X^42 
    + X^36 + X^33 + X^27 + X^24 + X^21 + X^18 + X^9 + 1
9
21
24
30
X^1279 + X^1103 + X^1091 + X^1084 + X^1079 + X^1077 + X^1073 + X^1072 + X^1067 +
    X^1065 + X^1061 + X^1060 + X^1058 + X^1055 + X^1054 + X^1053 + X^1049 + 
    X^1048 + X^1047 + X^1046 + X^1042 + X^1041 + X^1037 + X^1036 + X^1035 + 
    X^1034 + X^1030 + X^1029 + X^1028 + X^1027 + X^1025 + X^1023 + X^1022 + 
    X^1018 + X^1016 + X^1015 + X^1011 + X^1010 + X^1008 + X^1007 + X^1006 + 
    X^1004 + X^1003 + X^1001 + X^999 + X^997 + X^996 + X^995 + X^992 + X^991 + 
    X^989 + X^988 + X^985 + X^984 + X^983 + X^982 + X^981 + X^980 + X^979 + 
    X^978 + X^976 + X^973 + X^972 + X^970 + X^969 + X^966 + X^964 + X^962 + 
    X^961 + X^960 + X^957 + X^954 + X^950 + X^949 + X^947 + X^945 + X^942 + 
    X^941 + X^938 + X^935 + X^933 + X^931 + X^930 + X^929 + X^928 + X^926 + 
    X^925 + X^923 + X^922 + X^921 + X^919 + X^916 + X^914 + X^913 + X^912 + 
    X^910 + X^909 + X^907 + X^906 + X^905 + X^904 + X^902 + X^900 + X^897 + 
    X^894 + X^893 + X^890 + X^888 + X^886 + X^885 + X^881 + X^878 + X^874 + 
    X^873 + X^871 + X^869 + X^866 + X^865 + X^863 + X^862 + X^859 + X^857 + 
    X^855 + X^854 + X^853 + X^852 + X^851 + X^850 + X^849 + X^847 + X^846 + 
    X^845 + X^844 + X^843 + X^840 + X^839 + X^838 + X^836 + X^834 + X^832 + 
    X^831 + X^830 + X^829 + X^828 + X^827 + X^826 + X^825 + X^824 + X^820 + 
    X^817 + X^815 + X^813 + X^812 + X^810 + X^808 + X^807 + X^806 + X^805 + 
    X^801 + X^799 + X^798 + X^796 + X^794 + X^793 + X^788 + X^786 + X^785 + 
    X^782 + X^781 + X^780 + X^779 + X^777 + X^774 + X^766 + X^762 + X^761 + 
    X^760 + X^759 + X^758 + X^757 + X^753 + X^745 + X^742 + X^740 + X^739 + 
    X^738 + X^737 + X^734 + X^733 + X^731 + X^726 + X^725 + X^723 + X^721 + 
    X^720 + X^718 + X^714 + X^713 + X^712 + X^711 + X^709 + X^707 + X^706 + 
    X^704 + X^702 + X^699 + X^695 + X^694 + X^693 + X^692 + X^691 + X^690 + 
    X^689 + X^688 + X^685 + X^683 + X^681 + X^680 + X^679 + X^676 + X^674 + 
    X^673 + X^672 + X^670 + X^669 + X^667 + X^666 + X^665 + X^664 + X^663 + 
    X^662 + X^661 + X^660 + X^654 + X^653 + X^651 + X^650 + X^649 + X^648 + 
    X^646 + X^644 + X^642 + X^641 + X^639 + X^637 + X^634 + X^632 + X^630 + 
    X^629 + X^622 + X^621 + X^620 + X^618 + X^617 + X^615 + X^611 + X^610 + 
    X^605 + X^603 + X^602 + X^599 + X^598 + X^597 + X^596 + X^595 + X^593 + 
    X^592 + X^589 + X^587 + X^586 + X^585 + X^584 + X^583 + X^580 + X^579 + 
    X^578 + X^577 + X^576 + X^575 + X^574 + X^573 + X^570 + X^568 + X^567 + 
    X^566 + X^564 + X^563 + X^560 + X^559 + X^558 + X^556 + X^555 + X^554 + 
    X^549 + X^548 + X^547 + X^545 + X^544 + X^543 + X^540 + X^539 + X^537 + 
    X^536 + X^535 + X^533 + X^530 + X^529 + X^528 + X^527 + X^526 + X^525 + 
    X^524 + X^523 + X^520 + X^519 + X^518 + X^517 + X^516 + X^514 + X^511 + 
    X^510 + X^508 + X^507 + X^506 + X^505 + X^504 + X^501 + X^500 + X^498 + 
    X^493 + X^492 + X^488 + X^486 + X^485 + X^483 + X^482 + X^481 + X^474 + 
    X^473 + X^471 + X^469 + X^466 + X^464 + X^462 + X^461 + X^459 + X^457 + 
    X^455 + X^454 + X^453 + X^452 + X^450 + X^449 + X^443 + X^442 + X^441 + 
    X^440 + X^439 + X^438 + X^437 + X^436 + X^434 + X^433 + X^431 + X^430 + 
    X^429 + X^427 + X^424 + X^423 + X^422 + X^420 + X^418 + X^415 + X^414 + 
    X^413 + X^412 + X^411 + X^410 + X^409 + X^408 + X^404 + X^401 + X^399 + 
    X^397 + X^396 + X^394 + X^392 + X^391 + X^390 + X^389 + X^385 + X^383 + 
    X^382 + X^380 + X^378 + X^377 + X^372 + X^370 + X^369 + X^366 + X^365 + 
    X^364 + X^363 + X^361 + X^358 + X^350 + X^346 + X^345 + X^344 + X^343 + 
    X^342 + X^341 + X^337 + X^329 + X^326 + X^324 + X^323 + X^322 + X^321 + 
    X^318 + X^317 + X^315 + X^310 + X^309 + X^307 + X^305 + X^304 + X^302 + 
    X^298 + X^297 + X^296 + X^295 + X^293 + X^291 + X^290 + X^288 + X^286 + 
    X^283 + X^279 + X^278 + X^277 + X^276 + X^275 + X^274 + X^273 + X^272 + 
    X^271 + X^269 + X^267 + X^265 + X^264 + X^263 + X^260 + X^259 + X^258 + 
    X^257 + X^256 + X^254 + X^253 + X^252 + X^251 + X^250 + X^249 + X^248 + 
    X^246 + X^244 + X^241 + X^240 + X^238 + X^237 + X^234 + X^232 + X^230 + 
    X^229 + X^225 + X^222 + X^218 + X^217 + X^215 + X^213 + X^210 + X^209 + 
    X^206 + X^203 + X^201 + X^199 + X^198 + X^197 + X^196 + X^194 + X^193 + 
    X^191 + X^190 + X^189 + X^187 + X^184 + X^182 + X^181 + X^180 + X^178 + 
    X^177 + X^175 + X^174 + X^173 + X^172 + X^170 + X^168 + X^165 + X^162 + 
    X^161 + X^158 + X^156 + X^154 + X^153 + X^149 + X^146 + X^143 + X^142 + 
    X^141 + X^139 + X^137 + X^134 + X^133 + X^131 + X^130 + X^127 + X^125 + 
    X^124 + X^123 + X^122 + X^121 + X^120 + X^119 + X^118 + X^115 + X^114 + 
    X^112 + X^111 + X^108 + X^107 + X^106 + X^104 + X^102 + X^100 + X^99 + X^97 
    + X^96 + X^95 + X^93 + X^92 + X^88 + X^87 + X^85 + X^81 + X^80 + X^78 + X^76
    + X^75 + X^74 + X^73 + X^69 + X^68 + X^67 + X^66 + X^62 + X^61 + X^57 + X^56
    + X^55 + X^54 + X^50 + X^49 + X^48 + X^45 + X^43 + X^42 + X^38 + X^36 + X^31
    + X^30 + X^26 + X^24 + X^19 + X^12 + 1
12
19
26
30
X^1279 + X^1101 + X^1088 + X^1084 + X^1075 + X^1074 + X^1062 + X^1061 + X^1057 +
    X^1054 + X^1049 + X^1048 + X^1036 + X^1035 + X^1033 + X^1027 + X^1024 + 
    X^1023 + X^1022 + X^1020 + X^1016 + X^1010 + X^1009 + X^1007 + X^1006 + 
    X^997 + X^996 + X^993 + X^989 + X^986 + X^983 + X^965 + X^959 + X^956 + 
    X^953 + X^952 + X^950 + X^948 + X^939 + X^938 + X^925 + X^923 + X^921 + 
    X^920 + X^918 + X^916 + X^903 + X^902 + X^897 + X^893 + X^891 + X^889 + 
    X^888 + X^885 + X^884 + X^882 + X^880 + X^876 + X^871 + X^870 + X^861 + 
    X^857 + X^855 + X^853 + X^852 + X^850 + X^844 + X^825 + X^823 + X^822 + 
    X^820 + X^809 + X^796 + X^795 + X^793 + X^790 + X^783 + X^782 + X^777 + 
    X^770 + X^769 + X^764 + X^763 + X^756 + X^751 + X^750 + X^743 + X^740 + 
    X^738 + X^737 + X^724 + X^713 + X^711 + X^710 + X^708 + X^689 + X^683 + 
    X^681 + X^680 + X^678 + X^676 + X^672 + X^669 + X^663 + X^662 + X^657 + 
    X^656 + X^653 + X^652 + X^651 + X^649 + X^648 + X^645 + X^644 + X^643 + 
    X^640 + X^636 + X^631 + X^629 + X^625 + X^622 + X^616 + X^615 + X^613 + 
    X^612 + X^610 + X^608 + X^604 + X^603 + X^601 + X^594 + X^592 + X^591 + 
    X^590 + X^588 + X^585 + X^584 + X^583 + X^581 + X^580 + X^578 + X^575 + 
    X^568 + X^565 + X^564 + X^561 + X^557 + X^554 + X^551 + X^550 + X^547 + 
    X^544 + X^540 + X^537 + X^536 + X^533 + X^526 + X^523 + X^521 + X^520 + 
    X^518 + X^517 + X^516 + X^513 + X^511 + X^510 + X^509 + X^507 + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:25:54 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [30..31] do
for k in [22..29] do
for m in [15..21] do
for n in [9..14] do
        C := ((1 + X^n)^7)*((1 + X^m)^13)*((1 + X^k)^17)*((1 + X^j)^11)+ X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;


Output: Magma V2.10-22    Fri Jun 25 2004 09:25:41 on modular  [Seed = 2111904486]
   -------------------------------------

X^9 + X^4 + 1
9
21
23
30
9
21
24
30
12
19
26
30
13
17
27
30
12
17
29
30
13
20
25
31

Total time: 13.349 seconds, Total memory usage: 2.21MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:29:55 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C := ((1 + X^13)^7)*((1 + X^20)^13)*((1 + X^25)^17)*((1 + X^31)^11)+ X^1279;
if IsPrimitive(C) then 
C;
end if;
C := ((1 + X^12)^7)*((1 + X^17)^13)*((1 + X^29)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 09:29:51 on modular  [Seed = 227632524]
   -------------------------------------

X^1279 + X^1117 + X^1104 + X^1097 + X^1092 + X^1091 + X^1086 + X^1084 + X^1079 +
    X^1078 + X^1073 + X^1072 + X^1071 + X^1065 + X^1061 + X^1060 + X^1059 + 
    X^1058 + X^1055 + X^1052 + X^1048 + X^1047 + X^1046 + X^1045 + X^1042 + 
    X^1041 + X^1039 + X^1037 + X^1034 + X^1033 + X^1032 + X^1030 + X^1029 + 
    X^1028 + X^1026 + X^1021 + X^1020 + X^1019 + X^1016 + X^1015 + X^1012 + 
    X^1010 + X^1008 + X^1007 + X^1004 + X^1003 + X^1002 + X^997 + X^995 + X^994 
    + X^993 + X^992 + X^991 + X^990 + X^989 + X^988 + X^986 + X^984 + X^980 + 
    X^978 + X^977 + X^976 + X^973 + X^971 + X^968 + X^967 + X^965 + X^964 + 
    X^963 + X^962 + X^961 + X^960 + X^958 + X^954 + X^952 + X^949 + X^948 + 
    X^947 + X^945 + X^944 + X^941 + X^939 + X^936 + X^935 + X^934 + X^933 + 
    X^930 + X^928 + X^926 + X^924 + X^923 + X^922 + X^921 + X^919 + X^917 + 
    X^915 + X^912 + X^911 + X^910 + X^909 + X^906 + X^904 + X^901 + X^900 + 
    X^898 + X^897 + X^896 + X^893 + X^891 + X^887 + X^885 + X^884 + X^883 + 
    X^882 + X^881 + X^880 + X^878 + X^874 + X^872 + X^868 + X^867 + X^865 + 
    X^864 + X^861 + X^859 + X^855 + X^854 + X^853 + X^850 + X^849 + X^848 + 
    X^846 + X^842 + X^841 + X^839 + X^838 + X^837 + X^836 + X^835 + X^832 + 
    X^829 + X^826 + X^825 + X^823 + X^821 + X^820 + X^818 + X^816 + X^812 + 
    X^810 + X^805 + X^803 + X^802 + X^801 + X^799 + X^793 + X^792 + X^791 + 
    X^788 + X^787 + X^786 + X^784 + X^782 + X^780 + X^779 + X^778 + X^777 + 
    X^776 + X^775 + X^774 + X^770 + X^767 + X^764 + X^763 + X^761 + X^760 + 
    X^759 + X^758 + X^757 + X^756 + X^754 + X^753 + X^750 + X^747 + X^743 + 
    X^742 + X^741 + X^740 + X^739 + X^738 + X^737 + X^735 + X^733 + X^731 + 
    X^730 + X^729 + X^726 + X^725 + X^724 + X^718 + X^717 + X^716 + X^715 + 
    X^714 + X^712 + X^707 + X^705 + X^704 + X^701 + X^699 + X^696 + X^694 + 
    X^688 + X^686 + X^685 + X^684 + X^682 + X^681 + X^680 + X^676 + X^675 + 
    X^673 + X^672 + X^669 + X^668 + X^667 + X^665 + X^664 + X^663 + X^662 + 
    X^661 + X^660 + X^659 + X^656 + X^655 + X^653 + X^650 + X^649 + X^648 + 
    X^647 + X^646 + X^643 + X^642 + X^641 + X^636 + X^635 + X^629 + X^628 + 
    X^624 + X^617 + X^615 + X^613 + X^612 + X^611 + X^610 + X^606 + X^605 + 
    X^604 + X^603 + X^600 + X^598 + X^597 + X^596 + X^592 + X^590 + X^588 + 
    X^587 + X^586 + X^583 + X^582 + X^581 + X^580 + X^577 + X^572 + X^571 + 
    X^570 + X^569 + X^567 + X^564 + X^562 + X^561 + X^560 + X^559 + X^558 + 
    X^557 + X^556 + X^555 + X^553 + X^550 + X^548 + X^547 + X^546 + X^545 + 
    X^540 + X^537 + X^536 + X^535 + X^534 + X^531 + X^530 + X^529 + X^527 + 
    X^525 + X^521 + X^520 + X^519 + X^517 + X^514 + X^513 + X^512 + X^511 + 
    X^507 + X^506 + X^505 + X^504 + X^502 + X^500 + X^493 + X^489 + X^488 + 
    X^482 + X^481 + X^476 + X^475 + X^474 + X^471 + X^470 + X^469 + X^468 + 
    X^467 + X^464 + X^462 + X^461 + X^458 + X^457 + X^456 + X^455 + X^454 + 
    X^453 + X^452 + X^450 + X^449 + X^448 + X^445 + X^444 + X^442 + X^441 + 
    X^437 + X^436 + X^435 + X^433 + X^432 + X^431 + X^429 + X^423 + X^421 + 
    X^418 + X^416 + X^413 + X^412 + X^410 + X^405 + X^403 + X^402 + X^401 + 
    X^400 + X^399 + X^393 + X^392 + X^391 + X^388 + X^387 + X^386 + X^384 + 
    X^382 + X^380 + X^379 + X^378 + X^377 + X^376 + X^375 + X^374 + X^370 + 
    X^367 + X^364 + X^363 + X^361 + X^360 + X^359 + X^358 + X^357 + X^356 + 
    X^354 + X^353 + X^350 + X^347 + X^343 + X^342 + X^341 + X^340 + X^339 + 
    X^338 + X^337 + X^335 + X^333 + X^331 + X^330 + X^329 + X^326 + X^325 + 
    X^324 + X^318 + X^316 + X^315 + X^314 + X^312 + X^307 + X^305 + X^301 + 
    X^299 + X^297 + X^296 + X^294 + X^292 + X^291 + X^288 + X^285 + X^282 + 
    X^281 + X^280 + X^279 + X^278 + X^276 + X^275 + X^271 + X^269 + X^268 + 
    X^267 + X^264 + X^263 + X^262 + X^258 + X^256 + X^253 + X^252 + X^250 + 
    X^249 + X^245 + X^243 + X^239 + X^237 + X^236 + X^235 + X^234 + X^233 + 
    X^232 + X^230 + X^226 + X^224 + X^221 + X^220 + X^219 + X^217 + X^216 + 
    X^213 + X^211 + X^208 + X^207 + X^206 + X^205 + X^202 + X^200 + X^198 + 
    X^196 + X^195 + X^194 + X^193 + X^191 + X^189 + X^187 + X^184 + X^183 + 
    X^182 + X^181 + X^178 + X^176 + X^173 + X^172 + X^170 + X^169 + X^168 + 
    X^165 + X^163 + X^159 + X^157 + X^156 + X^155 + X^154 + X^153 + X^152 + 
    X^150 + X^149 + X^146 + X^144 + X^141 + X^140 + X^139 + X^137 + X^133 + 
    X^131 + X^129 + X^128 + X^127 + X^126 + X^125 + X^124 + X^123 + X^122 + 
    X^120 + X^115 + X^114 + X^113 + X^110 + X^109 + X^107 + X^105 + X^102 + 
    X^101 + X^98 + X^97 + X^96 + X^91 + X^89 + X^88 + X^87 + X^85 + X^84 + X^83 
    + X^80 + X^78 + X^76 + X^75 + X^72 + X^71 + X^70 + X^69 + X^65 + X^62 + X^59
    + X^58 + X^57 + X^56 + X^52 + X^46 + X^45 + X^44 + X^39 + X^38 + X^33 + X^31
    + X^26 + X^25 + X^20 + X^13 + 1
X^1279 + X^1128 + X^1116 + X^1111 + X^1104 + X^1098 + X^1092 + X^1086 + X^1082 +
    X^1081 + X^1080 + X^1074 + X^1070 + X^1062 + X^1060 + X^1058 + X^1052 + 
    X^1051 + X^1050 + X^1048 + X^1046 + X^1043 + X^1040 + X^1036 + X^1034 + 
    X^1032 + X^1030 + X^1028 + X^1024 + X^1021 + X^1020 + X^1018 + X^1016 + 
    X^1015 + X^1014 + X^1013 + X^1012 + X^1008 + X^1006 + X^1004 + X^996 + X^994
    + X^992 + X^986 + X^985 + X^983 + X^982 + X^980 + X^975 + X^974 + X^972 + 
    X^968 + X^964 + X^960 + X^955 + X^954 + X^953 + X^952 + X^948 + X^947 + 
    X^946 + X^945 + X^940 + X^936 + X^932 + X^928 + X^926 + X^925 + X^924 + 
    X^920 + X^918 + X^917 + X^915 + X^914 + X^912 + X^908 + X^907 + X^906 + 
    X^904 + X^900 + X^896 + X^892 + X^888 + X^887 + X^886 + X^885 + X^884 + 
    X^880 + X^879 + X^878 + X^877 + X^876 + X^872 + X^871 + X^868 + X^860 + 
    X^857 + X^850 + X^849 + X^847 + X^842 + X^841 + X^838 + X^836 + X^834 + 
    X^830 + X^828 + X^826 + X^824 + X^822 + X^819 + X^817 + X^816 + X^814 + 
    X^810 + X^806 + X^804 + X^803 + X^802 + X^798 + X^794 + X^790 + X^789 + 
    X^788 + X^786 + X^782 + X^778 + X^776 + X^775 + X^773 + X^770 + X^768 + 
    X^766 + X^764 + X^762 + X^758 + X^756 + X^754 + X^751 + X^750 + X^745 + 
    X^743 + X^742 + X^735 + X^732 + X^724 + X^721 + X^720 + X^716 + X^715 + 
    X^714 + X^713 + X^712 + X^708 + X^707 + X^706 + X^705 + X^704 + X^700 + 
    X^696 + X^692 + X^688 + X^686 + X^685 + X^684 + X^680 + X^678 + X^677 + 
    X^675 + X^674 + X^672 + X^668 + X^667 + X^666 + X^660 + X^656 + X^646 + 
    X^645 + X^644 + X^639 + X^638 + X^637 + X^634 + X^632 + X^624 + X^622 + 
    X^620 + X^616 + X^612 + X^609 + X^607 + X^600 + X^594 + X^587 + X^582 + 
    X^580 + X^578 + X^577 + X^574 + X^571 + X^570 + X^566 + X^562 + X^558 + 
    X^557 + X^554 + X^551 + X^550 + X^548 + X^546 + X^541 + X^534 + X^528 + 
    X^521 + X^519 + X^516 + X^512 + X^508 + X^506 + X^504 + X^496 + X^494 + 
    X^491 + X^490 + X^489 + X^484 + X^483 + X^482 + X^472 + X^468 + X^462 + 
    X^461 + X^460 + X^456 + X^454 + X^453 + X^451 + X^450 + X^448 + X^444 + 
    X^443 + X^442 + X^440 + X^436 + X^432 + X^428 + X^424 + X^423 + X^422 + 
    X^421 + X^420 + X^416 + X^415 + X^414 + X^413 + X^412 + X^408 + X^407 + 
    X^404 + X^396 + X^393 + X^386 + X^385 + X^383 + X^378 + X^377 + X^374 + 
    X^372 + X^370 + X^366 + X^364 + X^362 + X^360 + X^358 + X^355 + X^353 + 
    X^352 + X^350 + X^346 + X^342 + X^340 + X^339 + X^338 + X^334 + X^330 + 
    X^326 + X^325 + X^324 + X^322 + X^318 + X^314 + X^312 + X^311 + X^309 + 
    X^306 + X^304 + X^302 + X^300 + X^298 + X^294 + X^292 + X^290 + X^287 + 
    X^286 + X^281 + X^279 + X^278 + X^271 + X^268 + X^260 + X^257 + X^256 + 
    X^252 + X^251 + X^250 + X^249 + X^248 + X^244 + X^243 + X^242 + X^241 + 
    X^240 + X^236 + X^232 + X^228 + X^224 + X^222 + X^221 + X^220 + X^216 + 
    X^214 + X^213 + X^211 + X^210 + X^208 + X^204 + X^203 + X^202 + X^200 + 
    X^196 + X^192 + X^188 + X^183 + X^182 + X^181 + X^180 + X^176 + X^175 + 
    X^174 + X^173 + X^168 + X^164 + X^160 + X^156 + X^154 + X^153 + X^148 + 
    X^146 + X^145 + X^143 + X^142 + X^136 + X^134 + X^132 + X^124 + X^122 + 
    X^120 + X^116 + X^115 + X^114 + X^113 + X^112 + X^110 + X^108 + X^107 + 
    X^104 + X^100 + X^98 + X^96 + X^94 + X^92 + X^88 + X^85 + X^82 + X^80 + X^78
    + X^77 + X^76 + X^70 + X^68 + X^66 + X^58 + X^54 + X^48 + X^47 + X^46 + X^42
    + X^36 + X^30 + X^24 + X^17 + X^12 + 1

Total time: 3.939 seconds, Total memory usage: 2.21MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 09:59:52 2004

Input: C := ((1 + X^13)^7)*((1 + X^20)^13)*((1 + X^25)^17)*((1 + X^31)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^31)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^19)*((1 + X^16)^17)*((1 + X^22)^13)*((1 + X^31)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^17)^13)*((1 + X^29)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^21)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^23)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^24)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^19)^13)*((1 + X^26)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^7)*((1 + X^17)^13)*((1 + X^27)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 09:59:50 on modular  [Seed = 3712070213]
   -------------------------------------


>> C := ((1 + X^13)^7)*((1 + X^20)^13)*((1 + X^25)^17)*((1 + X^31)^11)+ X^1279
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^9)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^31)^11) + X^127
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^13)^19)*((1 + X^16)^17)*((1 + X^22)^13)*((1 + X^31)^11) + X^12
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^12)^7)*((1 + X^17)^13)*((1 + X^29)^17)*((1 + X^30)^11)+ X^1279
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^32)^11) + X^12
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^21)^13)*((1 + X^32)^11) + X^12
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^23)^17)*((1 + X^30)^11)+ X^1279;
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^24)^17)*((1 + X^30)^11)+ X^1279;
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^12)^7)*((1 + X^19)^13)*((1 + X^26)^17)*((1 + X^30)^11)+ X^1279
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

>> C := ((1 + X^13)^7)*((1 + X^17)^13)*((1 + X^27)^17)*((1 + X^30)^11)+ X^1279
              ^
User error: Identifier 'X' has not been declared or assigned

>> if IsPrimitive(C) then 
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 10:00:57 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C := ((1 + X^13)^7)*((1 + X^20)^13)*((1 + X^25)^17)*((1 + X^31)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^31)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^19)*((1 + X^16)^17)*((1 + X^22)^13)*((1 + X^31)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^17)^13)*((1 + X^29)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^21)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^23)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^24)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^19)^13)*((1 + X^26)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^7)*((1 + X^17)^13)*((1 + X^27)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 10:00:50 on modular  [Seed = 3783102909]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1117 + X^1104 + X^1097 + X^1092 + X^1091 + X^1086 + X^1084 + X^1079 +
    X^1078 + X^1073 + X^1072 + X^1071 + X^1065 + X^1061 + X^1060 + X^1059 + 
    X^1058 + X^1055 + X^1052 + X^1048 + X^1047 + X^1046 + X^1045 + X^1042 + 
    X^1041 + X^1039 + X^1037 + X^1034 + X^1033 + X^1032 + X^1030 + X^1029 + 
    X^1028 + X^1026 + X^1021 + X^1020 + X^1019 + X^1016 + X^1015 + X^1012 + 
    X^1010 + X^1008 + X^1007 + X^1004 + X^1003 + X^1002 + X^997 + X^995 + X^994 
    + X^993 + X^992 + X^991 + X^990 + X^989 + X^988 + X^986 + X^984 + X^980 + 
    X^978 + X^977 + X^976 + X^973 + X^971 + X^968 + X^967 + X^965 + X^964 + 
    X^963 + X^962 + X^961 + X^960 + X^958 + X^954 + X^952 + X^949 + X^948 + 
    X^947 + X^945 + X^944 + X^941 + X^939 + X^936 + X^935 + X^934 + X^933 + 
    X^930 + X^928 + X^926 + X^924 + X^923 + X^922 + X^921 + X^919 + X^917 + 
    X^915 + X^912 + X^911 + X^910 + X^909 + X^906 + X^904 + X^901 + X^900 + 
    X^898 + X^897 + X^896 + X^893 + X^891 + X^887 + X^885 + X^884 + X^883 + 
    X^882 + X^881 + X^880 + X^878 + X^874 + X^872 + X^868 + X^867 + X^865 + 
    X^864 + X^861 + X^859 + X^855 + X^854 + X^853 + X^850 + X^849 + X^848 + 
    X^846 + X^842 + X^841 + X^839 + X^838 + X^837 + X^836 + X^835 + X^832 + 
    X^829 + X^826 + X^825 + X^823 + X^821 + X^820 + X^818 + X^816 + X^812 + 
    X^810 + X^805 + X^803 + X^802 + X^801 + X^799 + X^793 + X^792 + X^791 + 
    X^788 + X^787 + X^786 + X^784 + X^782 + X^780 + X^779 + X^778 + X^777 + 
    X^776 + X^775 + X^774 + X^770 + X^767 + X^764 + X^763 + X^761 + X^760 + 
    X^759 + X^758 + X^757 + X^756 + X^754 + X^753 + X^750 + X^747 + X^743 + 
    X^742 + X^741 + X^740 + X^739 + X^738 + X^737 + X^735 + X^733 + X^731 + 
    X^730 + X^729 + X^726 + X^725 + X^724 + X^718 + X^717 + X^716 + X^715 + 
    X^714 + X^712 + X^707 + X^705 + X^704 + X^701 + X^699 + X^696 + X^694 + 
    X^688 + X^686 + X^685 + X^684 + X^682 + X^681 + X^680 + X^676 + X^675 + 
    X^673 + X^672 + X^669 + X^668 + X^667 + X^665 + X^664 + X^663 + X^662 + 
    X^661 + X^660 + X^659 + X^656 + X^655 + X^653 + X^650 + X^649 + X^648 + 
    X^647 + X^646 + X^643 + X^642 + X^641 + X^636 + X^635 + X^629 + X^628 + 
    X^624 + X^617 + X^615 + X^613 + X^612 + X^611 + X^610 + X^606 + X^605 + 
    X^604 + X^603 + X^600 + X^598 + X^597 + X^596 + X^592 + X^590 + X^588 + 
    X^587 + X^586 + X^583 + X^582 + X^581 + X^580 + X^577 + X^572 + X^571 + 
    X^570 + X^569 + X^567 + X^564 + X^562 + X^561 + X^560 + X^559 + X^558 + 
    X^557 + X^556 + X^555 + X^553 + X^550 + X^548 + X^547 + X^546 + X^545 + 
    X^540 + X^537 + X^536 + X^535 + X^534 + X^531 + X^530 + X^529 + X^527 + 
    X^525 + X^521 + X^520 + X^519 + X^517 + X^514 + X^513 + X^512 + X^511 + 
    X^507 + X^506 + X^505 + X^504 + X^502 + X^500 + X^493 + X^489 + X^488 + 
    X^482 + X^481 + X^476 + X^475 + X^474 + X^471 + X^470 + X^469 + X^468 + 
    X^467 + X^464 + X^462 + X^461 + X^458 + X^457 + X^456 + X^455 + X^454 + 
    X^453 + X^452 + X^450 + X^449 + X^448 + X^445 + X^444 + X^442 + X^441 + 
    X^437 + X^436 + X^435 + X^433 + X^432 + X^431 + X^429 + X^423 + X^421 + 
    X^418 + X^416 + X^413 + X^412 + X^410 + X^405 + X^403 + X^402 + X^401 + 
    X^400 + X^399 + X^393 + X^392 + X^391 + X^388 + X^387 + X^386 + X^384 + 
    X^382 + X^380 + X^379 + X^378 + X^377 + X^376 + X^375 + X^374 + X^370 + 
    X^367 + X^364 + X^363 + X^361 + X^360 + X^359 + X^358 + X^357 + X^356 + 
    X^354 + X^353 + X^350 + X^347 + X^343 + X^342 + X^341 + X^340 + X^339 + 
    X^338 + X^337 + X^335 + X^333 + X^331 + X^330 + X^329 + X^326 + X^325 + 
    X^324 + X^318 + X^316 + X^315 + X^314 + X^312 + X^307 + X^305 + X^301 + 
    X^299 + X^297 + X^296 + X^294 + X^292 + X^291 + X^288 + X^285 + X^282 + 
    X^281 + X^280 + X^279 + X^278 + X^276 + X^275 + X^271 + X^269 + X^268 + 
    X^267 + X^264 + X^263 + X^262 + X^258 + X^256 + X^253 + X^252 + X^250 + 
    X^249 + X^245 + X^243 + X^239 + X^237 + X^236 + X^235 + X^234 + X^233 + 
    X^232 + X^230 + X^226 + X^224 + X^221 + X^220 + X^219 + X^217 + X^216 + 
    X^213 + X^211 + X^208 + X^207 + X^206 + X^205 + X^202 + X^200 + X^198 + 
    X^196 + X^195 + X^194 + X^193 + X^191 + X^189 + X^187 + X^184 + X^183 + 
    X^182 + X^181 + X^178 + X^176 + X^173 + X^172 + X^170 + X^169 + X^168 + 
    X^165 + X^163 + X^159 + X^157 + X^156 + X^155 + X^154 + X^153 + X^152 + 
    X^150 + X^149 + X^146 + X^144 + X^141 + X^140 + X^139 + X^137 + X^133 + 
    X^131 + X^129 + X^128 + X^127 + X^126 + X^125 + X^124 + X^123 + X^122 + 
    X^120 + X^115 + X^114 + X^113 + X^110 + X^109 + X^107 + X^105 + X^102 + 
    X^101 + X^98 + X^97 + X^96 + X^91 + X^89 + X^88 + X^87 + X^85 + X^84 + X^83 
    + X^80 + X^78 + X^76 + X^75 + X^72 + X^71 + X^70 + X^69 + X^65 + X^62 + X^59
    + X^58 + X^57 + X^56 + X^52 + X^46 + X^45 + X^44 + X^39 + X^38 + X^33 + X^31
    + X^26 + X^25 + X^20 + X^13 + 1
X^1279 + X^1083 + X^1074 + X^1067 + X^1065 + X^1060 + X^1058 + X^1056 + X^1052 +
    X^1051 + X^1049 + X^1044 + X^1043 + X^1042 + X^1040 + X^1036 + X^1035 + 
    X^1034 + X^1033 + X^1029 + X^1027 + X^1026 + X^1025 + X^1021 + X^1020 + 
    X^1018 + X^1017 + X^1013 + X^1012 + X^1011 + X^1009 + X^1005 + X^1004 + 
    X^1003 + X^1002 + X^998 + X^996 + X^995 + X^994 + X^991 + X^990 + X^989 + 
    X^987 + X^986 + X^981 + X^980 + X^978 + X^975 + X^974 + X^972 + X^971 + 
    X^968 + X^967 + X^966 + X^965 + X^963 + X^960 + X^959 + X^958 + X^957 + 
    X^956 + X^955 + X^952 + X^950 + X^949 + X^948 + X^947 + X^944 + X^943 + 
    X^941 + X^940 + X^939 + X^937 + X^935 + X^934 + X^930 + X^929 + X^928 + 
    X^926 + X^925 + X^924 + X^923 + X^920 + X^919 + X^917 + X^916 + X^914 + 
    X^913 + X^911 + X^910 + X^908 + X^907 + X^906 + X^905 + X^904 + X^903 + 
    X^902 + X^900 + X^897 + X^896 + X^895 + X^894 + X^892 + X^891 + X^890 + 
    X^888 + X^886 + X^885 + X^881 + X^880 + X^879 + X^877 + X^875 + X^871 + 
    X^869 + X^866 + X^864 + X^863 + X^861 + X^859 + X^857 + X^856 + X^855 + 
    X^854 + X^850 + X^849 + X^848 + X^847 + X^846 + X^835 + X^833 + X^832 + 
    X^831 + X^830 + X^829 + X^827 + X^826 + X^825 + X^824 + X^823 + X^822 + 
    X^820 + X^819 + X^817 + X^816 + X^815 + X^813 + X^812 + X^811 + X^809 + 
    X^807 + X^804 + X^803 + X^801 + X^799 + X^792 + X^788 + X^787 + X^784 + 
    X^783 + X^781 + X^779 + X^777 + X^774 + X^769 + X^767 + X^765 + X^764 + 
    X^758 + X^757 + X^756 + X^755 + X^753 + X^750 + X^749 + X^743 + X^739 + 
    X^738 + X^737 + X^735 + X^734 + X^733 + X^730 + X^728 + X^727 + X^725 + 
    X^724 + X^722 + X^721 + X^720 + X^718 + X^717 + X^712 + X^710 + X^707 + 
    X^706 + X^703 + X^702 + X^701 + X^699 + X^697 + X^696 + X^694 + X^693 + 
    X^692 + X^691 + X^690 + X^689 + X^688 + X^687 + X^686 + X^681 + X^675 + 
    X^668 + X^666 + X^665 + X^663 + X^658 + X^657 + X^656 + X^653 + X^652 + 
    X^651 + X^648 + X^647 + X^646 + X^644 + X^642 + X^641 + X^640 + X^638 + 
    X^636 + X^634 + X^633 + X^632 + X^629 + X^628 + X^625 + X^622 + X^621 + 
    X^620 + X^618 + X^615 + X^613 + X^612 + X^611 + X^610 + X^607 + X^605 + 
    X^603 + X^602 + X^601 + X^600 + X^598 + X^597 + X^596 + X^594 + X^590 + 
    X^589 + X^581 + X^579 + X^578 + X^576 + X^575 + X^574 + X^573 + X^572 + 
    X^570 + X^567 + X^565 + X^564 + X^563 + X^562 + X^560 + X^558 + X^557 + 
    X^553 + X^551 + X^545 + X^538 + X^532 + X^530 + X^526 + X^525 + X^523 + 
    X^521 + X^520 + X^519 + X^518 + X^516 + X^513 + X^511 + X^510 + X^509 + 
    X^508 + X^507 + X^505 + X^504 + X^502 + X^494 + X^493 + X^489 + X^487 + 
    X^486 + X^485 + X^483 + X^482 + X^481 + X^480 + X^478 + X^476 + X^473 + 
    X^472 + X^471 + X^470 + X^468 + X^465 + X^463 + X^462 + X^461 + X^458 + 
    X^455 + X^454 + X^451 + X^450 + X^449 + X^447 + X^445 + X^443 + X^442 + 
    X^441 + X^439 + X^437 + X^436 + X^435 + X^432 + X^431 + X^430 + X^427 + 
    X^426 + X^425 + X^420 + X^418 + X^417 + X^415 + X^408 + X^402 + X^397 + 
    X^396 + X^395 + X^394 + X^393 + X^392 + X^391 + X^390 + X^389 + X^387 + 
    X^386 + X^384 + X^382 + X^381 + X^380 + X^377 + X^376 + X^373 + X^371 + 
    X^366 + X^365 + X^363 + X^362 + X^361 + X^359 + X^358 + X^356 + X^355 + 
    X^353 + X^350 + X^349 + X^348 + X^346 + X^345 + X^344 + X^340 + X^334 + 
    X^333 + X^330 + X^328 + X^327 + X^326 + X^325 + X^319 + X^318 + X^316 + 
    X^314 + X^309 + X^306 + X^304 + X^302 + X^300 + X^299 + X^296 + X^295 + 
    X^291 + X^284 + X^282 + X^280 + X^279 + X^276 + X^274 + X^272 + X^271 + 
    X^270 + X^268 + X^267 + X^266 + X^264 + X^263 + X^261 + X^260 + X^259 + 
    X^258 + X^257 + X^256 + X^254 + X^253 + X^252 + X^251 + X^250 + X^248 + 
    X^237 + X^236 + X^235 + X^234 + X^233 + X^229 + X^228 + X^227 + X^226 + 
    X^224 + X^222 + X^220 + X^219 + X^217 + X^214 + X^212 + X^208 + X^206 + 
    X^204 + X^203 + X^202 + X^198 + X^197 + X^195 + X^193 + X^192 + X^191 + 
    X^189 + X^188 + X^187 + X^186 + X^183 + X^181 + X^180 + X^179 + X^178 + 
    X^177 + X^176 + X^175 + X^173 + X^172 + X^170 + X^169 + X^167 + X^166 + 
    X^164 + X^163 + X^160 + X^159 + X^158 + X^157 + X^155 + X^154 + X^153 + 
    X^149 + X^148 + X^146 + X^144 + X^143 + X^142 + X^140 + X^139 + X^136 + 
    X^135 + X^134 + X^133 + X^131 + X^128 + X^127 + X^126 + X^125 + X^124 + 
    X^123 + X^120 + X^118 + X^117 + X^116 + X^115 + X^112 + X^111 + X^109 + 
    X^108 + X^105 + X^103 + X^102 + X^97 + X^96 + X^94 + X^93 + X^92 + X^89 + 
    X^88 + X^87 + X^85 + X^81 + X^80 + X^79 + X^78 + X^74 + X^72 + X^71 + X^70 +
    X^66 + X^65 + X^63 + X^62 + X^58 + X^57 + X^56 + X^54 + X^50 + X^49 + X^48 +
    X^47 + X^43 + X^41 + X^40 + X^39 + X^34 + X^32 + X^31 + X^27 + X^25 + X^23 +
    X^18 + X^16 + X^9 + 1
X^1279 + X^1146 + X^1133 + X^1130 + X^1124 + X^1120 + X^1117 + X^1115 + X^1111 +
    X^1108 + X^1107 + X^1104 + X^1102 + X^1099 + X^1098 + X^1095 + X^1093 + 
    X^1091 + X^1089 + X^1086 + X^1085 + X^1084 + X^1082 + X^1080 + X^1077 + 
    X^1076 + X^1073 + X^1071 + X^1069 + X^1068 + X^1067 + X
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 10:03:48 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C := ((1 + X^13)^19)*((1 + X^16)^17)*((1 + X^22)^13)*((1 + X^31)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^17)^13)*((1 + X^29)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^21)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^23)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^24)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^19)^13)*((1 + X^26)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^7)*((1 + X^17)^13)*((1 + X^27)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 10:03:43 on modular  [Seed = 2283075705]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1146 + X^1133 + X^1130 + X^1124 + X^1120 + X^1117 + X^1115 + X^1111 +
    X^1108 + X^1107 + X^1104 + X^1102 + X^1099 + X^1098 + X^1095 + X^1093 + 
    X^1091 + X^1089 + X^1086 + X^1085 + X^1084 + X^1082 + X^1080 + X^1077 + 
    X^1076 + X^1073 + X^1071 + X^1069 + X^1068 + X^1067 + X^1064 + X^1062 + 
    X^1060 + X^1055 + X^1054 + X^1053 + X^1051 + X^1049 + X^1046 + X^1040 + 
    X^1038 + X^1037 + X^1033 + X^1032 + X^1031 + X^1024 + X^1019 + X^1018 + 
    X^1016 + X^1015 + X^1010 + X^1003 + X^1002 + X^1001 + X^997 + X^996 + X^994 
    + X^988 + X^985 + X^983 + X^981 + X^980 + X^979 + X^974 + X^972 + X^967 + 
    X^966 + X^965 + X^963 + X^961 + X^958 + X^952 + X^950 + X^949 + X^945 + 
    X^944 + X^943 + X^938 + X^936 + X^931 + X^930 + X^928 + X^927 + X^925 + 
    X^916 + X^915 + X^914 + X^913 + X^912 + X^908 + X^907 + X^906 + X^903 + 
    X^899 + X^898 + X^897 + X^896 + X^895 + X^894 + X^893 + X^892 + X^887 + 
    X^886 + X^884 + X^883 + X^882 + X^881 + X^879 + X^877 + X^875 + X^873 + 
    X^870 + X^867 + X^865 + X^862 + X^861 + X^859 + X^857 + X^856 + X^850 + 
    X^840 + X^836 + X^835 + X^833 + X^829 + X^827 + X^825 + X^821 + X^820 + 
    X^819 + X^818 + X^817 + X^815 + X^814 + X^813 + X^812 + X^810 + X^809 + 
    X^807 + X^802 + X^801 + X^799 + X^798 + X^797 + X^796 + X^792 + X^791 + 
    X^790 + X^789 + X^788 + X^787 + X^786 + X^783 + X^780 + X^778 + X^776 + 
    X^774 + X^770 + X^769 + X^766 + X^765 + X^764 + X^759 + X^758 + X^757 + 
    X^756 + X^754 + X^751 + X^749 + X^748 + X^745 + X^744 + X^743 + X^742 + 
    X^741 + X^736 + X^734 + X^733 + X^731 + X^729 + X^727 + X^726 + X^722 + 
    X^720 + X^717 + X^716 + X^715 + X^714 + X^713 + X^712 + X^711 + X^709 + 
    X^706 + X^704 + X^700 + X^698 + X^697 + X^695 + X^694 + X^693 + X^692 + 
    X^690 + X^685 + X^684 + X^679 + X^678 + X^677 + X^676 + X^675 + X^674 + 
    X^672 + X^670 + X^668 + X^666 + X^664 + X^662 + X^657 + X^655 + X^654 + 
    X^653 + X^652 + X^650 + X^647 + X^646 + X^645 + X^644 + X^643 + X^641 + 
    X^633 + X^632 + X^631 + X^630 + X^626 + X^624 + X^623 + X^622 + X^621 + 
    X^620 + X^617 + X^616 + X^615 + X^613 + X^612 + X^610 + X^608 + X^607 + 
    X^599 + X^598 + X^593 + X^591 + X^590 + X^588 + X^587 + X^586 + X^581 + 
    X^580 + X^578 + X^577 + X^576 + X^575 + X^571 + X^570 + X^569 + X^568 + 
    X^566 + X^565 + X^560 + X^559 + X^558 + X^556 + X^555 + X^553 + X^548 + 
    X^547 + X^539 + X^538 + X^536 + X^534 + X^533 + X^531 + X^530 + X^529 + 
    X^526 + X^525 + X^524 + X^523 + X^522 + X^520 + X^516 + X^515 + X^514 + 
    X^513 + X^505 + X^503 + X^502 + X^501 + X^500 + X^499 + X^496 + X^494 + 
    X^493 + X^492 + X^491 + X^489 + X^484 + X^482 + X^480 + X^478 + X^476 + 
    X^474 + X^472 + X^471 + X^470 + X^469 + X^468 + X^467 + X^462 + X^461 + 
    X^456 + X^454 + X^453 + X^452 + X^451 + X^449 + X^448 + X^446 + X^442 + 
    X^440 + X^437 + X^435 + X^434 + X^433 + X^432 + X^431 + X^430 + X^429 + 
    X^426 + X^424 + X^420 + X^419 + X^417 + X^415 + X^413 + X^412 + X^410 + 
    X^405 + X^404 + X^403 + X^402 + X^401 + X^398 + X^397 + X^395 + X^392 + 
    X^390 + X^389 + X^388 + X^387 + X^382 + X^381 + X^380 + X^377 + X^376 + 
    X^372 + X^370 + X^368 + X^366 + X^363 + X^360 + X^359 + X^358 + X^357 + 
    X^356 + X^355 + X^354 + X^350 + X^349 + X^348 + X^347 + X^345 + X^344 + 
    X^339 + X^337 + X^336 + X^334 + X^333 + X^332 + X^331 + X^329 + X^328 + 
    X^327 + X^326 + X^325 + X^321 + X^319 + X^317 + X^313 + X^311 + X^310 + 
    X^306 + X^296 + X^290 + X^289 + X^287 + X^285 + X^284 + X^281 + X^279 + 
    X^276 + X^273 + X^271 + X^269 + X^267 + X^265 + X^264 + X^263 + X^262 + 
    X^260 + X^259 + X^254 + X^253 + X^252 + X^251 + X^250 + X^249 + X^248 + 
    X^247 + X^243 + X^240 + X^239 + X^238 + X^234 + X^233 + X^232 + X^231 + 
    X^230 + X^221 + X^219 + X^218 + X^216 + X^215 + X^210 + X^208 + X^203 + 
    X^202 + X^201 + X^197 + X^196 + X^194 + X^188 + X^185 + X^183 + X^181 + 
    X^180 + X^179 + X^174 + X^172 + X^167 + X^166 + X^165 + X^163 + X^161 + 
    X^158 + X^152 + X^150 + X^149 + X^145 + X^144 + X^143 + X^136 + X^131 + 
    X^130 + X^128 + X^127 + X^122 + X^115 + X^114 + X^113 + X^109 + X^108 + 
    X^106 + X^100 + X^97 + X^95 + X^93 + X^92 + X^91 + X^86 + X^84 + X^82 + X^79
    + X^78 + X^77 + X^75 + X^73 + X^70 + X^69 + X^66 + X^64 + X^62 + X^61 + X^60
    + X^57 + X^55 + X^53 + X^51 + X^48 + X^47 + X^44 + X^42 + X^39 + X^38 + X^35
    + X^31 + X^29 + X^26 + X^22 + X^16 + X^13 + 1
X^1279 + X^1128 + X^1116 + X^1111 + X^1104 + X^1098 + X^1092 + X^1086 + X^1082 +
    X^1081 + X^1080 + X^1074 + X^1070 + X^1062 + X^1060 + X^1058 + X^1052 + 
    X^1051 + X^1050 + X^1048 + X^1046 + X^1043 + X^1040 + X^1036 + X^1034 + 
    X^1032 + X^1030 + X^1028 + X^1024 + X^1021 + X^1020 + X^1018 + X^1016 + 
    X^1015 + X^1014 + X^1013 + X^1012 + X^1008 + X^1006 + X^1004 + X^996 + X^994
    + X^992 + X^986 + X^985 + X^983 + X^982 + X^980 + X^975 + X^974 + X^972 + 
    X^968 + X^964 + X^960 + X^955 + X^954 + X^953 + X^952 + X^948 + X^947 + 
    X^946 + X^945 + X^940 + X^936 + X^932 + X^928 + X^926 + X^925 + X^924 + 
    X^920 + X^918 + X^917 + X^915 + X^914 + X^912 + X^908 + X^907 + X^906 + 
    X^904 + X^900 + X^896 + X^892 + X^888 + X^887 + X^886 + X^885 + X^884 + 
    X^880 + X^879 + X^878 + X^877 + X^876 + X^872 + X^871 + X^868 + X^860 + 
    X^857 + X^850 + X^849 + X^847 + X^842 + X^841 + X^838 + X^836 + X^834 + 
    X^830 + X^828 + X^826 + X^824 + X^822 + X^819 + X^817 + X^816 + X^814 + 
    X^810 + X^806 + X^804 + X^803 + X^802 + X^798 + X^794 + X^790 + X^789 + 
    X^788 + X^786 + X^782 + X^778 + X^776 + X^775 + X^773 + X^770 + X^768 + 
    X^766 + X^764 + X^762 + X^758 + X^756 + X^754 + X^751 + X^750 + X^745 + 
    X^743 + X^742 + X^735 + X^732 + X^724 + X^721 + X^720 + X^716 + X^715 + 
    X^714 + X^713 + X^712 + X^708 + X^707 + X^706 + X^705 + X^704 + X^700 + 
    X^696 + X^692 + X^688 + X^686 + X^685 + X^684 + X^680 + X^678 + X^677 + 
    X^675 + X^674 + X^672 + X^668 + X^667 + X^666 + X^660 + X^656 + X^646 + 
    X^645 + X^644 + X^639 + X^638 + X^637 + X^634 + X^632 + X^624 + X^622 + 
    X^620 + X^616 + X^612 + X^609 + X^607 + X^600 + X^594 + X^587 + X^582 + 
    X^580 + X^578 + X^577 + X^574 + X^571 + X^570 + X^566 + X^562 + X^558 + 
    X^557 + X^554 + X^551 + X^550 + X^548 + X^546 + X^541 + X^534 + X^528 + 
    X^521 + X^519 + X^516 + X^512 + X^508 + X^506 + X^504 + X^496 + X^494 + 
    X^491 + X^490 + X^489 + X^484 + X^483 + X^482 + X^472 + X^468 + X^462 + 
    X^461 + X^460 + X^456 + X^454 + X^453 + X^451 + X^450 + X^448 + X^444 + 
    X^443 + X^442 + X^440 + X^436 + X^432 + X^428 + X^424 + X^423 + X^422 + 
    X^421 + X^420 + X^416 + X^415 + X^414 + X^413 + X^412 + X^408 + X^407 + 
    X^404 + X^396 + X^393 + X^386 + X^385 + X^383 + X^378 + X^377 + X^374 + 
    X^372 + X^370 + X^366 + X^364 + X^362 + X^360 + X^358 + X^355 + X^353 + 
    X^352 + X^350 + X^346 + X^342 + X^340 + X^339 + X^338 + X^334 + X^330 + 
    X^326 + X^325 + X^324 + X^322 + X^318 + X^314 + X^312 + X^311 + X^309 + 
    X^306 + X^304 + X^302 + X^300 + X^298 + X^294 + X^292 + X^290 + X^287 + 
    X^286 + X^281 + X^279 + X^278 + X^271 + X^268 + X^260 + X^257 + X^256 + 
    X^252 + X^251 + X^250 + X^249 + X^248 + X^244 + X^243 + X^242 + X^241 + 
    X^240 + X^236 + X^232 + X^228 + X^224 + X^222 + X^221 + X^220 + X^216 + 
    X^214 + X^213 + X^211 + X^210 + X^208 + X^204 + X^203 + X^202 + X^200 + 
    X^196 + X^192 + X^188 + X^183 + X^182 + X^181 + X^180 + X^176 + X^175 + 
    X^174 + X^173 + X^168 + X^164 + X^160 + X^156 + X^154 + X^153 + X^148 + 
    X^146 + X^145 + X^143 + X^142 + X^136 + X^134 + X^132 + X^124 + X^122 + 
    X^120 + X^116 + X^115 + X^114 + X^113 + X^112 + X^110 + X^108 + X^107 + 
    X^104 + X^100 + X^98 + X^96 + X^94 + X^92 + X^88 + X^85 + X^82 + X^80 + X^78
    + X^77 + X^76 + X^70 + X^68 + X^66 + X^58 + X^54 + X^48 + X^47 + X^46 + X^42
    + X^36 + X^30 + X^24 + X^17 + X^12 + 1
X^1279 + X^1151 + X^1139 + X^1135 + X^1128 + X^1127 + X^1123 + X^1119 + X^1116 +
    X^1115 + X^1112 + X^1111 + X^1107 + X^1104 + X^1103 + X^1100 + X^1099 + 
    X^1096 + X^1095 + X^1092 + X^1091 + X^1088 + X^1087 + X^1084 + X^1083 + 
    X^1080 + X^1079 + X^1076 + X^1075 + X^1072 + X^1071 + X^1068 + X^1067 + 
    X^1064 + X^1063 + X^1060 + X^1056 + X^1055 + X^1052 + X^1051 + X^1048 + 
    X^1044 + X^1040 + X^1039 + X^1032 + X^1028 + X^1023 + X^1016 + X^1011 + 
    X^1007 + X^1000 + X^999 + X^995 + X^991 + X^988 + X^987 + X^984 + X^983 + 
    X^979 + X^976 + X^975 + X^972 + X^971 + X^968 + X^964 + X^963 + X^960 + 
    X^956 + X^952 + X^948 + X^943 + X^940 + X^935 + X^927 + X^923 + X^920 + 
    X^912 + X^911 + X^904 + X^900 + X^888 + X^875 + X^867 + X^863 + X^859 + 
    X^855 + X^852 + X^847 + X^844 + X^840 + X^839 + X^836 + X^832 + X^831 + 
    X^827 + X^824 + X^823 + X^819 + X^816 + X^811 + X^808 + X^804 + X^800 + 
    X^796 + X^788 + X^775 + X^763 + X^759 + X^752 + X^751 + X^743 + X^740 + 
    X^736 + X^728 + X^723 + X^720 + X^715 + X^711 + X^707 + X^703 + X^700 + 
    X^699 + X^695 + X^692 + X^691 + X^688 + X^687 + X^684 + X^680 + X^679 + 
    X^676 + X^675 + X^672 + X^668 + X^664 + X^663 + X^656 + X^652 + X^647 + 
    X^640 + X^639 + X^635 + X^631 + X^627 + X^624 + X^619 + X^616 + X^612 + 
    X^608 + X^604 + X^596 + X^555 + X^547 + X^543 + X^539 + X^535 + X^532 + 
    X^527 + X^524 + X^520 + X^516 + X^512 + X^511 + X^504 + X^499 + X^495 + 
    X^488 + X^487 + X^483 + X^479 + X^476 + X^475 + X^472 + X^471 + X^467 + 
    X^464 + X^463 + X^460 + X^459 + X^456 + X^452 + X^451 + X^448 + X^444 + 
    X^440 + X^436 + X^431 + X^428 + X^423 + X^415 + X^411 + X^408 + X^400 + 
    X^399 + X^392 + X^388 + X^376 + X^363 + X^355 + X^351 + X^347 + X^343 + 
    X^340 + X^335 + X^332 + X^328 + X^327 + X^324 + X^320 + X^319 + X^315 + 
    X^312 + X^311 + X^307 + X^304 + X^299 + X^296 + X^292 + X^288 + X^284 + 
    X^276 + X^263 + X^251 + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 10:05:21 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^23)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^19)*((1 + X^16)^17)*((1 + X^21)^13)*((1 + X^32)^11) + X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^23)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^9)^7)*((1 + X^21)^13)*((1 + X^24)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^12)^7)*((1 + X^19)^13)*((1 + X^26)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^7)*((1 + X^17)^13)*((1 + X^27)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 10:05:16 on modular  [Seed = 2483611078]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1151 + X^1139 + X^1135 + X^1128 + X^1127 + X^1123 + X^1119 + X^1116 +
    X^1115 + X^1112 + X^1111 + X^1107 + X^1104 + X^1103 + X^1100 + X^1099 + 
    X^1096 + X^1095 + X^1092 + X^1091 + X^1088 + X^1087 + X^1084 + X^1083 + 
    X^1080 + X^1079 + X^1076 + X^1075 + X^1072 + X^1071 + X^1068 + X^1067 + 
    X^1064 + X^1063 + X^1060 + X^1056 + X^1055 + X^1052 + X^1051 + X^1048 + 
    X^1044 + X^1040 + X^1039 + X^1032 + X^1028 + X^1023 + X^1016 + X^1011 + 
    X^1007 + X^1000 + X^999 + X^995 + X^991 + X^988 + X^987 + X^984 + X^983 + 
    X^979 + X^976 + X^975 + X^972 + X^971 + X^968 + X^964 + X^963 + X^960 + 
    X^956 + X^952 + X^948 + X^943 + X^940 + X^935 + X^927 + X^923 + X^920 + 
    X^912 + X^911 + X^904 + X^900 + X^888 + X^875 + X^867 + X^863 + X^859 + 
    X^855 + X^852 + X^847 + X^844 + X^840 + X^839 + X^836 + X^832 + X^831 + 
    X^827 + X^824 + X^823 + X^819 + X^816 + X^811 + X^808 + X^804 + X^800 + 
    X^796 + X^788 + X^775 + X^763 + X^759 + X^752 + X^751 + X^743 + X^740 + 
    X^736 + X^728 + X^723 + X^720 + X^715 + X^711 + X^707 + X^703 + X^700 + 
    X^699 + X^695 + X^692 + X^691 + X^688 + X^687 + X^684 + X^680 + X^679 + 
    X^676 + X^675 + X^672 + X^668 + X^664 + X^663 + X^656 + X^652 + X^647 + 
    X^640 + X^639 + X^635 + X^631 + X^627 + X^624 + X^619 + X^616 + X^612 + 
    X^608 + X^604 + X^596 + X^555 + X^547 + X^543 + X^539 + X^535 + X^532 + 
    X^527 + X^524 + X^520 + X^516 + X^512 + X^511 + X^504 + X^499 + X^495 + 
    X^488 + X^487 + X^483 + X^479 + X^476 + X^475 + X^472 + X^471 + X^467 + 
    X^464 + X^463 + X^460 + X^459 + X^456 + X^452 + X^451 + X^448 + X^444 + 
    X^440 + X^436 + X^431 + X^428 + X^423 + X^415 + X^411 + X^408 + X^400 + 
    X^399 + X^392 + X^388 + X^376 + X^363 + X^355 + X^351 + X^347 + X^343 + 
    X^340 + X^335 + X^332 + X^328 + X^327 + X^324 + X^320 + X^319 + X^315 + 
    X^312 + X^311 + X^307 + X^304 + X^299 + X^296 + X^292 + X^288 + X^284 + 
    X^276 + X^263 + X^251 + X^247 + X^240 + X^239 + X^231 + X^228 + X^224 + 
    X^216 + X^211 + X^208 + X^203 + X^199 + X^195 + X^191 + X^188 + X^187 + 
    X^183 + X^180 + X^179 + X^176 + X^175 + X^172 + X^168 + X^167 + X^164 + 
    X^163 + X^160 + X^156 + X^152 + X^151 + X^144 + X^140 + X^135 + X^128 + 
    X^123 + X^119 + X^112 + X^111 + X^107 + X^103 + X^100 + X^99 + X^96 + X^95 +
    X^91 + X^88 + X^87 + X^84 + X^83 + X^80 + X^79 + X^76 + X^75 + X^72 + X^71 +
    X^68 + X^67 + X^64 + X^63 + X^60 + X^59 + X^56 + X^55 + X^52 + X^51 + X^48 +
    X^47 + X^44 + X^40 + X^39 + X^36 + X^35 + X^32 + X^28 + X^24 + X^23 + X^16 +
    X^12 + 1
X^1279 + X^1125 + X^1113 + X^1109 + X^1104 + X^1101 + X^1097 + X^1093 + X^1092 +
    X^1089 + X^1088 + X^1085 + X^1081 + X^1080 + X^1077 + X^1076 + X^1073 + 
    X^1072 + X^1069 + X^1068 + X^1065 + X^1064 + X^1061 + X^1060 + X^1057 + 
    X^1056 + X^1053 + X^1052 + X^1049 + X^1048 + X^1045 + X^1044 + X^1040 + 
    X^1037 + X^1036 + X^1033 + X^1032 + X^1028 + X^1024 + X^1021 + X^1016 + 
    X^1012 + X^1000 + X^997 + X^985 + X^981 + X^976 + X^973 + X^969 + X^965 + 
    X^964 + X^961 + X^960 + X^953 + X^952 + X^949 + X^948 + X^944 + X^940 + 
    X^937 + X^933 + X^932 + X^928 + X^921 + X^917 + X^916 + X^913 + X^912 + 
    X^909 + X^905 + X^900 + X^896 + X^893 + X^892 + X^888 + X^884 + X^873 + 
    X^872 + X^861 + X^857 + X^852 + X^845 + X^841 + X^840 + X^836 + X^824 + 
    X^820 + X^817 + X^813 + X^801 + X^797 + X^796 + X^792 + X^785 + X^780 + 
    X^776 + X^765 + X^764 + X^753 + X^749 + X^745 + X^744 + X^741 + X^737 + 
    X^732 + X^728 + X^725 + X^724 + X^721 + X^720 + X^716 + X^709 + X^705 + 
    X^704 + X^700 + X^697 + X^693 + X^689 + X^688 + X^685 + X^684 + X^677 + 
    X^676 + X^673 + X^672 + X^668 + X^664 + X^661 + X^656 + X^652 + X^640 + 
    X^637 + X^625 + X^621 + X^616 + X^609 + X^605 + X^604 + X^600 + X^593 + 
    X^588 + X^584 + X^572 + X^553 + X^541 + X^537 + X^532 + X^525 + X^521 + 
    X^520 + X^516 + X^509 + X^504 + X^500 + X^488 + X^485 + X^473 + X^469 + 
    X^464 + X^461 + X^457 + X^453 + X^452 + X^449 + X^448 + X^441 + X^440 + 
    X^437 + X^436 + X^432 + X^428 + X^425 + X^421 + X^420 + X^416 + X^409 + 
    X^405 + X^404 + X^401 + X^400 + X^397 + X^393 + X^388 + X^384 + X^381 + 
    X^380 + X^376 + X^372 + X^361 + X^360 + X^349 + X^345 + X^340 + X^333 + 
    X^329 + X^328 + X^324 + X^312 + X^308 + X^305 + X^301 + X^289 + X^285 + 
    X^284 + X^280 + X^273 + X^268 + X^264 + X^253 + X^252 + X^241 + X^237 + 
    X^233 + X^232 + X^229 + X^225 + X^220 + X^216 + X^213 + X^212 + X^209 + 
    X^208 + X^204 + X^197 + X^193 + X^192 + X^188 + X^185 + X^181 + X^177 + 
    X^176 + X^173 + X^172 + X^165 + X^164 + X^161 + X^160 + X^156 + X^152 + 
    X^149 + X^144 + X^140 + X^128 + X^125 + X^113 + X^109 + X^104 + X^101 + X^97
    + X^93 + X^92 + X^89 + X^88 + X^85 + X^81 + X^80 + X^77 + X^76 + X^73 + X^72
    + X^69 + X^68 + X^65 + X^64 + X^61 + X^60 + X^57 + X^56 + X^53 + X^52 + X^49
    + X^48 + X^45 + X^44 + X^40 + X^37 + X^36 + X^33 + X^32 + X^28 + X^24 + X^21
    + X^16 + X^12 + 1
X^1279 + X^1057 + X^1048 + X^1039 + X^1036 + X^1034 + X^1030 + X^1025 + X^1021 +
    X^1016 + X^1013 + X^1012 + X^1007 + X^1006 + X^1003 + X^998 + X^994 + X^989 
    + X^983 + X^980 + X^976 + X^973 + X^971 + X^955 + X^953 + X^952 + X^950 + 
    X^934 + X^932 + X^929 + X^922 + X^911 + X^904 + X^901 + X^899 + X^889 + 
    X^883 + X^881 + X^878 + X^871 + X^868 + X^866 + X^860 + X^850 + X^848 + 
    X^845 + X^838 + X^827 + X^820 + X^815 + X^808 + X^805 + X^797 + X^796 + 
    X^790 + X^787 + X^785 + X^784 + X^782 + X^781 + X^773 + X^772 + X^767 + 
    X^764 + X^763 + X^761 + X^758 + X^749 + X^740 + X^689 + X^685 + X^680 + 
    X^676 + X^671 + X^668 + X^667 + X^666 + X^664 + X^661 + X^658 + X^657 + 
    X^652 + X^648 + X^645 + X^643 + X^641 + X^640 + X^639 + X^630 + X^629 + 
    X^628 + X^626 + X^621 + X^620 + X^617 + X^615 + X^612 + X^610 + X^608 + 
    X^603 + X^598 + X^585 + X^584 + X^582 + X^580 + X^577 + X^575 + X^566 + 
    X^565 + X^564 + X^561 + X^559 + X^557 + X^547 + X^544 + X^543 + X^542 + 
    X^533 + X^531 + X^526 + X^524 + X^515 + X^514 + X^513 + X^510 + X^500 + 
    X^498 + X^496 + X^493 + X^492 + X^491 + X^482 + X^480 + X^477 + X^475 + 
    X^473 + X^472 + X^459 + X^454 + X^449 + X^447 + X^445 + X^442 + X^440 + 
    X^437 + X^436 + X^431 + X^429 + X^428 + X^427 + X^418 + X^417 + X^416 + 
    X^414 + X^412 + X^409 + X^405 + X^400 + X^399 + X^396 + X^393 + X^391 + 
    X^390 + X^389 + X^386 + X^381 + X^377 + X^372 + X^368 + X^317 + X^308 + 
    X^299 + X^296 + X^294 + X^293 + X^290 + X^285 + X^284 + X^276 + X^275 + 
    X^273 + X^272 + X^270 + X^267 + X^261 + X^260 + X^252 + X^249 + X^242 + 
    X^237 + X^230 + X^219 + X^212 + X^209 + X^207 + X^197 + X^191 + X^189 + 
    X^186 + X^179 + X^176 + X^174 + X^168 + X^158 + X^156 + X^153 + X^146 + 
    X^135 + X^128 + X^125 + X^123 + X^107 + X^105 + X^104 + X^102 + X^86 + X^84 
    + X^81 + X^77 + X^74 + X^68 + X^63 + X^59 + X^54 + X^51 + X^50 + X^45 + X^44
    + X^41 + X^36 + X^32 + X^27 + X^23 + X^21 + X^18 + X^9 + 1
X^1279 + X^1074 + X^1065 + X^1056 + X^1053 + X^1050 + X^1047 + X^1041 + X^1038 +
    X^1032 + X^1020 + X^1014 + X^1011 + X^1005 + X^999 + X^996 + X^993 + X^990 +
    X^987 + X^972 + X^966 + X^951 + X^948 + X^945 + X^939 + X^927 + X^921 + 
    X^918 + X^915 + X^906 + X^900 + X^897 + X^894 + X^888 + X^885 + X^882 + 
    X^876 + X^867 + X^864 + X^861 + X^855 + X^843 + X^837 + X^831 + X^825 + 
    X^822 + X^807 + X^804 + X^783 + X^777 + X^774 + X^765 + X^756 + X^702 + 
    X^693 + X^690 + X^684 + X^675 + X^672 + X^669 + X^666 + X^663 + X^657 + 
    X^651 + X^648 + X^633 + X^630 + X^612 + X^609 + X^606 + X^597 + X^594 + 
    X^591 + X^588 + X^576 + X^573 + X^570 + X^567 + X^558 + X^555 + X^552 + 
    X^540 + X^534 + X^522 + X^519 + X^516 + X^507 + X^504 + X^501 + X^498 + 
    X^486 + X^483 + X^480 + X^477 + X^468 + X^465 + X^462 + X^444 + X^441 + 
    X^426 + X^423 + X^417 + X^411 + X^408 + X^405 + X^402 + X^399 + X^390 + 
    X^384 + X^381 + X^372 + X^318 + X^309 + X^300 + X^297 + X^291 + X^270 + 
    X^267 + X^252 + X^249 + X^243 + X^237 + X^231 + X^219 + X^213 + X^210 + 
    X^207 + X^198 + X^192 + X^189 + X^186 + X^180 + X^177 + X^174 + X^168 + 
    X^159 + X^156 + X^153 + X^147 + X^135 + X^129 + X^126 + X^123 + X^108 + 
    X^102 + X^87 + X^84 + X^81 + X^78 + X^75 + X^69 + X^63 + X^60 + X^54 + X^42 
    + X^36 + X^33 + X^27 + X^24 + X^21 + X^18 + X^9 + 1
X^1279 + X^1103 + X^1091 + X^1084 + X^1079 + X^1077 + X^1073 + X^1072 + X^1067 +
    X^1065 + X^1061 + X^1060 + X^1058 + X^1055 + X^1054 + X^1053 + X^1049 + 
    X^1048 + X^1047 + X^1046 + X^1042 + X^1041 + X^1037 + X^1036 + X^1035 + 
    X^1034 + X^1030 + X^1029 + X^1028 + X^1027 + X^1025 + X^1023 + X^1022 + 
    X^1018 + X^1016 + X^1015 + X^1011 + X^1010 + X^1008 + X^1007 + X^1006 + 
    X^1004 + X^1003 + X^1001 + X^999 + X^997 + X^996 + X^995 + X^992 + X^991 + 
    X^989 + X^988 + X^985 + X^984 + X^983 + X^982 + X^981 + X^980 + X^979 + 
    X^978 + X^976 + X^973 + X^972 + X^970 + X^969 + X^966 + X^964 + X^962 + 
    X^961 + X^960 + X^957 + X^954 + X^950 + X^949 + X^947 + X^945 + X^942 + 
    X^941 + X^938 + X^935 + X^933 + X^931 + X^930 + X^929 + X^928 + X^926 + 
    X^925 + X^923 + X^922 + X^921 + X^919 + X^916 + X^914 + X^913 + X^912 + 
    X^910 + X^909 + X^907 + X^906 + X^905 + X^904 + X^902 + X^900 + X^897 + 
    X^894 + X^893 + X^890 + X^888 + X^886 + X^885 + X^881 + X^878 + X^874 + 
    X^873 + X^871 + X^869 + X^866 + X^865 + X^863 + X^862 + X^859 + X^857 + 
    X^855 + X^854 + X^853 + X^852 + X^851 + X^850 + X^849 + X^847 + X^846 + 
    X^845 + X^844 + X^843 + X^840 + X^839 + X^838 + X^836 + X^834 + X^832 + 
    X^831 + X^830 + X^829 + X^828 + X^827 + X^826 + X^825 + X^824 + X^820 + 
    X^817 + X^815 + X^813 + X^812 + X^810 + X^808 + X^807 + X^806 + X^805 + 
    X^801 + X^799 + X^798 + X^796 + X^794 + X^793 + X^788 + X^786 + X^785 + 
    X^782
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jun 25 10:09:29 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C := ((1 + X^12)^7)*((1 + X^19)^13)*((1 + X^26)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;
C := ((1 + X^13)^7)*((1 + X^17)^13)*((1 + X^27)^17)*((1 + X^30)^11)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;


Output: Magma V2.10-22    Fri Jun 25 2004 10:09:24 on modular  [Seed = 2805716477]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1103 + X^1091 + X^1084 + X^1079 + X^1077 + X^1073 + X^1072 + X^1067 +
    X^1065 + X^1061 + X^1060 + X^1058 + X^1055 + X^1054 + X^1053 + X^1049 + 
    X^1048 + X^1047 + X^1046 + X^1042 + X^1041 + X^1037 + X^1036 + X^1035 + 
    X^1034 + X^1030 + X^1029 + X^1028 + X^1027 + X^1025 + X^1023 + X^1022 + 
    X^1018 + X^1016 + X^1015 + X^1011 + X^1010 + X^1008 + X^1007 + X^1006 + 
    X^1004 + X^1003 + X^1001 + X^999 + X^997 + X^996 + X^995 + X^992 + X^991 + 
    X^989 + X^988 + X^985 + X^984 + X^983 + X^982 + X^981 + X^980 + X^979 + 
    X^978 + X^976 + X^973 + X^972 + X^970 + X^969 + X^966 + X^964 + X^962 + 
    X^961 + X^960 + X^957 + X^954 + X^950 + X^949 + X^947 + X^945 + X^942 + 
    X^941 + X^938 + X^935 + X^933 + X^931 + X^930 + X^929 + X^928 + X^926 + 
    X^925 + X^923 + X^922 + X^921 + X^919 + X^916 + X^914 + X^913 + X^912 + 
    X^910 + X^909 + X^907 + X^906 + X^905 + X^904 + X^902 + X^900 + X^897 + 
    X^894 + X^893 + X^890 + X^888 + X^886 + X^885 + X^881 + X^878 + X^874 + 
    X^873 + X^871 + X^869 + X^866 + X^865 + X^863 + X^862 + X^859 + X^857 + 
    X^855 + X^854 + X^853 + X^852 + X^851 + X^850 + X^849 + X^847 + X^846 + 
    X^845 + X^844 + X^843 + X^840 + X^839 + X^838 + X^836 + X^834 + X^832 + 
    X^831 + X^830 + X^829 + X^828 + X^827 + X^826 + X^825 + X^824 + X^820 + 
    X^817 + X^815 + X^813 + X^812 + X^810 + X^808 + X^807 + X^806 + X^805 + 
    X^801 + X^799 + X^798 + X^796 + X^794 + X^793 + X^788 + X^786 + X^785 + 
    X^782 + X^781 + X^780 + X^779 + X^777 + X^774 + X^766 + X^762 + X^761 + 
    X^760 + X^759 + X^758 + X^757 + X^753 + X^745 + X^742 + X^740 + X^739 + 
    X^738 + X^737 + X^734 + X^733 + X^731 + X^726 + X^725 + X^723 + X^721 + 
    X^720 + X^718 + X^714 + X^713 + X^712 + X^711 + X^709 + X^707 + X^706 + 
    X^704 + X^702 + X^699 + X^695 + X^694 + X^693 + X^692 + X^691 + X^690 + 
    X^689 + X^688 + X^685 + X^683 + X^681 + X^680 + X^679 + X^676 + X^674 + 
    X^673 + X^672 + X^670 + X^669 + X^667 + X^666 + X^665 + X^664 + X^663 + 
    X^662 + X^661 + X^660 + X^654 + X^653 + X^651 + X^650 + X^649 + X^648 + 
    X^646 + X^644 + X^642 + X^641 + X^639 + X^637 + X^634 + X^632 + X^630 + 
    X^629 + X^622 + X^621 + X^620 + X^618 + X^617 + X^615 + X^611 + X^610 + 
    X^605 + X^603 + X^602 + X^599 + X^598 + X^597 + X^596 + X^595 + X^593 + 
    X^592 + X^589 + X^587 + X^586 + X^585 + X^584 + X^583 + X^580 + X^579 + 
    X^578 + X^577 + X^576 + X^575 + X^574 + X^573 + X^570 + X^568 + X^567 + 
    X^566 + X^564 + X^563 + X^560 + X^559 + X^558 + X^556 + X^555 + X^554 + 
    X^549 + X^548 + X^547 + X^545 + X^544 + X^543 + X^540 + X^539 + X^537 + 
    X^536 + X^535 + X^533 + X^530 + X^529 + X^528 + X^527 + X^526 + X^525 + 
    X^524 + X^523 + X^520 + X^519 + X^518 + X^517 + X^516 + X^514 + X^511 + 
    X^510 + X^508 + X^507 + X^506 + X^505 + X^504 + X^501 + X^500 + X^498 + 
    X^493 + X^492 + X^488 + X^486 + X^485 + X^483 + X^482 + X^481 + X^474 + 
    X^473 + X^471 + X^469 + X^466 + X^464 + X^462 + X^461 + X^459 + X^457 + 
    X^455 + X^454 + X^453 + X^452 + X^450 + X^449 + X^443 + X^442 + X^441 + 
    X^440 + X^439 + X^438 + X^437 + X^436 + X^434 + X^433 + X^431 + X^430 + 
    X^429 + X^427 + X^424 + X^423 + X^422 + X^420 + X^418 + X^415 + X^414 + 
    X^413 + X^412 + X^411 + X^410 + X^409 + X^408 + X^404 + X^401 + X^399 + 
    X^397 + X^396 + X^394 + X^392 + X^391 + X^390 + X^389 + X^385 + X^383 + 
    X^382 + X^380 + X^378 + X^377 + X^372 + X^370 + X^369 + X^366 + X^365 + 
    X^364 + X^363 + X^361 + X^358 + X^350 + X^346 + X^345 + X^344 + X^343 + 
    X^342 + X^341 + X^337 + X^329 + X^326 + X^324 + X^323 + X^322 + X^321 + 
    X^318 + X^317 + X^315 + X^310 + X^309 + X^307 + X^305 + X^304 + X^302 + 
    X^298 + X^297 + X^296 + X^295 + X^293 + X^291 + X^290 + X^288 + X^286 + 
    X^283 + X^279 + X^278 + X^277 + X^276 + X^275 + X^274 + X^273 + X^272 + 
    X^271 + X^269 + X^267 + X^265 + X^264 + X^263 + X^260 + X^259 + X^258 + 
    X^257 + X^256 + X^254 + X^253 + X^252 + X^251 + X^250 + X^249 + X^248 + 
    X^246 + X^244 + X^241 + X^240 + X^238 + X^237 + X^234 + X^232 + X^230 + 
    X^229 + X^225 + X^222 + X^218 + X^217 + X^215 + X^213 + X^210 + X^209 + 
    X^206 + X^203 + X^201 + X^199 + X^198 + X^197 + X^196 + X^194 + X^193 + 
    X^191 + X^190 + X^189 + X^187 + X^184 + X^182 + X^181 + X^180 + X^178 + 
    X^177 + X^175 + X^174 + X^173 + X^172 + X^170 + X^168 + X^165 + X^162 + 
    X^161 + X^158 + X^156 + X^154 + X^153 + X^149 + X^146 + X^143 + X^142 + 
    X^141 + X^139 + X^137 + X^134 + X^133 + X^131 + X^130 + X^127 + X^125 + 
    X^124 + X^123 + X^122 + X^121 + X^120 + X^119 + X^118 + X^115 + X^114 + 
    X^112 + X^111 + X^108 + X^107 + X^106 + X^104 + X^102 + X^100 + X^99 + X^97 
    + X^96 + X^95 + X^93 + X^92 + X^88 + X^87 + X^85 + X^81 + X^80 + X^78 + X^76
    + X^75 + X^74 + X^73 + X^69 + X^68 + X^67 + X^66 + X^62 + X^61 + X^57 + X^56
    + X^55 + X^54 + X^50 + X^49 + X^48 + X^45 + X^43 + X^42 + X^38 + X^36 + X^31
    + X^30 + X^26 + X^24 + X^19 + X^12 + 1
X^1279 + X^1101 + X^1088 + X^1084 + X^1075 + X^1074 + X^1062 + X^1061 + X^1057 +
    X^1054 + X^1049 + X^1048 + X^1036 + X^1035 + X^1033 + X^1027 + X^1024 + 
    X^1023 + X^1022 + X^1020 + X^1016 + X^1010 + X^1009 + X^1007 + X^1006 + 
    X^997 + X^996 + X^993 + X^989 + X^986 + X^983 + X^965 + X^959 + X^956 + 
    X^953 + X^952 + X^950 + X^948 + X^939 + X^938 + X^925 + X^923 + X^921 + 
    X^920 + X^918 + X^916 + X^903 + X^902 + X^897 + X^893 + X^891 + X^889 + 
    X^888 + X^885 + X^884 + X^882 + X^880 + X^876 + X^871 + X^870 + X^861 + 
    X^857 + X^855 + X^853 + X^852 + X^850 + X^844 + X^825 + X^823 + X^822 + 
    X^820 + X^809 + X^796 + X^795 + X^793 + X^790 + X^783 + X^782 + X^777 + 
    X^770 + X^769 + X^764 + X^763 + X^756 + X^751 + X^750 + X^743 + X^740 + 
    X^738 + X^737 + X^724 + X^713 + X^711 + X^710 + X^708 + X^689 + X^683 + 
    X^681 + X^680 + X^678 + X^676 + X^672 + X^669 + X^663 + X^662 + X^657 + 
    X^656 + X^653 + X^652 + X^651 + X^649 + X^648 + X^645 + X^644 + X^643 + 
    X^640 + X^636 + X^631 + X^629 + X^625 + X^622 + X^616 + X^615 + X^613 + 
    X^612 + X^610 + X^608 + X^604 + X^603 + X^601 + X^594 + X^592 + X^591 + 
    X^590 + X^588 + X^585 + X^584 + X^583 + X^581 + X^580 + X^578 + X^575 + 
    X^568 + X^565 + X^564 + X^561 + X^557 + X^554 + X^551 + X^550 + X^547 + 
    X^544 + X^540 + X^537 + X^536 + X^533 + X^526 + X^523 + X^521 + X^520 + 
    X^518 + X^517 + X^516 + X^513 + X^511 + X^510 + X^509 + X^507 + X^500 + 
    X^498 + X^497 + X^493 + X^491 + X^489 + X^488 + X^486 + X^485 + X^479 + 
    X^476 + X^472 + X^470 + X^465 + X^461 + X^458 + X^457 + X^456 + X^453 + 
    X^452 + X^450 + X^449 + X^448 + X^445 + X^444 + X^439 + X^438 + X^432 + 
    X^429 + X^425 + X^423 + X^421 + X^420 + X^418 + X^412 + X^393 + X^391 + 
    X^390 + X^388 + X^377 + X^364 + X^363 + X^361 + X^358 + X^351 + X^350 + 
    X^345 + X^338 + X^337 + X^332 + X^331 + X^324 + X^319 + X^318 + X^311 + 
    X^308 + X^306 + X^305 + X^292 + X^281 + X^279 + X^278 + X^276 + X^257 + 
    X^251 + X^249 + X^248 + X^246 + X^244 + X^240 + X^231 + X^230 + X^225 + 
    X^221 + X^219 + X^217 + X^216 + X^213 + X^212 + X^210 + X^208 + X^204 + 
    X^199 + X^198 + X^185 + X^183 + X^181 + X^180 + X^178 + X^176 + X^163 + 
    X^162 + X^153 + X^151 + X^149 + X^148 + X^145 + X^142 + X^136 + X^118 + 
    X^115 + X^112 + X^108 + X^105 + X^104 + X^95 + X^94 + X^92 + X^91 + X^85 + 
    X^81 + X^79 + X^78 + X^77 + X^74 + X^68 + X^66 + X^65 + X^53 + X^52 + X^47 +
    X^44 + X^40 + X^39 + X^27 + X^26 + X^17 + X^13 + 1

Total time: 4.009 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 12:54:28 2004

Input: // compute first slopes

setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;


// compute conditions for NP through bendpoint.
// C is a set of coefficients.

comp:=function(g,C,bendpoint)
   print "Compute conditions for bending point",bendpoint;

   

   n:=bendpoint[2]; k:=bendpoint[1];
   Cmin:=Min(C);
   Cmax:=Max(C);
   RR<[A]>:=PolynomialRing(GF(2),Cmax);
   relation:=RR!0;
   i:=func<n,k | ((n-1) mod k) +1>;
   
   part:=Partitions(n);
   
   
   for p in part do
      if #p eq k then
   
         Bt:=[];result:=[];
   
         perm(p,result,~Bt);
         for B in Bt do
   
     
           print B;
     
           B2:=[2^b : b in B];
           R<[Cbound]>:=PolynomialRing(Rationals(),k);
           Abound:=[
              (&+[ case<j1 | 0 : 1,
                     default : (&*[B2[i(j+j2,k)] : j2 in [1..j1]])>
                  *Cbound[i(j+1+j1,k)]  : j1 in [0..k-1]])/(-1+&*B2)
                 : j in [1..k]];
     
     
           checklow:=function(count,ind,k)
              return count[ind] ge Evaluate(Abound[ind],[Cmin : j in [1..k]]);
           end function;
     
           checkup:=function(count,ind,k)
              return count[ind] le Evaluate(Abound[ind],[Cmax : j in [1..k]]);
           end function;
      
     
           procedure increase(~count,ind,k)
              if IsZero(ind) then count[1]:=0;
              else
                for j in [ind+1..k] do count[j]:=1; end for;
                repeat
                   count[ind]+:=2; 
                until checklow(count,ind,k); 
                if not checkup(count,ind,k) then
                   increase(~count,ind-1,k);
                end if;
              end if;
           end procedure;
     
     
     
     

           count:=[1 : j in [1..k]]; 
           repeat
              QQ:=[B2[i(j,k)]*count[i(j,k)]-count[i(j-1,k)] : j in [1..k]];
              if #{j : j in count} eq k and
                 {j : j in QQ} subset C
              then 
                 print [count,QQ],&*[A[j] : j in QQ];
                 relation+:=&*[A[j] : j in QQ];
              end if;
              increase(~count,k,k);
           until count[1] eq 0;
         end for;
      end if;
   end for;
     
   return relation;
   
   
end function;
   
comp(9,{1,9,19},[3,7]);

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 12:59:59 2004

Input: // compute first slopes

setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;


// compute conditions for NP through bendpoint.
// C is a set of coefficients.

comp:=function(g,C,bendpoint)
   print "Compute conditions for bending point",bendpoint;

   

   n:=bendpoint[2]; k:=bendpoint[1];
   Cmin:=Min(C);
   Cmax:=Max(C);
   RR<[A]>:=PolynomialRing(GF(2),Cmax);
   relation:=RR!0;
   i:=func<n,k | ((n-1) mod k) +1>;
   
   part:=Partitions(n);
   
   
   for p in part do
      if #p eq k then
   
         Bt:=[];result:=[];
   
         perm(p,result,~Bt);
         for B in Bt do
   
     
           print B;
     
           B2:=[2^b : b in B];
           R<[Cbound]>:=PolynomialRing(Rationals(),k);
           Abound:=[
              (&+[ case<j1 | 0 : 1,
                     default : (&*[B2[i(j+j2,k)] : j2 in [1..j1]])>
                  *Cbound[i(j+1+j1,k)]  : j1 in [0..k-1]])/(-1+&*B2)
                 : j in [1..k]];
     
     
           checklow:=function(count,ind,k)
              return count[ind] ge Evaluate(Abound[ind],[Cmin : j in [1..k]]);
           end function;
     
           checkup:=function(count,ind,k)
              return count[ind] le Evaluate(Abound[ind],[Cmax : j in [1..k]]);
           end function;
      
     
           procedure increase(~count,ind,k)
              if IsZero(ind) then count[1]:=0;
              else
                for j in [ind+1..k] do count[j]:=1; end for;
                repeat
                   count[ind]+:=2; 
                until checklow(count,ind,k); 
                if not checkup(count,ind,k) then
                   increase(~count,ind-1,k);
                end if;
              end if;
           end procedure;
     
     
     
     

           count:=[1 : j in [1..k]]; 
           repeat
              QQ:=[B2[i(j,k)]*count[i(j,k)]-count[i(j-1,k)] : j in [1..k]];
              if #{j : j in count} eq k and
                 {j : j in QQ} subset C
              then 
                 print [count,QQ],&*[A[j] : j in QQ];
                 relation+:=&*[A[j] : j in QQ];
              end if;
              increase(~count,k,k);
           until count[1] eq 0;
         end for;
      end if;
   end for;
     
   return relation;
   
   
end function;

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:00:22 2004

Input: // compute first slopes

setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;



Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:00:46 2004

Input: // compute first slopes

setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition


Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:01:59 2004

Input: A:={2,3};
Append(~A,9);
A;



Output: Magma V2.10-22    Fri Jun 25 2004 13:01:57 on modular  [Seed = 294456263]
   -------------------------------------


>> Append(~A,9);
         ^
Runtime error in 'Append': Bad argument types
Argument types given: SetEnum[RngIntElt] ~, RngIntElt
{ 2, 3 }

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:02:24 2004

Input: A:=[2,3];
Append(~A,9);
A;



Output: Magma V2.10-22    Fri Jun 25 2004 13:02:22 on modular  [Seed = 428147668]
   -------------------------------------

[ 2, 3, 9 ]

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:10:33 2004

Input: a:=function(b) return b+2; end function;

a(4);



Output: Magma V2.10-22    Fri Jun 25 2004 13:10:31 on modular  [Seed = 143922396]
   -------------------------------------

6

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:23:31 2004

Input: procedure a(b)
  print b;
end procedure;


Output: Magma V2.10-22    Fri Jun 25 2004 13:23:29 on modular  [Seed = 3728916764]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:23:45 2004

Input: procedure a(b)
  print b;
end procedure;

a(4);

Output: Magma V2.10-22    Fri Jun 25 2004 13:23:43 on modular  [Seed = 3327842570]
   -------------------------------------

4

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:24:42 2004

Input: procedure a(~b)
    b:=3;
end procedure;

a(4);

b;


Output: Magma V2.10-22    Fri Jun 25 2004 13:24:39 on modular  [Seed = 3444691529]
   -------------------------------------


>> a(4);
    ^
Runtime error in procedure call: Argument 1 must be a variable reference (use ~)

>> b;
   ^
User error: Identifier 'b' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 13:24:59 2004

Input: procedure a(~b)
    b:=3;
end procedure;

b:=5;
a(~b);

b;


Output: Magma V2.10-22    Fri Jun 25 2004 13:24:56 on modular  [Seed = 4100516687]
   -------------------------------------

3

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E690C8.dip.t-dialin.net. (217.230.144.200)
Time: Fri Jun 25 14:15:02 2004

Input: P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4));
D := QuadraticTwist(C,1);

Output: Magma V2.10-22    Fri Jun 25 2004 14:15:00 on modular  [Seed = 1794523546]
   -------------------------------------


Total time: 2.519 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host pD9E690C8.dip.t-dialin.net. (217.230.144.200)
Time: Fri Jun 25 14:15:21 2004

Input: m:=1;
upperBound:=10;
for p in [5..upperBound] do
if IsPrime(p) then
F<x> := PolynomialRing(FiniteField(p^m));
C := HyperellipticCurve(x^3-1);
#C;
end if;
end for;

Output: Magma V2.10-22    Fri Jun 25 2004 14:15:18 on modular  [Seed = 311310832]
   -------------------------------------

6
4

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E690C8.dip.t-dialin.net. (217.230.144.200)
Time: Fri Jun 25 14:15:33 2004

Input: m:=1;
upperBound:=20;
for p in [5..upperBound] do
if IsPrime(p) then
F<x> := PolynomialRing(FiniteField(p^m));
C := HyperellipticCurve(x^3-1);
#C;
end if;
end for;

Output: Magma V2.10-22    Fri Jun 25 2004 14:15:30 on modular  [Seed = 445002124]
   -------------------------------------

6
4
12
12
18
28

Total time: 2.489 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pD9E690C8.dip.t-dialin.net. (217.230.144.200)
Time: Fri Jun 25 14:15:44 2004

Input: m:=1;
upperBound:=200;
for p in [5..upperBound] do
if IsPrime(p) then
F<x> := PolynomialRing(FiniteField(p^m));
C := HyperellipticCurve(x^3-1);
#C;
end if;
end for;

Output: Magma V2.10-22    Fri Jun 25 2004 14:15:41 on modular  [Seed = 43919771]
   -------------------------------------

6
4
12
12
18
28
24
30
28
48
42
52
48
54
60
48
52
72
84
76
84
90
84
102
124
108
108
114
148
132
138
124
150
148
144
172
168
174
180
156
192
192
198
172

Total time: 2.559 seconds, Total memory usage: 2.20MB


************** MAGMA *****************
Host pD9E690C8.dip.t-dialin.net. (217.230.144.200)
Time: Fri Jun 25 14:16:03 2004

Input: F<x> := PolynomialRing(FiniteField(7));
C := HyperellipticCurve(x^3-1);
ZetaFunction(C);

Output: Magma V2.10-22    Fri Jun 25 2004 14:16:01 on modular  [Seed = 194453694]
   -------------------------------------

(7*$.1^2 - 4*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1)

Total time: 2.479 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9E690C8.dip.t-dialin.net. (217.230.144.200)
Time: Fri Jun 25 14:16:16 2004

Input: F<x> := PolynomialRing(FiniteField(7));
C := HyperellipticCurve(x^3-1);
ZetaFunction(C,x);

Output: Magma V2.10-22    Fri Jun 25 2004 14:16:13 on modular  [Seed = 867113098]
   -------------------------------------


>> ZetaFunction(C,x);;
               ^
Runtime error in 'ZetaFunction': Bad argument types
Argument types given: CrvHyp, RngUPolElt

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 14:54:55 2004

Input: 
setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;

setslopes(9);

Output: Magma V2.10-22    Fri Jun 25 2004 14:54:53 on modular  [Seed = 2333589282]
   -------------------------------------

[
    [ 1, 9 ],
    [ 1, 8 ],
    [ 1, 7 ],
    [ 1, 6 ],
    [ 1, 5 ],
    [ 2, 9 ],
    [ 1, 4 ],
    [ 2, 8 ],
    [ 2, 7 ],
    [ 1, 3 ],
    [ 2, 6 ],
    [ 3, 9 ],
    [ 3, 8 ],
    [ 2, 5 ],
    [ 3, 7 ],
    [ 4, 9 ]
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 14:55:31 2004

Input: setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;

setslopes(9);

Output: Magma V2.10-22    Fri Jun 25 2004 14:55:28 on modular  [Seed = 3006236359]
   -------------------------------------

[
    [ 1, 9 ],
    [ 1, 8 ],
    [ 1, 7 ],
    [ 1, 6 ],
    [ 1, 5 ],
    [ 2, 9 ],
    [ 1, 4 ],
    [ 2, 8 ],
    [ 2, 7 ],
    [ 1, 3 ],
    [ 2, 6 ],
    [ 3, 9 ],
    [ 3, 8 ],
    [ 2, 5 ],
    [ 3, 7 ],
    [ 4, 9 ]
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 14:55:47 2004

Input: setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;

setslopes(9);

Output: Magma V2.10-22    Fri Jun 25 2004 14:55:44 on modular  [Seed = 3139931871]
   -------------------------------------

[
    [ 1, 9 ],
    [ 1, 8 ],
    [ 1, 7 ],
    [ 1, 6 ],
    [ 1, 5 ],
    [ 2, 9 ],
    [ 1, 4 ],
    [ 2, 8 ],
    [ 2, 7 ],
    [ 1, 3 ],
    [ 2, 6 ],
    [ 3, 9 ],
    [ 3, 8 ],
    [ 2, 5 ],
    [ 3, 7 ],
    [ 4, 9 ]
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 14:57:21 2004

Input: setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;

setslopes(9);
result:=[];Bt:=[];
perm({2,3,4,4,5},result,~Bt);


Output: Magma V2.10-22    Fri Jun 25 2004 14:57:18 on modular  [Seed = 2905708663]
   -------------------------------------

[
    [ 1, 9 ],
    [ 1, 8 ],
    [ 1, 7 ],
    [ 1, 6 ],
    [ 1, 5 ],
    [ 2, 9 ],
    [ 1, 4 ],
    [ 2, 8 ],
    [ 2, 7 ],
    [ 1, 3 ],
    [ 2, 6 ],
    [ 3, 9 ],
    [ 3, 8 ],
    [ 2, 5 ],
    [ 3, 7 ],
    [ 4, 9 ]
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 14:57:37 2004

Input: setslopes:=function(g)   
  slopes:=[];
  slopesset:={a/b : a in [1..Floor((b-1)/2)], b in [1..g]};
  repeat 
    n:=Denominator(Min(slopesset));
    k:=Numerator(Min(slopesset));
    j:=1;
    while j*n le g do
       Append(~slopes,[j*k,j*n]);
       j+:=1;
    end while; 
    Exclude(~slopesset,Min(slopesset));
  until IsZero(#slopesset);
  return slopes;
end function;



// create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;

setslopes(9);
result:=[];Bt:=[];
perm({2,3,4,4,5},result,~Bt);
Bt;

Output: Magma V2.10-22    Fri Jun 25 2004 14:57:35 on modular  [Seed = 1422418334]
   -------------------------------------

[
    [ 1, 9 ],
    [ 1, 8 ],
    [ 1, 7 ],
    [ 1, 6 ],
    [ 1, 5 ],
    [ 2, 9 ],
    [ 1, 4 ],
    [ 2, 8 ],
    [ 2, 7 ],
    [ 1, 3 ],
    [ 2, 6 ],
    [ 3, 9 ],
    [ 3, 8 ],
    [ 2, 5 ],
    [ 3, 7 ],
    [ 4, 9 ]
]
[
    [ 2, 3, 4, 5 ],
    [ 2, 3, 5, 4 ],
    [ 2, 4, 3, 5 ],
    [ 2, 4, 5, 3 ],
    [ 2, 5, 3, 4 ],
    [ 2, 5, 4, 3 ]
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129)
Time: Fri Jun 25 14:58:21 2004

Input: // create a list of all relevant permutations of a partition

procedure perm(par,result,~Bt)  
   if IsZero(#result) then      
      parset:={Min(par)};
   else
      parset:=Set(par);
      if (#parset eq 2) and (result[1] in  parset) then
         if #Set(Exclude(par,Max(parset))) eq 1 then
            parset:={result[1]};
         end if;
      end if;
   end if;

   for j in parset do
      par2:=Exclude(par,j);
      result2:=Append(result,j);
      if IsZero(#par2) then
        Append(~Bt,result2);
      else 
        perm(par2,result2,~Bt);
      end if;
   end for; 
end procedure;


// compute conditions for NP through bendpoint.
// C is a set of coefficients.

comp:=function(g,C,bendpoint)
   print "Compute conditions for bending point",bendpoint;

   

   n:=bendpoint[2]; k:=bendpoint[1];
   Cmin:=Min(C);
   Cmax:=Max(C);
   RR<[A]>:=PolynomialRing(GF(2),Cmax);
   relation:=RR!0;
   i:=func<n,k | ((n-1) mod k) +1>;
   
   part:=Partitions(n);
   
   
   for p in part do
      if #p eq k then
   
         Bt:=[];result:=[];
   
         perm(p,result,~Bt);
         for B in Bt do
   
     
           print B;
     
           B2:=[2^b : b in B];
           R<[Cbound]>:=PolynomialRing(Rationals(),k);
           Abound:=[
              (&+[ case<j1 | 0 : 1,
                     default : (&*[B2[i(j+j2,k)] : j2 in [1..j1]])>
                  *Cbound[i(j+1+j1,k)]  : j1 in [0..k-1]])/(-1+&*B2)
                 : j in [1..k]];
     
     
           checklow:=function(count,ind,k)
              return count[ind] ge Evaluate(Abound[ind],[Cmin : j in [1..k]]);
           end function;
     
           checkup:=function(count,ind,k)
              return count[ind] le Evaluate(Abound[ind],[Cmax : j in [1..k]]);
           end function;
      
     
           procedure increase(~count,ind,k)
              if IsZero(ind) then count[1]:=0;
              else
                for j in [ind+1..k] do count[j]:=1; end for;
                repeat
                   count[ind]+:=2; 
                until checklow(count,ind,k); 
                if not checkup(count,ind,k) then
                   increase(~count,ind-1,k);
                end if;
              end if;
           end procedure;
     
     
     
     

           count:=[1 : j in [1..k]]; 
           repeat
              QQ:=[B2[i(j,k)]*count[i(j,k)]-count[i(j-1,k)] : j in [1..k]];
              if #{j : j in count} eq k and
                 {j : j in QQ} subset C
              then 
                 print [count,QQ],&*[A[j] : j in QQ];
                 relation+:=&*[A[j] : j in QQ];
              end if;
              increase(~count,k,k);
           until count[1] eq 0;
         end for;
      end if;
   end for;
     
   return relation;
   
   
end function;
   
   



Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host 3(NXDOMAIN) (203.195.105.34)
Time: Fri Jun 25 17:14:44 2004

Input: fsolve(poly(cos(Pi/13)))

Output: Magma V2.10-22    Fri Jun 25 2004 17:14:41 on modular  [Seed = 2838854719]
   -------------------------------------


>> fsolve(poly(cos(Pi/13)));
               ^
User error: Identifier 'cos' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-67-174-181-202.client.comcast.net. (67.174.181.202)
Time: Fri Jun 25 19:12:07 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Fri Jun 25 2004 19:12:04 on modular  [Seed = 2111933539]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-67-174-181-202.client.comcast.net. (67.174.181.202)
Time: Fri Jun 25 19:12:15 2004

Input: 2+3

Output: Magma V2.10-22    Fri Jun 25 2004 19:12:12 on modular  [Seed = 1978238051]
   -------------------------------------

5

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-67-174-181-202.client.comcast.net. (67.174.181.202)
Time: Fri Jun 25 19:12:27 2004

Input: NullSpace(A)

Output: Magma V2.10-22    Fri Jun 25 2004 19:12:25 on modular  [Seed = 1844550766]
   -------------------------------------


>> NullSpace(A);
             ^
User error: Identifier 'A' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9535ECF.dip.t-dialin.net. (217.83.94.207)
Time: Fri Jun 25 19:38:09 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
F;
Order(F);

Output: Magma V2.10-22    Fri Jun 25 2004 19:38:05 on modular  [Seed = 733469740]
   -------------------------------------

Finitely presented group F on 2 generators
Relations
    a * b * a = b * a * b
    a^4 = Id(F)
96

Total time: 4.109 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535ECF.dip.t-dialin.net. (217.83.94.207)
Time: Fri Jun 25 19:38:29 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
F;
Order(F);

Output: Magma V2.10-22    Fri Jun 25 2004 19:38:26 on modular  [Seed = 599774219]
   -------------------------------------

Finitely presented group F on 2 generators
Relations
    a * b * a = b * a * b
    a^3 = Id(F)
24

Total time: 2.619 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535ECF.dip.t-dialin.net. (217.83.94.207)
Time: Fri Jun 25 19:38:39 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2>;
F;
Order(F);

Output: Magma V2.10-22    Fri Jun 25 2004 19:38:36 on modular  [Seed = 3678874877]
   -------------------------------------

Finitely presented group F on 2 generators
Relations
    a * b * a = b * a * b
    a^2 = Id(F)
6

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535ECF.dip.t-dialin.net. (217.83.94.207)
Time: Fri Jun 25 19:38:47 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^5>;
F;
Order(F);

Output: Magma V2.10-22    Fri Jun 25 2004 19:38:44 on modular  [Seed = 3545179149]
   -------------------------------------

Finitely presented group F on 2 generators
Relations
    a * b * a = b * a * b
    a^5 = Id(F)
600

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535ECF.dip.t-dialin.net. (217.83.94.207)
Time: Fri Jun 25 19:39:55 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
F;
Order(F);

Output: Magma V2.10-22    Fri Jun 25 2004 19:39:50 on modular  [Seed = 3411491927]
   -------------------------------------

Finitely presented group F on 2 generators
Relations
    a * b * a = b * a * b
    a^6 = Id(F)
0

Total time: 5.549 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host matist-207.science.ankara.edu.tr. (80.251.35.207)
Time: Sat Jun 26 07:49:23 2004

Input: restore "g2.ws";
echpar:=-1;
h11 := sub<g |a2,a1*a2*a1>;
print "W(J) kesisim W(J')",#(h meet h11);
subgp := procedure( gss, gsn, gsl, h11, ~h11ss, ~h11sn, ~h11sl )
        h11ss := [];
        h11sn := [];
        h11sl := [];
        for i := 1 to #(gss)  do
                if  gss[i] in h11  then
                        h11ss := h11ss cat [gss[i]];
                        h11sn := h11sn cat [gsn[i]];
                        h11sl := h11sl cat [gsl[i]];
                end if;
        end for;
end procedure;
organ := procedure( g,h11ss,gss, h11, ~ntrl, ~h11cos )
        ntrl := [];
        h11cos := [];
        g1 := {  };
        for i := 1 to #(gss)  do
                h1:={}; 
                z := gss[i];
                if not (z in g1) then
                        for j:=1 to #(h11ss) do
                        z1:=h11ss[j]*z;
                        h1:=h1 join {z1};
                        end for;
                        h11cos := h11cos cat [h1];
                        ntrl := ntrl cat [z];
                        g1 := g1 join h1;
                end if;
        end for;
end procedure;
subgp( gss, gsn, gsl, h11, ~h11ss, ~h11sn, ~h11sl );
organ ( g,h11ss,gss, h11, ~ntrl, ~h11cos );
vclst := [];
gplst := [];
for i := 1 to #(ntrl)  do
        gg := ntrl[i];
        cst:={};     
   for j:=1 to #(hss) do
        z2:= hss[j]*gg;    
        cst := cst join {z2};
    end for;    
        ww := zz;
        h12 := h11^gg;
        for x in h12 do
           cst2:=Setseq(cst); 
           cst1:={};
           for k:=1 to #(cst2) do
               z3:= cst2[k]*x;     
               cst1 := cst1 join {z3};
           end for;    
               pos := Position(hcos,cst1);
                if pos eq 0 then
                       print "error";
                else
                        pos1 := Position(gss, x);
                if (gsn[pos1] mod 2) eq 0 then
                                ww[pos] := ww[pos]+1;
                            else
                                ww[pos] := ww[pos]-1;
                end if;
            end if;     
      end for;
        vclst := vclst cat [ww];
        pos := Position(gss, gg);
        gplst := gplst cat [gsl[pos]];
end for;
ms :=  sub< vs | zz >;
vc1set := {  };
vc1lst := [];
msdim := 0;
for i := 1 to #(vclst)  do
        ww := vclst[i];
        ms := sub< vs | ms, ww >;
        msd := Dimension(ms);
        if msd gt msdim then
                msdim := msd;
                vc1set := vc1set join { vclst[i] };
                vc1lst := vc1lst cat [vclst[i]];
        end if;
end for;
vsb := sub< vs | vc1set >;
n := Dimension(vsb);
if echpar eq 0 then
        echa := EchelonForm(vc1set);
else
        newech( vc1lst, m, k, ~echa );
end if;
vsa := VectorSpace(k,n);
glva := GeneralLinearGroup(vsa);
mats := [];
for i := 1 to n  do
        coords( vc1lst[i], echa, m, vsa, k, n, ~vco, ~sco );
        mats := mats cat sco;
end for;
mata := glva!mats;
mata := mata^(-1);
gs1q := [];
for i := 1 to #(gsq)  do
        mats := [];
        for j := 1 to n  do
                vn := vc1lst[j]*gsq[i];
                coords( vn, echa, m, vsa, k, n, ~vco, ~sco );
                vn := vco*mata;
                for jj := 1 to n  do
                        sco[jj] := vn[jj];
                end for;
                mats := mats cat sco;
        end for;
        matg := glva!mats;
        gs1q := gs1q cat [matg];
end for;
cls := Classes(g);
fi := hom< g -> glv |gsq>;
fia := hom< g -> glva |gs1q>;
print "generators of subgroup h11";
for x in Generators(h11) do
        pos := Position(gss, x);
        print gsl[pos];
end for;
print" __________________________";
d1 := Seqset(trl);
d2 := Seqset(ntrl);
d3 := d1 meet d2;
K:=Classes(g);
for i:=1 to #(K) do
    gg:=K[i,3];
        pos := Position(gss, gg);
        print gsl[pos], Trace(fi(gg)), Trace((gg) @ fia);
end for;
print" __________________________";
if #(d3) eq n then
        print " H , H11  IS A PERFECT SYSTEM";
end if;
quit;



Output: WARNING: MAGMA command contains unsafe command 'system', so it will not be executed.

************** MAGMA *****************
Host KHP222009073098.ppp-bb.dion.ne.jp. (222.9.73.98)
Time: Sat Jun 26 10:39:01 2004

Input: x:=13;
y := x^2-2;
x, y;

Output: Magma V2.10-22    Sat Jun 26 2004 10:38:59 on modular  [Seed = 1556190905]
   -------------------------------------

13 167

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host KHP222009073098.ppp-bb.dion.ne.jp. (222.9.73.98)
Time: Sat Jun 26 10:39:46 2004

Input:  s := [ [1], [1, 2], [1, 2, 3] ];
s;

Output: Magma V2.10-22    Sat Jun 26 2004 10:39:43 on modular  [Seed = 632877036]
   -------------------------------------

[
    [ 1 ],
    [ 1, 2 ],
    [ 1, 2, 3 ]
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE0006258f7ffc-CM000f9f54e45c.cpe.net.cable.rogers.com. (69.198.148.130)
Time: Sat Jun 26 12:32:52 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sat Jun 26 2004 12:32:49 on modular  [Seed = 4084078245]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.117.66.246)
Time: Sat Jun 26 13:26:28 2004

Input: arcsin30

Output: Magma V2.10-22    Sat Jun 26 2004 13:26:26 on modular  [Seed = 1539746545]
   -------------------------------------


>> arcsin30;
   ^
User error: Identifier 'arcsin30' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E51A42.dip.t-dialin.net. (217.229.26.66)
Time: Sat Jun 26 14:55:31 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*a*b*b>;
Index(F,G);
Order(F);

Output: Magma V2.10-22    Sat Jun 26 2004 14:55:28 on modular  [Seed = 3595259934]
   -------------------------------------

24
96

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A42.dip.t-dialin.net. (217.229.26.66)
Time: Sat Jun 26 14:56:06 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*a*b*b>;
Index(F,G);
Order(F);
5/6;


Output: Magma V2.10-22    Sat Jun 26 2004 14:56:04 on modular  [Seed = 2922588162]
   -------------------------------------

24
96
5/6

Total time: 2.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A42.dip.t-dialin.net. (217.229.26.66)
Time: Sat Jun 26 14:56:28 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*a*b*b>;
Order(F)/Index(F,G);


Output: Magma V2.10-22    Sat Jun 26 2004 14:56:26 on modular  [Seed = 2788892692]
   -------------------------------------

4

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A42.dip.t-dialin.net. (217.229.26.66)
Time: Sat Jun 26 14:56:50 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*a*b*b*a*a*b*b>;
Order(F)/Index(F,G);


Output: Magma V2.10-22    Sat Jun 26 2004 14:56:47 on modular  [Seed = 3189979193]
   -------------------------------------

2

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A42.dip.t-dialin.net. (217.229.26.66)
Time: Sat Jun 26 14:57:02 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a>;
Order(F)/Index(F,G);


Output: Magma V2.10-22    Sat Jun 26 2004 14:56:59 on modular  [Seed = 3056283685]
   -------------------------------------

4

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A42.dip.t-dialin.net. (217.229.26.66)
Time: Sat Jun 26 14:57:12 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b>;
Order(F)/Index(F,G);


Output: Magma V2.10-22    Sat Jun 26 2004 14:57:09 on modular  [Seed = 2383612387]
   -------------------------------------

12

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host c-24-14-71-44.client.comcast.net. (24.14.71.44)
Time: Sat Jun 26 19:00:02 2004

Input: G:=CongruenceSubgroup(5);
Index(G);


Output: Magma V2.10-22    Sat Jun 26 2004 18:59:58 on modular  [Seed = 110868867]
   -------------------------------------

60

Total time: 3.679 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host c-24-14-71-44.client.comcast.net. (24.14.71.44)
Time: Sat Jun 26 19:01:05 2004

Input: G:=CongruenceSubgroup(25);
Index(G);


Output: Magma V2.10-22    Sat Jun 26 2004 19:00:43 on modular  [Seed = 3799818898]
   -------------------------------------



************** MAGMA *****************
Host dsl-linz7-17-188.utaonline.at. (81.189.17.188)
Time: Sat Jun 26 19:22:21 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sat Jun 26 2004 19:22:18 on modular  [Seed = 2283195848]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-66-123-238-155.dsl.snfc21.pacbell.net. (66.123.238.155)
Time: Sun Jun 27 16:39:12 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sun Jun 27 2004 16:39:09 on modular  [Seed = 2199712658]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host opac15.cie.bib.uab.es. (158.109.53.68)
Time: Mon Jun 28 05:22:14 2004

Input: Matrix([1,1,1],[2,2,3]);

Output: Magma V2.10-22    Mon Jun 28 2004 05:22:11 on modular  [Seed = 1405939733]
   -------------------------------------


>> Matrix([1,1,1],[2,2,3]);;
         ^
Runtime error in 'Matrix': Bad argument types
Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host opac15.cie.bib.uab.es. (158.109.53.68)
Time: Mon Jun 28 05:22:41 2004

Input: Matrix({[1,1,1],[2,2,3]});

Output: Magma V2.10-22    Mon Jun 28 2004 05:22:38 on modular  [Seed = 1710933566]
   -------------------------------------


>> Matrix({[1,1,1],[2,2,3]});;
         ^
Runtime error in 'Matrix': Bad argument types
Argument types given: SetEnum[SeqEnum]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host opac15.cie.bib.uab.es. (158.109.53.68)
Time: Mon Jun 28 05:23:05 2004

Input: Matrix([[1,1,1],[2,2,3]]);

Output: Magma V2.10-22    Mon Jun 28 2004 05:23:02 on modular  [Seed = 1878051868]
   -------------------------------------

[1 1 1]
[2 2 3]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host opac15.cie.bib.uab.es. (158.109.53.68)
Time: Mon Jun 28 05:23:34 2004

Input: Matrix([[1-x,1-y,1-z],[2-x,2-y,3-z]]);

Output: Magma V2.10-22    Mon Jun 28 2004 05:23:32 on modular  [Seed = 2011747558]
   -------------------------------------


>> Matrix([[1-x,1-y,1-z],[2-x,2-y,3-z]]);;
              ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:03:53 2004

Input: F<a,b>=Group<a,b|a*b*a=b*a*b,a^6>;
a^6;
G<x>=sub<F|a*b>;
Index(F,G);

Output: Magma V2.10-22    Mon Jun 28 2004 07:03:49 on modular  [Seed = 227718672]
   -------------------------------------


>> F<a,b>=Group<a,b|a*b*a=b*a*b,a^6>;
         ^
User error: bad syntax

>> a^6;
   ^
User error: Identifier 'a' has not been declared or assigned

>> G<x>=sub<F|a*b>;
       ^
User error: bad syntax

>> Index(F,G);;
         ^
User error: Identifier 'F' has not been declared or assigned

Total time: 2.619 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:04:07 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
a^6;
G<x>:=sub<F|a*b>;
Index(F,G);

Output: Magma V2.10-22    Mon Jun 28 2004 07:04:02 on modular  [Seed = 94027311]
   -------------------------------------

a^6
0

Total time: 4.969 seconds, Total memory usage: 29.67MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:09:10 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
a^6;
G<x>:=sub<F|a*b>;
Index(F,G);
H:=RWSGroup(F);
H;

Output: Magma V2.10-22    Mon Jun 28 2004 07:08:47 on modular  [Seed = 394832672]
   -------------------------------------

a^6
0
Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:10:13 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
H:=RWSGroup(F);
H;

Output: Magma V2.10-22    Mon Jun 28 2004 07:10:11 on modular  [Seed = 566140346]
   -------------------------------------

Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0
#System is confluent.
#Halting with 35 equations.
A confluent rewrite group.
Generator Ordering = [ $.1, $.1^-1, $.2, $.2^-1 ]
Ordering = ShortLex.
The reduction machine has 44 states.
    $.1 * $.1^-1 = Id($)
    $.1^-1 * $.1 = Id($)
    $.2 * $.2^-1 = Id($)
    $.2^-1 * $.2 = Id($)
    $.2 * $.1 * $.2 = $.1 * $.2 * $.1
    $.1^3 = $.1^-1
    $.1^$.2 = $.1 * $.2 * $.1^-1
    $.1^-2 = $.1^2
    $.2 * $.1 * $.2^-1 = $.2^$.1
    $.2^-1 * $.1^-1 * $.2 = $.1 * $.2^-1 * $.1^-1
    $.2 * $.1^-1 * $.2^-1 = $.1^-1 * $.2^-1 * $.1
    $.2^-1 * $.1^-1 * $.2^-1 = $.1^-1 * $.2^-1 * $.1^-1
    $.2 * $.1^2 * $.2 * $.1 = $.1 * $.2 * $.1^2 * $.2
    $.2 * $.1^2 * $.2 * $.1^-1 = $.1^-1 * $.2 * $.1^2 * $.2
    ($.2 * $.1 * $.2^-1)^2 = ($.1^-1 * $.2 * $.1)^2
    ($.2^-1 * $.1 * $.2)^2 = ($.1 * $.2 * $.1^-1)^2
    $.2^-2 = $.2^2
    $.2^3 = $.2^-1
    $.2^-1 * $.1^2 * $.2^-1 * $.1 = $.1 * $.2^-1 * $.1^2 * $.2^-1
    $.2^-1 * $.1^2 * $.2^-1 * $.1^-1 = $.1^-1 * $.2^-1 * $.1^2 * $.2^-1
    $.2 * $.1^2 * $.2^2 = $.1^-1 * $.2 * $.1^-1 * $.2 * $.1
    $.2 * $.1^-1 * $.2 * $.1^2 * $.2 = $.1 * $.2 * $.1^-1 * $.2 * $.1^2
    $.2^2 * $.1^2 * $.2 = $.1 * $.2 * $.1^-1 * $.2 * $.1^-1
    ($.2 * $.1^-1)^3 = ($.1 * $.2^-1)^3
    $.2 * $.1^-1 * $.2 * $.1^-1 * $.2 * $.1 = $.1 * $.2 * $.1^-1 * $.2 * $.1^-1 
        * $.2
    $.2^2 * $.1^-1 * $.2 * $.1 = $.2^-1 * $.1 * $.2^-1
    $.2^-1 * $.1 * $.2^-1 * $.1^-1 = $.2^2 * $.1^-1 * $.2
    $.2 * $.1^-1 * $.2^2 = $.1^-1 * $.2^-1 * $.1 * $.2^-1
    $.2^-1 * $.1 * $.2^-1 * $.1^2 = $.2^2 * $.1^-1 * $.2 * $.1^-1
    ($.1^-1 * $.2)^3 = ($.1 * $.2^-1)^3
    $.1^2 * $.2^-1 * $.1 * $.2^-1 * $.1 * $.2^-1 = $.2 * $.1^-1 * $.2 * $.1^-1 *
        $.2
    ($.2^-1 * $.1)^3 = ($.1 * $.2^-1)^3
    $.1^2 * $.2 * $.1^-1 * $.2 * $.1^-1 * $.2 = $.2^-1 * $.1 * $.2^-1 * $.1 * 
        $.2^-1
    $.1^-1 * $.2^-1 * $.1 * $.2^-1 * $.1 * $.2^-1 = $.1 * $.2 * $.1^-1 * $.2 * 
        $.1^-1 * $.2
    $.2^2 * $.1^-1 * $.2 * $.1^-1 * $.2 = $.1 * $.2^2 * $.1^-1 * $.2 * $.1^-1


Total time: 2.549 seconds, Total memory usage: 4.72MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:11:39 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^4>;
H:=RWSGroup(F);
H;

Output: Magma V2.10-22    Mon Jun 28 2004 07:11:36 on modular  [Seed = 1000638427]
   -------------------------------------

Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0
#System is confluent.
#Halting with 35 equations.
A confluent rewrite group.
Generator Ordering = [ a, a^-1, b, b^-1 ]
Ordering = ShortLex.
The reduction machine has 44 states.
    a * a^-1 = Id(FG)
    a^-1 * a = Id(FG)
    b * b^-1 = Id(FG)
    b^-1 * b = Id(FG)
    b * a * b = a * b * a
    a^3 = a^-1
    a^b = a * b * a^-1
    a^-2 = a^2
    b * a * b^-1 = b^a
    b^-1 * a^-1 * b = a * b^-1 * a^-1
    b * a^-1 * b^-1 = a^-1 * b^-1 * a
    b^-1 * a^-1 * b^-1 = a^-1 * b^-1 * a^-1
    b * a^2 * b * a = a * b * a^2 * b
    b * a^2 * b * a^-1 = a^-1 * b * a^2 * b
    (b * a * b^-1)^2 = (a^-1 * b * a)^2
    (b^-1 * a * b)^2 = (a * b * a^-1)^2
    b^-2 = b^2
    b^3 = b^-1
    b^-1 * a^2 * b^-1 * a = a * b^-1 * a^2 * b^-1
    b^-1 * a^2 * b^-1 * a^-1 = a^-1 * b^-1 * a^2 * b^-1
    b * a^2 * b^2 = a^-1 * b * a^-1 * b * a
    b * a^-1 * b * a^2 * b = a * b * a^-1 * b * a^2
    b^2 * a^2 * b = a * b * a^-1 * b * a^-1
    (b * a^-1)^3 = (a * b^-1)^3
    b * a^-1 * b * a^-1 * b * a = a * b * a^-1 * b * a^-1 * b
    b^2 * a^-1 * b * a = b^-1 * a * b^-1
    b^-1 * a * b^-1 * a^-1 = b^2 * a^-1 * b
    b * a^-1 * b^2 = a^-1 * b^-1 * a * b^-1
    b^-1 * a * b^-1 * a^2 = b^2 * a^-1 * b * a^-1
    (a^-1 * b)^3 = (a * b^-1)^3
    a^2 * b^-1 * a * b^-1 * a * b^-1 = b * a^-1 * b * a^-1 * b
    (b^-1 * a)^3 = (a * b^-1)^3
    a^2 * b * a^-1 * b * a^-1 * b = b^-1 * a * b^-1 * a * b^-1
    a^-1 * b^-1 * a * b^-1 * a * b^-1 = a * b * a^-1 * b * a^-1 * b
    b^2 * a^-1 * b * a^-1 * b = a * b^2 * a^-1 * b * a^-1


Total time: 2.529 seconds, Total memory usage: 4.71MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:12:46 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^4>;
H:=RWSGroup(F);
H;
Order(F);
Order(H);

Output: Magma V2.10-22    Mon Jun 28 2004 07:12:43 on modular  [Seed = 900368406]
   -------------------------------------

Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0
#System is confluent.
#Halting with 35 equations.
A confluent rewrite group.
Generator Ordering = [ a, a^-1, b, b^-1 ]
Ordering = ShortLex.
The reduction machine has 44 states.
    a * a^-1 = Id(FG)
    a^-1 * a = Id(FG)
    b * b^-1 = Id(FG)
    b^-1 * b = Id(FG)
    b * a * b = a * b * a
    a^3 = a^-1
    a^b = a * b * a^-1
    a^-2 = a^2
    b * a * b^-1 = b^a
    b^-1 * a^-1 * b = a * b^-1 * a^-1
    b * a^-1 * b^-1 = a^-1 * b^-1 * a
    b^-1 * a^-1 * b^-1 = a^-1 * b^-1 * a^-1
    b * a^2 * b * a = a * b * a^2 * b
    b * a^2 * b * a^-1 = a^-1 * b * a^2 * b
    (b * a * b^-1)^2 = (a^-1 * b * a)^2
    (b^-1 * a * b)^2 = (a * b * a^-1)^2
    b^-2 = b^2
    b^3 = b^-1
    b^-1 * a^2 * b^-1 * a = a * b^-1 * a^2 * b^-1
    b^-1 * a^2 * b^-1 * a^-1 = a^-1 * b^-1 * a^2 * b^-1
    b * a^2 * b^2 = a^-1 * b * a^-1 * b * a
    b * a^-1 * b * a^2 * b = a * b * a^-1 * b * a^2
    b^2 * a^2 * b = a * b * a^-1 * b * a^-1
    (b * a^-1)^3 = (a * b^-1)^3
    b * a^-1 * b * a^-1 * b * a = a * b * a^-1 * b * a^-1 * b
    b^2 * a^-1 * b * a = b^-1 * a * b^-1
    b^-1 * a * b^-1 * a^-1 = b^2 * a^-1 * b
    b * a^-1 * b^2 = a^-1 * b^-1 * a * b^-1
    b^-1 * a * b^-1 * a^2 = b^2 * a^-1 * b * a^-1
    (a^-1 * b)^3 = (a * b^-1)^3
    a^2 * b^-1 * a * b^-1 * a * b^-1 = b * a^-1 * b * a^-1 * b
    (b^-1 * a)^3 = (a * b^-1)^3
    a^2 * b * a^-1 * b * a^-1 * b = b^-1 * a * b^-1 * a * b^-1
    a^-1 * b^-1 * a * b^-1 * a * b^-1 = a * b * a^-1 * b * a^-1 * b
    b^2 * a^-1 * b * a^-1 * b = a * b^2 * a^-1 * b * a^-1

96
96

Total time: 2.669 seconds, Total memory usage: 20.72MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:13:20 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^6>;
H:=RWSGroup(F);
H;
Order(F);
Order(H);

Output: Magma V2.10-22    Mon Jun 28 2004 07:12:57 on modular  [Seed = 1305669756]
   -------------------------------------

Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:13:32 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^5>;
H:=RWSGroup(F);
H;
Order(F);
Order(H);

Output: Magma V2.10-22    Mon Jun 28 2004 07:13:29 on modular  [Seed = 1171978260]
   -------------------------------------

Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0
#System is confluent.
#Halting with 161 equations.
A confluent rewrite group.
Generator Ordering = [ a, a^-1, b, b^-1 ]
Ordering = ShortLex.
The reduction machine has 293 states.
    a * a^-1 = Id(FG)
    a^-1 * a = Id(FG)
    b * b^-1 = Id(FG)
    b^-1 * b = Id(FG)
    b * a * b = a * b * a
    a^3 = a^-2
    a^b = a * b * a^-1
    a^-3 = a^2
    b * a * b^-1 = b^a
    b^-1 * a^-1 * b = a * b^-1 * a^-1
    b * a^-1 * b^-1 = a^-1 * b^-1 * a
    b^-1 * a^-1 * b^-1 = a^-1 * b^-1 * a^-1
    b * a^2 * b * a = a * b * a^2 * b
    b * a^2 * b * a^-1 = a^-1 * b * a^2 * b
    (b * a * b^-1)^2 = (a^-1 * b * a)^2
    (b^-1 * a * b)^2 = (a * b * a^-1)^2
    (b * a^-1 * b^-1)^2 = (a^-1 * b^-1 * a)^2
    (b^-1 * a^-1 * b)^2 = (a * b^-1 * a^-1)^2
    b^-1 * a^-2 * b^-1 * a = a * b^-1 * a^-2 * b^-1
    b^-1 * a^-2 * b^-1 * a^-1 = a^-1 * b^-1 * a^-2 * b^-1
    a * b * a^2 * b^2 = b * a^-2 * b * a
    a^-1 * b * a^-2 * b * a = b * a^2 * b^2
    b * a^2 * b^2 * a^-1 = a^-1 * b * a^-2 * b
    b * a^-2 * b * a^2 * b = a * b * a^-2 * b * a^2
    a * b * a^-2 * b * a^-1 = b^2 * a^2 * b
    a^-1 * b^2 * a^2 * b = b * a^-2 * b * a^-1
    a^-2 * b * a^-2 * b * a^-1 = a^2 * b^2 * a^2 * b
    b^3 = b^-2
    b^-3 = b^2
    b^2 * a^-2 * b * a = b^-2 * a * b^-2
    b * a^-2 * b^2 * a^-1 = a^-1 * b^2 * a^-2 * b
    a * b * a^-1 * b^2 = b^-1 * a * b^-2
    a^-1 * b^-1 * a * b^-2 = b * a^-1 * b^2
    b^-1 * a^-2 * b^-2 * a = a * b^-1 * a^2 * b^-1
    a * b^-1 * a^2 * b^-1 * a^-1 = b^-1 * a^-2 * b^-2
    a^-1 * b^-1 * a^-2 * b^-2 = b^-1 * a^2 * b^-1 * a^-1
    a * b^-2 * a^-2 * b^-1 = b^-1 * a^2 * b^-1 * a
    a^-1 * b^-1 * a^2 * b^-1 * a = b^-2 * a^-2 * b^-1
    b^-2 * a * b^-1 * a^-1 = b^2 * a^-1 * b
    b^2 * a^-1 * b * a = b^-2 * a * b^-1
    b^-1 * a^2 * b^-2 * a = a * b^-2 * a^2 * b^-1
    b^-2 * a^2 * b^-1 * a^-1 = b^2 * a^-1 * b^2
    b^-1 * a^2 * b^-1 * a^-2 * b^-1 = a^-1 * b^-1 * a^2 * b^-1 * a^-2
    a^-2 * b * a^2 * b^2 = a^2 * b * a^-2 * b * a
    a^-1 * b * a^-1 * b * a^2 * b = (b * a^-2)^2
    b * a^2 * b^2 * a^2 = a^-1 * b * a^-2 * b * a^-2
    b^2 * a^-2 * b * a^-1 * b * a = b^-2 * a * b^-1 * a * b^-2
    b * a^-1 * b * a^2 * b^2 * a = a * b * a^-1 * b * a^2 * b^2
    a^-1 * b * a^-1 * b * a^-2 * b * a^-2 = b * a^-2 * b * a^-1 * b * a^2
    b * a^-2 * b * a^-1 * b * a^-1 = a^-1 * b * a^-1 * b * a^-2 * b
    b * a^-1 * b * a^-2 * b * a^-1 * b * a = a * b * a^-1 * b * a^-2 * b * a^-1 
        * b
    b^2 * a^-1 * b^2 * a = b^-2 * a^2 * b^-1
    a^-1 * b^-1 * a^2 * b^-2 = b^2 * a^-1 * b^2
    a * b^2 * a^-1 * b^2 = b^-1 * a^2 * b^-2
    b^2 * a^-1 * b * a^-2 * b = a * b * a^-1 * b * a^-1 * b * a^-1
    b^-2 * a * b^-1 * a^2 = b^2 * a^-1 * b * a^-2
    a^-2 * b * a^-1 * b^2 = a^2 * b^-1 * a * b^-2
    a * b * a^-2 * b^2 = b^-2 * a * b^-2
    a^-1 * b^-2 * a * b^-2 = b * a^-2 * b^2
    b^-2 * a * b^-2 * a^-1 = b^2 * a^-2 * b
    b^-2 * a * b^-2 * a^2 = b^2 * a^-2 * b * a^-2
    b * a^-1 * b * a^-1 * b^2 * a^-1 = a^-1 * b^2 * a^-1 * b * a^-1 * b
    b^2 * a^-1 * b * a^-1 * b * a = b^-2 * a^2 * b^-2
    a * b * a^-1 * b * a^-1 * b * a = (b^-1 * a * b^-1)^2
    b^2 * a^-2 * b^2 * a = b^-2 * a * b^-1 * a * b^-1
    b^-2 * a * b^-1 * a * b^-1 * a^-1 = b^2 * a^-2 * b^2
    b^-2 * a * b^-2 * a * b^-1 = b^2 * a^2 * b^2 * a
    a^-1 * b^-1 * a * b^-1 * a^2 * b^-2 = b^2 * a^-1 * b * a^-1 * b^2
    a * b^2 * a^-1 * b * a^-1 * b^2 = b^-1 * a * b^-1 * a^2 * b^-2
    a^-1 * b^2 * a^-2 * b * a^-2 = b * a^-2 * b^2 * a^2
    b^2 * a^-1 * b^2 * a^-2 * b = b^-1 * a * b^-1 * a * b^-1 * a^-2
    a * b^-1 * a * b^-1 * a^-2 * b^-1 = (b^-1 * a^2)^2
    a * b * a^-1 * b * a^-1 * b^2 = b^-2 * a^2 * b^-2
    a^-1 * b^-2 * a^2 * b^-2 = b * a^-1 * b * a^-1 * b^2
    a * b^2 * a^-2 * b^2 = b^-1 * a * b^-1 * a * b^-2
    a^-1 * b^-1 * a * b^-1 * a * b^-2 = b^2 * a^-2 * b^2
    b^-1 * a^2 * b^-1 * a * b^-2 = a * b^-1 * a * b^-1 * a * b^-1 * a^-1
    a^-1 * b^-1 * a * b^-1 * a * b^-1 * a^-1 = (b * a^-1 * b)^2
    b^-1 * a^-2 * b^-2 * a^-2 = a * b^-1 * a^2 * b^-1 * a^2
    b^-1 * a^2 * b^-1 * a * b^-1 * a = a * b^-1 * a * b^-1 * a^2 * b^-1
    a^-2 * b^-1 * a^2 * b^-1 * a^-1 = a^2 * b^-1 * a^-2 * b^-2
    b^-1 * a^2 * b^-1 * a^2 * b^-2 = a * b^-1 * a^2 * b^-1 * a * b^-1 * a^-1
    b^-2 * a^2 * b^-1 * a * b^-1 * a^-1 = b^2 * a^-1 * b * a^-1 * b^2
    b^2 * a^-1 * b * a^-1 * b^2 * a = b^-2 * a^2 * b^-1 * a * b^-1
    b^-1 * a^2 * b^-1 * a^2 * b^-1 * a = a * b^-1 * a^2 * b^-1 * a^2 * b^-1
    a^-2 * b^-2 * a^-2 * b^-1 = a^2 * b^-1 * a^2 * b^-1 * a
    b^-2 * a^2 * b^-1 * a^2 = b^2 * a^-1 * b^2 * a^-2
    b^-1 * a * b^-1 * a^-2 * b^-2 * a^-1 = a^-1 * b^-1 * a * b^-1 * a^-2 * b^-2
    b^-1 * a * b^-1 * a^2 * b^-1 * a * b^-1 * a^-1 = a^-1 * b^-1 * a * b^-1 * 
        a^2 * b^-1 * a * b^-1
    b^-2 * a^2 * b^-2 * a^-1 = b^2 * a^-1 * b * a^-1 * b
    b^2 * a^-1 * b * a^-1 * b * a^-2 * b = b^-1 * a * b^-1 * a * b^-2 * a^-2
    b^-1 * a * b^-2 * a^2 * b^-1 * a = b^2 * a^-1 * b * a^-1 * b * a^-2
    a * b * a^-1 * b * a^-2 * b^2 = b^-2 * a * b^-1 * a * b^-2
    b^-2 * a * b^-1 * a * b^-2 * a^-1 = b^2 * a^-2 * b * a^-1 * b
    a^-1 * b^-2 * a * b^-1 * a * b^-2 = b * a^-1 * b * a^-2 * b^2
    b^2 * a^-2 * b * a^-2 * b = a * b * a^-1 * b * a^-2 * b * a^-1
    b * a^-1 * b * a^-1 * b * a^-1 * b * a^2 = b^-2 * a * b^-1 * a * b^-1 * a * 
        b^-1
    b^-2 * a * b^-1 * a * b^-1 * a * b^-1 * a^-1 = b * a^-1 * b * a^-1 * b * 
        a^-1 * b * a
    b^2 * a^-1 * b * a^-1 * b * a^-1 * b * a = b^-1 * a * b^-1 * a * b^-1 * a * 
        b^-1 * a^-1
    b^-1 * a * b^-1 * a * b^-1 * a * b^-1 * a^-2 = b^2 * a^-1 * b * a^-1 * b * 
        a^-1 * b
    b * a^-1 * b^2 * a^-1 * b^2 = a^-1 * b^-2 * a^-2 * b^-2
    b^-2 * a^-2 * b^-2 * a^-1 = b^2 * a^-1 * b^2 * a^-1 * b
    b^-1 * a * b^-1 * a^2 * b^-1 * a^2 = b^2 * a^-1 * b^2 * a^-1 * b * a^-1
    b * a^-1 * b^2 * a^-1 * b * a^-2 = (a^-1 * b^-1 * a^2)^3
    b * a^-1 * b * a^-2 * b * a^-2 * b = a * b * a^-1 * b * a^-2 * b * a^-2
    a^-2 * b * a^-2 * b^2 = a^2 * b^-2 * a * b^-2
    b^-1 * a * b^-1 * a * b^-2 * a = a * b^-2 * a * b^-1 * a * b^-1
    a^-1 * b * a^-1 * b * a^-1 * b * a^-2 * b * a^-1 = b * a^-1 * b * a^-2 * b^2
        * a^2
    b^-1 * a * b^-2 * a * b^-1 * a * b^-1 * a = b * a^-1 * b * a^-1 * b * a^-2 *
        b * a^-1
    b * a^-1 * b * a^-1 * b * a^-2 * b * a^-1 * b = a * b * a^-1 * b * a^-1 * b 
        * a^-2 * b * a^-1
    a^2 * b * a^-1 * b * a^-2 * b * a^-1 * b = b^-1 * a * b^-2 * a * b^-1 * a * 
        b^-2
    b * a^-1 * b * a^-1 * b * a^-1 * b * a^-1 * b * a = a * b * a^-1 * b * a^-1 
        * b * a^-1 * b * a^-1 * b
    (b * a^-1)^5 = (a * b^-1)^5
    a^2 * b^-1 * a * b^-1 * a * b^-1 * a * b^-2 = (a^-1 * b)^4
    a^-2 * b * a^-1 * b * a^-1 * b * a^-1 * b = a * b^-1 * a * b^-1 * a * b^-1 *
        a * b^-2
    a^-1 * b * a^-1 * b * a^-1 * b * a^-1 * b^2 = a^2 * b^-1 * a * b^-1 * a * 
        b^-1 * a * b^-1
    a^-2 * b^-1 * a * b^-1 * a * b^-1 * a * b^-1 = b * a^-1 * b * a^-1 * b * 
        a^-1 * b^2
    a * b * a^-1 * b * a^-1 * b * a^-1 * b^2 = a^-1 * b^-1 * a * b^-1 * a * b^-1
        * a * b^-1
    a^-1 * b^-1 * a * b^-1 * a * b^-1 * a * b^-2 = a * b * a^-1 * b * a^-1 * b *
        a^-1 * b
    a^2 * b * a^-1 * b * a^-1 * b * a^-1 * b = b^-1 * a * b^-1 * a * b^-1 * a * 
        b^-2
    b * a^-1 * b * a^-1 * b * a^-2 * b^2 * a = b^-2 * a * b^-1 * a * b^-1 * a * 
        b^-2
    b^-2 * a * b^-1 * a * b^-1 * a * b^-2 * a^-1 = b * a^-1 * b * a^-1 * b * 
        a^-2 * b^2
    (a^-2 * b * a^-1 * b)^2 = (a * b^-1 * a * b^-2)^2
    a^2 * b^-1 * a * b^-2 * a * b^-1 * a * b^-2 = a^-1 * b * a^-1 * b * a^-2 * b
        * a^-1 * b
    a^-1 * b^-2 * a * b^-1 * a * b^-1 * a * b^-2 = b * a^-1 * b * a^-1 * b * 
        a^-2 * b^2
    a * b * a^-1 * b * a^-1 * b * a^-2 * b^2 = b^-2 * a * b^-1 * a * b^-1 * a * 
        b^-2
    b^-2 * a * b^-1 * a * b^-1 * a^2 = b * a^-1 * b^2 * a^-2 * b * a^-1
    b * a^-1 * b * a^-1 * b * a^-1 * b * a^-2 * b = (a * b * a^-2)^4
    b^-2 * a * b^-1 * a * b^-1 * a * b^-1 * a = b * a^-1 * b * a^-1 * b * a^-1 *
        b * a^-2
    b^2 * a^-1 * b * a^-1 * b * a^-1 * b * a^-2 = (b^-1 * a)^4
    b^-1 * a * b^-1 * a * b^-1 * a * b^-1 * a^2 = b^2 * a^-1 * b * a^-1 * b * 
        a^-1 * b * a^-1
    b^-1 * a * b^-1 * a * b^-1 * a * b^-1 * a * b^-2 = a * b^-1 * a * b^-1 * a *
        b^-1 * a * b^-2 * a^-1
    (a^-1 * b)^5 = (a * b^-1)^5
    a^2 * b^-1 * a * b^-1 * a * b^-1 * a * b^-1 * a * b^-1 = b * a^-1 * b * a^-1
        * b * a^-1 * b * a^-1 * b
    (b^-1 * a)^5 = (a * b^-1)^5
    b^-1 * a * b^-1 * a * b^-1 * a * b^-1 * a * b^-1 * a^-1 = a^-1 * b^-1 * a * 
        b^-1 * a * b^-1 * a * b^-1 * a * b^-1
    a * b * a^-1 * b * a^-1 * b * a^-1 * b * a = b^-1 * a * b^-2 * a^2 * b^-2
    b * a^-1 * b^2 * a^-2 * b * a^-1 * b = a * b * a^-1 * b * a^-1 * b * a^-1 * 
        b * a^-1
    a^-2 * b^2 * a^-1 * b^2 = a^2 * b^-1 * a^2 * b^-2
    b^-1 * a * b^-2 * a * b^-2 = a * b^2 * a^2 * b^2
    (a^-2 * b * a)^3 = a^2 * b^-1 * a * b^-2 * a * b^-1
    a^-1 * b^-1 * a * b^-1 * a * b^-1 * a^2 * b^-2 = b^2 * a^-1 * b * a^-1 * b *
        a^-1 * b^2
    a * b^2 * a^-1 * b * a^-1 * b * a^-1 * b^2 = b^-1 * a * b^-1 * a * b^-1 * 
        a^2 * b^-2
    b^2 * a^-1 * b^2 * a^-1 * b * a^-1 * b = b^-1 * a^2 * b^-1 * a * b^-1 * a^-2
    a^-2 * b^-1 * a * b^-1 * a^2 * b^-1 * a * b^-1 = b * a^-1 * b^2 * a^-1 * b *
        a^-1 * b^2
    a^-1 * b^2 * a^-1 * b * a^-1 * b * a^-2 = b * a^-1 * b * a^-1 * b^2 * a^2
    b * a^-1 * b^2 * a^-1 * b * a^-1 * b * a^-1 * b = b^-1 * a * b^-1 * a^2 * 
        b^-2 * a^-2
    b^-1 * a * b^-1 * a * b^-1 * a^2 * b^-1 * a = b * a^-1 * b^2 * a^-1 * b * 
        a^-1 * b * a^-1
    b^2 * a^-1 * b * a^-1 * b * a^-1 * b^2 * a = b^-1 * a * b^-1 * a * b^-1 * 
        a^2 * b^-2
    b^-1 * a * b^-1 * a * b^-1 * a^
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:13:58 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^5>;
H:=RWSGroup(F);
Order(F);
Order(H);

Output: Magma V2.10-22    Mon Jun 28 2004 07:13:55 on modular  [Seed = 1589764901]
   -------------------------------------

Running Knuth-Bendix with the following parameter values
MaxRelations  = 32767
MaxStates     = 0
TidyInt       = 100
MaxWdiffs     = 512
HaltingFactor = 0
MinTime       = 0
#System is confluent.
#Halting with 161 equations.
600
600

Total time: 2.719 seconds, Total memory usage: 20.72MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:14:33 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^7>;
Order(F);

Output: Magma V2.10-22    Mon Jun 28 2004 07:14:28 on modular  [Seed = 1456073674]
   -------------------------------------

0

Total time: 4.869 seconds, Total memory usage: 18.24MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:14:44 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^8>;
Order(F);

Output: Magma V2.10-22    Mon Jun 28 2004 07:14:39 on modular  [Seed = 1878053624]
   -------------------------------------

0

Total time: 4.649 seconds, Total memory usage: 18.24MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:15:27 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^12,b^12,a^3*b^3=b^3*a^3>;
Order(F);

Output: Magma V2.10-22    Mon Jun 28 2004 07:15:24 on modular  [Seed = 2028455357]
   -------------------------------------

6144

Total time: 2.659 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:16:09 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F);

Output: Magma V2.10-22    Mon Jun 28 2004 07:16:01 on modular  [Seed = 1911475336]
   -------------------------------------

0

Total time: 7.439 seconds, Total memory usage: 19.01MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:18:15 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.10-22    Mon Jun 28 2004 07:18:08 on modular  [Seed = 2366780405]
   -------------------------------------

0

Total time: 7.449 seconds, Total memory usage: 19.01MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:18:24 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=10000000);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Mon Jun 28 2004 07:18:21 on modular  [Seed = 2233089008]
   -------------------------------------


Current total memory usage: 77.9MB, failed memory request: 38.1MB
System Error: User memory limit has been reached

Total time: 3.249 seconds, Total memory usage: 81.67MB


************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:18:58 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=5000000);

Output: Magma V2.10-22    Mon Jun 28 2004 07:18:35 on modular  [Seed = 2634162974]
   -------------------------------------



************** MAGMA *****************
Host pD953561B.dip.t-dialin.net. (217.83.86.27)
Time: Mon Jun 28 07:21:26 2004

Input: FG<a,b>:=FreeGroup(2);
F:=quo<FG|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 07:21:05 on modular  [Seed = 3039431324]
   -------------------------------------

0

Total time: 20.359 seconds, Total memory usage: 68.04MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:09:08 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:08:47 on modular  [Seed = 1408440597]
   -------------------------------------

0

Total time: 20.389 seconds, Total memory usage: 68.04MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:11:27 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,b^12,a^6*b^6=b^6*a^6>;
G<x,y>:=Group<x,y|x^3=y^2,(x^-1*y)^6,(y*x^-1)^6>;
Order(G : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:11:12 on modular  [Seed = 1623206537]
   -------------------------------------

0

Total time: 14.679 seconds, Total memory usage: 68.04MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:13:14 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
G<x,y>:=Group<x,y|x^3=y^2,(x^-1*y)^6>;
Order(G : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:13:01 on modular  [Seed = 2111649337]
   -------------------------------------

0

Total time: 13.419 seconds, Total memory usage: 68.04MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:16:41 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(G : CosetLimit:=4000000, Lookahead=1);

Output: Magma V2.10-22    Mon Jun 28 2004 08:16:38 on modular  [Seed = 2301216166]
   -------------------------------------


>> Order(G : CosetLimit:=4000000, Lookahead=1);;
                                           ^
User error: bad syntax

Total time: 2.569 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:16:51 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(G : CosetLimit:=4000000, Lookahead:=1);

Output: Magma V2.10-22    Mon Jun 28 2004 08:16:48 on modular  [Seed = 2233846204]
   -------------------------------------


>> Order(G : CosetLimit:=4000000, Lookahead:=1);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:17:21 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Lookahead:=1);

Output: Magma V2.10-22    Mon Jun 28 2004 08:16:59 on modular  [Seed = 2621231278]
   -------------------------------------

0

Total time: 21.839 seconds, Total memory usage: 71.11MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:17:59 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Lookahead:=2);

Output: Magma V2.10-22    Mon Jun 28 2004 08:17:37 on modular  [Seed = 2520177406]
   -------------------------------------

0

Total time: 21.959 seconds, Total memory usage: 71.11MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:19:35 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Hard");

Output: Magma V2.10-22    Mon Jun 28 2004 08:19:19 on modular  [Seed = 2684415086]
   -------------------------------------

0

Total time: 16.529 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:19:56 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Easy");

Output: Magma V2.10-22    Mon Jun 28 2004 08:19:52 on modular  [Seed = 3088643161]
   -------------------------------------

0

Total time: 4.179 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:20:29 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Felsch");

Output: Magma V2.10-22    Mon Jun 28 2004 08:20:13 on modular  [Seed = 3345451827]
   -------------------------------------

0

Total time: 16.000 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:21:15 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="HLT");

Output: Magma V2.10-22    Mon Jun 28 2004 08:21:06 on modular  [Seed = 3732837349]
   -------------------------------------

0

Total time: 9.219 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:21:43 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="CT");

Output: Magma V2.10-22    Mon Jun 28 2004 08:21:29 on modular  [Seed = 3598097302]
   -------------------------------------

0

Total time: 14.079 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:22:00 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="RT");

Output: Magma V2.10-22    Mon Jun 28 2004 08:21:56 on modular  [Seed = 3998131075]
   -------------------------------------

0

Total time: 4.369 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:22:32 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Sims1");

Output: Magma V2.10-22    Mon Jun 28 2004 08:22:28 on modular  [Seed = 4183405684]
   -------------------------------------

0

Total time: 4.379 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:23:05 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Sims3");

Output: Magma V2.10-22    Mon Jun 28 2004 08:22:48 on modular  [Seed = 4031823201]
   -------------------------------------

0

Total time: 16.720 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:23:16 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Sims5");

Output: Magma V2.10-22    Mon Jun 28 2004 08:23:11 on modular  [Seed = 246301611]
   -------------------------------------

0

Total time: 4.549 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:24:02 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Sims7");

Output: Magma V2.10-22    Mon Jun 28 2004 08:23:43 on modular  [Seed = 111561667]
   -------------------------------------

0

Total time: 19.259 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:24:24 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000, Strategy:="Sims9");

Output: Magma V2.10-22    Mon Jun 28 2004 08:24:10 on modular  [Seed = 532632319]
   -------------------------------------

0

Total time: 14.249 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:24:52 2004

Input: F<a,b>:=Group<a,b|a^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:24:39 on modular  [Seed = 397891866]
   -------------------------------------

0

Total time: 12.799 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:25:11 2004

Input: F<a,b>:=Group<a,b|a^12>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:25:08 on modular  [Seed = 747397634]
   -------------------------------------

Infinity

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:25:23 2004

Input: F<a,b>:=Group<a,b|a^12,b^12>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:25:18 on modular  [Seed = 629500673]
   -------------------------------------

0

Total time: 5.119 seconds, Total memory usage: 65.76MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:25:57 2004

Input: F<a,b>:=Group<a,b|a^2,b^2>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:25:53 on modular  [Seed = 1223165459]
   -------------------------------------

0

Total time: 3.919 seconds, Total memory usage: 33.76MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:27:20 2004

Input: F<a,b>:=Group<a,b|a^12,b^12,a^6*b^6=b^6*a^6>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:27:06 on modular  [Seed = 1105268689]
   -------------------------------------

0

Total time: 14.309 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:27:48 2004

Input: F<a,b>:=Group<a,b|a^4,b^4,a^2*b^2=b^2*a^2>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:27:39 on modular  [Seed = 1560023789]
   -------------------------------------

0

Total time: 8.769 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host p50825CA2.dip.t-dialin.net. (80.130.92.162)
Time: Mon Jun 28 08:28:30 2004

Input: F<a,b>:=Group<a,b|a^4,b^4,a^2*b^2=b^2*a^2,a*b*a=b*a*b>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 08:28:26 on modular  [Seed = 1757947528]
   -------------------------------------

48

Total time: 3.159 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host pD9E51F08.dip.t-dialin.net. (217.229.31.8)
Time: Mon Jun 28 09:17:35 2004

Input: F:=Group<a,s,t|a^12,s*a=a*t,t*a=a*s,s*t=t*s,s^2,t^2>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 09:17:32 on modular  [Seed = 4267615384]
   -------------------------------------

48

Total time: 3.109 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host pD9E51F08.dip.t-dialin.net. (217.229.31.8)
Time: Mon Jun 28 09:22:39 2004

Input: F:=Group<a,s|a^12,s^2,s*a^2=a*s>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 09:22:36 on modular  [Seed = 296831622]
   -------------------------------------

6

Total time: 2.939 seconds, Total memory usage: 49.76MB


************** MAGMA *****************
Host pD9E51F08.dip.t-dialin.net. (217.229.31.8)
Time: Mon Jun 28 09:23:41 2004

Input: F:=Group<a,s|a^12,s^2,s*a^2=a^2*s>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 09:23:33 on modular  [Seed = 578976252]
   -------------------------------------

0

Total time: 8.489 seconds, Total memory usage: 49.77MB


************** MAGMA *****************
Host pD9E51F08.dip.t-dialin.net. (217.229.31.8)
Time: Mon Jun 28 09:27:19 2004

Input: F:=Group<a,s|a^12,s^2,s*a^2=a^2*s,s*a^-1*s*a=a^-1*s*a*s>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Mon Jun 28 2004 09:27:16 on modular  [Seed = 898984330]
   -------------------------------------

48

Total time: 2.969 seconds, Total memory usage: 49.77MB


************** MAGMA *****************
Host dialin-145-254-111-034.arcor-ip.net. (145.254.111.34)
Time: Mon Jun 28 11:19:42 2004

Input: hg


Output: Magma V2.10-22    Mon Jun 28 2004 11:19:39 on modular  [Seed = 2852838829]
   -------------------------------------


>> hg
   ^
User error: Identifier 'hg' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dialin-145-254-111-034.arcor-ip.net. (145.254.111.34)
Time: Mon Jun 28 11:24:36 2004

Input: function u1(s,r)
return s^-2*r^-1*s;
end function;
F<x,y>:=FreeGroup(2);


Output: Magma V2.10-22    Mon Jun 28 2004 11:24:34 on modular  [Seed = 3715999203]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dialin-145-254-111-034.arcor-ip.net. (145.254.111.34)
Time: Mon Jun 28 11:25:03 2004

Input: function u1(s,r)
return s^-2*r^-1*s;
end function;
F<x,y>:=FreeGroup(2);
f;

Output: Magma V2.10-22    Mon Jun 28 2004 11:25:00 on modular  [Seed = 3581259157]
   -------------------------------------


>> f;;
   ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dialin-145-254-111-034.arcor-ip.net. (145.254.111.34)
Time: Mon Jun 28 11:25:26 2004

Input: function u1(s,r)
return s^-2*r^-1*s;
end function;
F<x,y>:=FreeGroup(2);
F;

Output: Magma V2.10-22    Mon Jun 28 2004 11:25:23 on modular  [Seed = 4014970752]
   -------------------------------------

Finitely presented group F on 2 generators (free)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dialin-145-254-111-034.arcor-ip.net. (145.254.111.34)
Time: Mon Jun 28 11:28:35 2004

Input: function u1(s,r)
return s^-2*r^-1*s;
end function;
F<x,y>:=FreeGroup(4);
F;

Output: Magma V2.10-22    Mon Jun 28 2004 11:28:32 on modular  [Seed = 296839228]
   -------------------------------------

Finitely presented group F on 4 generators (free)

Total time: 2.740 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E511F2.dip.t-dialin.net. (217.229.17.242)
Time: Mon Jun 28 11:32:59 2004

Input: F<a,s>:=Group<a,s|a^12,s^2,s*a^2=a^2*s,s*a^-1*s*a=a^-1*s*a*s>;
Order(F : CosetLimit:=4000000);
G<x>:=sub<F|a>;
H:=Rewrite(F,G);
H;

Output: WARNING: MAGMA command contains unsafe command 'write', so it will not be executed.

************** MAGMA *****************
Host pD9E511F2.dip.t-dialin.net. (217.229.17.242)
Time: Mon Jun 28 11:35:47 2004

Input: F<a,s>:=Group<a,s|a^12,s^2,s*a^2=a^2*s,s*a^-1*s*a=a^-1*s*a*s>;
Order(F : CosetLimit:=4000000);
G<x>:=sub<F|a>;
Order(G);


Output: Magma V2.10-22    Mon Jun 28 2004 11:35:41 on modular  [Seed = 1189493893]
   -------------------------------------

48
12

Total time: 3.329 seconds, Total memory usage: 49.67MB


************** MAGMA *****************
Host pD9E511F2.dip.t-dialin.net. (217.229.17.242)
Time: Mon Jun 28 11:38:34 2004

Input: F<a,s,t>:=Group<a,s,t|a^12,s^2,t^2,s*t=t*s,s*a=a*t,t*a=a*s>;
Order(F : CosetLimit:=4000000);
G:=Simplify(F);
Order(G);
G;


Output: Magma V2.10-22    Mon Jun 28 2004 11:38:31 on modular  [Seed = 1741102109]
   -------------------------------------

48
48
Finitely presented group G on 2 generators
Index in group F is 1
Generators as words in group F
    G.1 = a
    G.2 = s
Relations
    G.2^2 = Id(G)
    G.1^-1 * G.2 * G.1^2 * G.2 * G.1^-1 = Id(G)
    G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2 * G.1 = Id(G)
    G.1^12 = Id(G)

Total time: 3.269 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host pD9E511F2.dip.t-dialin.net. (217.229.17.242)
Time: Mon Jun 28 11:40:29 2004

Input: F<a,s,t>:=Group<a,s,t|a^12,s^2,t^2,s*t=t*s,s*a=a*t,t*a=a*s>;
Order(F : CosetLimit:=4000000);
G,phi:=Simplify(F);
Order(G);
G;
phi(t);

Output: Magma V2.10-22    Mon Jun 28 2004 11:40:26 on modular  [Seed = 2604392572]
   -------------------------------------

48
48
Finitely presented group G on 2 generators
Index in group F is 1
Generators as words in group F
    G.1 = a
    G.2 = s
Relations
    G.2^2 = Id(G)
    G.1^-1 * G.2 * G.1^2 * G.2 * G.1^-1 = Id(G)
    G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2 * G.1 = Id(G)
    G.1^12 = Id(G)
G.2^G.1

Total time: 3.249 seconds, Total memory usage: 65.77MB


************** MAGMA *****************
Host d213-102-220-207.cust.tele2.fr. (213.102.220.207)
Time: Mon Jun 28 14:03:01 2004

Input: R=QQ[x_0..x_2]
I1=ideal(x_0,x_1)
I2=ideal(x_0,x_2)
I3=ideal(x_2,x_1)
I=intersect(I1,I2,I3) 

hilbertSeries I 

Output: Magma V2.10-22    Mon Jun 28 2004 14:02:58 on modular  [Seed = 2604369606]
   -------------------------------------


>> I1=ideal(x_0,x_1)
   ^
User error: bad syntax

>> I3=ideal(x_2,x_1)
   ^
User error: bad syntax

>> hilbertSeries I ;
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:03:22 2004

Input: B<a,b>:=BraidGroup(2);
a*b*a eq b*a*b;

Output: Magma V2.10-22    Mon Jun 28 2004 15:03:19 on modular  [Seed = 2267524325]
   -------------------------------------


>> B<a,b>:=BraidGroup(2);
    ^
Runtime error in 'AssignNames': Too many names given for this object

>> a*b*a eq b*a*b;;
   ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:03:37 2004

Input: B<a,b>:=BraidGroup(3);
a*b*a eq b*a*b;

Output: Magma V2.10-22    Mon Jun 28 2004 15:03:34 on modular  [Seed = 2402264092]
   -------------------------------------

true

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:04:12 2004

Input: B<a,b>:=BraidGroup(3);
(a^3*b)^3 eq (a*b)^6;

Output: Magma V2.10-22    Mon Jun 28 2004 15:04:09 on modular  [Seed = 3071777803]
   -------------------------------------

true

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:04:44 2004

Input: B<a,b>:=BraidGroup(3);
(a^4*b)^4 eq (a*b)^10;

Output: Magma V2.10-22    Mon Jun 28 2004 15:04:41 on modular  [Seed = 3105460837]
   -------------------------------------

false

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:12:45 2004

Input: B<a,b>:=BraidGroup(3);
(a^4*b)^6 eq (a*b)^15;

Output: Magma V2.10-22    Mon Jun 28 2004 15:12:42 on modular  [Seed = 3497065839]
   -------------------------------------

false

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:12:57 2004

Input: B<a,b>:=BraidGroup(3);
(a^4*b)^8 eq (a*b)^20;

Output: Magma V2.10-22    Mon Jun 28 2004 15:12:55 on modular  [Seed = 3631805818]
   -------------------------------------

false

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:14:49 2004

Input: B<a,b>:=BraidGroup(3);
(a^4*b)^16 eq (a*b)^40;

Output: Magma V2.10-22    Mon Jun 28 2004 15:14:47 on modular  [Seed = 3227578098]
   -------------------------------------

false

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:16:03 2004

Input: B<a,b>:=BraidGroup(3);
(a^4*b)^160 eq (a*b)^400;

Output: Magma V2.10-22    Mon Jun 28 2004 15:16:01 on modular  [Seed = 3412845999]
   -------------------------------------

false

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:17:06 2004

Input: B<a,b>:=BraidGroup(3);
(a^4*b)^1600 eq (a*b)^4000;

Output: Magma V2.10-22    Mon Jun 28 2004 15:17:03 on modular  [Seed = 4250784583]
   -------------------------------------

false

Total time: 3.109 seconds, Total memory usage: 2.65MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:20:51 2004

Input: B<a,b>:=BraidGroup(3);
NormalForm(a);
NormalForm(b);
NormalForm(a*b);


Output: Magma V2.10-22    Mon Jun 28 2004 15:20:48 on modular  [Seed = 313671060]
   -------------------------------------

a
<Artin, 0, [
    (1, 2)
], 0>
b
<Artin, 0, [
    (2, 3)
], 0>
a * b
<Artin, 0, [
    (1, 2, 3)
], 0>

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:21:37 2004

Input: B<a,b>:=BraidGroup(3);
NormalForm(a);
NormalForm(b);
NormalForm(a*b);
NormalForm(a*b*a);
NormalForm(a^2);
NormalForm(a^3);


Output: Magma V2.10-22    Mon Jun 28 2004 15:21:34 on modular  [Seed = 448411058]
   -------------------------------------

a
<Artin, 0, [
    (1, 2)
], 0>
b
<Artin, 0, [
    (2, 3)
], 0>
a * b
<Artin, 0, [
    (1, 2, 3)
], 0>
b * a * b
<Artin, 1, [], 0>
a^2
<Artin, 0, [
    (1, 2),
    (1, 2)
], 0>
a^3
<Artin, 0, [
    (1, 2),
    (1, 2),
    (1, 2)
], 0>

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:23:17 2004

Input: B<a,b>:=BraidGroup(3);
a;

Output: Magma V2.10-22    Mon Jun 28 2004 15:23:14 on modular  [Seed = 27341108]
   -------------------------------------

a
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:28:15 2004

Input: B<a,b>:=BraidGroup(3);
a^-1;

Output: Magma V2.10-22    Mon Jun 28 2004 15:28:12 on modular  [Seed = 831586411]
   -------------------------------------

b^-1 * a^-1 * b^-1 * a * b
<Artin, -1, [
    (1, 2, 3)
], 0>

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:29:05 2004

Input: B<a,b>:=BraidGroup(3);
a^5;

Output: Magma V2.10-22    Mon Jun 28 2004 15:29:02 on modular  [Seed = 966330449]
   -------------------------------------

a^5
<Artin, 0, [
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2)
], 0>

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:29:15 2004

Input: B<a,b>:=BraidGroup(3);
b*a^5;

Output: Magma V2.10-22    Mon Jun 28 2004 15:29:12 on modular  [Seed = 562106559]
   -------------------------------------

b * a^5
<Artin, 0, [
    (2, 3),
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2)
], 0>

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:29:27 2004

Input: B<a,b>:=BraidGroup(3);
a^5*b;

Output: Magma V2.10-22    Mon Jun 28 2004 15:29:24 on modular  [Seed = 696850603]
   -------------------------------------

a^5 * b
<Artin, 0, [
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (2, 3)
], 0>

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:29:42 2004

Input: B<a,b>:=BraidGroup(3);
a^5*b*a;

Output: Magma V2.10-22    Mon Jun 28 2004 15:29:39 on modular  [Seed = 1374773476]
   -------------------------------------

a^5 * b * a
<Artin, 0, [
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (2, 3),
    (1, 2)
], 0>

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:32:30 2004

Input: B<a,b>:=BraidGroup(3);
a^5*b*a;
b*a*b^5;

Output: Magma V2.10-22    Mon Jun 28 2004 15:32:28 on modular  [Seed = 1206351133]
   -------------------------------------

a^5 * b * a
<Artin, 0, [
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (1, 2),
    (2, 3),
    (1, 2)
], 0>
b * a * b^5
<Artin, 0, [
    (2, 3),
    (1, 2),
    (2, 3),
    (2, 3),
    (2, 3),
    (2, 3),
    (2, 3)
], 0>

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825F14.dip.t-dialin.net. (80.130.95.20)
Time: Mon Jun 28 15:32:58 2004

Input: B<a,b>:=BraidGroup(3);
NormalForm(a^5*b*a);
NormalForm(b*a*b^5);

Output: Magma V2.10-22    Mon Jun 28 2004 15:32:55 on modular  [Seed = 1290567229]
   -------------------------------------

b * a * b^5
<Artin, 1, [
    (2, 3),
    (2, 3),
    (2, 3),
    (2, 3)
], 0>
b * a * b^5
<Artin, 1, [
    (2, 3),
    (2, 3),
    (2, 3),
    (2, 3)
], 0>

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ppp1-181.her.forthnet.gr. (213.16.187.181)
Time: Mon Jun 28 20:59:30 2004

Input: 5+3


Output: Magma V2.10-22    Mon Jun 28 2004 20:59:27 on modular  [Seed = 1425320610]
   -------------------------------------

8

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ppp1-181.her.forthnet.gr. (213.16.187.181)
Time: Mon Jun 28 21:00:48 2004

Input: (x^2+5*x)/(x^2+1)

Output: Magma V2.10-22    Mon Jun 28 2004 21:00:45 on modular  [Seed = 1892716372]
   -------------------------------------


>> (x^2+5*x)/(x^2+1);
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-1-243-43.ilm.bellsouth.net. (65.1.243.43)
Time: Mon Jun 28 21:30:12 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Mon Jun 28 2004 21:30:09 on modular  [Seed = 2166425529]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.62.138.196)
Time: Tue Jun 29 03:29:01 2004

Input: 1+1

Output: Magma V2.10-22    Tue Jun 29 2004 03:28:58 on modular  [Seed = 2654979257]
   -------------------------------------

2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.62.138.196)
Time: Tue Jun 29 03:29:54 2004

Input: (a*x+b*y)^2 +(b*x-a*y)^2

Output: Magma V2.10-22    Tue Jun 29 2004 03:29:51 on modular  [Seed = 2520239332]
   -------------------------------------


>> (a*x+b*y)^2 +(b*x-a*y)^2;
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ilya.ttk.ru. (195.170.233.240)
Time: Tue Jun 29 03:55:10 2004

Input: x^2 + y^3(x - y)

Output: Magma V2.10-22    Tue Jun 29 2004 03:55:01 on modular  [Seed = 1067343733]
   -------------------------------------


>> x^2 + y^3(x - y);
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dsl254-023-142.sea1.dsl.speakeasy.net. (216.254.23.142)
Time: Tue Jun 29 04:30:44 2004

Input: E := EllipticCurve([0,-3,-1,2,0]);
IntegralPoints(E);


Output: Magma V2.10-22    Tue Jun 29 2004 04:30:40 on modular  [Seed = 3105411371]
   -------------------------------------


IntegralPoints(
    E: Elliptic Curve defined by y^2 - y = x^3 - 3*x^2 + 2*x over R...
)
SIntegralPoints(
    E: Elliptic Curve defined by y^2 - y = x^3 - 3*x^2 + 2*x over R...,
    S: []
)
IntPoints(
    E: E
)
IntPointsUpperBound(
    E: E,
    MWG2: [ (0 : 108 : 1) ],
    lambda: 0.05111140823996884047231148429091263096779584884643
)
ReduceBound(
    E: E,
    MWG: [ (0 : 108 : 1) ],
    lambda: 0.05111140823996884047231148429091263096779584884643,
    N: 13
)
In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 988, 
column 20:
>>         N:= Ceiling(x);
                      ^
Runtime error in 'Ceiling': Argument 1 should be real

Total time: 2.879 seconds, Total memory usage: 2.16MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:16:33 2004

Input: 2^(2000000);


Output: Magma V2.10-22    Tue Jun 29 2004 11:16:09 on modular  [Seed = 3139075114]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:16:58 2004

Input: 2^(20);


Output: Magma V2.10-22    Tue Jun 29 2004 11:16:55 on modular  [Seed = 3021304699]
   -------------------------------------

1048576

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:17:32 2004

Input: 2^(200);


Output: Magma V2.10-22    Tue Jun 29 2004 11:17:29 on modular  [Seed = 2385462959]
   -------------------------------------

1606938044258990275541962092341162602522202993782792835301376

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:17:41 2004

Input: 2^(2000);


Output: Magma V2.10-22    Tue Jun 29 2004 11:17:38 on modular  [Seed = 2250723004]
   -------------------------------------

1148130695274254524232833201177681984022317702088695200477642736825766261392370\
3138566594863165062699184459646389874627734471189608630553314259313561666531853\
9129989145312280000688779148240044871428926990063486244781615463646388363947317\
0260404663539709049965581623988089446296056233116495361642219703326813441689089\
8445850560237948480791405890093477650042900271670662583052200813223628129176126\
7883317206598995396418127021779858404042159853183251540889433902091920554957783\
5896720391600819572166305827553804255837260155283487864194320545089152757838826\
25175435528800822842770817965453762184851149029376

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:17:52 2004

Input: 2^(20000);


Output: Magma V2.10-22    Tue Jun 29 2004 11:17:49 on modular  [Seed = 2654951083]
   -------------------------------------

3980276840337966592354307206191202453704772780492425938713426865652386359749300\
5704267600974997559551083646113750491270283140037693531914362175347041582702598\
1215282426893498224826615977707595539466961019588699726772279731941315198182787\
2640348528212001645661279303907103981829799353277180168737848213495164061149829\
1669186736187537002454587214079382727748256282419243923780158869781416852033865\
0090909697535966525032757049430286459482977357373598020450589927318365663076719\
1369341325931267619066960037703853052845703311196910015265843477220123863818817\
7942554921085169645825394357855769907215463965563079388394196137897184684111380\
4188730258903839103669626086974468150655710480841592465655211805257863007811676\
8888395550175367317581134486567525141586014440516451546655143884316190423961067\
1675576233872818346136985464892397290442755615882182377872919311145344584421697\
9095435045778144571378954652122396061615147642540250745857228893999875491625014\
9460138393408913260609339010362499992386378275777746666448097340338616194203639\
3646517873091923367311424456391505843899662583411213296799849557624932046287174\
7777012165543887156255858358784852335060574881876552025685704823768078710818951\
8607413794292421108556449739774204138103735145845040068963926758549978668708185\
6420723908387432495387127637571610150657515320574736396374074986751468261975677\
5534507006871485887812402927738227576635284174246988540785975240020481266853076\
1271722280243305615501201820087775982305420337024634083166711208861692609340068\
0579986459863631117978777673860899234606306309965964827966387817407478717923716\
9752957046404584525301384153358344055908219695854852185210739761460551596658211\
0131599154095661454268097375504175782284658358308902944975354631120815376726640\
5689162434577931152456001998431545614212628289848672834500476787349975268347140\
9587367450593302392307908004590644754012537113320493601682133709318222647489080\
5316440153213911573871782321541268280077603137168722422096142009675221804757161\
9997368946771401040467396145414646604585523221719668766514314761219915192127743\
2309700460321430381533385245877431330533479476152339364503436322919665631042328\
7404636125658425604119470201740065078933962761038344362331409150253910143861192\
0117646265955638834305860032671061890368374651657702121427693328917902105995692\
5949717956040857979165914170970056212869933593589268626151996676594370800885093\
0482306871528032132547355947417990760394530572723198843223418832410363826175984\
0188943913030187697549868173617421571128705344701371159600457480356270138824682\
2510391522419061320663740921321754344166744899588160649291823535983386025904942\
0407245810176159684295770158080903609685440592045942000693046124173663987768315\
3226559622471575030179220772560793253454369375877226201038736043556763523271834\
3420679693057360004073679493008945813961012439574397373178636054628207647520675\
1944202442710363437293188584308714619788669647723620572905773260806644631296575\
9024985974854410133384209271365309665606626682744607914559019664464341740372322\
0085696202719321533233027169599734928971588850348415000070034027025298183104148\
3439802976631489715866079037717178806831754364455858106105468820735715561623246\
5935131032656080444897422934974342563716483424279999142714505089946951195483477\
4847172360693568437689147399455672090773686782511054291185172381917008889957645\
3113399509930447797836071405937665080179359925813578583065253037832317524252420\
0834784486798833302541724994409211857811368740315816270707515400605341637407576\
5162668533127078605316562826337193606242535290683224423660462222408680300498714\
1496072655504412207380759416339884350515944872568028741822648144259231111931882\
8063201312780289788960533878308953274087720230412249819362545476834377553549887\
2821099981620497070810489137457106892573248498734243717184800822956334469415666\
8188580732186539779543090231828517232465220427924014613820016019205012844393252\
1408421073640063088492994227298294361370812301135526091554583104316024352359937\
2006226150289664982113944898886610710824955096724626895416484521819026132177640\
5986916580359862853763550337190945680831222193457220636136097791583380843753314\
3127652754848256621007134774454129287187613476424970485984095027622762732889742\
4208932988115108907187647698491814375639614313178092528678007370045871748218421\
7863961972842132090226237627346308360068641924146052372489832890069052689884751\
9759978152415891358370132519909035227425260834297130390766936304565623218397875\
5853064004010895030834921988601355201181158877254807798058635127708445592064519\
5631150947492766066975595293328072214140210249052417889749177550347005104320398\
9019739369172291112688917439431212725479314162497583042909799770553178190824208\
3922068769027355129212617244130640289994777413026624013157329948333586377955103\
1958448171638224842327007638592902534003765157019867535968900758185444854757857\
8003184357906575409509997094050464021285080999705112897656388088639241076632144\
9987529690463262182894272302749154535447233331028841215215533602398281107050696\
0175078276027615478163247432979381772041837658211178188699597950318482013224360\
5310377899354138477985726231146589575408553837196904092242093691507665350031017\
5006188572019017358300979056992161958286882575984331858170857303361269891312794\
3692448965403231924516788306681804550592897435806407360762335619358881095258458\
0312591238896552416681985597706139904349922984351793016911803681246079461566780\
8961600389778306540324849286501515292799391304510997298128228258006156017389878\
0862727899933214163492059216356969637035589713911231748773537575367740133150349\
5694278440382418155174162918065841408190565033367263898341678638809502616949660\
5199749691595798835947189777822765198767949699778106683862989103096006505865271\
0035663461913824060116739584040091948521100169152224334596417871709178721403678\
7102359646405164794738858057077446230434789620167619719552142878231360858371439\
9238092208362933211302942806480175589402387976531080436906856834377344137698180\
7895626459743741554004977548439050322311882521258021803535775105198695706752348\
92321663406309376

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:18:16 2004

Input: 2^(200000);


Output: Magma V2.10-22    Tue Jun 29 2004 11:18:13 on modular  [Seed = 2520211083]
   -------------------------------------

9980051818471209560859346309213505420041765610346220829126570959195807493223281\
0090344916884594500291804056197724652993840208785217853809690514645183408328250\
9402726791838696368444875295871898027402085079821331102776321213781388328995964\
7384877546795977235831526317325470277184725609174807369684823136976033122822961\
9044316945416995480226413366970077655937438323193255485036644933460082715332045\
3983118896114991575072864292096458416956403761646426772121248411624699569184283\
6056561529719175223592360220756433047198880083551717213289166286863081641180682\
4514869142993260088381373631262004530298771097082280052096264921122583943147923\
5046980809413304371297959042825781931136432350165028081254333893091680495211821\
9992682428018534057429148399639327041310355439174730911496947880801432967813077\
3379674593066476713838133767708266330819071156308574848806184940145762056026910\
3109796838192439478767736981477186772343800792411539379587023823986268442688667\
2688910033774190792664850845372822677311588590203850112414194636871679023208090\
3502437965974429265003926875956738209665568756642601632371986503819935750870882\
8966729391089498571708284794505518791885423774732615107304584368178319948215523\
2827723292941974953771613798991794680841351256463580273523590587809269583545359\
6455903696295558101672758847965243077030004769663333370693073698254301367191797\
7937539838236383396171006485675780030583551000355738714585645500142030899617822\
3785489268695448888482970389741087389524524235123429442462978424281736544613729\
5218008381093874616472167738177782572329768938016512448596154223643471482967214\
8922126123867148953042173646075766114697824521246503846872572821425467834473681\
8804438902569719528362742262077040757620129120609980995190751944542710664939865\
7158487860070320129460743685009882920451019617521602060623715835175228451465481\
1620300250831292505936116506745776244025821511400366952601952462282361442951572\
2224882045796677167645684321251919589859880158824025971966762304747630209662670\
1030800100048065172961629582861198945852680960170041638651872615159208417070928\
8903599472331124693278176915679093714760851284964475856470306169060854519083870\
9421497386086225813848618631147488096290122298840787044860128881792387109786755\
7755088882335690773560605458579831364089258301270662607699507426434127224288290\
8284288864997801730335816629949204315439298021629770986039943674982883383809135\
3518999658970576390806819879926544787510471037806156868572592378555215293804478\
9728014097947216600357264326770097317476625893194709750622782116332559490278955\
7283002354897977820517036309877692691301463708977972669601423493844107954142881\
8269184544202525201859604993114285151571168658902741985969687824592669921006108\
8808674816913878264757424183406297610332705841394861985637270023371607443990717\
5628752746588534161293287654419927535430390924334678326436146672330379440204787\
9198613218700233495579277397865166979530359969811703628030637197246158869017455\
2184703438215220054131811728605262306762439336633244714265473943396899414511255\
4468891618790887338289121520365885384281733278178180665579814936568058220774803\
3932494215455190366825417159996063173922436905764162667771383522982865607976621\
3253531264769925945604938388423173737589397021708790991918905383615160819258074\
8259833079392277484646636529602712121420800715902028396325562174778763298049495\
6390985301024250751183333221534746242556300162899916065605898393217264950997198\
5091775881855607340982120616380247407765688709112535105929938234478430766762272\
9165416413568082588420839119030938105526143479355127829617273549483700992848311\
5046233138666632946812405593056565014171295574415859664453254730970620708197260\
8363544568219191939577441563032861476452954343145478048021484050699599288654388\
6121161012558501741512817695727144593539459579579969178096886897475449943430469\
4570306038347097427831203214844262794347061252871214358346066395364339046035658\
2691046971899239437679937608809992180574480421249939543711601481183569171385549\
9858525957645193101946026291635475236558154312481760658258111985019271365648743\
0388701835663148494438680070713803534142045233661781861292884033673194580631359\
7927433366673971525306436527744827440011342746410735993977441006948094341456774\
1975665092933891185608367399730592478146984992115510944954370813329536236155320\
9820759310904609313121778867739730692352159651681385438464087870109630087016328\
2237340979472253237231866042025180617287138637756903583363694627567436864918637\
5802457092464036432277823984879592792662624417932094155987835148629604710238486\
0744347972894966419632071249566688701831288905981179216836503682067533022352469\
2355532999890697488757879084074854624577441261300538997326679644168765078658634\
9382364945314756111151598927314730858659506106986221234093387699520351367458956\
6826746061072316261671373502714785049192001603417229108982012226088309908617629\
8872070243489939663610795811346363752181017554067425431559752550601382026156911\
3780895100534050732742127966592345435818085582694306976848223585665141172437642\
6246183053602016462500195041535455321849232707705714074346606848407533803095503\
0662092756903793560627795243602853592453814028038969325651651807834474016995015\
7145297660005105877738618967057434788165276561254283825749039212656443222071115\
9507133990050236357646039987078345837269261544531913234428573145047779638872024\
7231961873508543480335183925651362384560894816684002096907735636882928114063019\
8639404186671163330219048797536596095894515534088611078767555349245600810456086\
1691100992933226190463633693667420583952343845215794790321798039951594321541889\
3812134523883771149960956344721703393349973266640872642090563261224144022945059\
7506843386714409464614942390425245103703967155598265069597508734988402525962257\
2841952403383515837339037069116441077574901963864518532532376894687903148420536\
1275120421919647171778602465459469638033594256291015041199804351276935933706256\
6773307772119059113978607006966678527518507957463667350659115929171731941434920\
5116812514686680876543460435856593986928606550172516272287782741214624250761872\
5097380000091557667624195142281952797977547681023761748173084620132175384011831\
0221545904754070123830817170364688854948437384997228445618983489811173222999562\
7427270612033576579630007562482953353016901482854335848026500581679303105295299\
5988502785748478956135422156926920701610660197125767274816806637904005614403047\
7206943092469230040901978747282735864532153657034177468394395842685837329460320\
1968517313287158000187815049623921902104856870494090665589580732048760469124810\
8489971776137976776840869303263385368327581270947132834079341759444360269637927\
4951607546556152260458240963513674708294085845623139832224843763156453020816357\
3687668999026747846283350347904689412092360417799882209638756077965926439097218\
1026131840136258758154205069314765494266367179743240176915539029673868226517745\
4521653328095411224480331260702455779648169967785367164378914834397483554870432\
8466481761663972890805147448178558228544694286876810398651227935278079504967493\
2113990006656449458428131212534623270164433714062902171000724508367876607553017\
3685797333883904124846254182373088265269823554273785287700481020121338506883297\
5566843157121954125342612720310463502290002694653401689723727284386091144259496\
0279901848639547414923897868398503973157435265613502860748558532625553994889755\
9893195964573142248354702505806423966948144414352577224059851808184284926256841\
9196629841355265892789345143803195084577402486877929389820419236437718134472563\
3578073492758881024919085865828951953834196431429683427192899080002798436641955\
9692002471049919751064121252226539949152070130543605435752845797872214480359419\
2192908982001098506454100340001284282484841522793519057757894743539618358742188\
6054206015836632707479860431800784666695831521031752598041723694673684624804785\
2367881681500317467197795030433428950868582962617767982438362531758944660361832\
9242297079218624817787385972565837555472485810493851097294564536072476755875843\
8315148316320304075214495550957785682486495734034687570365124098158957230965862\
2451320991198548588001975256128700771758790861998861695632554540971801382553496\
4437381193150972037710826337016929255144984167455204189058764046679023909577486\
1177073449085648347791444452609775100171479794523884528213470064629470366529953\
9141558119424203230396841497503826812358023288483734876597925720344152304620598\
4032464049681143211432118619508954321515001506759862787702507961515659682587470\
9807002230652908393071952728587883647428611010285830149994526477909159804280395\
6031619601332684104705017156987473898358203487955039088638703220032247679254070\
8583618421977195520665651827409500265623856201157521549889164782090497501048123\
6544374560296347604941852380697554954952137689481028522552822629508908078678380\
6224146806700380049208215142508260786296227927216919140729150245748398197502479\
1162561448252564443481131452698660741288905316405185871148587088967120217429913\
5268982251247829458741807242228791766730704604385074127325061063405095368785055\
4149457234445393870979043340401128511528888309519250560818500106402072313452110\
2394679315938235838495341014491582561113911333426627700135235514654067818631070\
7261029131758964379625803308075812023239286476382267519557018250915396201724052\
6799743504556151394552677060489817993402794828072269755509827904322670226723751\
0601798699000928990170513546909301794189707299535459899549780066566900202379802\
5707725581523282904234650222324105296283707210296545305467627999325123561749981\
1651071952557810585362461905795107959005778213224555645977473058203058954554295\
5745707117699763678874048929041982380781323650871804047122438617214374601279514\
1118720783733448364379281350507591937473800836615193925593647352682747760051925\
6
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:18:59 2004

Input: a:=2^(2000000):


Output: Magma V2.10-22    Tue Jun 29 2004 11:18:56 on modular  [Seed = 3762366632]
   -------------------------------------


>> a:=2^(2000000):
                 ^
User error: bad syntax

Total time: 2.759 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:19:07 2004

Input: 2^(2000000);


Output: Magma V2.10-22    Tue Jun 29 2004 11:18:44 on modular  [Seed = 3998164626]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:19:11 2004

Input: a:=2^(2000000);



Output: Magma V2.10-22    Tue Jun 29 2004 11:19:08 on modular  [Seed = 4284364731]
   -------------------------------------


Total time: 2.539 seconds, Total memory usage: 1.91MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:19:49 2004

Input: ?sqrt;



Output: Magma V2.10-22    Tue Jun 29 2004 11:19:46 on modular  [Seed = 3412722545]
   -------------------------------------

15 matches:
     1   I   /magma/ring-field-algebra/algebraic-field/ideal/roots/SquareRoot
     2   I   /magma/ring-field-algebra/algebraic-field/operation-element/\
             field-element/Sqrt
     3   I   /magma/ring-field-algebra/algebraically-closed-field/creation/\
             roots/SquareRoot
     4   I   /magma/ring-field-algebra/finite-Galois-field/operation-element/\
             order-root/SquareRoot
     5   I   /magma/ring-field-algebra/function-field/ideals/ideals-roots/\
             SquareRoot
     6   I   /magma/ring-field-algebra/integer/residue-class-rings/special/Sqrt
     7   I   /magma/ring-field-algebra/lazy/elements/other/SquareRoot
     8   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
     9   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    10   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    11   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    12   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    13   I   /magma/ring-field-algebra/local/elt-roots/SquareRoot
    14   I   /magma/ring-field-algebra/real-complex/operation-element/simple/\
             SquareRoot
    15   I   /magma/ring-field-algebra/series-power-Laurent/operation-element/\
             square-root/SquareRoot
To view an entry, type ? followed by the number next to it

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:20:05 2004

Input: a:=1;



Output: Magma V2.10-22    Tue Jun 29 2004 11:20:02 on modular  [Seed = 3598130781]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jun 29 11:20:13 2004

Input: a;



Output: Magma V2.10-22    Tue Jun 29 2004 11:20:11 on modular  [Seed = 797894573]
   -------------------------------------


>> a;
   ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:48:37 2004

Input: F<a,b>=Group<a,b|a*b*a=b*a*b>;
(a*b)^3 eq (a*b*a)^2;

Output: Magma V2.10-22    Tue Jun 29 2004 12:48:34 on modular  [Seed = 2587576273]
   -------------------------------------


>> F<a,b>=Group<a,b|a*b*a=b*a*b>;
         ^
User error: bad syntax

>> (a*b)^3 eq (a*b*a)^2;;
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:48:47 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b>;
(a*b)^3 eq (a*b*a)^2;

Output: Magma V2.10-22    Tue Jun 29 2004 12:48:44 on modular  [Seed = 2503231696]
   -------------------------------------

false

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:49:56 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b>;
G<x>:=sub<F|(a*b)^3>;
H<y>:=sub<F|(a*b*a)^2>;
G eq H;


Output: Magma V2.10-22    Tue Jun 29 2004 12:49:41 on modular  [Seed = 3981193313]
   -------------------------------------

true

Total time: 14.689 seconds, Total memory usage: 29.67MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:50:50 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b>;
G<x>:=sub<F|a^3>;
H<y>:=sub<F|a^2>;
G eq H;


Output: Magma V2.10-22    Tue Jun 29 2004 12:50:44 on modular  [Seed = 3829741865]
   -------------------------------------


>> G eq H;
     ^
Runtime error in 'eq': Could not construct a closed coset table

Total time: 6.839 seconds, Total memory usage: 29.66MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:52:04 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12>;
G<x>:=sub<F|a^6*b^6>;
H<y>:=sub<F|b^6*a^6>;
G eq H;


Output: Magma V2.10-22    Tue Jun 29 2004 12:51:47 on modular  [Seed = 4233962230]
   -------------------------------------

true

Total time: 16.989 seconds, Total memory usage: 30.34MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:53:11 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12>;
G<x>:=sub<F|a^6*b^6*(b^6*a^6)^-1>;
H:=sub<F|>;
G eq H;


Output: Magma V2.10-22    Tue Jun 29 2004 12:52:59 on modular  [Seed = 4132907188]
   -------------------------------------


>> G eq H;
     ^
Runtime error in 'eq': Could not construct a closed coset table

Total time: 12.159 seconds, Total memory usage: 30.34MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:53:50 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12>;
G<x>:=sub<F|a*b*a*(b*a*b)^-1>;
H:=sub<F|>;
G eq H;


Output: Magma V2.10-22    Tue Jun 29 2004 12:53:38 on modular  [Seed = 3227590267]
   -------------------------------------

true

Total time: 12.209 seconds, Total memory usage: 30.34MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:54:22 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12>;
G<x>:=sub<F|a*b*a*(b*a*b)^-1>;
H:=sub<F|>;
G eq H;
IsIdentity(a*b*a*(b*a*b)^-1);

Output: Magma V2.10-22    Tue Jun 29 2004 12:54:09 on modular  [Seed = 3631810115]
   -------------------------------------

true

>> IsIdentity(a*b*a*(b*a*b)^-1);;
             ^
Runtime error in 'IsIdentity': Bad argument types
Argument types given: GrpFPElt

Total time: 12.189 seconds, Total memory usage: 30.34MB


************** MAGMA *****************
Host pD95350C3.dip.t-dialin.net. (217.83.80.195)
Time: Tue Jun 29 12:56:31 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2*b^2*(b^2*a^2)^-1>;
H:=sub<F|>;
G eq H;

Output: Magma V2.10-22    Tue Jun 29 2004 12:56:28 on modular  [Seed = 3547466950]
   -------------------------------------

false

Total time: 2.729 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A04.dip.t-dialin.net. (217.229.26.4)
Time: Tue Jun 29 13:19:12 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<c,d>:=Group<a,b|a*b*a=b*a*b,a^4,a^2*b^2=b^2*a^2>;
Index(F);
Index(G);

Output: Magma V2.10-22    Tue Jun 29 2004 13:19:09 on modular  [Seed = 465239996]
   -------------------------------------


>> Index(F);
        ^
Runtime error in 'Index': Bad argument types
Argument types given: GrpFP

>> Index(G);;
        ^
Runtime error in 'Index': Bad argument types
Argument types given: GrpFP

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E51A04.dip.t-dialin.net. (217.229.26.4)
Time: Tue Jun 29 13:19:32 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<c,d>:=Group<a,b|a*b*a=b*a*b,a^4,a^2*b^2=b^2*a^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 13:19:29 on modular  [Seed = 330495899]
   -------------------------------------

96
48

Total time: 2.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51A04.dip.t-dialin.net. (217.229.26.4)
Time: Tue Jun 29 13:20:32 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 13:20:30 on modular  [Seed = 2094897288]
   -------------------------------------

96
48

Total time: 2.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host 66-178-22-82.reverse.newskies.net. (66.178.22.82)
Time: Tue Jun 29 14:45:51 2004

Input: k:=GF(172316432754274362361);  E:= EllipticCurve([k | 3141, 5926]);
P1 := E![2718,73035449260546778840]; P2:=E![271828,53265169777564442543];
Log(P2,P1); 

Output: Magma V2.10-22    Tue Jun 29 2004 14:45:48 on modular  [Seed = 882232515]
   -------------------------------------

-1

Total time: 3.089 seconds, Total memory usage: 3.32MB


************** MAGMA *****************
Host fiber-83.aub.edu.lb. (69.60.65.83)
Time: Tue Jun 29 14:46:04 2004

Input: k:=GF(172316432754274362361);  E:= EllipticCurve([k | 3141, 5926]);
P1 := E![2718,73035449260546778840]; P2:=E![271828,53265169777564442543];
Log(P2,P1); 

Output: Magma V2.10-22    Tue Jun 29 2004 14:46:01 on modular  [Seed = 212726990]
   -------------------------------------

-1

Total time: 3.009 seconds, Total memory usage: 3.32MB


************** MAGMA *****************
Host 66-178-22-82.reverse.newskies.net. (66.178.22.82)
Time: Tue Jun 29 14:48:11 2004

Input: k:=GF(172316432754274362361);  E:= EllipticCurve([k | 3141, 5926]);
P1 := E![2718,73035449260546778840]; P2:=E![271828,53265169777564442543];
Log(P1,P2); 

Output: Magma V2.10-22    Tue Jun 29 2004 14:48:03 on modular  [Seed = 465232467]
   -------------------------------------

134712877515817113540

Total time: 7.759 seconds, Total memory usage: 3.32MB


************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:49:13 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2,a^2*c^2=c^2*a^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:49:06 on modular  [Seed = 3846464123]
   -------------------------------------

0
1536

Total time: 7.309 seconds, Total memory usage: 19.02MB


************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:50:08 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:50:00 on modular  [Seed = 4200299838]
   -------------------------------------

0
1536

Total time: 7.239 seconds, Total memory usage: 19.02MB


************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:50:57 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F : CosetLimit:=400000);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:50:51 on modular  [Seed = 3429713147]
   -------------------------------------

0
1536

Total time: 5.299 seconds, Total memory usage: 17.67MB


************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:51:17 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F : CosetLimit:=1000000);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:51:07 on modular  [Seed = 3294973123]
   -------------------------------------

0
1536

Total time: 9.799 seconds, Total memory usage: 28.04MB


************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:51:43 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F : CosetLimit:=4000000);
Order(G);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Tue Jun 29 2004 15:51:26 on modular  [Seed = 3699201230]
   -------------------------------------


Current total memory usage: 94.4MB, failed memory request: 1.0MB
System Error: User memory limit has been reached

Current total memory usage: 94.1MB, failed memory request: 2.5MB
System Error: User memory limit has been reached

Total time: 17.349 seconds, Total memory usage: 99.02MB


************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:52:13 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F : CosetLimit:=3000000);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:51:51 on modular  [Seed = 730506065]
   -------------------------------------



************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:52:41 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F : CosetLimit:=3000000);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:52:19 on modular  [Seed = 595766141]
   -------------------------------------



************** MAGMA *****************
Host pD9E51E70.dip.t-dialin.net. (217.229.30.112)
Time: Tue Jun 29 15:53:06 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
G:=quo<F|a^2*b^2=b^2*a^2,b^2*c^2=c^2*b^2>;
Order(F : CosetLimit:=2000000);
Order(G);

Output: Magma V2.10-22    Tue Jun 29 2004 15:52:48 on modular  [Seed = 983282311]
   -------------------------------------

0
1536

Total time: 17.779 seconds, Total memory usage: 55.12MB


************** MAGMA *****************
Host Toronto-HSE-ppp3694960.sympatico.ca. (65.95.88.59)
Time: Tue Jun 29 21:34:33 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Tue Jun 29 2004 21:34:30 on modular  [Seed = 10639505]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dsl254-023-142.sea1.dsl.speakeasy.net. (216.254.23.142)
Time: Tue Jun 29 22:51:56 2004

Input: C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);


Output: Magma V2.10-22    Tue Jun 29 2004 22:51:54 on modular  [Seed = 3682185517]
   -------------------------------------


>> C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
              ^
User error: Identifier 'P2' has not been declared or assigned

>> pt := C![0,0,1];
         ^
User error: Identifier 'C' has not been declared or assigned

>> E1,phi1 := EllipticCurve(C,pt);
                            ^
User error: Identifier 'C' has not been declared or assigned

>> E1,phi1;
   ^
User error: Identifier 'E1' has not been declared or assigned

>> IntegralPoints(E1);
                  ^
User error: Identifier 'E1' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dsl254-023-142.sea1.dsl.speakeasy.net. (216.254.23.142)
Time: Tue Jun 29 22:52:22 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);


Output: Magma V2.10-22    Tue Jun 29 2004 22:52:13 on modular  [Seed = 3547445554]
   -------------------------------------

Elliptic Curve defined by y^2 - 48*x*y - 23520*y = x^3 + 976*x^2 + 238112*x over
Rational Field
Mapping from: Crv: C to CrvEll: E1
with equations : 
-488*X^3 - 48*X^2*Z - 4*X*Y*Z + 4*X*Z^2
-976*X^2*Z - 96*X*Z^2 - 8*Y*Z^2 + 8*Z^3
X^3
and inverse
2*$.1*$.2*$.3
-$.1^3 - 488*$.1^2*$.3 - 24*$.1*$.2*$.3 + $.2^2*$.3
$.2^2*$.3
[ (-504 : -336 : 1), (-512 : -544 : 1), (-532 : -952 : 1), (-479 : 49 : 1), 
(-500 : -280 : 1), (-448 : 1568 : 1), (-536 : -1136 : 1), (-511 : -497 : 1), (0 
: 0 : 1) ]
[
    [ <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 1> ],
    [ <(-512 : -544 : 1), 1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 2> ],
    [ <(-500 : -200 : 1), -1> ],
    [ <(-500 : -200 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 1>, <(-500 : -200 : 1), -1> ],
    [ <(-512 : -544 : 1), 1>, <(-500 : -200 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 2>, <(-500 : -200 : 1), -1>, <(-504 : -336 : 1), 1> ]
]

Total time: 9.069 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host dsl254-023-142.sea1.dsl.speakeasy.net. (216.254.23.142)
Time: Tue Jun 29 22:55:27 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);


Output: Magma V2.10-22    Tue Jun 29 2004 22:55:18 on modular  [Seed = 2027557843]
   -------------------------------------

Elliptic Curve defined by y^2 - 48*x*y - 23520*y = x^3 + 976*x^2 + 238112*x over
Rational Field
Mapping from: Crv: C to CrvEll: E1
with equations : 
-488*X^3 - 48*X^2*Z - 4*X*Y*Z + 4*X*Z^2
-976*X^2*Z - 96*X*Z^2 - 8*Y*Z^2 + 8*Z^3
X^3
and inverse
2*$.1*$.2*$.3
-$.1^3 - 488*$.1^2*$.3 - 24*$.1*$.2*$.3 + $.2^2*$.3
$.2^2*$.3
[ (-504 : -336 : 1), (-512 : -512 : 1), (-532 : -1064 : 1), (-479 : 479 : 1), 
(-500 : -200 : 1), (-448 : 448 : 1), (-536 : -1072 : 1), (-511 : -511 : 1), (0 :
23520 : 1) ]
[
    [ <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), 1> ],
    [ <(-512 : -512 : 1), 1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), 2> ],
    [ <(-500 : -280 : 1), -1> ],
    [ <(-500 : -280 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), 1>, <(-500 : -280 : 1), -1> ],
    [ <(-512 : -512 : 1), 1>, <(-500 : -280 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), 2>, <(-500 : -280 : 1), -1>, <(-504 : -336 : 1), 1> ]
]

Total time: 9.099 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host dsl254-023-142.sea1.dsl.speakeasy.net. (216.254.23.142)
Time: Tue Jun 29 22:56:08 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);


Output: Magma V2.10-22    Tue Jun 29 2004 22:55:59 on modular  [Seed = 1610429661]
   -------------------------------------

Elliptic Curve defined by y^2 - 48*x*y - 23520*y = x^3 + 976*x^2 + 238112*x over
Rational Field
Mapping from: Crv: C to CrvEll: E1
with equations : 
-488*X^3 - 48*X^2*Z - 4*X*Y*Z + 4*X*Z^2
-976*X^2*Z - 96*X*Z^2 - 8*Y*Z^2 + 8*Z^3
X^3
and inverse
2*$.1*$.2*$.3
-$.1^3 - 488*$.1^2*$.3 - 24*$.1*$.2*$.3 + $.2^2*$.3
$.2^2*$.3
[ (-504 : -336 : 1), (-512 : -544 : 1), (-532 : -952 : 1), (-479 : 49 : 1), 
(-500 : -280 : 1), (-448 : 1568 : 1), (-536 : -1136 : 1), (-511 : -497 : 1), (0 
: 0 : 1) ]
[
    [ <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 1> ],
    [ <(-512 : -544 : 1), 1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 2> ],
    [ <(-500 : -200 : 1), -1> ],
    [ <(-500 : -200 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 1>, <(-500 : -200 : 1), -1> ],
    [ <(-512 : -544 : 1), 1>, <(-500 : -200 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -544 : 1), 2>, <(-500 : -200 : 1), -1>, <(-504 : -336 : 1), 1> ]
]

Total time: 9.099 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Tue Jun 29 22:56:27 2004

Input: 34523452345234523452345234523462367245734563456*23456234512345213534643574567456345234

Output: Magma V2.10-22    Tue Jun 29 2004 22:56:24 on modular  [Seed = 3172980312]
   -------------------------------------

8097901943855953307489710911779458872037890286734767867869559302480778984142161\
68704

Total time: 2.530 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host client-200.60.187.164.speedy.net.pe. (200.60.187.164)
Time: Tue Jun 29 22:56:27 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);

Output: Magma V2.10-22    Tue Jun 29 2004 22:56:17 on modular  [Seed = 1358052284]
   -------------------------------------

Elliptic Curve defined by y^2 - 48*x*y - 23520*y = x^3 + 976*x^2 + 238112*x over
Rational Field
Mapping from: Crv: C to CrvEll: E1
with equations : 
-488*X^3 - 48*X^2*Z - 4*X*Y*Z + 4*X*Z^2
-976*X^2*Z - 96*X*Z^2 - 8*Y*Z^2 + 8*Z^3
X^3
and inverse
2*$.1*$.2*$.3
-$.1^3 - 488*$.1^2*$.3 - 24*$.1*$.2*$.3 + $.2^2*$.3
$.2^2*$.3
[ (-504 : -336 : 1), (-500 : -280 : 1), (-448 : 1568 : 1), (-479 : 49 : 1), (0 :
0 : 1), (-512 : -544 : 1), (-532 : -952 : 1), (-536 : -1136 : 1), (-511 : -497 :
1) ]
[
    [ <(-504 : -336 : 1), 1> ],
    [ <(-500 : -280 : 1), 1> ],
    [ <(-500 : -280 : 1), 1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), -2> ],
    [ <(-500 : -280 : 1), 1>, <(-512 : -512 : 1), -2>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), -1> ],
    [ <(-512 : -512 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-500 : -280 : 1), 1>, <(-512 : -512 : 1), -1> ],
    [ <(-500 : -280 : 1), 1>, <(-512 : -512 : 1), -1>, <(-504 : -336 : 1), 1> ]
]

Total time: 9.249 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host CPE-24-163-232-254.mn.rr.com. (24.163.232.254)
Time: Tue Jun 29 22:56:36 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);

Output: Magma V2.10-22    Tue Jun 29 2004 22:56:33 on modular  [Seed = 3004291183]
   -------------------------------------


>> C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)));
             ^
Runtime error in 'Curve': Defining polynomials must be non-constant and 
homogeneous with respect to all the gradings of the ambient

>> pt := C![0,0,1];
         ^
User error: Identifier 'C' has not been declared or assigned

>> E1,phi1 := EllipticCurve(C,pt);
                            ^
User error: Identifier 'C' has not been declared or assigned

>> E1,phi1;
   ^
User error: Identifier 'E1' has not been declared or assigned

>> IntegralPoints(E1);;
                  ^
User error: Identifier 'E1' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cable-68-184-68-23.abr.al.charter.com. (68.184.68.23)
Time: Tue Jun 29 22:57:10 2004

Input: // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
// TEST1
RandomHEC_3_2();


Output: Magma V2.10-22    Tue Jun 29 2004 22:57:08 on modular  [Seed = 2570843552]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + y = x^7 + x^4 + x^3 + x^2 + x + 1 over
GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host CPE-24-163-232-254.mn.rr.com. (24.163.232.254)
Time: Tue Jun 29 22:57:39 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z - Y*Z^2 - (2*X*(X-Z)*(X-2*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);

Output: Magma V2.10-22    Tue Jun 29 2004 22:57:30 on modular  [Seed = 2436103606]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 2904*x^2 + 1874048*x + 113379904 over 
Rational Field
Mapping from: Crv: C to CrvEll: E1
with equations : 
-242*X^2 + 2662*X*Z
10648*X^2 - 2662*X*Y + 5324*X*Z + 58564*Y*Z - 58564*Z^2
X^2 + 1/4*X*Y
and inverse
-1/4*$.1^2 + 2662*$.1*$.3
$.1^2 + 242*$.1*$.3 + 121*$.2*$.3 - 1288408*$.3^2
$.1^2 + 1/88*$.1*$.2 + 121*$.1*$.3
[ (968 : -10648 : 1), (2904 : -74536 : 1), (121 : -17303 : 1), (356 : 21392 : 
1), (6776 : 436568 : 1), (1089 : 1331 : 1), (10648 : -947672 : 1), (1936 : 
-10648 : 1), (0 : 10648 : 1), (2420 : 42592 : 1), (56144 : 12958616 : 1), (484 :
21296 : 1), (5808 : 330088 : 1), (-24 : 8168 : 1), (617584 : 484196504 : 1) ]
[
    [ <(968 : -10648 : 1), 1> ],
    [ <(968 : -10648 : 1), 2> ],
    [ <(968 : -10648 : 1), 3> ],
    [ <(968 : -10648 : 1), 3>, <(1936 : 10648 : 1), -3> ],
    [ <(1936 : 10648 : 1), -2> ],
    [ <(968 : -10648 : 1), 1>, <(1936 : 10648 : 1), -2> ],
    [ <(968 : -10648 : 1), 2>, <(1936 : 10648 : 1), -2> ],
    [ <(1936 : 10648 : 1), -1> ],
    [ <(968 : -10648 : 1), 1>, <(1936 : 10648 : 1), -1> ],
    [ <(968 : -10648 : 1), 2>, <(1936 : 10648 : 1), -1> ],
    [ <(968 : -10648 : 1), 4>, <(1936 : 10648 : 1), -1> ],
    [ <(968 : -10648 : 1), 1>, <(1936 : 10648 : 1), 1> ],
    [ <(968 : -10648 : 1), 2>, <(1936 : 10648 : 1), 1> ],
    [ <(968 : -10648 : 1), 3>, <(1936 : 10648 : 1), 2> ],
    [ <(968 : -10648 : 1), 2>, <(1936 : 10648 : 1), 3> ]
]

Total time: 8.899 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Tue Jun 29 23:01:00 2004

Input: phi(1345)

Output: Magma V2.10-22    Tue Jun 29 2004 23:00:58 on modular  [Seed = 515666634]
   -------------------------------------


>> phi(1345);
   ^
User error: Identifier 'phi' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Tue Jun 29 23:10:27 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, ab = ba>;
CharacterTable(G);

Output: Magma V2.10-22    Tue Jun 29 2004 23:10:24 on modular  [Seed = 499085826]
   -------------------------------------


>> G<b, a> := PolycyclicGroup< b, a | b^4, a^3, ab = ba>;
                                                     ^
User error: Identifier 'ba' has not been declared or assigned

>> CharacterTable(G);;
                  ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Tue Jun 29 23:10:43 2004

Input: G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a*b = b*a>;
CharacterTable(G);

Output: Magma V2.10-22    Tue Jun 29 2004 23:10:41 on modular  [Seed = 364345883]
   -------------------------------------


>> G<b, a> := PolycyclicGroup< b, a | b^4, a^3, a*b = b*a>;
                             ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : $.2 *
$.1 = $.1 * $.2

>> CharacterTable(G);;
                  ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Tue Jun 29 23:13:18 2004

Input: G := Group< b, a | b^4, a^3, a*b = b*a>;
CharacterTable(G);

Output: Magma V2.10-22    Tue Jun 29 2004 23:13:15 on modular  [Seed = 1273570495]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Tue Jun 29 23:13:50 2004

Input: G<a, b> := Group< b, a | b^4, a^3, a*b = b*a>;
CharacterTable(G);

Output: Magma V2.10-22    Tue Jun 29 2004 23:13:47 on modular  [Seed = 2987449702]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:05:12 2004

Input: G := Group<a, b | a^2, b^2, ab>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:05:09 on modular  [Seed = 2553996072]
   -------------------------------------


>> G := Group<a, b | a^2, b^2, ab>;
                               ^
User error: Identifier 'ab' has not been declared or assigned

>> CharacterTable(G);;
                  ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:05:25 2004

Input: G := Group<a, b | a^2, b^2, a*b>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:05:22 on modular  [Seed = 3004289012]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:05:44 2004

Input: G := Group<a, b | a^2, c^2, a*b^2>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:05:41 on modular  [Seed = 3122185962]
   -------------------------------------


>> G := Group<a, b | a^2, c^2, a*b^2>;
                          ^
User error: Identifier 'c' has not been declared or assigned

>> CharacterTable(G);;
                  ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.709 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:05:56 2004

Input: G := Group<a, b | a^2, b^2, a*b^2>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:05:53 on modular  [Seed = 1408315188]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:06:16 2004

Input: G := Group<a, b | a^2, b^3, a*b^2>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:06:14 on modular  [Seed = 1758073880]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:06:35 2004

Input: G := Group<a, b | a^2, b^3, a*b^2*a>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:06:32 on modular  [Seed = 1909656959]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:10:27 2004

Input: G<a, b> := Group<a, b | a^2, b^3, a*b^2*a>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:10:24 on modular  [Seed = 3311909043]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:10:47 2004

Input: G<a, b> := Group<a, b | a^2, b^3, a*b^2*a*b>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:10:45 on modular  [Seed = 3514019026]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:11:13 2004

Input: G<a, b> := Group<a, b | a^2, b^3, a*b^2*a*b^2>;
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:11:10 on modular  [Seed = 3947468531]
   -------------------------------------


>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:12:23 2004

Input: G<a, b> := Group<a, b | a^2, b^3, a*b^2*a*b^2>;
Order(G);
CharacterTable(G);

Output: Magma V2.10-22    Wed Jun 30 2004 00:12:20 on modular  [Seed = 2671633021]
   -------------------------------------

6

>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:30:09 2004

Input: Order(Group<a, b | a^2, b^3, a*b^2*a*b^2>);

Output: Magma V2.10-22    Wed Jun 30 2004 00:30:06 on modular  [Seed = 1509644510]
   -------------------------------------

6

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:30:25 2004

Input: CharacterTable(Group<a, b | a^2, b^3, a*b^2*a*b^2>);

Output: Magma V2.10-22    Wed Jun 30 2004 00:30:22 on modular  [Seed = 1374900422]
   -------------------------------------


>> CharacterTable(Group<a, b | a^2, b^3, a*b^2*a*b^2>);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:50:27 2004

Input: CharacterTable(pQuotient(Group<a, b | a^2, b^3, a*b^2*a*b^2>, 2, 0));

Output: Magma V2.10-22    Wed Jun 30 2004 00:50:25 on modular  [Seed = 2785321085]
   -------------------------------------

Class limit set to 127.


Character Table
---------------


-------------
Class |   1 2
Size  |   1 1
Order |   1 2
-------------
p  =  2   1 1
-------------
X.1   +   1 1
X.2   +   1-1




Total time: 2.559 seconds, Total memory usage: 21.67MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:51:26 2004

Input: CharacterTable(pQuotient(Group<a, b | a^2, b^4, a*b^2*a*b^2>, 2, 0));

Output: Magma V2.10-22    Wed Jun 30 2004 00:51:03 on modular  [Seed = 1223315124]
   -------------------------------------

Class limit set to 127.


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:52:55 2004

Input: CharacterTable(Sym(5));

Output: Magma V2.10-22    Wed Jun 30 2004 00:52:53 on modular  [Seed = 482220914]
   -------------------------------------



Character Table
---------------


-----------------------------
Class |   1  2  3  4  5  6  7
Size  |   1 10 15 20 30 24 20
Order |   1  2  2  3  4  5  6
-----------------------------
p  =  2   1  1  1  4  3  6  4
p  =  3   1  2  3  1  5  6  2
p  =  5   1  2  3  4  5  1  7
-----------------------------
X.1   +   1  1  1  1  1  1  1
X.2   +   1 -1  1  1 -1  1 -1
X.3   +   4  2  0  1  0 -1 -1
X.4   +   4 -2  0  1  0 -1  1
X.5   +   5  1  1 -1 -1  0  1
X.6   +   5 -1  1 -1  1  0 -1
X.7   +   6  0 -2  0  0  1  0




Total time: 2.479 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:53:21 2004

Input: CharacterTable(Sym(7));

Output: Magma V2.10-22    Wed Jun 30 2004 00:53:18 on modular  [Seed = 966475340]
   -------------------------------------



Character Table
---------------


------------------------------------------------------------------
Class |    1  2   3   4  5   6   7   8   9  10  11  12  13  14  15
Size  |    1 21 105 105 70 280 210 630 504 210 420 840 720 504 420
Order |    1  2   2   2  3   3   4   4   5   6   6   6   7  10  12
------------------------------------------------------------------
p  =  2    1  1   1   1  5   6   4   4   9   5   5   6  13   9  10
p  =  3    1  2   3   4  1   1   7   8   9   4   2   3  13  14   7
p  =  5    1  2   3   4  5   6   7   8   1  10  11  12  13   2  15
p  =  7    1  2   3   4  5   6   7   8   9  10  11  12   1  14  15
------------------------------------------------------------------
X.1   +    1  1   1   1  1   1   1   1   1   1   1   1   1   1   1
X.2   +    1 -1  -1   1  1   1  -1   1   1   1  -1  -1   1  -1  -1
X.3   +    6  4   0   2  3   0   2   0   1  -1   1   0  -1  -1  -1
X.4   +    6 -4   0   2  3   0  -2   0   1  -1  -1   0  -1   1   1
X.5   +   14  4   0   2 -1   2  -2   0  -1  -1   1   0   0  -1   1
X.6   +   14  6   2   2  2  -1   0   0  -1   2   0  -1   0   1   0
X.7   +   14 -6  -2   2  2  -1   0   0  -1   2   0   1   0  -1   0
X.8   +   14 -4   0   2 -1   2   2   0  -1  -1  -1   0   0   1  -1
X.9   +   15  5  -3  -1  3   0   1  -1   0  -1  -1   0   1   0   1
X.10  +   15 -5   3  -1  3   0  -1  -1   0  -1   1   0   1   0  -1
X.11  +   20  0   0  -4  2   2   0   0   0   2   0   0  -1   0   0
X.12  +   21  1  -3   1 -3   0  -1  -1   1   1   1   0   0   1  -1
X.13  +   21 -1   3   1 -3   0   1  -1   1   1  -1   0   0  -1   1
X.14  +   35  5   1  -1 -1  -1  -1   1   0  -1  -1   1   0   0  -1
X.15  +   35 -5  -1  -1 -1  -1   1   1   0  -1   1  -1   0   0   1




Total time: 2.549 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:54:37 2004

Input: CharacterTable(Sym(12));

Output: Magma V2.10-22    Wed Jun 30 2004 00:54:33 on modular  [Seed = 3930647848]
   -------------------------------------



Character Table
---------------


----------------------------------------------------------------------------
Class |      1   2    3     4     5     6     7   8     9     10     11   12
Size  |      1  66 1485 10395 13860 51975 62370 440 36960 246400 492800 2970
Order |      1   2    2     2     2     2     2   3     3      3      3    4
----------------------------------------------------------------------------
p  =  2      1   1    1     1     1     1     1   8     9     10     11    3
p  =  3      1   2    3     4     5     6     7   1     1      1      1   12
p  =  5      1   2    3     4     5     6     7   8     9     10     11   12
p  =  7      1   2    3     4     5     6     7   8     9     10     11   12
p  = 11      1   2    3     4     5     6     7   8     9     10     11   12
----------------------------------------------------------------------------
X.1   +      1   1    1     1     1     1     1   1     1      1      1    1
X.2   +      1  -1    1     1    -1     1    -1   1     1      1      1   -1
X.3   +     11   9    7    -1     5     3     1   8     5     -1      2    7
X.4   +     11  -9    7    -1    -5     3    -1   8     5     -1      2   -7
X.5   +     54  36   22     6    12     6     4  27     9      0      0   20
X.6   +     54 -36   22     6   -12     6    -4  27     9      0      0  -20
X.7   +     55  35   19    -5     7    -1    -5  28    10      1      1   21
X.8   +     55 -35   19    -5    -7    -1     5  28    10      1      1  -21
X.9   +    132  48   20    20     8     4     0   6     6      6     -3   -8
X.10  +    132 -48   20    20    -8     4     0   6     6      6     -3    8
X.11  +    154  84   42    -6    20    10     4  49     7      4      1   28
X.12  +    154 -84   42    -6   -20    10    -4  49     7      4      1  -28
X.13  +    165  75   21     5    -5   -11    -5  57    12      3      3   35
X.14  +    165 -75   21     5     5   -11     5  57    12      3      3  -35
X.15  +    275 125   55    15    25    11     5  50     5     -4      5   15
X.16  +    275-125   55    15   -25    11    -5  50     5     -4      5  -15
X.17  +    297 117   49   -15    21     9     5  27     9      0      0   -7
X.18  +    297-117   49   -15   -21     9    -5  27     9      0      0    7
X.19  +    320 160   64     0    16     0     0 104    14     -4     -4   64
X.20  +    320-160   64     0   -16     0     0 104    14     -4     -4  -64
X.21  +    330  90   -6    10   -22    -6    10  78    15     -3      6   34
X.22  +    330 -90   -6    10    22    -6   -10  78    15     -3      6  -34
X.23  +    462 -42  -42   -10    14    14   -10  84    21      3      3  -14
X.24  +    462 -42   14    30    -2    -2   -10 -42     3     12      3   14
X.25  +    462  42  -42   -10   -14    14    10  84    21      3      3   14
X.26  +    462  42   14    30     2    -2    10 -42     3     12      3  -14
X.27  +    616 224   56    24     8     8    16 112    -5      4     -5   56
X.28  +    616-224   56    24    -8     8   -16 112    -5      4     -5  -56
X.29  +    891 351  111    -9    27     3    -9 162     0      0      0   69
X.30  +    891-351  111    -9   -27     3     9 162     0      0      0  -69
X.31  +    945 315   49   -15   -21   -15    -5 189     9      0      0   91
X.32  +    945-315   49   -15    21   -15     5 189     9      0      0  -91
X.33  +   1155 315   91    -5    19     3    -5  21    21     -6     -6  -49
X.34  +   1155-315   91    -5   -19     3     5  21    21     -6     -6   49
X.35  +   1320 240   56   -40     8     8     0 -48    15      6     -3  -56
X.36  +   1320-240   56   -40    -8     8     0 -48    15      6     -3   56
X.37  +   1408 448  128     0    32     0     0 112     4      4      4    0
X.38  +   1408-448  128     0   -32     0     0 112     4      4      4    0
X.39  +   1485 225   29    45   -15    -3   -15 -27    18      0      0  -55
X.40  +   1485-225   29    45    15    -3    15 -27    18      0      0   55
X.41  +   1650 300   50   -30    20     2   -20 -15   -15     12      3  -20
X.42  +   1650-300   50   -30   -20     2    20 -15   -15     12      3   20
X.43  +   1728 288  -64     0   -48     0     0 216    18      0      0   64
X.44  +   1728-288  -64     0    48     0     0 216    18      0      0  -64
X.45  +   1925-175  -35    45   -15    21   -15  35   -10      8      8  -35
X.46  +   1925 175  -35    45    15    21    15  35   -10      8      8   35
X.47  +   1925 525  105   -15    25    13     5 140   -25     -4     -1   35
X.48  +   1925-525  105   -15   -25    13    -5 140   -25     -4     -1  -35
X.49  +   2079 441    7    -9   -15    15     9 189   -18      0      0   77
X.50  +   2079-441    7    -9    15    15    -9 189   -18      0      0  -77
X.51  +   2100   0 -140    20     0    20     0 210    30     -6     -6    0
X.52  +   2112 288   64     0    16     0     0-120     6    -12      6  -64
X.53  +   2112-288   64     0   -16     0     0-120     6    -12      6   64
X.54  +   2376 576   56    24   -24   -24   -16 216    -9      0      0   56
X.55  +   2376-576   56    24    24   -24    16 216    -9      0      0  -56
X.56  +   2640   0   16    80     0    16     0-168    12     -6     -6    0
X.57  +   2673 567  117    45    27     9    15   0     0      0      0  -63
X.58  +   2673-567  117    45   -27     9   -15   0     0      0      0   63
X.59  +   2970  90   34   -30    -6    -6    10-216     9      0      0  -34
X.60  +   2970 -90   34   -30     6    -6   -10-216     9      0      0   34
X.61  +   3080 560   56   -40   -24   -24     0  56    11      2      2  -56
X.62  +   3080-560   56   -40    24   -24     0  56    11      2      2   56
X.63  +   3520 160  -64     0   -48     0     0  -8    10     -8     10  -64
X.64  +   3520-160  -64     0    48     0     0  -8    10     -8     10   64
X.65  +   3564 216 -132   -36     0    12   -24 162     0      0      0   48
X.66  +   3564-216 -132   -36     0    12    24 162     0      0      0  -48
X.67  +   3696-336 -112    16    48   -16   -16 168     6      6     -3    0
X.68  +   3696 336 -112    16   -48   -16    16 168     6      6     -3    0
X.69  +   4158 252   14    30    12   -18   -20-189    -9      0      0  -28
X.70  +   4158-252   14    30   -12   -18    20-189    -9      0      0   28
X.71  +   4455 135  -21   -45    27    15    15-162     0      0      0   21
X.72  +   4455-135  -21   -45   -27    15   -15-162     0      0      0  -21
X.73  +   5632 768    0     0     0     0     0  64   -32     -8     -2    0
X.74  +   5632-768    0     0     0     0     0  64   -32     -8     -2    0
X.75  +   5775-525   35    -5    15     7    -5-210    15      6     -3  105
X.76  +   5775 525   35    -5   -15     7     5-210    15      6     -3 -105
X.77  +   7700   0 -140    20     0   -12     0 -70   -10      2     -4    0


--------------------------------------------------------------------------
Class |      13     14     15     16      17      18      19      20    21
Size  |   83160 311850 623700 623700 1247400 1247400 1871100 3742200 19008
Order |       4      4      4      4       4       4       4       4     5
--------------------------------------------------------------------------
p  =  2       3      3      6      3       4       3       6       6    21
p  =  3      13     14     15     16      17      18      19      20    21
p  =  5      13     14     15     16      17      18      19      20     1
p  =  7      13     14     15     16      17      18      19      20    21
p  = 11      13     14     15     16      17      18      19      20    21
--------------------------------------------------------------------------
X.1   +       1      1      1      1       1       1       1       1     1
X.2   +       1     -1      1     -1      -1       1       1      -1     1
X.3   +       5     -1      3      3      -1       1      -1       1     6
X.4   +       5      1      3     -3       1       1      -1      -1     6
X.5   +      10      4      2      4       0       2       2       0    14
X.6   +      10     -4      2     -4       0       2       2       0    14
X.7   +       9     -3      3      1       1      -3      -1      -1    15
X.8   +       9      3      3     -1      -1      -3      -1       1    15
X.9   +       0      8      4      0       0       0       4       0    -8
X.10  +       0     -8      4      0       0       0       4       0    -8
X.11  +      10     -4     -2      4       0       2      -2       0    14
X.12  +      10      4     -2     -4       0       2      -2       0    14
X.13  +       5      3      1     -5      -1      -3       1      -1    20
X.14  +       5     -3      1      5       1      -3       1       1    20
X.15  +       5      7     -1      3       3       1       3       1     0
X.16  +       5     -7     -1     -3      -3       1       3      -1     0
X.17  +       1     -7      5      1      -3       1      -3       1   -13
X.18  +       1      7      5     -1       3       1      -3      -1   -13
X.19  +      16      0      0      0       0       0       0       0    35
X.20  +      16      0      0      0       0       0       0       0    35
X.21  +      -6      2     -2     -6      -2       2      -2      -2    15
X.22  +      -6     -2     -2      6       2       2      -2       2    15
X.23  +     -14      2     -6      2      -2       2       2       2     7
X.24  +      -6     -2      2     -2      -6       2       2       2     7
X.25  +     -14     -2     -6     -2       2       2       2      -2     7
X.26  +      -6      2      2      2       6       2       2      -2     7
X.27  +       4      8      0      0       0       4       0       0    21
X.28  +       4     -8      0      0       0       4       0       0    21
X.29  +       9     -3     -5      1      -3      -3      -1      -1    21
X.30  +       9      3     -5     -1       3      -3      -1       1 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:55:40 2004

Input: CharacterTable(PSL(2,7));

Output: Magma V2.10-22    Wed Jun 30 2004 00:55:37 on modular  [Seed = 2183169280]
   -------------------------------------



Character Table
---------------


------------------------------
Class |   1  2  3  4    5    6
Size  |   1 21 56 42   24   24
Order |   1  2  3  4    7    7
------------------------------
p  =  2   1  1  3  2    5    6
p  =  3   1  2  1  4    6    5
p  =  7   1  2  3  4    1    1
------------------------------
X.1   +   1  1  1  1    1    1
X.2   0   3 -1  0  1   Z1 Z1#3
X.3   0   3 -1  0  1 Z1#3   Z1
X.4   +   6  2  0  0   -1   -1
X.5   +   7 -1  1 -1    0    0
X.6   +   8  0 -1  0    1    1


Explanation of Symbols:
-----------------------

# denotes algebraic conjugation, that is,
#k indicates replacing the root of unity w by w^k

Z1     = (CyclotomicField(7)) ! [ RationalField() | -1, -1, -1, 0, -1, 0 ]



Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 00:56:49 2004

Input: CharacterTable(Alt(8));

Output: Magma V2.10-22    Wed Jun 30 2004 00:56:47 on modular  [Seed = 2836111853]
   -------------------------------------



Character Table
---------------


--------------------------------------------------------------------------
Class |    1   2   3   4    5    6    7    8    9   10   11   12   13   14
Size  |    1 105 210 112 1120 1260 2520 1344 1680 3360 2880 2880 1344 1344
Order |    1   2   2   3    3    4    4    5    6    6    7    7   15   15
--------------------------------------------------------------------------
p  =  2    1   1   1   4    5    2    3    8    4    5   11   12   13   14
p  =  3    1   2   3   1    1    6    7    8    3    2   12   11    8    8
p  =  5    1   2   3   4    5    6    7    1    9   10   12   11    4    4
p  =  7    1   2   3   4    5    6    7    8    9   10    1    1   14   13
--------------------------------------------------------------------------
X.1   +    1   1   1   1    1    1    1    1    1    1    1    1    1    1
X.2   +    7  -1   3   4    1   -1    1    2    0   -1    0    0   -1   -1
X.3   +   14   6   2  -1    2    2    0   -1   -1    0    0    0   -1   -1
X.4   +   20   4   4   5   -1    0    0    0    1    1   -1   -1    0    0
X.5   +   21  -3   1   6    0    1   -1    1   -2    0    0    0    1    1
X.6   0   21  -3   1  -3    0    1   -1    1    1    0    0    0   Z2 Z2#7
X.7   0   21  -3   1  -3    0    1   -1    1    1    0    0    0 Z2#7   Z2
X.8   +   28  -4   4   1    1    0    0   -2    1   -1    0    0    1    1
X.9   +   35   3  -5   5    2   -1   -1    0    1    0    0    0    0    0
X.10  0   45  -3  -3   0    0    1    1    0    0    0   Z1 Z1#3    0    0
X.11  0   45  -3  -3   0    0    1    1    0    0    0 Z1#3   Z1    0    0
X.12  +   56   8   0  -4   -1    0    0    1    0   -1    0    0    1    1
X.13  +   64   0   0   4   -2    0    0   -1    0    0    1    1   -1   -1
X.14  +   70  -2   2  -5    1   -2    0    0   -1    1    0    0    0    0


Explanation of Symbols:
-----------------------

# denotes algebraic conjugation, that is,
#k indicates replacing the root of unity w by w^k

Z1     = (CyclotomicField(7)) ! [ RationalField() | 0, 1, 1, 0, 1, 0 ]

Z2     = (CyclotomicField(15)) ! [ RationalField() | -2, 2, 1, -1, 2, -1, 0, 1 ]



Total time: 2.659 seconds, Total memory usage: 2.10MB


************** MAGMA *****************
Host blackhole.uhkt.cz. (62.168.16.194)
Time: Wed Jun 30 02:35:37 2004

Input: x:=53:y:=21:x*y

Output: Magma V2.10-22    Wed Jun 30 2004 02:35:34 on modular  [Seed = 2351862766]
   -------------------------------------


>> x:=53:y:=21:x*y;
        ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host blackhole.uhkt.cz. (62.168.16.194)
Time: Wed Jun 30 02:36:18 2004

Input: x:=53
y:=21
x*y

Output: Magma V2.10-22    Wed Jun 30 2004 02:36:15 on modular  [Seed = 3122177457]
   -------------------------------------


>> y:=21
   ^
User error: bad syntax

>> x*y;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (80.253.171.75)
Time: Wed Jun 30 07:59:08 2004

Input: 25

Output: Magma V2.10-22    Wed Jun 30 2004 07:59:05 on modular  [Seed = 865196118]
   -------------------------------------

25

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 13:57:40 2004

Input: CharacterTable(Sym(5));

Output: Magma V2.10-22    Wed Jun 30 2004 13:57:37 on modular  [Seed = 4234036126]
   -------------------------------------



Character Table
---------------


-----------------------------
Class |   1  2  3  4  5  6  7
Size  |   1 10 15 20 30 24 20
Order |   1  2  2  3  4  5  6
-----------------------------
p  =  2   1  1  1  4  3  6  4
p  =  3   1  2  3  1  5  6  2
p  =  5   1  2  3  4  5  1  7
-----------------------------
X.1   +   1  1  1  1  1  1  1
X.2   +   1 -1  1  1 -1  1 -1
X.3   +   4  2  0  1  0 -1 -1
X.4   +   4 -2  0  1  0 -1  1
X.5   +   5  1  1 -1 -1  0  1
X.6   +   5 -1  1 -1  1  0 -1
X.7   +   6  0 -2  0  0  1  0




Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 14:03:55 2004

Input: CharacterTable(Sym(16));

Output: Magma V2.10-22    Wed Jun 30 2004 14:03:33 on modular  [Seed = 3732774616]
   -------------------------------------



************** MAGMA *****************
Host client-200.60.187.164.speedy.net.pe. (200.60.187.164)
Time: Wed Jun 30 17:44:07 2004

Input: P2<X, Y, Z> := ProjectiveSpace(Rationals(), 2);
C := Curve(P2, Y^2*Z^2 - Y*Z^3 - (2*X*(X-Z)*(X-2*Z)*(X-3*Z)));
pt := C![0,0,1];
E1,phi1 := EllipticCurve(C,pt);
E1,phi1;
IntegralPoints(E1);
TorsionSubgroup(E1);
TorsionSubgroupScheme(E1,2);
MordellWeilGroup(E1);
Generators(E1);

Output: Magma V2.10-22    Wed Jun 30 2004 17:43:57 on modular  [Seed = 2638145930]
   -------------------------------------

Elliptic Curve defined by y^2 - 48*x*y - 23520*y = x^3 + 976*x^2 + 238112*x over
Rational Field
Mapping from: Crv: C to CrvEll: E1
with equations : 
-488*X^3 - 48*X^2*Z - 4*X*Y*Z + 4*X*Z^2
-976*X^2*Z - 96*X*Z^2 - 8*Y*Z^2 + 8*Z^3
X^3
and inverse
2*$.1*$.2*$.3
-$.1^3 - 488*$.1^2*$.3 - 24*$.1*$.2*$.3 + $.2^2*$.3
$.2^2*$.3
[ (-504 : -336 : 1), (-500 : -280 : 1), (-448 : 1568 : 1), (-479 : 49 : 1), (0 :
0 : 1), (-512 : -544 : 1), (-532 : -952 : 1), (-536 : -1136 : 1), (-511 : -497 :
1) ]
[
    [ <(-504 : -336 : 1), 1> ],
    [ <(-500 : -280 : 1), 1> ],
    [ <(-500 : -280 : 1), 1>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), -2> ],
    [ <(-500 : -280 : 1), 1>, <(-512 : -512 : 1), -2>, <(-504 : -336 : 1), 1> ],
    [ <(-512 : -512 : 1), -1> ],
    [ <(-512 : -512 : 1), -1>, <(-504 : -336 : 1), 1> ],
    [ <(-500 : -280 : 1), 1>, <(-512 : -512 : 1), -1> ],
    [ <(-500 : -280 : 1), 1>, <(-512 : -512 : 1), -1>, <(-504 : -336 : 1), 1> ]
]
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0
Subgroup scheme of E1 defined by x^3 + 1552*x^2 + 802592*x + 138297600
Abelian Group isomorphic to Z/2 + Z + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
[ (-504 : -336 : 1), (-512 : -544 : 1), (-500 : -280 : 1) ]

Total time: 9.139 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 23:08:54 2004

Input: EulerPhi(196883);

Output: Magma V2.10-22    Wed Jun 30 2004 23:08:51 on modular  [Seed = 713681510]
   -------------------------------------

186760

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host proxy1.bezeqint.net. (192.115.106.236)
Time: Wed Jun 30 23:09:10 2004

Input: Factor(EulerPhi(196883));

Output: Magma V2.10-22    Wed Jun 30 2004 23:09:07 on modular  [Seed = 578937470]
   -------------------------------------


>> Factor(EulerPhi(196883));;
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngIntElt

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (139.91.254.18)
Time: Thu Jul  1 03:11:31 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Thu Jul  1 2004 03:11:28 on modular  [Seed = 2419288481]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 2(SERVFAIL) (139.91.254.18)
Time: Thu Jul  1 03:11:55 2004

Input: x=4+5

Output: Magma V2.10-22    Thu Jul  1 2004 03:11:52 on modular  [Seed = 2604163762]
   -------------------------------------


>> x=4+5;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-14-71-44.client.comcast.net. (24.14.71.44)
Time: Thu Jul  1 03:20:53 2004

Input: Index(Gamma1(5));

Output: Magma V2.10-22    Thu Jul  1 2004 03:20:50 on modular  [Seed = 3138928889]
   -------------------------------------

12

Total time: 2.519 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:33:07 2004

Input: 3+4

Output: Magma V2.10-22    Thu Jul  1 2004 04:33:05 on modular  [Seed = 1223410715]
   -------------------------------------

7

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:33:17 2004

Input: a+b

Output: Magma V2.10-22    Thu Jul  1 2004 04:33:15 on modular  [Seed = 1909652776]
   -------------------------------------


>> a+b;
   ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:34:17 2004

Input: [1 2;3 4]+[ 4 3;2 1]

Output: Magma V2.10-22    Thu Jul  1 2004 04:34:14 on modular  [Seed = 2452692486]
   -------------------------------------


>> [1 2;3 4]+[ 4 3;2 1];
      ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:39:39 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);


Output: Magma V2.10-22    Thu Jul  1 2004 04:39:36 on modular  [Seed = 3446554647]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:39:47 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4])


Output: Magma V2.10-22    Thu Jul  1 2004 04:39:44 on modular  [Seed = 4116084791]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:39:53 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4])


Output: Magma V2.10-22    Thu Jul  1 2004 04:39:50 on modular  [Seed = 4250824760]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:40:04 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4])
X

Output: Magma V2.10-22    Thu Jul  1 2004 04:40:02 on modular  [Seed = 431658216]
   -------------------------------------


>> X;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:40:50 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);


Output: Magma V2.10-22    Thu Jul  1 2004 04:40:48 on modular  [Seed = 10718723]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:41:14 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);
y := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);

Output: Magma V2.10-22    Thu Jul  1 2004 04:41:11 on modular  [Seed = 262963515]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:41:29 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);
y := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);
X*y

Output: Magma V2.10-22    Thu Jul  1 2004 04:41:27 on modular  [Seed = 932493587]
   -------------------------------------

[ 7 10]
[15 22]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:41:41 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);
y := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);
X

Output: Magma V2.10-22    Thu Jul  1 2004 04:41:39 on modular  [Seed = 1067233647]
   -------------------------------------

[1 2]
[3 4]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mela156.uku.fi. (193.167.234.156)
Time: Thu Jul  1 04:42:14 2004

Input: X := Matrix(IntegerRing(), 2, 2, [a,b, c,d]);
y := Matrix(IntegerRing(), 2, 2, [d,c, b,a]);
X

Output: Magma V2.10-22    Thu Jul  1 2004 04:42:11 on modular  [Seed = 663005527]
   -------------------------------------


>> X := Matrix(IntegerRing(), 2, 2, [a,b, c,d]);
                                     ^
User error: Identifier 'a' has not been declared or assigned

>> y := Matrix(IntegerRing(), 2, 2, [d,c, b,a]);
                                     ^
User error: Identifier 'd' has not been declared or assigned

>> X;
   ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mykonos.ubn.kun.nl. (131.174.248.33)
Time: Thu Jul  1 10:25:21 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Thu Jul  1 2004 10:25:15 on modular  [Seed = 3004689762]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.619 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mykonos.ubn.kun.nl. (131.174.248.33)
Time: Thu Jul  1 10:31:18 2004

Input: 5+13

Output: Magma V2.10-22    Thu Jul  1 2004 10:31:15 on modular  [Seed = 3429412066]
   -------------------------------------

18

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mykonos.ubn.kun.nl. (131.174.248.33)
Time: Thu Jul  1 10:31:47 2004

Input: 3423423423523324/111

Output: Magma V2.10-22    Thu Jul  1 2004 10:31:44 on modular  [Seed = 4267351731]
   -------------------------------------

3423423423523324/111

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 11:23:10 2004

Input: list := SmallGroups(12, func<x|not IsAbelian(x)> );
G := list[1]; G;
ConjugacyClasses(G);
CharacterTable(G);
CommutatorSubgroup(G, G, G);

Output: Magma V2.10-22    Thu Jul  1 2004 11:23:07 on modular  [Seed = 2267278274]
   -------------------------------------

GrpPC : G of order 12 = 2^2 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.3^G.1 = G.3^2
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1      
        Rep G.2

[3]     Order 3       Length 2      
        Rep G.3

[4]     Order 4       Length 3      
        Rep G.1

[5]     Order 4       Length 3      
        Rep G.1 * G.2

[6]     Order 6       Length 2      
        Rep G.2 * G.3




Character Table of Group G
--------------------------


-----------------------
Class |   1 2 3  4  5 6
Size  |   1 1 2  3  3 2
Order |   1 2 3  4  4 6
-----------------------
p  =  2   1 1 3  2  2 3
p  =  3   1 2 1  5  4 2
-----------------------
X.1   +   1 1 1  1  1 1
X.2   0   1-1 1  I -I-1
X.3   +   1 1 1 -1 -1 1
X.4   0   1-1 1 -I  I-1
X.5   +   2 2-1  0  0-1
X.6   -   2-2-1  0  0 1


Explanation of Symbols:
-----------------------

I = RootOfUnity(4)


GrpPC of order 3
PC-Relations:
    $.1^3 = Id($)

Total time: 2.599 seconds, Total memory usage: 22.06MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:34:19 2004

Input: k := FiniteField(17);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3 - 4*x*z^2);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:34:16 on modular  [Seed = 747131195]
   -------------------------------------

Algebraic function field defined over GF(17) by
u^3 + 4*u + 16*v^2
1

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:35:33 2004

Input: k := FiniteField(3);
P<x,y,z> := ProjectiveSpace(k, 2);
E := Curve(P, y^2*z - x^3 + x*z^2);
F<a,b> := FunctionField(E);
F;
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:35:29 on modular  [Seed = 612391273]
   -------------------------------------

Algebraic function field defined over GF(3) by
$.1^3 + 2*$.1 + 2*$.2^2
1

Total time: 2.989 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:35:53 2004

Input: k := FiniteField(17);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3 - 4*x*z^2);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:35:50 on modular  [Seed = 1559765285]
   -------------------------------------

Algebraic function field defined over GF(17) by
u^3 + 4*u + 16*v^2
1

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:36:26 2004

Input: k := FiniteField(17);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3 + x*z^2);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:36:24 on modular  [Seed = 1408708292]
   -------------------------------------

Algebraic function field defined over GF(17) by
u^3 + 16*u + 16*v^2
1

Total time: 2.579 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:36:37 2004

Input: k := FiniteField(3);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3 + x*z^2);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:36:34 on modular  [Seed = 1240282308]
   -------------------------------------

Algebraic function field defined over GF(3) by
u^3 + 2*u + 2*v^2
1

Total time: 2.999 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:38:49 2004

Input: k := FiniteField(3);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3 + x*z^2);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(E);
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:38:46 on modular  [Seed = 2078213490]
   -------------------------------------

Algebraic function field defined over GF(3) by
u^3 + 2*u + 2*v^2
true
1

Total time: 2.989 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:39:05 2004

Input: k := FiniteField(3);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(E);
Genus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:39:02 on modular  [Seed = 1943473482]
   -------------------------------------

Algebraic function field defined over GF(3) by
u^3 + 2*v^2
false
0

Total time: 3.019 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:39:20 2004

Input: k := FiniteField(3);
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(E);
Genus(E);
ArithmeticGenus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:39:17 on modular  [Seed = 1791890496]
   -------------------------------------

Algebraic function field defined over GF(3) by
u^3 + 2*v^2
false
0
1

Total time: 3.009 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:47:05 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, (x^5 - x) * (y^5 - y) - 1 );
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(E);
Genus(E);
ArithmeticGenus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:47:02 on modular  [Seed = 2166718872]
   -------------------------------------

Algebraic function field defined over GF(3) by
u^3 + 2*v^2
false
0
1

Total time: 3.029 seconds, Total memory usage: 8.25MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:47:38 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, (x^5 - x) * (y^5 - y) - 1 );
D<X,Y,Z> := ProjectiveClosure(C); D
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(E);
Genus(E);
ArithmeticGenus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:47:36 on modular  [Seed = 3054679681]
   -------------------------------------


>> P<x,y,z> := ProjectiveSpace(k,2);
   ^
User error: bad syntax

>> E := Curve(P, y^2*z - x^3);
              ^
User error: Identifier 'P' has not been declared or assigned

>> E1<u,v> := AffinePatch(E,1);
                          ^
User error: Identifier 'E' has not been declared or assigned

>> F<a,b> := FunctionField(E);
                           ^
User error: Identifier 'E' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

>> IsNonsingular(E);
                 ^
User error: Identifier 'E' has not been declared or assigned

>> Genus(E);
         ^
User error: Identifier 'E' has not been declared or assigned

>> ArithmeticGenus(E);
                   ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:47:59 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, (x^5 - x) * (y^5 - y) - 1 );
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(E);
Genus(E);
ArithmeticGenus(E);


Output: Magma V2.10-22    Thu Jul  1 2004 12:47:56 on modular  [Seed = 2919935629]
   -------------------------------------

Curve over GF(3) defined by
X^5*Y^5 + 2*X^5*Y*Z^4 + 2*X*Y^5*Z^4 + X*Y*Z^8 + 2*Z^10
Algebraic function field defined over GF(3) by
u^3 + 2*v^2
false
0
1

Total time: 3.009 seconds, Total memory usage: 8.25MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:48:24 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, (x^5 - x) * (y^5 - y) - 1 );
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 12:48:21 on modular  [Seed = 2785191660]
   -------------------------------------

Curve over GF(3) defined by
X^5*Y^5 + 2*X^5*Y*Z^4 + 2*X*Y^5*Z^4 + X*Y*Z^8 + 2*Z^10
Algebraic function field defined over GF(3) by
u^3 + 2*v^2
false
12
36

Total time: 3.229 seconds, Total memory usage: 8.35MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:49:00 2004

Input: k := FiniteField(5);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, (x^5 - x) * (y^5 - y) - 1 );
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 12:48:57 on modular  [Seed = 3732594360]
   -------------------------------------

Curve over GF(5) defined by
X^5*Y^5 + 4*X^5*Y*Z^4 + 4*X*Y^5*Z^4 + X*Y*Z^8 + 4*Z^10
Algebraic function field defined over GF(5) by
u^3 + 4*v^2
false
16
36

Total time: 3.069 seconds, Total memory usage: 6.61MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:58:52 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, y^2 - x^3 + x);
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 12:58:49 on modular  [Seed = 3345204497]
   -------------------------------------

Curve over GF(3) defined by
X^3 + 2*X*Z^2 + 2*Y^2*Z
Algebraic function field defined over GF(3) by
u^3 + 2*v^2
true
1
1

Total time: 3.019 seconds, Total memory usage: 8.35MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:59:13 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, y^2 - x^3 + x);
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
% E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:59:22 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, y^2 - x^3 + x);
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
- E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 12:59:18 on modular  [Seed = 4149474574]
   -------------------------------------

Curve over GF(3) defined by
X^3 + 2*X*Z^2 + 2*Y^2*Z

>> - E1<u,v> := AffinePatch(E,1);
       ^
User error: bad syntax
Algebraic function field defined over GF(3) by
$.1^3 + 2*$.2^2
true
1
1

Total time: 3.009 seconds, Total memory usage: 8.35MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 12:59:27 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, y^2 - x^3 + x);
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
-- E1<u,v> := AffinePatch(E,1);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 12:59:24 on modular  [Seed = 4014730524]
   -------------------------------------

Curve over GF(3) defined by
X^3 + 2*X*Z^2 + 2*Y^2*Z

>> -- E1<u,v> := AffinePatch(E,1);
        ^
User error: bad syntax
Algebraic function field defined over GF(3) by
$.1^3 + 2*$.2^2
true
1
1

Total time: 3.009 seconds, Total memory usage: 8.35MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:00:29 2004

Input: k := FiniteField(3);
A<x,y> := AffineSpace(k, 2);
C := Curve(A, y^2 - x^3 + x);
D<X,Y,Z> := ProjectiveClosure(C); D;
P<x,y,z> := ProjectiveSpace(k,2);
E := Curve(P, y^2*z - x^3);
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 13:00:25 on modular  [Seed = 730802210]
   -------------------------------------

Curve over GF(3) defined by
X^3 + 2*X*Z^2 + 2*Y^2*Z
Algebraic function field defined over GF(3) by
$.1^3 + 2*$.2^2
true
1
1

Total time: 3.009 seconds, Total memory usage: 8.35MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:02:26 2004

Input: k := FiniteField(3);
A<x, z> := AffineSpace(k, 2);
C := Curve(A, z - x^3 + x*z^2);
P := Origin(C); P;
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 13:02:24 on modular  [Seed = 881866676]
   -------------------------------------


>> P := Origin(C); P;
              ^
Runtime error in 'Origin': Bad argument types
Argument types given: Crv

>> P := Origin(C); P;
                   ^
User error: Identifier 'P' has not been declared or assigned

>> F<a,b> := FunctionField(E);
                           ^
User error: Identifier 'E' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

>> IsNonsingular(D);
                 ^
User error: Identifier 'D' has not been declared or assigned

>> Genus(D);
         ^
User error: Identifier 'D' has not been declared or assigned

>> ArithmeticGenus(D);
                   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:02:53 2004

Input: k := FiniteField(3);
A<x, z> := AffineSpace(k, 2);
C := Curve(A, z - x^3 + x*z^2);
P := Origin(A); P;
F<a,b> := FunctionField(E);
F;
IsNonsingular(D);
Genus(D);
ArithmeticGenus(D);


Output: Magma V2.10-22    Thu Jul  1 2004 13:02:50 on modular  [Seed = 1016610726]
   -------------------------------------

(0, 0)

>> F<a,b> := FunctionField(E);
                           ^
User error: Identifier 'E' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

>> IsNonsingular(D);
                 ^
User error: Identifier 'D' has not been declared or assigned

>> Genus(D);
         ^
User error: Identifier 'D' has not been declared or assigned

>> ArithmeticGenus(D);
                   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:03:06 2004

Input: k := FiniteField(3);
A<x, z> := AffineSpace(k, 2);
C := Curve(A, z - x^3 + x*z^2);
P := Origin(A); P;
Genus(C);

Output: Magma V2.10-22    Thu Jul  1 2004 13:03:03 on modular  [Seed = 77596643]
   -------------------------------------

(0, 0)
1

Total time: 3.049 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:07:06 2004

Input: P<x,y,z> := ProjectiveSpace(Rationals(),2);
C := Curve(P, y^2*z - x^3 + x*z^2);
F<a,b> := FunctionField(C);
f := a/b;
f;
p := C ! [0,0,1];
Evaluate(f,p);
Valuation(f,p);
vp := Valuation(p);
vp(a), vp(b);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:07:04 on modular  [Seed = 229181845]
   -------------------------------------

b/(a^2 - 1)
0
1
2 1
a + b

Total time: 2.559 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:13:28 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(P, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X/Y;
f;
p := C ! [0,1,0];
Evaluate(f,p);
Valuation(f,p);
vp := Valuation(p);
vp(a), vp(b);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:13:25 on modular  [Seed = 448666639]
   -------------------------------------


>> C := Curve(P, y^2 - x^3 + x);
              ^
User error: Identifier 'P' has not been declared or assigned

>> F<X,Y> := FunctionField(C);
                           ^
User error: Identifier 'C' has not been declared or assigned

>> f := X/Y;
        ^
User error: Identifier 'X' has not been declared or assigned

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

>> p := C ! [0,1,0];
        ^
User error: Identifier 'C' has not been declared or assigned

>> Evaluate(f,p);
            ^
User error: Identifier 'f' has not been declared or assigned

>> Valuation(f,p);
             ^
User error: Identifier 'f' has not been declared or assigned

>> vp := Valuation(p);
                   ^
User error: Identifier 'p' has not been declared or assigned

>> vp(a), vp(b);
      ^
User error: Identifier 'a' has not been declared or assigned

>> UniformizingParameter(p);
                         ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:13:50 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(A, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X/Y;
f;
p := C ! [0,1,0];
Evaluate(f,p);
Valuation(f,p);
vp := Valuation(p);
vp(a), vp(b);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:13:47 on modular  [Seed = 1657168905]
   -------------------------------------

Y/(X^2 + 2)

>> p := C ! [0,1,0];
          ^
Runtime error in '!': Illegal coercion
LHS: Crv
RHS: [RngIntElt]

>> Evaluate(f,p);
              ^
User error: Identifier 'p' has not been declared or assigned

>> Valuation(f,p);
               ^
User error: Identifier 'p' has not been declared or assigned

>> vp := Valuation(p);
                   ^
User error: Identifier 'p' has not been declared or assigned

>> vp(a), vp(b);
      ^
User error: Identifier 'a' has not been declared or assigned

>> UniformizingParameter(p);
                         ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 8.24MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:14:06 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(A, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X/Y;
f;
p := Origin(A);
Evaluate(f,p);
Valuation(f,p);
vp := Valuation(p);
vp(a), vp(b);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:14:03 on modular  [Seed = 1791912977]
   -------------------------------------

Y/(X^2 + 2)

>> Evaluate(f,p);
           ^
Runtime error in 'Evaluate': No routine to work with this function

>> Valuation(f,p);
            ^
Runtime error in 'Valuation': Point must be a nonsingular point of some curve

>> vp := Valuation(p);
                  ^
Runtime error in 'Valuation': Point must be a nonsingular point of some curve

>> vp(a), vp(b);
      ^
User error: Identifier 'a' has not been declared or assigned

>> UniformizingParameter(p);
                        ^
Runtime error in 'UniformizingParameter': Argument must be a nonsingular point 
of a curve

Total time: 2.999 seconds, Total memory usage: 8.34MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:14:45 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(A, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X/Y;
f;
p := Origin(A);
P := Place(p);
Valuation(f,p);
vp := Valuation(p);
vp(a), vp(b);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:14:42 on modular  [Seed = 1926657232]
   -------------------------------------

Y/(X^2 + 2)

>> P := Place(p);
             ^
Runtime error in 'Place': Scheme of point must be a curve

>> Valuation(f,p);
            ^
Runtime error in 'Valuation': Point must be a nonsingular point of some curve

>> vp := Valuation(p);
                  ^
Runtime error in 'Valuation': Point must be a nonsingular point of some curve

>> vp(a), vp(b);
      ^
User error: Identifier 'a' has not been declared or assigned

>> UniformizingParameter(p);
                        ^
Runtime error in 'UniformizingParameter': Argument must be a nonsingular point 
of a curve

Total time: 2.979 seconds, Total memory usage: 8.34MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:15:03 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(A, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X/Y;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
vp := Valuation(p);
vp(a), vp(b);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:15:00 on modular  [Seed = 2078244303]
   -------------------------------------

Y/(X^2 + 2)
1

>> vp(a), vp(b);
      ^
User error: Identifier 'a' has not been declared or assigned
X + Y

Total time: 3.019 seconds, Total memory usage: 8.45MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:15:12 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(A, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X/Y;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:15:09 on modular  [Seed = 1139230206]
   -------------------------------------

Y/(X^2 + 2)
1
X + Y

Total time: 3.049 seconds, Total memory usage: 8.45MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:15:29 2004

Input: A<x,y> := AffineSpace(GF(3),2);
C := Curve(A, y^2 - x^3 + x);
F<X,Y> := FunctionField(C);
f := X;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:15:26 on modular  [Seed = 1273974213]
   -------------------------------------

X
2
X + Y

Total time: 3.039 seconds, Total memory usage: 8.45MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:15:54 2004

Input: A<x,z> := AffineSpace(GF(3),2);
C := Curve(A, z - x^3 + x*z^2);
F<X,Y> := FunctionField(C);
f := X;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:15:51 on modular  [Seed = 1408718260]
   -------------------------------------

X
1
X

Total time: 3.059 seconds, Total memory usage: 8.45MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:16:07 2004

Input: A<x,z> := AffineSpace(GF(3),2);
C := Curve(A, z - x^3 + x*z^2);
F<X,Z> := FunctionField(C);
f := Z;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:16:04 on modular  [Seed = 1559780008]
   -------------------------------------

Z
3
X

Total time: 3.069 seconds, Total memory usage: 8.45MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:16:29 2004

Input: A<x,z> := AffineSpace(GF(3),2);
C := Curve(A, z - x^3 + x*z^2);
F<X,Z> := FunctionField(C);
f := 2*X + Z;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:16:26 on modular  [Seed = 2751505006]
   -------------------------------------

2*X + Z
1
X

Total time: 3.059 seconds, Total memory usage: 8.45MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:17:10 2004

Input: q := 5;
A<x,z> := AffineSpace(GF(q),2);
C := Curve(A, z - x^3 + x*z^2);
F<X,Z> := FunctionField(C);
f := 2*X + Z;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:17:07 on modular  [Seed = 2919934365]
   -------------------------------------

2*X + Z
1
X

Total time: 2.879 seconds, Total memory usage: 6.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:18:22 2004

Input: p := 5;
A<y,z> := AffineSpace(GF(p),2);
C := Curve(A, (1 - z^(p-1) ) * (y^p - y*z^(p-1) - z^p);
F<Y,Z> := FunctionField(C);
f := 2*X + Z;
f;
p := C ! [0, 0];
P := Place(p);
Valuation(f,p);
UniformizingParameter(p);




Output: Magma V2.10-22    Thu Jul  1 2004 13:18:19 on modular  [Seed = 3054678477]
   -------------------------------------


>> C := Curve(A, (1 - z^(p-1) ) * (y^p - y*z^(p-1) - z^p);
                                                         ^
User error: bad syntax

>> F<Y,Z> := FunctionField(C);
                           ^
User error: Identifier 'C' has not been declared or assigned

>> f := 2*X + Z;
          ^
User error: Identifier 'X' has not been declared or assigned

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

>> p := C ! [0, 0];
        ^
User error: Identifier 'C' has not been declared or assigned

>> P := Place(p);
             ^
Runtime error in 'Place': Bad argument types
Argument types given: RngIntElt

>> Valuation(f,p);
             ^
User error: Identifier 'f' has not been declared or assigned

>> UniformizingParameter(p);
                        ^
Runtime error in 'UniformizingParameter': Bad argument types
Argument types given: RngIntElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:18:36 2004

Input: p := 5;
A<y,z> := AffineSpace(GF(p),2);
C := Curve(A, (1 - z^(p-1) ) * (y^p - y*z^(p-1) - z^p);
F<Y,Z> := FunctionField(C);
f := 2*X + Z;
f;
q := C ! [0, 0];
Q := Place(q);
Valuation(f, q);
UniformizingParameter(q);




Output: Magma V2.10-22    Thu Jul  1 2004 13:18:34 on modular  [Seed = 3189422580]
   -------------------------------------


>> C := Curve(A, (1 - z^(p-1) ) * (y^p - y*z^(p-1) - z^p);
                                                         ^
User error: bad syntax

>> F<Y,Z> := FunctionField(C);
                           ^
User error: Identifier 'C' has not been declared or assigned

>> f := 2*X + Z;
          ^
User error: Identifier 'X' has not been declared or assigned

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

>> q := C ! [0, 0];
        ^
User error: Identifier 'C' has not been declared or assigned

>> Q := Place(q);
              ^
User error: Identifier 'q' has not been declared or assigned

>> Valuation(f, q);
             ^
User error: Identifier 'f' has not been declared or assigned

>> UniformizingParameter(q);
                         ^
User error: Identifier 'q' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:18:45 2004

Input: p := 5;
A<y,z> := AffineSpace(GF(p),2);
C := Curve(A, (1 - z^(p-1) ) * (y^p - y*z^(p-1)) - z^p);
F<Y,Z> := FunctionField(C);
f := 2*X + Z;
f;
q := C ! [0, 0];
Q := Place(q);
Valuation(f, q);
UniformizingParameter(q);




Output: Magma V2.10-22    Thu Jul  1 2004 13:18:42 on modular  [Seed = 2250408404]
   -------------------------------------


>> f := 2*X + Z;
          ^
User error: Identifier 'X' has not been declared or assigned

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

>> Q := Place(q);
             ^
Runtime error in 'Place': Argument 1 is not non-singular

>> Valuation(f, q);
             ^
User error: Identifier 'f' has not been declared or assigned

>> UniformizingParameter(q);
                        ^
Runtime error in 'UniformizingParameter': Argument must be a nonsingular point 
of a curve

Total time: 2.829 seconds, Total memory usage: 6.59MB


************** MAGMA *****************
Host drl4n16-5.math.upenn.edu. (130.91.51.137)
Time: Thu Jul  1 13:18:55 2004

Input: p := 5;
A<y,z> := AffineSpace(GF(p),2);
C := Curve(A, (1 - z^(p-1) ) * (y^p - y*z^(p-1)) - z^p);
F<Y,Z> := FunctionField(C);
f := Y;
f;
q := C ! [0, 0];
Q := Place(q);
Valuation(f, q);
UniformizingParameter(q);




Output: Magma V2.10-22    Thu Jul  1 2004 13:18:52 on modular  [Seed = 2385152466]
   -------------------------------------

Y

>> Q := Place(q);
             ^
Runtime error in 'Place': Argument 1 is not non-singular


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Wed Apr 23 11:13:24 EST 2003
Initial seed: 2385152466
Time to this point: 2.87
Segmentation fault

Errors: Magma: Fatal Error: Magma: Irrecoverable error; exiting


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Thu Jul  1 15:09:16 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![3/5,0,2/5,4/5,1/5,0,2/5,2/5,1/5];
Eigenvalues(M);
Eigenspace(M,1);


Output: Magma V2.10-22    Thu Jul  1 2004 15:09:14 on modular  [Seed = 545522008]
   -------------------------------------

{
    <1, 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
(  1 1/4 1/2)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Thu Jul  1 15:12:03 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![3/5,0,2/5,4/5,1/5,0,2/5,2/5,1/5];
Eigenvalues(M);
Eigenspace(M,1);
EchelonForm(M);


Output: Magma V2.10-22    Thu Jul  1 2004 15:12:00 on modular  [Seed = 179185704]
   -------------------------------------

{
    <1, 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
(  1 1/4 1/2)
[1 0 0]
[0 1 0]
[0 0 1]

Total time: 2.490 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Thu Jul  1 15:13:40 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![3/5,0,2/5,4/5,1/5,0,2/5,2/5,1/5];
Eigenvalues(M);
Eigenspace(M,1);
EchelonForm(M);
CharacteristicPolynomial(M)

Output: Magma V2.10-22    Thu Jul  1 2004 15:13:37 on modular  [Seed = 448673882]
   -------------------------------------

{
    <1, 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
(  1 1/4 1/2)
[1 0 0]
[0 1 0]
[0 0 1]
$.1^3 - $.1^2 + 3/25*$.1 - 3/25

Total time: 2.619 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Thu Jul  1 15:15:43 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![3/5,0,2/5,4/5,1/5,0,2/5,2/5,1/5];
Eigenvalues(M);
Eigenspace(M,1);
JordanForm(M);
CharacteristicPolynomial(M)


Output: Magma V2.10-22    Thu Jul  1 2004 15:15:40 on modular  [Seed = 1740850585]
   -------------------------------------

{
    <1, 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
(  1 1/4 1/2)
[    1     0     0]
[    0     0     1]
[    0 -3/25     0]
$.1^3 - $.1^2 + 3/25*$.1 - 3/25

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Thu Jul  1 15:22:53 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![2/4,1/4,1/4,0,0,1,2/3,0,1/3];
Eigenvalues(M);
Eigenspace(M,1);
JordanForm(M);
CharacteristicPolynomial(M)


Output: Magma V2.10-22    Thu Jul  1 2004 15:22:50 on modular  [Seed = 1543471091]
   -------------------------------------

{
    <1, 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
(  1 1/4 3/4)
[   1    0    0]
[   0    0    1]
[   0 -1/6 -1/6]
$.1^3 - 5/6*$.1^2 - 1/6

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:51:10 2004

Input: F<a,b>:=Group<a,b|a^2,b^2,(a*b)^2>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:51:07 on modular  [Seed = 1441890347]
   -------------------------------------

4

Total time: 2.659 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:52:11 2004

Input: F<a,b>:=Group<a,b|a^2,b^2,(a*b)^3>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:52:08 on modular  [Seed = 1576634593]
   -------------------------------------

6

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:52:25 2004

Input: F<a,b>:=Group<a,b|a^2,b^2,(a*b)^4>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:52:22 on modular  [Seed = 2768334886]
   -------------------------------------

8

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:52:50 2004

Input: F<a,b>:=Group<a,b|a^2,b^2,(a*b)^5>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:52:47 on modular  [Seed = 2903078967]
   -------------------------------------

10

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:53:16 2004

Input: F<a,b>:=Group<a,b|a^3,b^3,(a*b)^2>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:53:14 on modular  [Seed = 3071500872]
   -------------------------------------

12

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:53:31 2004

Input: F<a,b>:=Group<a,b|a^3,b^3,(a*b)^3>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:53:27 on modular  [Seed = 3206244989]
   -------------------------------------

0

Total time: 3.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:53:48 2004

Input: F<a,b>:=Group<a,b|a^3,b^3,(a*b)^4>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:53:44 on modular  [Seed = 2200393310]
   -------------------------------------

0

Total time: 3.539 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:54:05 2004

Input: F<a,b>:=Group<a,b|a^3,b^3,(a*b)^5>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:54:01 on modular  [Seed = 2335137191]
   -------------------------------------

0

Total time: 3.419 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:54:15 2004

Input: F<a,b>:=Group<a,b|a^3,b^3,(a*b)^6>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:54:12 on modular  [Seed = 2469873058]
   -------------------------------------

0

Total time: 3.389 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:54:42 2004

Input: F<a,b>:=Group<a,b|a^4,b^4,(a*b)^2>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:54:38 on modular  [Seed = 3829412591]
   -------------------------------------

0

Total time: 3.609 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:54:57 2004

Input: F<a,b>:=Group<a,b|a^4,b^4,(a*b)^3>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:54:53 on modular  [Seed = 3964156660]
   -------------------------------------

0

Total time: 3.439 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:55:06 2004

Input: F<a,b>:=Group<a,b|a^4,b^4,(a*b)^4>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:55:03 on modular  [Seed = 4098892438]
   -------------------------------------

0

Total time: 3.359 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:56:46 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:56:43 on modular  [Seed = 4284164465]
   -------------------------------------

6

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:56:59 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:56:56 on modular  [Seed = 3345158490]
   -------------------------------------

24

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:57:11 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:57:09 on modular  [Seed = 3413056811]
   -------------------------------------

96

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:57:27 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^5>;
Order(F);

Output: Magma V2.10-22    Thu Jul  1 2004 18:57:24 on modular  [Seed = 3547792674]
   -------------------------------------

600

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:57:53 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : CosetLimit=1000000);

Output: Magma V2.10-22    Thu Jul  1 2004 18:57:50 on modular  [Seed = 3682536720]
   -------------------------------------


>> Order(F : CosetLimit=1000000);;
                       ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:58:05 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.10-22    Thu Jul  1 2004 18:57:59 on modular  [Seed = 545584881]
   -------------------------------------

0

Total time: 5.549 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 18:58:30 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Thu Jul  1 2004 18:58:14 on modular  [Seed = 680328968]
   -------------------------------------

0

Total time: 16.299 seconds, Total memory usage: 65.99MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 19:02:31 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^2>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Thu Jul  1 2004 19:02:27 on modular  [Seed = 229233960]
   -------------------------------------

24

Total time: 3.249 seconds, Total memory usage: 81.67MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 19:02:44 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^3>;
Order(F : CosetLimit:=4000000);

Output: Magma V2.10-22    Thu Jul  1 2004 19:02:41 on modular  [Seed = 313969189]
   -------------------------------------

648

Total time: 3.389 seconds, Total memory usage: 97.68MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 19:03:39 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F : CosetLimit:=4000000);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Thu Jul  1 2004 19:03:22 on modular  [Seed = 1690352760]
   -------------------------------------


Current total memory usage: 94.4MB, failed memory request: 1.0MB
System Error: User memory limit has been reached

Total time: 17.149 seconds, Total memory usage: 99.02MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 19:04:12 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^4>;
Order(F : CosetLimit:=3500000);

Output: Magma V2.10-22    Thu Jul  1 2004 19:03:50 on modular  [Seed = 1825092636]
   -------------------------------------



************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 19:05:46 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^2>;
Order(F : CosetLimit:=3500000);

Output: Magma V2.10-22    Thu Jul  1 2004 19:05:42 on modular  [Seed = 1959832724]
   -------------------------------------

120

Total time: 3.419 seconds, Total memory usage: 99.69MB


************** MAGMA *****************
Host pD9E511CD.dip.t-dialin.net. (217.229.17.205)
Time: Thu Jul  1 19:06:04 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^3>;
Order(F : CosetLimit:=3500000);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Thu Jul  1 2004 19:06:00 on modular  [Seed = 1189256888]
   -------------------------------------


Current total memory usage: 95.1MB, failed memory request: 13.4MB
System Error: User memory limit has been reached

Total time: 3.389 seconds, Total memory usage: 99.69MB


************** MAGMA *****************
Host adsl-68-122-12-123.dsl.pltn13.pacbell.net. (68.122.12.123)
Time: Thu Jul  1 21:15:16 2004

Input: 2+2

Output: Magma V2.10-22    Thu Jul  1 2004 21:15:13 on modular  [Seed = 1340848201]
   -------------------------------------

4

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:46:32 2004

Input: a=2047;
n=1;
b=(3^n) - 1;
while Mod(((3^n)-1),a) != 0 do

 n=n+1;
end while
print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:46:30 on modular  [Seed = 949798502]
   -------------------------------------


>> a=2047;
   ^
User error: Identifier 'a' has not been declared or assigned

>> n=1;
   ^
User error: Identifier 'n' has not been declared or assigned

>> b=(3^n) - 1;
        ^
User error: Identifier 'n' has not been declared or assigned

>> while Mod(((3^n)-1),a) != 0 do
                           ^
User error: bad syntax

>>  n=n+1;
      ^
User error: Identifier 'n' has not been declared or assigned

>> end while
   ^
User error: bad syntax

>> print(a);
         ^
User error: Identifier 'a' has not been declared or assigned

>> print(b);
         ^
User error: Identifier 'b' has not been declared or assigned

>> print(n);;
         ^
User error: Identifier 'n' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:47:19 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while Mod(((3^n)-1),a) != 0 do

 n:=n+1;
end while;

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:47:17 on modular  [Seed = 44498063]
   -------------------------------------


>> while Mod(((3^n)-1),a) != 0 do
                           ^
User error: bad syntax

>> end while;
   ^
User error: bad syntax
2047
2
2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:47:38 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while Mod(((3^n)-1),a) <> 0 do

 n:=n+1;
end while;

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:47:36 on modular  [Seed = 448717962]
   -------------------------------------


>> while Mod(((3^n)-1),a) <> 0 do
                          ^
User error: bad syntax

>> end while;
   ^
User error: bad syntax
2047
2
2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:48:14 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while Mod(((3^n)-1),a) ne 0 do

 n:=n+1;
end while;

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:48:11 on modular  [Seed = 330821088]
   -------------------------------------


>> while Mod(((3^n)-1),a) ne 0 do
            ^
Runtime error: Attempting to call something that is not callable
2047
2
1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:48:36 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while ((3^n)-1) mod a ne 0 do

 n:=n+1;
end while;

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:48:33 on modular  [Seed = 1808766386]
   -------------------------------------

2047
2
88

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:52:56 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047)

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:52:53 on modular  [Seed = 1724029371]
   -------------------------------------


>> print(a);
   ^
User error: bad syntax
2
88

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:53:06 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047);

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:53:03 on modular  [Seed = 1892978599]
   -------------------------------------


>> print(Gcd((3^n)-1,2047);
                          ^
User error: bad syntax
2047
2
88

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:53:27 2004

Input: a:=2047;
n:=1;
b:=(3^n) - 1;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));

print(a);
print(b);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:53:25 on modular  [Seed = 1240320372]
   -------------------------------------

2047
2047
2
88

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:55:39 2004

Input: a:=2047;
n:=1;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));
print((3^n)-1,n+1);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:55:37 on modular  [Seed = 1105576432]
   -------------------------------------

2047

>> print((3^n)-1,n+1);
        ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle
2047
88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:56:13 2004

Input: a:=2047;
n:=1;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));
print((3^n)-1/(n+1));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:56:11 on modular  [Seed = 1526651593]
   -------------------------------------

2047
86309861951089600656037152852603192584854328/89
2047
88

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:57:01 2004

Input: a:=2047;
n:=1;
d:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));
d := (3^n)-1/(n+1));
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:56:58 on modular  [Seed = 1391907472]
   -------------------------------------

2047

>> d := (3^n)-1/(n+1));
                     ^
User error: bad syntax
0
2047
88

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:57:12 2004

Input: a:=2047;
n:=1;
d:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));
d := (3^n)-1/(n+1);
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:57:10 on modular  [Seed = 2853055092]
   -------------------------------------

2047
86309861951089600656037152852603192584854328/89
2047
88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:58:11 2004

Input: a:=2047;
n:=1;
d:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));
d := (3^n)-1/(88);
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:58:09 on modular  [Seed = 2718311355]
   -------------------------------------

2047
85340088221302077053160330910439111769294167/88
2047
88

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 21:59:06 2004

Input: a:=2047;
n:=1;
d:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;

print(Gcd((3^n)-1,2047));
d := (3^n)-1/(23);
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 21:59:03 on modular  [Seed = 3139386100]
   -------------------------------------

2047
22304795785113042866166904669773858757883702/23
2047
88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:02:40 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));
d := ((3^n))-1 div(88);
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:02:38 on modular  [Seed = 2554075790]
   -------------------------------------

2047
969773729787523602876821942164080815560161
2047
88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:03:26 2004

Input: a:=8388607;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));
d := ((3^n))-1 div(88);
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:03:03 on modular  [Seed = 2419331823]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:03:55 2004

Input: a:=8191;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));
d := ((3^n))-1 div(88);
print(d);

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:03:53 on modular  [Seed = 3914165064]
   -------------------------------------

8191
1514752907900222770124030320216999503871460299633998900366003366218781151216959\
5269377706922383208272786162775877084943746053583044175700191704698752699647454\
7925973830885866863152615431504058184264417354225280130745436996269644963441205\
7089596137759323872224559144532728780656272145005194261540809389061989485017480\
9640213882709126457491239524501791199733881850480602098296151948950255657870090\
9237404646686828570620836929481375261049
8191
910

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:05:00 2004

Input: a:=8191;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:04:57 on modular  [Seed = 3779420928]
   -------------------------------------

8191
8191
910

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:05:48 2004

Input: a:=127;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:05:45 on modular  [Seed = 4183653160]
   -------------------------------------

127
127
126

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:08:09 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:08:07 on modular  [Seed = 4098914139]
   -------------------------------------

2047
2047
88

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:17:37 2004

Input: a:=31;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:17:34 on modular  [Seed = 3497284934]
   -------------------------------------

31
31
30

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:18:20 2004

Input: a:=8388607;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:17:58 on modular  [Seed = 697150678]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:21:31 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,n));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:21:29 on modular  [Seed = 932426167]
   -------------------------------------

8
2047
88

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:23:28 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,89));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:23:25 on modular  [Seed = 27625013]
   -------------------------------------

89
2047
88

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:25:28 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(((3^n)-1) div (n+1));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:25:26 on modular  [Seed = 448699813]
   -------------------------------------

2047
10896334042556444976144066765888548489440
2047
88

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:28:48 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(((3^n)-1) div (n+3));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:28:45 on modular  [Seed = 347118688]
   -------------------------------------

2047
10656854173489270361283757606198690280880
2047
88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:28:59 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(((3^n)-1) / (n+3));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:28:57 on modular  [Seed = 1825104940]
   -------------------------------------

2047
969773729787523602876821942164080815560160/91
2047
88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 22:29:12 2004

Input: a:=2047;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(((3^n)-1) / (n+1));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 22:29:09 on modular  [Seed = 1690364984]
   -------------------------------------

2047
10896334042556444976144066765888548489440
2047
88

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul  1 23:09:36 2004

Input: a:=89;
n:=1;
d:=0;
x:=0;
while ((3^n)-1) mod a ne 0 do
 n:=n+1;
end while;
print(Gcd((3^n)-1,a));

print(((3^n)-1) / (n+1));

print(a);
print(n);

Output: Magma V2.10-22    Thu Jul  1 2004 23:09:33 on modular  [Seed = 2587757406]
   -------------------------------------

89
10896334042556444976144066765888548489440
89
88

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host barolo-gw.osaka-gu.ac.jp. (210.163.44.76)
Time: Fri Jul  2 00:12:16 2004

Input: nextprime(10^10)

Output: Magma V2.10-22    Fri Jul  2 2004 00:12:13 on modular  [Seed = 1640350166]
   -------------------------------------


>> nextprime(10^10);
   ^
User error: Identifier 'nextprime' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host barolo-gw.osaka-gu.ac.jp. (210.163.44.76)
Time: Fri Jul  2 00:12:32 2004

Input: prime(10^10)

Output: Magma V2.10-22    Fri Jul  2 2004 00:12:29 on modular  [Seed = 2044582398]
   -------------------------------------


>> prime(10^10);
   ^
User error: Identifier 'prime' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 04:10:05 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C: = ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^1279          
 if IsPrimitive(C) then 
    C;
end if;


Output: Magma V2.10-22    Fri Jul  2 2004 04:10:03 on modular  [Seed = 2785279697]
   -------------------------------------

X^9 + X^4 + 1

>> C: = ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^127
      ^
User error: bad syntax
X^9 + X^4 + 1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 04:11:27 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C: = ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^1279; if IsPrimitive(C) then 
    C;
end if;


Output: Magma V2.10-22    Fri Jul  2 2004 04:11:25 on modular  [Seed = 3206211390]
   -------------------------------------

X^9 + X^4 + 1

>> C: = ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^127
      ^
User error: bad syntax
X^9 + X^4 + 1

>> end if;
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 04:13:24 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^12)*((1+X^11)^18)*((1+X^13)^25)*((1+X^19)^33)+X^1279;
if IsPrimitive(C) then 
    C;
end if;


Output: Magma V2.10-22    Fri Jul  2 2004 04:13:20 on modular  [Seed = 3071471291]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1258 + X^1245 + X^1239 + X^1236 + X^1226 + X^1223 + X^1222 + X^1217 +
    X^1209 + X^1204 + X^1203 + X^1200 + X^1190 + X^1187 + X^1186 + X^1181 + 
    X^1173 + X^1168 + X^1167 + X^1164 + X^1151 + X^1150 + X^1145 + X^1141 + 
    X^1137 + X^1135 + X^1131 + X^1128 + X^1122 + X^1119 + X^1115 + X^1113 + 
    X^1109 + X^1105 + X^1100 + X^1099 + X^1086 + X^1083 + X^1077 + X^1064 + 
    X^1050 + X^1037 + X^1031 + X^1028 + X^1018 + X^1015 + X^1014 + X^1010 + 
    X^1009 + X^1001 + X^997 + X^996 + X^995 + X^992 + X^991 + X^988 + X^982 + 
    X^979 + X^978 + X^975 + X^974 + X^973 + X^969 + X^961 + X^960 + X^956 + 
    X^955 + X^952 + X^946 + X^942 + X^939 + X^927 + X^924 + X^920 + X^914 + 
    X^911 + X^910 + X^906 + X^905 + X^897 + X^893 + X^892 + X^891 + X^888 + 
    X^887 + X^884 + X^878 + X^875 + X^874 + X^871 + X^870 + X^869 + X^865 + 
    X^857 + X^856 + X^852 + X^851 + X^848 + X^838 + X^835 + X^829 + X^816 + 
    X^802 + X^789 + X^783 + X^780 + X^767 + X^766 + X^761 + X^757 + X^753 + 
    X^751 + X^747 + X^744 + X^738 + X^735 + X^731 + X^729 + X^725 + X^721 + 
    X^716 + X^715 + X^702 + X^699 + X^698 + X^693 + X^685 + X^680 + X^679 + 
    X^676 + X^666 + X^663 + X^662 + X^657 + X^650 + X^649 + X^644 + X^643 + 
    X^640 + X^637 + X^631 + X^630 + X^628 + X^627 + X^621 + X^618 + X^615 + 
    X^614 + X^609 + X^608 + X^601 + X^596 + X^595 + X^592 + X^582 + X^579 + 
    X^578 + X^573 + X^565 + X^560 + X^559 + X^556 + X^543 + X^542 + X^537 + 
    X^533 + X^529 + X^527 + X^523 + X^520 + X^514 + X^511 + X^507 + X^505 + 
    X^501 + X^497 + X^492 + X^491 + X^478 + X^475 + X^469 + X^456 + X^442 + 
    X^429 + X^423 + X^420 + X^410 + X^407 + X^406 + X^402 + X^401 + X^393 + 
    X^389 + X^388 + X^387 + X^384 + X^383 + X^380 + X^374 + X^371 + X^370 + 
    X^367 + X^366 + X^365 + X^361 + X^353 + X^352 + X^348 + X^347 + X^344 + 
    X^338 + X^334 + X^331 + X^319 + X^316 + X^312 + X^306 + X^303 + X^302 + 
    X^298 + X^297 + X^289 + X^285 + X^284 + X^283 + X^280 + X^279 + X^276 + 
    X^270 + X^267 + X^266 + X^263 + X^262 + X^261 + X^257 + X^249 + X^248 + 
    X^244 + X^243 + X^240 + X^230 + X^227 + X^221 + X^208 + X^194 + X^181 + 
    X^175 + X^172 + X^159 + X^158 + X^153 + X^149 + X^145 + X^143 + X^139 + 
    X^136 + X^130 + X^127 + X^123 + X^121 + X^117 + X^113 + X^108 + X^107 + X^94
    + X^91 + X^90 + X^85 + X^77 + X^72 + X^71 + X^68 + X^58 + X^55 + X^54 + X^49
    + X^41 + X^36 + X^35 + X^32 + X^22 + X^19 + X^13 + 1

Total time: 3.729 seconds, Total memory usage: 2.11MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:11:52 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C := ((1 + X^9)^23)*((1 + X^14)^17)*((1 + X^17)^19)*((1 + X^22)^23)+ X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:11:49 on modular  [Seed = 949837504]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:12:37 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^23)*((1+X^14)^17)*((1+X^17)^19)*((1+X^22)^23)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:12:34 on modular  [Seed = 815093535]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:13:08 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^23)*((1+X^14)^17)*((1+X^17)^19)*((1+X^32)^23)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:13:06 on modular  [Seed = 145583879]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:14:56 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^19)*((1+X^16)^17)*((1+X^23)^13)*((1+X^31)^11)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:14:52 on modular  [Seed = 44524963]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1083 + X^1074 + X^1067 + X^1065 + X^1060 + X^1058 + X^1056 + X^1052 +
    X^1051 + X^1049 + X^1044 + X^1043 + X^1042 + X^1040 + X^1036 + X^1035 + 
    X^1034 + X^1033 + X^1029 + X^1027 + X^1026 + X^1025 + X^1021 + X^1020 + 
    X^1018 + X^1017 + X^1013 + X^1012 + X^1011 + X^1009 + X^1005 + X^1004 + 
    X^1003 + X^1002 + X^998 + X^996 + X^995 + X^994 + X^991 + X^990 + X^989 + 
    X^987 + X^986 + X^981 + X^980 + X^978 + X^975 + X^974 + X^972 + X^971 + 
    X^968 + X^967 + X^966 + X^965 + X^963 + X^960 + X^959 + X^958 + X^957 + 
    X^956 + X^955 + X^952 + X^950 + X^949 + X^948 + X^947 + X^944 + X^943 + 
    X^941 + X^940 + X^939 + X^937 + X^935 + X^934 + X^930 + X^929 + X^928 + 
    X^926 + X^925 + X^924 + X^923 + X^920 + X^919 + X^917 + X^916 + X^914 + 
    X^913 + X^911 + X^910 + X^908 + X^907 + X^906 + X^905 + X^904 + X^903 + 
    X^902 + X^900 + X^897 + X^896 + X^895 + X^894 + X^892 + X^891 + X^890 + 
    X^888 + X^886 + X^885 + X^881 + X^880 + X^879 + X^877 + X^875 + X^871 + 
    X^869 + X^866 + X^864 + X^863 + X^861 + X^859 + X^857 + X^856 + X^855 + 
    X^854 + X^850 + X^849 + X^848 + X^847 + X^846 + X^835 + X^833 + X^832 + 
    X^831 + X^830 + X^829 + X^827 + X^826 + X^825 + X^824 + X^823 + X^822 + 
    X^820 + X^819 + X^817 + X^816 + X^815 + X^813 + X^812 + X^811 + X^809 + 
    X^807 + X^804 + X^803 + X^801 + X^799 + X^792 + X^788 + X^787 + X^784 + 
    X^783 + X^781 + X^779 + X^777 + X^774 + X^769 + X^767 + X^765 + X^764 + 
    X^758 + X^757 + X^756 + X^755 + X^753 + X^750 + X^749 + X^743 + X^739 + 
    X^738 + X^737 + X^735 + X^734 + X^733 + X^730 + X^728 + X^727 + X^725 + 
    X^724 + X^722 + X^721 + X^720 + X^718 + X^717 + X^712 + X^710 + X^707 + 
    X^706 + X^703 + X^702 + X^701 + X^699 + X^697 + X^696 + X^694 + X^693 + 
    X^692 + X^691 + X^690 + X^689 + X^688 + X^687 + X^686 + X^681 + X^675 + 
    X^668 + X^666 + X^665 + X^663 + X^658 + X^657 + X^656 + X^653 + X^652 + 
    X^651 + X^648 + X^647 + X^646 + X^644 + X^642 + X^641 + X^640 + X^638 + 
    X^636 + X^634 + X^633 + X^632 + X^629 + X^628 + X^625 + X^622 + X^621 + 
    X^620 + X^618 + X^615 + X^613 + X^612 + X^611 + X^610 + X^607 + X^605 + 
    X^603 + X^602 + X^601 + X^600 + X^598 + X^597 + X^596 + X^594 + X^590 + 
    X^589 + X^581 + X^579 + X^578 + X^576 + X^575 + X^574 + X^573 + X^572 + 
    X^570 + X^567 + X^565 + X^564 + X^563 + X^562 + X^560 + X^558 + X^557 + 
    X^553 + X^551 + X^545 + X^538 + X^532 + X^530 + X^526 + X^525 + X^523 + 
    X^521 + X^520 + X^519 + X^518 + X^516 + X^513 + X^511 + X^510 + X^509 + 
    X^508 + X^507 + X^505 + X^504 + X^502 + X^494 + X^493 + X^489 + X^487 + 
    X^486 + X^485 + X^483 + X^482 + X^481 + X^480 + X^478 + X^476 + X^473 + 
    X^472 + X^471 + X^470 + X^468 + X^465 + X^463 + X^462 + X^461 + X^458 + 
    X^455 + X^454 + X^451 + X^450 + X^449 + X^447 + X^445 + X^443 + X^442 + 
    X^441 + X^439 + X^437 + X^436 + X^435 + X^432 + X^431 + X^430 + X^427 + 
    X^426 + X^425 + X^420 + X^418 + X^417 + X^415 + X^408 + X^402 + X^397 + 
    X^396 + X^395 + X^394 + X^393 + X^392 + X^391 + X^390 + X^389 + X^387 + 
    X^386 + X^384 + X^382 + X^381 + X^380 + X^377 + X^376 + X^373 + X^371 + 
    X^366 + X^365 + X^363 + X^362 + X^361 + X^359 + X^358 + X^356 + X^355 + 
    X^353 + X^350 + X^349 + X^348 + X^346 + X^345 + X^344 + X^340 + X^334 + 
    X^333 + X^330 + X^328 + X^327 + X^326 + X^325 + X^319 + X^318 + X^316 + 
    X^314 + X^309 + X^306 + X^304 + X^302 + X^300 + X^299 + X^296 + X^295 + 
    X^291 + X^284 + X^282 + X^280 + X^279 + X^276 + X^274 + X^272 + X^271 + 
    X^270 + X^268 + X^267 + X^266 + X^264 + X^263 + X^261 + X^260 + X^259 + 
    X^258 + X^257 + X^256 + X^254 + X^253 + X^252 + X^251 + X^250 + X^248 + 
    X^237 + X^236 + X^235 + X^234 + X^233 + X^229 + X^228 + X^227 + X^226 + 
    X^224 + X^222 + X^220 + X^219 + X^217 + X^214 + X^212 + X^208 + X^206 + 
    X^204 + X^203 + X^202 + X^198 + X^197 + X^195 + X^193 + X^192 + X^191 + 
    X^189 + X^188 + X^187 + X^186 + X^183 + X^181 + X^180 + X^179 + X^178 + 
    X^177 + X^176 + X^175 + X^173 + X^172 + X^170 + X^169 + X^167 + X^166 + 
    X^164 + X^163 + X^160 + X^159 + X^158 + X^157 + X^155 + X^154 + X^153 + 
    X^149 + X^148 + X^146 + X^144 + X^143 + X^142 + X^140 + X^139 + X^136 + 
    X^135 + X^134 + X^133 + X^131 + X^128 + X^127 + X^126 + X^125 + X^124 + 
    X^123 + X^120 + X^118 + X^117 + X^116 + X^115 + X^112 + X^111 + X^109 + 
    X^108 + X^105 + X^103 + X^102 + X^97 + X^96 + X^94 + X^93 + X^92 + X^89 + 
    X^88 + X^87 + X^85 + X^81 + X^80 + X^79 + X^78 + X^74 + X^72 + X^71 + X^70 +
    X^66 + X^65 + X^63 + X^62 + X^58 + X^57 + X^56 + X^54 + X^50 + X^49 + X^48 +
    X^47 + X^43 + X^41 + X^40 + X^39 + X^34 + X^32 + X^31 + X^27 + X^25 + X^23 +
    X^18 + X^16 + X^9 + 1

Total time: 3.669 seconds, Total memory usage: 2.10MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:15:34 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^23)*((1+X^16)^17)*((1+X^23)^13)*((1+X^31)^11)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:15:31 on modular  [Seed = 448757124]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:16:24 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^23)*((1+X^14)^17)*((1+X^23)^13)*((1+X^31)^11)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:16:21 on modular  [Seed = 1858800038]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:17:01 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^23)*((1+X^14)^17)*((1+X^17)^19)*((1+X^22)^32)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:16:59 on modular  [Seed = 1724059200]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:17:19 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C:=((1+X^9)^23)*((1+X^14)^17)*((1+X^17)^19)*((1+X^22)^23)+X^1279;
if IsPrimitive(C) then 
   C;
end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:17:17 on modular  [Seed = 2027753544]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.559 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:20:41 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [24..31] do
for k in [17..23] do
for m in [14..17] do
for n in [8..13] do
        C :=((1+X^n)^23)*((1+X^m)^17)*((1+X^k)^19)*((1+X^j)^23)+X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;




Output: Magma V2.10-22    Fri Jul  2 2004 05:20:18 on modular  [Seed = 1610233760]
   -------------------------------------

X^9 + X^4 + 1
9
15
18
24


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:22:49 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1+X^9)^23)*((1+X^15)^17)*((1+X^18)^19)*((1+X^24)^23)+X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:22:41 on modular  [Seed = 1458781978]
   -------------------------------------

X^9 + X^4 + 1
X^1356 + X^1347 + X^1341 + X^1323 + X^1320 + X^1317 + X^1311 + X^1305 + X^1299 +
    X^1293 + X^1287 + X^1284 + X^1281 + X^1279 + X^1263 + X^1257 + X^1248 + 
    X^1212 + X^1203 + X^1197 + X^1179 + X^1176 + X^1173 + X^1167 + X^1164 + 
    X^1161 + X^1143 + X^1140 + X^1137 + X^1131 + X^1128 + X^1125 + X^1116 + 
    X^1104 + X^1095 + X^1092 + X^1089 + X^1083 + X^1080 + X^1077 + X^1068 + 
    X^1056 + X^1047 + X^1044 + X^1041 + X^1035 + X^1032 + X^1029 + X^1020 + 
    X^1008 + X^999 + X^996 + X^993 + X^987 + X^984 + X^981 + X^963 + X^960 + 
    X^957 + X^951 + X^948 + X^945 + X^927 + X^921 + X^912 + X^876 + X^867 + 
    X^861 + X^843 + X^840 + X^837 + X^831 + X^825 + X^819 + X^813 + X^807 + 
    X^804 + X^801 + X^783 + X^777 + X^768 + X^588 + X^579 + X^573 + X^555 + 
    X^552 + X^549 + X^543 + X^537 + X^531 + X^525 + X^519 + X^516 + X^513 + 
    X^495 + X^489 + X^480 + X^444 + X^435 + X^429 + X^411 + X^408 + X^405 + 
    X^399 + X^396 + X^393 + X^375 + X^372 + X^369 + X^363 + X^360 + X^357 + 
    X^348 + X^336 + X^327 + X^324 + X^321 + X^315 + X^312 + X^309 + X^300 + 
    X^288 + X^279 + X^276 + X^273 + X^267 + X^264 + X^261 + X^252 + X^240 + 
    X^231 + X^228 + X^225 + X^219 + X^216 + X^213 + X^195 + X^192 + X^189 + 
    X^183 + X^180 + X^177 + X^159 + X^153 + X^144 + X^108 + X^99 + X^93 + X^75 +
    X^72 + X^69 + X^63 + X^57 + X^51 + X^45 + X^39 + X^36 + X^33 + X^15 + X^9 + 
    1

Total time: 7.649 seconds, Total memory usage: 3.02MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:25:44 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1+X^9)^23)*((1+X^14)^17)*((1+X^17)^19)*((1+X^22)^23)+X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:25:41 on modular  [Seed = 2869870992]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:26:50 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1+X^9)^23)*((1+X^14)^17)*((1+X^17)^19)*((1+X^22)^21)+X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:26:47 on modular  [Seed = 2718419160]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.569 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:30:20 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1 + X^10)^21)*((1 + X^14)^19)*((1 + X^16)^17)*((1 + X^22)^23) + X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:30:17 on modular  [Seed = 3021070256]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1254 + X^1244 + X^1240 + X^1238 + X^1232 + X^1230 + X^1228 + X^1226 +
    X^1224 + X^1222 + X^1218 + X^1212 + X^1208 + X^1206 + X^1200 + X^1198 + 
    X^1188 + X^1186 + X^1178 + X^1174 + X^1172 + X^1170 + X^1166 + X^1164 + 
    X^1162 + X^1160 + X^1152 + X^1150 + X^1148 + X^1146 + X^1144 + X^1142 + 
    X^1140 + X^1138 + X^1130 + X^1128 + X^1126 + X^1124 + X^1122 + X^1120 + 
    X^1118 + X^1116 + X^1108 + X^1106 + X^1104 + X^1102 + X^1100 + X^1098 + 
    X^1096 + X^1086 + X^1082 + X^1078 + X^1076 + X^1074 + X^1070 + X^1066 + 
    X^1064 + X^1062 + X^1060 + X^1052 + X^1034 + X^1030 + X^1026 + X^1024 + 
    X^1022 + X^1014 + X^1012 + X^1010 + X^1006 + X^1002 + X^994 + X^990 + X^988 
    + X^986 + X^984 + X^982 + X^980 + X^978 + X^972 + X^962 + X^960 + X^958 + 
    X^954 + X^952 + X^942 + X^934 + X^932 + X^930 + X^928 + X^922 + X^916 + 
    X^914 + X^912 + X^910 + X^892 + X^890 + X^888 + X^886 + X^880 + X^878 + 
    X^872 + X^862 + X^860 + X^854 + X^848 + X^844 + X^842 + X^838 + X^834 + 
    X^832 + X^830 + X^828 + X^812 + X^810 + X^806 + X^804 + X^802 + X^796 + 
    X^794 + X^790 + X^784 + X^780 + X^772 + X^766 + X^762 + X^760 + X^756 + 
    X^754 + X^752 + X^748 + X^746 + X^740 + X^736 + X^734 + X^732 + X^726 + 
    X^724 + X^722 + X^718 + X^716 + X^714 + X^712 + X^710 + X^708 + X^704 + 
    X^700 + X^696 + X^694 + X^692 + X^690 + X^684 + X^682 + X^676 + X^670 + 
    X^664 + X^662 + X^660 + X^658 + X^652 + X^650 + X^648 + X^646 + X^644 + 
    X^642 + X^638 + X^636 + X^632 + X^630 + X^624 + X^622 + X^618 + X^616 + 
    X^612 + X^610 + X^608 + X^606 + X^604 + X^602 + X^596 + X^594 + X^592 + 
    X^590 + X^584 + X^578 + X^572 + X^570 + X^564 + X^562 + X^560 + X^558 + 
    X^554 + X^550 + X^546 + X^544 + X^542 + X^540 + X^538 + X^536 + X^532 + 
    X^530 + X^528 + X^522 + X^520 + X^518 + X^514 + X^508 + X^506 + X^502 + 
    X^500 + X^498 + X^494 + X^492 + X^488 + X^482 + X^474 + X^470 + X^464 + 
    X^460 + X^458 + X^452 + X^450 + X^448 + X^444 + X^442 + X^426 + X^424 + 
    X^422 + X^420 + X^416 + X^412 + X^410 + X^406 + X^400 + X^394 + X^392 + 
    X^382 + X^376 + X^374 + X^368 + X^366 + X^364 + X^362 + X^344 + X^342 + 
    X^340 + X^338 + X^332 + X^326 + X^324 + X^322 + X^320 + X^312 + X^302 + 
    X^300 + X^296 + X^294 + X^292 + X^282 + X^276 + X^274 + X^272 + X^270 + 
    X^268 + X^266 + X^264 + X^260 + X^252 + X^248 + X^244 + X^242 + X^240 + 
    X^232 + X^230 + X^228 + X^224 + X^220 + X^202 + X^194 + X^192 + X^190 + 
    X^188 + X^184 + X^180 + X^178 + X^176 + X^172 + X^168 + X^158 + X^156 + 
    X^154 + X^152 + X^150 + X^148 + X^146 + X^138 + X^136 + X^134 + X^132 + 
    X^130 + X^128 + X^126 + X^124 + X^116 + X^114 + X^112 + X^110 + X^108 + 
    X^106 + X^104 + X^102 + X^94 + X^92 + X^90 + X^88 + X^84 + X^82 + X^80 + 
    X^76 + X^68 + X^66 + X^56 + X^54 + X^48 + X^46 + X^42 + X^36 + X^32 + X^30 +
    X^28 + X^26 + X^24 + X^22 + X^16 + X^14 + X^10 + 1

Total time: 3.679 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:31:48 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1 + X^08)^11)*((1 + X^14)^13)*((1 + X^31)^17)*((1 + X^21)^19) + X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 05:31:44 on modular  [Seed = 2385241379]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1196 + X^1188 + X^1182 + X^1180 + X^1175 + X^1174 + X^1172 + X^1167 +
    X^1166 + X^1165 + X^1161 + X^1159 + X^1158 + X^1157 + X^1154 + X^1153 + 
    X^1149 + X^1146 + X^1145 + X^1144 + X^1143 + X^1141 + X^1138 + X^1137 + 
    X^1136 + X^1135 + X^1133 + X^1132 + X^1128 + X^1127 + X^1126 + X^1125 + 
    X^1124 + X^1123 + X^1122 + X^1120 + X^1117 + X^1116 + X^1115 + X^1114 + 
    X^1111 + X^1109 + X^1108 + X^1107 + X^1106 + X^1105 + X^1103 + X^1102 + 
    X^1101 + X^1099 + X^1098 + X^1093 + X^1087 + X^1086 + X^1085 + X^1080 + 
    X^1078 + X^1074 + X^1073 + X^1072 + X^1070 + X^1067 + X^1066 + X^1064 + 
    X^1063 + X^1056 + X^1049 + X^1046 + X^1045 + X^1039 + X^1038 + X^1035 + 
    X^1021 + X^1018 + X^1017 + X^1011 + X^1010 + X^1007 + X^993 + X^990 + X^989 
    + X^983 + X^982 + X^979 + X^972 + X^965 + X^964 + X^962 + X^961 + X^958 + 
    X^956 + X^955 + X^954 + X^950 + X^948 + X^943 + X^942 + X^941 + X^935 + 
    X^930 + X^929 + X^927 + X^926 + X^925 + X^923 + X^922 + X^921 + X^920 + 
    X^919 + X^917 + X^914 + X^913 + X^912 + X^911 + X^908 + X^906 + X^905 + 
    X^904 + X^903 + X^902 + X^901 + X^900 + X^896 + X^895 + X^893 + X^892 + 
    X^891 + X^890 + X^887 + X^885 + X^884 + X^883 + X^882 + X^879 + X^875 + 
    X^874 + X^871 + X^870 + X^869 + X^867 + X^863 + X^862 + X^861 + X^860 + 
    X^856 + X^854 + X^853 + X^852 + X^848 + X^844 + X^840 + X^839 + X^838 + 
    X^836 + X^832 + X^831 + X^830 + X^829 + X^825 + X^823 + X^822 + X^821 + 
    X^818 + X^817 + X^813 + X^810 + X^809 + X^808 + X^807 + X^805 + X^802 + 
    X^801 + X^800 + X^799 + X^797 + X^796 + X^792 + X^791 + X^790 + X^789 + 
    X^788 + X^787 + X^786 + X^784 + X^781 + X^780 + X^779 + X^778 + X^775 + 
    X^773 + X^772 + X^771 + X^770 + X^769 + X^767 + X^766 + X^765 + X^763 + 
    X^762 + X^757 + X^751 + X^750 + X^749 + X^744 + X^742 + X^738 + X^737 + 
    X^736 + X^734 + X^731 + X^730 + X^728 + X^727 + X^720 + X^713 + X^710 + 
    X^709 + X^703 + X^702 + X^700 + X^699 + X^692 + X^686 + X^685 + X^684 + 
    X^682 + X^681 + X^679 + X^678 + X^676 + X^675 + X^674 + X^670 + X^669 + 
    X^665 + X^663 + X^662 + X^661 + X^658 + X^654 + X^650 + X^649 + X^648 + 
    X^646 + X^645 + X^643 + X^642 + X^641 + X^640 + X^639 + X^637 + X^632 + 
    X^631 + X^630 + X^627 + X^625 + X^624 + X^622 + X^621 + X^615 + X^614 + 
    X^613 + X^611 + X^610 + X^609 + X^603 + X^602 + X^599 + X^597 + X^594 + 
    X^593 + X^587 + X^586 + X^585 + X^583 + X^582 + X^581 + X^575 + X^574 + 
    X^572 + X^571 + X^569 + X^566 + X^565 + X^564 + X^559 + X^557 + X^556 + 
    X^555 + X^554 + X^553 + X^551 + X^550 + X^548 + X^547 + X^546 + X^542 + 
    X^538 + X^535 + X^534 + X^533 + X^531 + X^527 + X^526 + X^522 + X^521 + 
    X^520 + X^518 + X^517 + X^515 + X^514 + X^512 + X^511 + X^510 + X^504 + 
    X^497 + X^496 + X^494 + X^493 + X^487 + X^486 + X^483 + X^476 + X^469 + 
    X^468 + X^466 + X^465 + X^462 + X^460 + X^459 + X^458 + X^454 + X^452 + 
    X^447 + X^446 + X^445 + X^439 + X^434 + X^433 + X^431 + X^430 + X^429 + 
    X^427 + X^426 + X^425 + X^424 + X^423 + X^421 + X^418 + X^417 + X^416 + 
    X^415 + X^412 + X^410 + X^409 + X^408 + X^407 + X^406 + X^405 + X^404 + 
    X^400 + X^399 + X^397 + X^396 + X^395 + X^394 + X^391 + X^389 + X^388 + 
    X^387 + X^386 + X^383 + X^379 + X^378 + X^375 + X^374 + X^373 + X^371 + 
    X^367 + X^366 + X^365 + X^364 + X^360 + X^358 + X^357 + X^356 + X^352 + 
    X^348 + X^344 + X^343 + X^342 + X^340 + X^336 + X^335 + X^334 + X^333 + 
    X^329 + X^327 + X^326 + X^325 + X^322 + X^321 + X^317 + X^314 + X^313 + 
    X^312 + X^311 + X^309 + X^306 + X^305 + X^304 + X^303 + X^301 + X^300 + 
    X^296 + X^295 + X^294 + X^293 + X^292 + X^291 + X^290 + X^288 + X^285 + 
    X^284 + X^283 + X^282 + X^279 + X^277 + X^276 + X^275 + X^274 + X^273 + 
    X^271 + X^270 + X^269 + X^267 + X^266 + X^261 + X^255 + X^254 + X^253 + 
    X^248 + X^246 + X^242 + X^241 + X^240 + X^238 + X^235 + X^234 + X^232 + 
    X^231 + X^224 + X^217 + X^214 + X^213 + X^207 + X^206 + X^203 + X^189 + 
    X^186 + X^185 + X^179 + X^178 + X^175 + X^161 + X^158 + X^157 + X^151 + 
    X^150 + X^147 + X^140 + X^133 + X^132 + X^130 + X^129 + X^126 + X^124 + 
    X^123 + X^122 + X^118 + X^116 + X^111 + X^110 + X^109 + X^103 + X^98 + X^97 
    + X^95 + X^94 + X^93 + X^91 + X^90 + X^89 + X^88 + X^87 + X^85 + X^82 + X^81
    + X^80 + X^79 + X^76 + X^74 + X^73 + X^72 + X^71 + X^70 + X^69 + X^68 + X^64
    + X^63 + X^61 + X^60 + X^59 + X^58 + X^55 + X^53 + X^52 + X^51 + X^50 + X^47
    + X^43 + X^42 + X^39 + X^38 + X^37 + X^35 + X^31 + X^30 + X^29 + X^24 + X^22
    + X^21 + X^16 + X^14 + X^8 + 1

Total time: 3.729 seconds, Total memory usage: 2.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:33:28 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [21..31] do
for k in [16..20] do
for m in [13..15] do
for n in [9..12] do
        C :=((1+X^n)^23)*((1+X^m)^17)*((1+X^k)^19)*((1+X^j)^23)+X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;




Output: Magma V2.10-22    Fri Jul  2 2004 05:33:09 on modular  [Seed = 2250501502]
   -------------------------------------

X^9 + X^4 + 1
9
15
18
24

Total time: 18.079 seconds, Total memory usage: 2.94MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:37:01 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for j in [21..31] do
for k in [16..20] do
for m in [13..15] do
for n in [1..12] do
        C :=((1+X^n)^23)*((1+X^m)^17)*((1+X^k)^19)*((1+X^j)^23)+X^1279;
        if IsPrimitive(C) then 
           n;
           m;
           k;
           j;
        end if;
end for;
end for;
end for;
end for;




Output: Magma V2.10-22    Fri Jul  2 2004 05:36:38 on modular  [Seed = 2554197011]
   -------------------------------------

X^9 + X^4 + 1
8
14
16
21
6
13
19
22
6
13
19
23
9
15
18
24
6
13
19
24


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:39:23 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for m in [1..15] do
for n in [1..15] do
        C :=((1+X^n)^23)*((1+X^m)^17)*((1+X^17)^19)*((1+X^22)^23)+X^1279;
        if IsPrimitive(C) then 
           n;
           m;
        end if;
end for;
end for;




Output: Magma V2.10-22    Fri Jul  2 2004 05:39:18 on modular  [Seed = 3897394563]
   -------------------------------------

X^9 + X^4 + 1

Total time: 4.479 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 05:40:02 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for m in [1..15] do
for n in [1..15] do
        C :=((1+X^n)^23)*((1+X^m)^17)*((1+X^17)^19)*((1+X^23)^22)+X^1279;
        if IsPrimitive(C) then 
           n;
           m;
        end if;
end for;
end for;




Output: Magma V2.10-22    Fri Jul  2 2004 05:39:56 on modular  [Seed = 3762654625]
   -------------------------------------

X^9 + X^4 + 1
15
2

Total time: 5.939 seconds, Total memory usage: 2.23MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 06:14:47 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1 + X^09)^23)*((1 + X^17)^19)*((1 + X^14)^17)*((1 + X^22)^23) + X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 06:14:44 on modular  [Seed = 1657214936]
   -------------------------------------

X^9 + X^4 + 1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (217.172.99.3)
Time: Fri Jul  2 06:17:28 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
C :=((1 + X^09)^23)*((1 + X^17)^17)*((1 + X^14)^19)*((1 + X^22)^23) + X^1279;
        if IsPrimitive(C) then 
           C;
        end if;



Output: Magma V2.10-22    Fri Jul  2 2004 06:17:24 on modular  [Seed = 1324038228]
   -------------------------------------

X^9 + X^4 + 1
X^1279 + X^1268 + X^1259 + X^1254 + X^1251 + X^1250 + X^1246 + X^1245 + X^1242 +
    X^1241 + X^1240 + X^1236 + X^1233 + X^1231 + X^1229 + X^1227 + X^1226 + 
    X^1223 + X^1222 + X^1220 + X^1217 + X^1215 + X^1214 + X^1213 + X^1211 + 
    X^1210 + X^1209 + X^1208 + X^1207 + X^1206 + X^1205 + X^1200 + X^1199 + 
    X^1198 + X^1197 + X^1196 + X^1193 + X^1191 + X^1190 + X^1189 + X^1185 + 
    X^1184 + X^1182 + X^1181 + X^1176 + X^1175 + X^1173 + X^1172 + X^1171 + 
    X^1168 + X^1167 + X^1164 + X^1162 + X^1159 + X^1155 + X^1154 + X^1153 + 
    X^1151 + X^1150 + X^1149 + X^1145 + X^1142 + X^1140 + X^1137 + X^1133 + 
    X^1132 + X^1131 + X^1129 + X^1128 + X^1127 + X^1124 + X^1123 + X^1120 + 
    X^1118 + X^1111 + X^1109 + X^1105 + X^1102 + X^1097 + X^1093 + X^1088 + 
    X^1084 + X^1083 + X^1082 + X^1075 + X^1073 + X^1066 + X^1065 + X^1060 + 
    X^1056 + X^1051 + X^1050 + X^1044 + X^1043 + X^1041 + X^1035 + X^1034 + 
    X^1033 + X^1032 + X^1030 + X^1028 + X^1027 + X^1026 + X^1023 + X^1022 + 
    X^1021 + X^1019 + X^1018 + X^1017 + X^1016 + X^1014 + X^1012 + X^1011 + 
    X^1009 + X^1003 + X^1002 + X^999 + X^996 + X^992 + X^991 + X^990 + X^988 + 
    X^987 + X^986 + X^981 + X^978 + X^975 + X^974 + X^972 + X^971 + X^970 + 
    X^968 + X^964 + X^963 + X^962 + X^961 + X^960 + X^959 + X^958 + X^957 + 
    X^955 + X^950 + X^948 + X^947 + X^943 + X^942 + X^939 + X^937 + X^936 + 
    X^935 + X^933 + X^932 + X^930 + X^929 + X^928 + X^927 + X^926 + X^925 + 
    X^924 + X^923 + X^920 + X^918 + X^916 + X^912 + X^911 + X^909 + X^907 + 
    X^906 + X^903 + X^898 + X^896 + X^895 + X^894 + X^892 + X^890 + X^888 + 
    X^887 + X^884 + X^882 + X^881 + X^880 + X^876 + X^870 + X^869 + X^866 + 
    X^865 + X^864 + X^863 + X^859 + X^857 + X^854 + X^853 + X^852 + X^849 + 
    X^848 + X^847 + X^845 + X^844 + X^842 + X^838 + X^836 + X^829 + X^827 + 
    X^826 + X^825 + X^824 + X^823 + X^820 + X^817 + X^815 + X^811 + X^810 + 
    X^809 + X^808 + X^807 + X^804 + X^802 + X^798 + X^797 + X^795 + X^794 + 
    X^787 + X^785 + X^784 + X^783 + X^780 + X^778 + X^777 + X^776 + X^775 + 
    X^774 + X^772 + X^766 + X^765 + X^764 + X^762 + X^758 + X^757 + X^756 + 
    X^754 + X^753 + X^752 + X^751 + X^750 + X^749 + X^746 + X^744 + X^743 + 
    X^740 + X^738 + X^736 + X^733 + X^732 + X^730 + X^728 + X^727 + X^725 + 
    X^724 + X^723 + X^718 + X^717 + X^713 + X^711 + X^709 + X^704 + X^702 + 
    X^700 + X^699 + X^698 + X^697 + X^696 + X^695 + X^694 + X^693 + X^690 + 
    X^689 + X^688 + X^687 + X^685 + X^684 + X^682 + X^680 + X^677 + X^676 + 
    X^675 + X^674 + X^673 + X^672 + X^671 + X^669 + X^667 + X^666 + X^664 + 
    X^663 + X^661 + X^658 + X^656 + X^652 + X^651 + X^649 + X^648 + X^647 + 
    X^646 + X^645 + X^644 + X^642 + X^640 + X^638 + X^636 + X^635 + X^633 + 
    X^632 + X^630 + X^628 + X^626 + X^624 + X^623 + X^622 + X^621 + X^620 + 
    X^619 + X^617 + X^616 + X^612 + X^610 + X^607 + X^605 + X^604 + X^602 + 
    X^601 + X^599 + X^597 + X^596 + X^595 + X^594 + X^593 + X^592 + X^591 + 
    X^588 + X^586 + X^584 + X^583 + X^581 + X^580 + X^579 + X^578 + X^575 + 
    X^574 + X^573 + X^572 + X^571 + X^570 + X^569 + X^568 + X^566 + X^564 + 
    X^559 + X^557 + X^555 + X^551 + X^550 + X^545 + X^544 + X^543 + X^541 + 
    X^540 + X^538 + X^536 + X^535 + X^532 + X^530 + X^528 + X^525 + X^524 + 
    X^522 + X^519 + X^518 + X^517 + X^516 + X^515 + X^514 + X^512 + X^511 + 
    X^510 + X^506 + X^504 + X^503 + X^502 + X^496 + X^494 + X^493 + X^492 + 
    X^491 + X^490 + X^488 + X^485 + X^484 + X^483 + X^481 + X^474 + X^473 + 
    X^471 + X^470 + X^466 + X^464 + X^461 + X^460 + X^459 + X^458 + X^457 + 
    X^453 + X^451 + X^448 + X^445 + X^444 + X^443 + X^442 + X^441 + X^439 + 
    X^432 + X^430 + X^426 + X^424 + X^423 + X^421 + X^420 + X^419 + X^416 + 
    X^415 + X^414 + X^411 + X^409 + X^405 + X^404 + X^403 + X^402 + X^399 + 
    X^398 + X^392 + X^388 + X^387 + X^386 + X^384 + X^381 + X^380 + X^378 + 
    X^376 + X^374 + X^373 + X^372 + X^370 + X^365 + X^362 + X^361 + X^359 + 
    X^357 + X^356 + X^352 + X^350 + X^348 + X^345 + X^344 + X^343 + X^342 + 
    X^341 + X^340 + X^339 + X^338 + X^336 + X^335 + X^333 + X^332 + X^331 + 
    X^329 + X^326 + X^325 + X^321 + X^320 + X^318 + X^313 + X^311 + X^310 + 
    X^309 + X^308 + X^307 + X^306 + X^305 + X^304 + X^300 + X^298 + X^297 + 
    X^296 + X^294 + X^293 + X^290 + X^287 + X^282 + X^281 + X^280 + X^278 + 
    X^277 + X^276 + X^272 + X^269 + X^266 + X^265 + X^259 + X^257 + X^256 + 
    X^254 + X^252 + X^251 + X^250 + X^249 + X^247 + X^246 + X^245 + X^242 + 
    X^241 + X^240 + X^238 + X^236 + X^235 + X^234 + X^233 + X^227 + X^225 + 
    X^224 + X^218 + X^217 + X^212 + X^208 + X^203 + X^202 + X^195 + X^193 + 
    X^186 + X^185 + X^184 + X^180 + X^175 + X^171 + X^166 + X^163 + X^159 + 
    X^157 + X^150 + X^148 + X^145 + X^144 + X^141 + X^140 + X^139 + X^137 + 
    X^136 + X^135 + X^131 + X^128 + X^126 + X^123 + X^119 + X^118 + X^117 + 
    X^115 + X^114 + X^113 + X^109 + X^106 + X^104 + X^101 + X^100 + X^97 + X^96 
    + X^95 + X^93 + X^92 + X^87 + X^86 + X^84 + X^83 + X^79 + X^78 + X^77 + X^75
    + X^72 + X^71 + X^70 + X^69 + X^68 + X^63 + X^62 + X^61 + X^60 + X^59 + X^58
    + X^57 + X^55 + X^54 + X^53 + X^51 + X^48 + X^46 + X^45 + X^42 + X^41 + X^39
    + X^37 + X^35 + X^32 + X^28 + X^27 + X^26 + X^23 + X^22 + X^18 + X^17 + X^14
    + X^9 + 1

Total time: 3.669 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.149.47.186)
Time: Fri Jul  2 09:07:23 2004

Input: AAAAA

Output: Magma V2.10-22    Fri Jul  2 2004 09:07:17 on modular  [Seed = 4166903502]
   -------------------------------------


>> AAAAA;
   ^
User error: Identifier 'AAAAA' has not been declared or assigned

Total time: 2.710 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (128.192.179.231)
Time: Fri Jul  2 12:26:14 2004

Input: 31.99=5U+3v+w+2x
6.88=11u+4v+2w+6x+y+2z
25.44=2u+2v+4z
16.96=u+x+z
18.65=u+2w+y

Output: Magma V2.10-22    Fri Jul  2 2004 12:26:09 on modular  [Seed = 3227847762]
   -------------------------------------


>> 31.99=5U+3v+w+2x
          ^
User error: bad syntax

>> 6.88=11u+4v+2w+6x+y+2z
          ^
User error: bad syntax

>> 25.44=2u+2v+4z
          ^
User error: bad syntax

>> 18.65=u+2w+y;
   ^
User error: bad syntax

Total time: 2.619 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host io.yourlibrary.ca. (208.181.90.67)
Time: Fri Jul  2 15:28:01 2004

Input: EllipticCurve(Stein-WatkinsDatabase(),21987);

Output: Magma V2.10-22    Fri Jul  2 2004 15:27:58 on modular  [Seed = 2919979429]
   -------------------------------------


>> EllipticCurve(Stein-WatkinsDatabase(),21987);;
                 ^
User error: Identifier 'Stein' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host io.yourlibrary.ca. (208.181.90.67)
Time: Fri Jul  2 15:28:24 2004

Input: EllipticCurve(CremonaDatabase(),21987);

Output: Magma V2.10-22    Fri Jul  2 2004 15:28:20 on modular  [Seed = 2519949815]
   -------------------------------------


>> EllipticCurve(CremonaDatabase(),21987);;
                ^
Runtime error in 'EllipticCurve': Bad argument types
Argument types given: DB, RngIntElt

Total time: 2.499 seconds, Total memory usage: 2.57MB


************** MAGMA *****************
Host io.yourlibrary.ca. (208.181.90.67)
Time: Fri Jul  2 15:28:53 2004

Input: EllipticCurve(CremonaDatabase(),21987,1);

Output: Magma V2.10-22    Fri Jul  2 2004 15:28:51 on modular  [Seed = 2654693848]
   -------------------------------------


>> EllipticCurve(CremonaDatabase(),21987,1);;
                ^
Runtime error in 'EllipticCurve': Bad argument types
Argument types given: DB, RngIntElt, RngIntElt

Total time: 2.499 seconds, Total memory usage: 2.57MB


************** MAGMA *****************
Host io.yourlibrary.ca. (208.181.90.67)
Time: Fri Jul  2 15:29:16 2004

Input: EllipticCurve(CremonaDatabase(),1987,1);

Output: Magma V2.10-22    Fri Jul  2 2004 15:29:14 on modular  [Seed = 2250469689]
   -------------------------------------


>> EllipticCurve(CremonaDatabase(),1987,1);;
                ^
Runtime error in 'EllipticCurve': Bad argument types
Argument types given: DB, RngIntElt, RngIntElt

Total time: 2.499 seconds, Total memory usage: 2.57MB


************** MAGMA *****************
Host io.yourlibrary.ca. (208.181.90.67)
Time: Fri Jul  2 15:31:17 2004

Input: LargestConductor(CremonaDatabase());

Output: Magma V2.10-22    Fri Jul  2 2004 15:31:15 on modular  [Seed = 2284679358]
   -------------------------------------

20000

Total time: 2.529 seconds, Total memory usage: 2.57MB


************** MAGMA *****************
Host io.yourlibrary.ca. (208.181.90.67)
Time: Fri Jul  2 15:31:38 2004

Input: LargestConductor(EllipticCurveDatabase());

Output: Magma V2.10-22    Fri Jul  2 2004 15:31:36 on modular  [Seed = 4032104669]
   -------------------------------------

20000

Total time: 2.619 seconds, Total memory usage: 2.57MB


************** MAGMA *****************
Host lns-th2-3-82-64-44-128.adsl.proxad.net. (82.64.44.128)
Time: Fri Jul  2 15:35:08 2004

Input: (1+x+y)^2

Output: Magma V2.10-22    Fri Jul  2 2004 15:35:05 on modular  [Seed = 4217242407]
   -------------------------------------


>> (1+x+y)^2;
      ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host lns-th2-3-82-64-44-128.adsl.proxad.net. (82.64.44.128)
Time: Fri Jul  2 15:35:22 2004

Input: (1+x+y)^2

Output: Magma V2.10-22    Fri Jul  2 2004 15:35:20 on modular  [Seed = 3931050535]
   -------------------------------------


>> (1+x+y)^2;
      ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host leastsquares.com. (207.188.167.61)
Time: Fri Jul  2 15:48:50 2004

Input: diff(sin(x),x)

Output: Magma V2.10-22    Fri Jul  2 2004 15:48:47 on modular  [Seed = 612489229]
   -------------------------------------


>> diff(sin(x),x);
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9535436.dip.t-dialin.net. (217.83.84.54)
Time: Fri Jul  2 21:35:05 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  2 2004 21:35:02 on modular  [Seed = 2819548627]
   -------------------------------------

4

Total time: 2.659 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535436.dip.t-dialin.net. (217.83.84.54)
Time: Fri Jul  2 21:35:18 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  2 2004 21:35:14 on modular  [Seed = 2684808655]
   -------------------------------------

0

Total time: 4.139 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535436.dip.t-dialin.net. (217.83.84.54)
Time: Fri Jul  2 21:40:22 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  2 2004 21:40:19 on modular  [Seed = 2150026814]
   -------------------------------------

24

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535436.dip.t-dialin.net. (217.83.84.54)
Time: Fri Jul  2 21:40:53 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  2 2004 21:40:51 on modular  [Seed = 4166956646]
   -------------------------------------

96

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:31:26 2004

Input: a:=2048;
n:=1;
while 3^n div a ne 0 do
n:=n+1;
end while
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:31:23 on modular  [Seed = 2836389747]
   -------------------------------------


>> print(n);;
   ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:31:38 2004

Input: a:=2048;
n:=1;
while 3^n div a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:31:36 on modular  [Seed = 2971125592]
   -------------------------------------

1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:31:59 2004

Input: a:=128;
n:=1;
while 3^n div a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:31:56 on modular  [Seed = 3105869636]
   -------------------------------------

1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:32:19 2004

Input: a:=4;
n:=1;
while 3^n div a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:32:17 on modular  [Seed = 1122251985]
   -------------------------------------

1

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:33:04 2004

Input: a:=4;
n:=1;
while 3^n+2 div a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:32:42 on modular  [Seed = 1256996066]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:33:32 2004

Input: a:=9;
n:=1;
while 3^n div a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:33:30 on modular  [Seed = 1375151625]
   -------------------------------------

1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:34:02 2004

Input: a:=9;
n:=1;
while 3^n div a eq 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:33:59 on modular  [Seed = 1509895724]
   -------------------------------------

2

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:34:19 2004

Input: a:=4;
n:=1;
while 3^n div a eq 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:34:17 on modular  [Seed = 1640437354]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:35:30 2004

Input: a:=2048;
n:=1;
while 3^n mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:35:07 on modular  [Seed = 1893074761]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:36:02 2004

Input: a:=8;
n:=1;
while 3^n mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:35:40 on modular  [Seed = 2144929953]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:36:36 2004

Input: a:=2047;
n:=1;
while 3^n mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:36:14 on modular  [Seed = 94597881]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:37:19 2004

Input: a:=127;
n:=1;
while 3^n mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:36:56 on modular  [Seed = 229341863]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:37:39 2004

Input: a:=127;
n:=1;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:37:37 on modular  [Seed = 448553545]
   -------------------------------------

126

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:38:06 2004

Input: a:=2047;
n:=1;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:38:04 on modular  [Seed = 545675342]
   -------------------------------------

88

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:38:40 2004

Input: a:=8388607;
n:=1;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:38:18 on modular  [Seed = 697258321]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:39:15 2004

Input: a:=8388607;
n:=230;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:38:53 on modular  [Seed = 3947729908]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:39:45 2004

Input: a:=8388607;
n:=45;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:39:22 on modular  [Seed = 4032202952]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:40:18 2004

Input: a:=8388607;
n:=47;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:39:56 on modular  [Seed = 4166942758]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:40:51 2004

Input: a:=8388607;
n:=46;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:40:28 on modular  [Seed = 2654529120]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:41:41 2004

Input: a:=8388607;
n:=178480;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:41:38 on modular  [Seed = 2801917671]
   -------------------------------------

178480

Total time: 2.579 seconds, Total memory usage: 2.21MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:41:51 2004

Input: a:=8388607;
n:=178479;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:41:49 on modular  [Seed = 2936657632]
   -------------------------------------

178480

Total time: 2.649 seconds, Total memory usage: 2.21MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:42:04 2004

Input: a:=8388607;
n:=178478;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:42:01 on modular  [Seed = 3021131247]
   -------------------------------------

178480

Total time: 2.719 seconds, Total memory usage: 2.21MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:43:38 2004

Input: x:=29;
a:=(2^x)-1;
n:=256997;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:43:15 on modular  [Seed = 3172713628]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:44:14 2004

Input: x:=29;
a:=(2^x)-1;
n:=2304165;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:43:52 on modular  [Seed = 1155677583]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:44:45 2004

Input: x:=29;
a:=(2^x)-1;
n:=231;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:44:23 on modular  [Seed = 1290417576]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:45:20 2004

Input: x:=29;
a:=(2^x)-1;
n:=1101;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:44:57 on modular  [Seed = 1425157598]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:45:51 2004

Input: x:=29;
a:=(2^x)-1;
n:=2087;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:45:29 on modular  [Seed = 1559897590]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:46:14 2004

Input: x:=23;
a:=(2^x)-1;
n:=178479;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:46:11 on modular  [Seed = 1808601403]
   -------------------------------------

178480

Total time: 2.639 seconds, Total memory usage: 2.21MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:46:51 2004

Input: x:=29;
a:=(2^x)-1;
n:=486735;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:46:28 on modular  [Seed = 1943341332]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 00:47:22 2004

Input: x:=29;
a:=(2^x)-1;
n:=232;
while ((3^n)-1) mod a ne 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul  3 2004 00:47:00 on modular  [Seed = 2078081404]
   -------------------------------------



************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Sat Jul  3 01:14:08 2004

Input: ((3^164511352)-1)/((2^41)-1)

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Sat Jul  3 2004 01:14:05 on modular  [Seed = 2200273757]
   -------------------------------------


Current total memory usage: 1.6MB, failed memory request: 551.2MB
System Error: User memory limit has been reached

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:25:45 2004

Input: R<x,y,z,t,u,v>:=PolynomialRing(RationalField(),[1,2,3,4,5,6]);
SyzygyModule(xz-y^2,xt-zy,xv-uy,yt-z^2,yv-uz,zv-ut);

Output: Magma V2.10-22    Sat Jul  3 2004 05:25:42 on modular  [Seed = 2684787571]
   -------------------------------------


>> SyzygyModule(xz-y^2,xt-zy,xv-uy,yt-z^2,yv-uz,zv-ut);;
                ^
User error: Identifier 'xz' has not been declared or assigned

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:26:08 2004

Input: R<x,y,z,t,u,v>:=PolynomialRing(RationalField(),[1,2,3,4,5,6]);
SyzygyModule(x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t);

Output: Magma V2.10-22    Sat Jul  3 2004 05:26:06 on modular  [Seed = 2869792832]
   -------------------------------------


>> SyzygyModule(x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t);;
               ^
Runtime error in 'SyzygyModule': Bad argument types
Argument types given: RngMPolElt, RngMPolElt, RngMPolElt, RngMPolElt, 
RngMPolElt, RngMPolElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:26:33 2004

Input: R<x,y,z,t,u,v>:=PolynomialRing(RationalField(),[1,2,3,4,5,6]);
SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t]);

Output: Magma V2.10-22    Sat Jul  3 2004 05:26:30 on modular  [Seed = 3004532784]
   -------------------------------------

Module of degree 6
TOP Order
Coefficient ring:
    Graded Polynomial ring of rank 6 over Rational Field
    Lexicographical Order
    Variables: x, y, z, t, u, v
    Variable weights: 1 2 3 4 5 6
Basis:
(        -t          z          0         -y          0          0)
(        -v          0          z          0         -y          0)
(-y*t + z^2          0          0  x*z - y^2          0          0)
(-y*v + z*u          0          0          0  x*z - y^2          0)
(        -v          u          0          0         -y          x)
(         0         -v          t          u         -z          0)
(         z         -y          0          x          0          0)
(       t*u       -y*v          0        y*u  x*t - y*z          0)
(         0 -z*v + t*u          0        z*u       -z^2        x*t)
(       z*v          0       -y*t  x*v - y*u        y*z          0)
(         u          0         -y          0          x          0)
(         0          u         -z          0          0          x)
(         0          0          0         -v          t         -z)
(         0          0          0 -z*v + t*u          0  y*t - z^2)
(         0          0          0          u         -z          y)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:27:39 2004

Input: R<x,y,z,t,u,v>:=PolynomialRing(RationalField(),[1,2,3,4,5,6]);
SyzygyMatrix([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t]);

Output: Magma V2.10-22    Sat Jul  3 2004 05:27:36 on modular  [Seed = 3139274742]
   -------------------------------------

[        -t          z          0         -y          0          0]
[        -v          0          z          0         -y          0]
[-y*t + z^2          0          0  x*z - y^2          0          0]
[-y*v + z*u          0          0          0  x*z - y^2          0]
[        -v          u          0          0         -y          x]
[         0         -v          t          u         -z          0]
[         z         -y          0          x          0          0]
[       t*u       -y*v          0        y*u  x*t - y*z          0]
[         0 -z*v + t*u          0        z*u       -z^2        x*t]
[       z*v          0       -y*t  x*v - y*u        y*z          0]
[         u          0         -y          0          x          0]
[         0          u         -z          0          0          x]
[         0          0          0         -v          t         -z]
[         0          0          0 -z*v + t*u          0  y*t - z^2]
[         0          0          0          u         -z          y]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:28:38 2004

Input: R<x,y,z,t,u,v>:=PolynomialRing(RationalField(),[1,2,3,4,5,6]);
M:=SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t]);
Groebner(M);

Output: Magma V2.10-22    Sat Jul  3 2004 05:28:35 on modular  [Seed = 1088846917]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:29:05 2004

Input: R<x,y,z,t,u,v>:=PolynomialRing(RationalField(),[1,2,3,4,5,6]);
M:=SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t]);
Groebner(M);
BasisMatrix(M);

Output: Magma V2.10-22    Sat Jul  3 2004 05:29:03 on modular  [Seed = 1223586897]
   -------------------------------------

[-x*v + y*u          0  x*z - y^2          0          0          0]
[-x*t + y*z  x*z - y^2          0          0          0          0]
[         0 -x*v + y*u  x*t - y*z          0          0          0]
[         0          u         -z          0          0          x]
[         u          0         -y          0          x          0]
[         z         -y          0          x          0          0]
[ z*v - t*u -y*v + z*u  y*t - z^2          0          0          0]
[         0          v         -t          0          0          y]
[         v          0         -z          0          y          0]
[         t         -z          0          y          0          0]
[         0          0          0          v         -t          z]
[         0          v         -t         -u          z          0]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:30:44 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,8,9]);
M:=SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,B*x+A*y-u^2,B*y+A*z-u*v,B*z+A*t-v^2]);
Groebner(M);
BasisMatrix(M);

Output: Magma V2.10-22    Sat Jul  3 2004 05:30:41 on modular  [Seed = 1375170006]
   -------------------------------------

[-x*B - y*A + u^2   0   0   0   0   0   x*z - y^2   0   0]
[-x*v + y*u   0   x*z - y^2   0   0   0   0   0   0]
[-x*t + y*z   x*z - y^2   0   0   0   0   0   0   0]
[0   -x*B - y*A + u^2   0   0   0   0   x*t - y*z   0   0]
[0   -x*v + y*u   x*t - y*z   0   0   0   0   0   0]
[0   0   -x*B - y*A + u^2   0   0   0   x*v - y*u   0   0]
[0   -A   v   0   u   0   -z   0   x]
[-A   0   u   0   0   0   -y   x   0]
[0   u   -z   0   0   x   0   0   0]
[u   0   -y   0   x   0   0   0   0]
[z   -y   0   x   0   0   0   0   0]
[z*B + t*A   -y*B - z*A   0   u^2   0   0   y*t - z^2   0   0]
[z*v - t*u   -y*v + z*u   y*t - z^2   0   0   0   0   0   0]
[u*B + v*A   0   -y*B - z*A   0   u^2   0   y*v - z*u   0   0]
[0   B   0   0   v   u   -t   0   y]
[B   0   0   0   u   0   -z   y   0]
[0   v   -t   0   0   y   0   0   0]
[v   0   -z   0   y   0   0   0   0]
[t   -z   0   y   0   0   0   0   0]
[0   u*B + v*A   -z*B - t*A   0   0   u^2   z*v - t*u   0   0]
[0   0   0   B   0   v   0   -t   z]
[0   B   0   A   0   u   -t   z   0]
[0   0   0   v   -t   z   0   0   0]
[0   v   -t   -u   z   0   0   0   0]
[0   0   0   0   B   A   0   -v   u]
[0   0   B   0   A   0   -v   u   0]

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 05:38:48 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
M:=SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,A*x+B*z^2-u^2,A*y+B*z*t-u*v,A*z+B*t^2-v^2]);
Groebner(M);
BasisMatrix(M);

Output: Magma V2.10-22    Sat Jul  3 2004 05:38:45 on modular  [Seed = 1673878912]
   -------------------------------------

[-x*A - z^2*B + u^2   0   0   0   0   0   x*z - y^2   0   0]
[-x*v + y*u   0   x*z - y^2   0   0   0   0   0   0]
[-x*t + y*z   x*z - y^2   0   0   0   0   0   0   0]
[0   -x*A - z^2*B + u^2   0   0   0   0   x*t - y*z   0   0]
[0   -x*v + y*u   x*t - y*z   0   0   0   0   0   0]
[0   0   -x*A - z^2*B + u^2   0   0   0   x*v - y*u   0   0]
[0   -t*B   v   -z*B   u   0   -z   0   x]
[0   -z*B   u   0   0   0   -y   x   0]
[0   u   -z   0   0   x   0   0   0]
[u   0   -y   0   x   0   0   0   0]
[z   -y   0   x   0   0   0   0   0]
[z*A   -y*A   0   -z^2*B + u^2   0   0   y*t - z^2   0   0]
[z*v - t*u   -y*v + z*u   y*t - z^2   0   0   0   0   0   0]
[u*A   z*v*B   -y*A - z*t*B   -z*u*B   u^2   0   y*v - z*u   0   0]
[0   A   0   -t*B   v   u   -t   0   y]
[A   0   0   -z*B   u   0   -z   y   0]
[0   v   -t   0   0   y   0   0   0]
[v   0   -z   0   y   0   0   0   0]
[t   -z   0   y   0   0   0   0   0]
[0   t*v*B + u*A   -z*A - t^2*B   z*v*B - t*u*B   0   u^2   z*v - t*u   0   0]
[0   0   0   A   0   v   0   -t   z]
[0   A   0   0   0   u   -t   z   0]
[0   0   0   v   -t   z   0   0   0]
[0   v   -t   -u   z   0   0   0   0]
[0   0   0   0   A   t*B   0   -v   u]
[0   0   A   -v*B   t*B   0   -v   u   0]

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (80.125.88.82)
Time: Sat Jul  3 08:34:36 2004

Input: RealTamagawa := function(N : M:=CuspidalSubspace(ModularSymbols(N)),
F:=FiniteField(2),
C:=StarInvolution(M),
n:=Dimension(M),
U:=Matrix(F,n,n,[<i,j,F!C[i][j]>: i, j in [1..n]])-ScalarMatrix(n,F!1))
return 2^(n/2-Rank(U));
end function;
RealTamagawa(8*3*5*7*11);


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host pD9FF0CB6.dip.t-dialin.net. (217.255.12.182)
Time: Sat Jul  3 09:42:34 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
Order(F);

Output: Magma V2.10-22    Sat Jul  3 2004 09:42:30 on modular  [Seed = 662818984]
   -------------------------------------

96

Total time: 2.679 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF0CB6.dip.t-dialin.net. (217.255.12.182)
Time: Sat Jul  3 09:43:46 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b>;
Index(F,G);
Order(F);
Order(F)/Index(F,G);

Output: Magma V2.10-22    Sat Jul  3 2004 09:43:43 on modular  [Seed = 1067042681]
   -------------------------------------

8
96
12

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF0CB6.dip.t-dialin.net. (217.255.12.182)
Time: Sat Jul  3 09:44:26 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a*b>;
Index(F,G);
Order(F);
Order(F)/Index(F,G);

Output: Magma V2.10-22    Sat Jul  3 2004 09:44:07 on modular  [Seed = 932302681]
   -------------------------------------

0
0

>> Order(F)/Index(F,G);;
           ^
Runtime error in '/': Division by zero

Total time: 18.389 seconds, Total memory usage: 29.67MB


************** MAGMA *****************
Host pD9535E46.dip.t-dialin.net. (217.83.94.70)
Time: Sat Jul  3 10:06:40 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b>;
Index(F,G);
Order(F);
Order(F)/Index(F,G);

Output: Magma V2.10-22    Sat Jul  3 2004 10:06:37 on modular  [Seed = 3947697871]
   -------------------------------------

8
96
12

Total time: 2.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 11:52:14 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,8,9]);
SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,B*x+A*y-u^2,B*y+A*z-u*v,B*z+A*t-v^2]);

Output: Magma V2.10-22    Sat Jul  3 2004 11:52:11 on modular  [Seed = 515410047]
   -------------------------------------

Module of degree 9
TOP Order
Coefficient ring:
    Graded Polynomial ring of rank 8 over Rational Field
    Lexicographical Order
    Variables: x, y, z, t, u, v, A, B
    Variable weights: 1 2 3 4 5 6 8 9
Basis:
(-t   z   0   -y   0   0   0   0   0)
(-v   0   z   0   -y   0   0   0   0)
(-B   0   0   0   -u   0   z   -y   0)
(-y*t + z^2   0   0   x*z - y^2   0   0   0   0   0)
(-y*v + z*u   0   0   0   x*z - y^2   0   0   0   0)
(-y*B - z*A + u*v   0   0   0   0   0   0   x*z - y^2   0)
(-v   u   0   0   -y   x   0   0   0)
(-B   -A   v   0   0   0   0   -y   x)
(-t*u*B - t*v*A + v^3   0   0   -y*u*B - y*v*A   y*v^2 - z^2*A + z*u*v   -x*z*B 
    0   -z^2*u   x*z*v)
(0   -v   t   u   -z   0   0   0   0)
(0   -B   0   -A   0   -u   t   -z   0)
(z   -y   0   x   0   0   0   0   0)
(t*u   -y*v   0   y*u   x*t - y*z   0   0   0   0)
(-t*A   -y*B + u*v   0   -y*A   0   0   0   x*t - y*z   0)
(0   -z*v + t*u   0   z*u   -z^2   x*t   0   0   0)
(0   -z*B - t*A + v^2   0   -z*A   z*v   0   0   -z^2   x*t)
(0   -u*B - v*A   v^2   0   -z*A + u*v   -x*B   0   -z*u   x*v)
(0   0   -B   0   -A   0   v   -u   0)
(z*v   0   -y*t   x*v - y*u   y*z   0   0   0   0)
(u   0   -y   0   x   0   0   0   0)
(-v*A   0   -y*B + u*v   0   -y*A   0   0   x*v - y*u   0)
(0   u   -z   0   0   x   0   0   0)
(0   -v*A   -z*B + v^2   0   -z*A + u*v   0   0   -z*u   x*v)
(0   -v^2*A   -t*u*B + v^3   -u^2*B   -z*v*A + u*v^2   -x*v*B - z*u*A   0   0   
    x*v^2 - z*u^2)
(z*B   0   0   x*B + y*A - u^2   z*u   0   -y*t   y*z   0)
(u*B   0   0   0   x*B + y*A   0   -y*v   y*u   0)
(-A   0   u   0   0   0   -y   x   0)
(0   u*B   0   0   z*A   x*B   -z*v   z*u   0)
(0   -A   v   0   u   0   -z   0   x)
(0   -v*A   v^2   u*A   -z*A + u*v   -x*B + u^2   -t*u   0   x*v)
(0   0   0   -v   t   -z   0   0   0)
(0   0   0   -B   0   -v   0   t   -z)
(0   0   0   -z*v + t*u   0   y*t - z^2   0   0   0)
(0   0   0   -z*B - t*A + v^2   0   0   0   0   y*t - z^2)
(0   0   0   -u*B - v*A   v^2   -y*B - z*A   0   0   y*v - z*u)
(0   0   0   0   -B   -A   0   v   -u)
(0   0   0   u   -z   y   0   0   0)
(0   0   0   -v*A   -z*B + v^2   -z*A   0   0   y*v - z*u)
(0   0   0   -v^2*A   -t*u*B + v^3   -y*v*B - z*v*A - t*u*A + u*v^2   0   0   
    y*v^2 - t*u^2)
(0   0   0   u*B   0   y*B + z*A   0   -z*v   z*u)
(0   0   0   -A   v   0   0   -z   y)
(0   0   0   -v*A   v^2   -y*B - z*A + u*v   0   -t*u   y*v)
(0   0   0   0   0   -z*v*B - t*v*A + v^3   0   0   z*v^2 - t*u*v)
(0   0   0   0   0   -z*B - t*A + v^2   0   0   z*v - t*u)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 11:53:32 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,8,9]);
SyzygyMatrix([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,B*x+A*y-u^2,B*y+A*z-u*v,B*z+A*t-v^2]);

Output: Magma V2.10-22    Sat Jul  3 2004 11:53:30 on modular  [Seed = 347243044]
   -------------------------------------

[-t   z   0   -y   0   0   0   0   0]
[-v   0   z   0   -y   0   0   0   0]
[-B   0   0   0   -u   0   z   -y   0]
[-y*t + z^2   0   0   x*z - y^2   0   0   0   0   0]
[-y*v + z*u   0   0   0   x*z - y^2   0   0   0   0]
[-y*B - z*A + u*v   0   0   0   0   0   0   x*z - y^2   0]
[-v   u   0   0   -y   x   0   0   0]
[-B   -A   v   0   0   0   0   -y   x]
[-t*u*B - t*v*A + v^3   0   0   -y*u*B - y*v*A   y*v^2 - z^2*A + z*u*v   -x*z*B 
    0   -z^2*u   x*z*v]
[0   -v   t   u   -z   0   0   0   0]
[0   -B   0   -A   0   -u   t   -z   0]
[z   -y   0   x   0   0   0   0   0]
[t*u   -y*v   0   y*u   x*t - y*z   0   0   0   0]
[-t*A   -y*B + u*v   0   -y*A   0   0   0   x*t - y*z   0]
[0   -z*v + t*u   0   z*u   -z^2   x*t   0   0   0]
[0   -z*B - t*A + v^2   0   -z*A   z*v   0   0   -z^2   x*t]
[0   -u*B - v*A   v^2   0   -z*A + u*v   -x*B   0   -z*u   x*v]
[0   0   -B   0   -A   0   v   -u   0]
[z*v   0   -y*t   x*v - y*u   y*z   0   0   0   0]
[u   0   -y   0   x   0   0   0   0]
[-v*A   0   -y*B + u*v   0   -y*A   0   0   x*v - y*u   0]
[0   u   -z   0   0   x   0   0   0]
[0   -v*A   -z*B + v^2   0   -z*A + u*v   0   0   -z*u   x*v]
[0   -v^2*A   -t*u*B + v^3   -u^2*B   -z*v*A + u*v^2   -x*v*B - z*u*A   0   0   
    x*v^2 - z*u^2]
[z*B   0   0   x*B + y*A - u^2   z*u   0   -y*t   y*z   0]
[u*B   0   0   0   x*B + y*A   0   -y*v   y*u   0]
[-A   0   u   0   0   0   -y   x   0]
[0   u*B   0   0   z*A   x*B   -z*v   z*u   0]
[0   -A   v   0   u   0   -z   0   x]
[0   -v*A   v^2   u*A   -z*A + u*v   -x*B + u^2   -t*u   0   x*v]
[0   0   0   -v   t   -z   0   0   0]
[0   0   0   -B   0   -v   0   t   -z]
[0   0   0   -z*v + t*u   0   y*t - z^2   0   0   0]
[0   0   0   -z*B - t*A + v^2   0   0   0   0   y*t - z^2]
[0   0   0   -u*B - v*A   v^2   -y*B - z*A   0   0   y*v - z*u]
[0   0   0   0   -B   -A   0   v   -u]
[0   0   0   u   -z   y   0   0   0]
[0   0   0   -v*A   -z*B + v^2   -z*A   0   0   y*v - z*u]
[0   0   0   -v^2*A   -t*u*B + v^3   -y*v*B - z*v*A - t*u*A + u*v^2   0   0   
    y*v^2 - t*u^2]
[0   0   0   u*B   0   y*B + z*A   0   -z*v   z*u]
[0   0   0   -A   v   0   0   -z   y]
[0   0   0   -v*A   v^2   -y*B - z*A + u*v   0   -t*u   y*v]
[0   0   0   0   0   -z*v*B - t*v*A + v^3   0   0   z*v^2 - t*u*v]
[0   0   0   0   0   -z*B - t*A + v^2   0   0   z*v - t*u]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 11:56:18 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,8,9]);
MinimalSyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,B*x+A*y-u^2,B*y+A*z-u*v,B*z+A*t-v^2]);

Output: Magma V2.10-22    Sat Jul  3 2004 11:56:16 on modular  [Seed = 579122504]
   -------------------------------------


>> MinimalSyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,B*x+A*
                      ^
Runtime error in 'MinimalSyzygyModule': Bad argument types
Argument types given: SeqEnum[RngMPolElt]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host webcacheB02a.cache.pol.co.uk. (195.92.168.164)
Time: Sat Jul  3 11:56:59 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,8,9]);
M:=SyzygyModule([x*z-y^2,x*t-z*y,x*v-u*y,y*t-z^2,y*v-u*z,z*v-u*t,B*x+A*y-u^2,B*y+A*z-u*v,B*z+A*t-v^2]);
MinimalSyzygyModule(M);

Output: Magma V2.10-22    Sat Jul  3 2004 11:56:56 on modular  [Seed = 983346488]
   -------------------------------------


>> MinimalSyzygyModule(M);;
                      ^
Runtime error in 'MinimalSyzygyModule': Argument 1 must be homogeneous

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pcp08867223pcs.sabrna01.az.comcast.net. (69.137.185.218)
Time: Sat Jul  3 23:45:35 2004

Input: factor(x^15 - 1)


Output: Magma V2.10-22    Sat Jul  3 2004 23:45:32 on modular  [Seed = 1240364104]
   -------------------------------------


>> factor(x^15 - 1)
          ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host IP-213157024181.dialin.heagmedianet.de. (213.157.24.181)
Time: Sun Jul  4 12:23:32 2004

Input: 10+10

Output: Magma V2.10-22    Sun Jul  4 2004 12:23:29 on modular  [Seed = 2852308431]
   -------------------------------------

20

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host IP-213157024181.dialin.heagmedianet.de. (213.157.24.181)
Time: Sun Jul  4 12:24:19 2004

Input: 10^199994324

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Sun Jul  4 2004 12:24:16 on modular  [Seed = 2351227864]
   -------------------------------------


Current total memory usage: 1.6MB, failed memory request: 607.3MB
System Error: User memory limit has been reached

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host IP-213157024181.dialin.heagmedianet.de. (213.157.24.181)
Time: Sun Jul  4 12:24:39 2004

Input: 10^199

Output: Magma V2.10-22    Sun Jul  4 2004 12:24:36 on modular  [Seed = 2487024564]
   -------------------------------------

1000000000000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000000000000000

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host IP-213157024181.dialin.heagmedianet.de. (213.157.24.181)
Time: Sun Jul  4 12:25:04 2004

Input: 3^199

Output: Magma V2.10-22    Sun Jul  4 2004 12:25:01 on modular  [Seed = 1875312727]
   -------------------------------------

8853799629195825644626044067859320894307781755113149865819165391303083030043406\
0998128233014667

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 20:17:41 2004

Input: 100000!

Output: Magma V2.10-22    Sun Jul  4 2004 20:17:39 on modular  [Seed = 696383328]
   -------------------------------------


>> 100000!;
          ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:15:04 2004

Input: Q = QuadraticField(14);

Output: Magma V2.10-22    Sun Jul  4 2004 21:15:02 on modular  [Seed = 3648074277]
   -------------------------------------


>> Q = QuadraticField(14);;
   ^
User error: Identifier 'Q' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:15:42 2004

Input: R<S> = QuadraticField(14);

Output: Magma V2.10-22    Sun Jul  4 2004 21:15:40 on modular  [Seed = 3514382855]
   -------------------------------------


>> R<S> = QuadraticField(14);;
        ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:15:54 2004

Input: R<S> := QuadraticField(14);

Output: Magma V2.10-22    Sun Jul  4 2004 21:15:52 on modular  [Seed = 2835431947]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:16:25 2004

Input: R<S> := QuadraticField(14);
R<O> := RingOfIntegers(S);

Output: Magma V2.10-22    Sun Jul  4 2004 21:16:23 on modular  [Seed = 2785955115]
   -------------------------------------


>> R<O> := RingOfIntegers(S);;
                         ^
Runtime error in 'RingOfIntegers': Bad argument types
Argument types given: FldQuadElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:18:16 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-14);
I := 43*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Sun Jul  4 2004 21:18:14 on modular  [Seed = 3155447936]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [43, 0]
        [53, 1], 1>,
    <Prime Ideal
    Two element generators:
        [43, 0]
        [76, 1], 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:22:28 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-14);
I := 41*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Sun Jul  4 2004 21:22:25 on modular  [Seed = 2570155170]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [41, 0], 1>
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:22:44 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 41*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Sun Jul  4 2004 21:22:42 on modular  [Seed = 2436463769]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [41, 0], 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:22:55 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 37*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Sun Jul  4 2004 21:22:52 on modular  [Seed = 1757447535]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [37, 0]
        [46, 1], 1>,
    <Prime Ideal
    Two element generators:
        [37, 0]
        [65, 1], 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Sun Jul  4 21:33:29 2004

Input: gcd(1849, 989);

Output: Magma V2.10-22    Sun Jul  4 2004 21:33:27 on modular  [Seed = 2077463799]
   -------------------------------------


>> gcd(1849, 989);;
   ^
User error: Identifier 'gcd' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 01:09:41 2004

Input: R<x> = PolynomialRing(RationalField());
K<a> = NumberField(x^2-14);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 01:09:38 on modular  [Seed = 95266811]
   -------------------------------------


>> R<x> = PolynomialRing(RationalField());
        ^
User error: bad syntax

>> K<a> = NumberField(x^2-14);
        ^
User error: bad syntax

>> I := 43 * MaximalOrder(K);
                          ^
User error: Identifier 'K' has not been declared or assigned

>> Factorization(I);;
                 ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 01:10:02 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-14);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 01:09:59 on modular  [Seed = 498450390]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [43, 0]
        [53, 1], 1>,
    <Prime Ideal
    Two element generators:
        [43, 0]
        [76, 1], 1>
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 200-168-118-162.dsl.telesp.net.br. (200.168.118.162)
Time: Mon Jul  5 01:50:04 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Mon Jul  5 2004 01:50:02 on modular  [Seed = 3715461563]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.490 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:09:24 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 43*MaximalOrder(K);
Factorize(I);

Output: Magma V2.10-22    Mon Jul  5 2004 02:09:22 on modular  [Seed = 3121744452]
   -------------------------------------


>> Factorize(I);;
   ^
User error: Identifier 'Factorize' has not been declared or assigned

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:09:35 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 43*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 02:09:33 on modular  [Seed = 2988048963]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0], 1>
]

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:10:14 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 11*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 02:10:12 on modular  [Seed = 2268018479]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [11, 0], 1>
]

Total time: 2.619 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:10:25 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 13*MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 02:10:22 on modular  [Seed = 2671193917]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [13, 0], 1>
]

Total time: 2.579 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:16:30 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 13*MaximalOrder(K);
Factorization(I);
LegendreSymbol(13, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 02:16:27 on modular  [Seed = 2436441030]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [13, 0], 1>
]
-1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:16:44 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 11*MaximalOrder(K);
Factorization(I);
LegendreSymbol(11, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 02:16:41 on modular  [Seed = 1757469260]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [11, 0], 1>
]
1

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:16:59 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 11*MaximalOrder(K);
Factorization(I);
LegendreSymbol(7, 11);

Output: Magma V2.10-22    Mon Jul  5 2004 02:16:57 on modular  [Seed = 1623773780]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [11, 0], 1>
]
-1

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:17:14 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 13*MaximalOrder(K);
Factorization(I);
LegendreSymbol(7, 13);

Output: Magma V2.10-22    Mon Jul  5 2004 02:17:12 on modular  [Seed = 2060634239]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [13, 0], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 02:17:27 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-7);
I := 17*MaximalOrder(K);
Factorization(I);
LegendreSymbol(7, 17);

Output: Magma V2.10-22    Mon Jul  5 2004 02:17:25 on modular  [Seed = 1926938730]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [17, 0], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host tachyon.mathematik.uni-kl.de. (131.246.164.32)
Time: Mon Jul  5 08:52:55 2004

Input: Matrix(GF(2),2,2,[0,1,1,0]);
 

Output: Magma V2.10-22    Mon Jul  5 2004 08:52:51 on modular  [Seed = 1222723354]
   -------------------------------------

[0 1]
[1 0]

Total time: 2.740 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host tachyon.mathematik.uni-kl.de. (131.246.164.32)
Time: Mon Jul  5 09:11:38 2004

Input: M:=Matrix(GF(2),2,2,[0,1,1,0]);
Determinant(M);

Output: Magma V2.10-22    Mon Jul  5 2004 09:11:36 on modular  [Seed = 347932653]
   -------------------------------------

1

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host tachyon.mathematik.uni-kl.de. (131.246.164.32)
Time: Mon Jul  5 09:11:55 2004

Input: M:=Matrix(GF(2),2,2,[0,1,1,0]);
Determinant(M);
M;

Output: Magma V2.10-22    Mon Jul  5 2004 09:11:53 on modular  [Seed = 481628148]
   -------------------------------------

1
[0 1]
[1 0]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825EDD.dip.t-dialin.net. (80.130.94.221)
Time: Mon Jul  5 10:35:36 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2=b^2>;
Order(F);

Output: Magma V2.10-22    Mon Jul  5 2004 10:35:31 on modular  [Seed = 2401675469]
   -------------------------------------

0

Total time: 4.419 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825EDD.dip.t-dialin.net. (80.130.94.221)
Time: Mon Jul  5 10:35:56 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2,b^2>;
Order(F);

Output: Magma V2.10-22    Mon Jul  5 2004 10:35:53 on modular  [Seed = 1960661839]
   -------------------------------------

6

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:40:05 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 17*MaximalOrder(K);
Factorization(I);
LegendreSymbol(7, 17);

Output: Magma V2.10-22    Mon Jul  5 2004 12:40:02 on modular  [Seed = 2200586131]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [17, 0], 1>
]
-1

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:40:26 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 13*MaximalOrder(K);
Factorization(I);
LegendreSymbol(7, 13);

Output: Magma V2.10-22    Mon Jul  5 2004 12:40:24 on modular  [Seed = 2334281601]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [13, 0], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:40:39 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 11*MaximalOrder(K);
Factorization(I);
LegendreSymbol(7, 11);

Output: Magma V2.10-22    Mon Jul  5 2004 12:40:37 on modular  [Seed = 1927001732]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [11, 0]
        [12, 2], 1>,
    <Prime Ideal
    Two element generators:
        [11, 0]
        [19, 2], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:41:14 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 11*MaximalOrder(K);
Factorization(I);
LegendreSymbol(11, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 12:41:11 on modular  [Seed = 2060697262]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [11, 0]
        [12, 2], 1>,
    <Prime Ideal
    Two element generators:
        [11, 0]
        [19, 2], 1>
]
1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:41:31 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 13*MaximalOrder(K);
Factorization(I);
LegendreSymbol(13, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 12:41:29 on modular  [Seed = 1640539563]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [13, 0], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:41:42 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 19*MaximalOrder(K);
Factorization(I);
LegendreSymbol(19, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 12:41:40 on modular  [Seed = 1774235102]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [19, 0], 1>
]
-1

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:41:55 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 23*MaximalOrder(K);
Factorization(I);
LegendreSymbol(23, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 12:41:53 on modular  [Seed = 1375245811]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [23, 0]
        [26, 2], 1>,
    <Prime Ideal
    Two element generators:
        [23, 0]
        [41, 2], 1>
]
1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:42:10 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+7);
I := 29*MaximalOrder(K);
Factorization(I);
LegendreSymbol(29, 7);

Output: Magma V2.10-22    Mon Jul  5 2004 12:42:07 on modular  [Seed = 1508941258]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [29, 0]
        [42, 2], 1>,
    <Prime Ideal
    Two element generators:
        [29, 0]
        [43, 2], 1>
]
1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:42:27 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-5);
I := 29*MaximalOrder(K);
Factorization(I);
LegendreSymbol(29, 5);

Output: Magma V2.10-22    Mon Jul  5 2004 12:42:25 on modular  [Seed = 1105757635]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [29, 0]
        [39, 2], 1>,
    <Prime Ideal
    Two element generators:
        [29, 0]
        [46, 2], 1>
]
1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 12:42:44 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-5);
I := 37*MaximalOrder(K);
Factorization(I);
LegendreSymbol(37, 5);

Output: Magma V2.10-22    Mon Jul  5 2004 12:42:41 on modular  [Seed = 1239452731]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [37, 0], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 13:36:21 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+11);
I := 37*MaximalOrder(K);
Factorization(I);
LegendreSymbol(37, 11);

Output: Magma V2.10-22    Mon Jul  5 2004 13:36:18 on modular  [Seed = 4233440541]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [37, 0]
        [46, 2], 1>,
    <Prime Ideal
    Two element generators:
        [37, 0]
        [63, 2], 1>
]
1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 13:36:38 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+11);
I := 123*MaximalOrder(K);
Factorization(I);
LegendreSymbol(123, 11);

Output: Magma V2.10-22    Mon Jul  5 2004 13:36:35 on modular  [Seed = 3830265140]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [3, 0]
        [3, 2], 1>,
    <Prime Ideal
    Two element generators:
        [3, 0]
        [4, 2], 1>,
    <Principal Prime Ideal
    Generator:
        [41, 0], 1>
]
-1

Total time: 2.519 seconds, Total memory usage: 1.87MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 13:36:59 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+11);
I := 127*MaximalOrder(K);
Factorization(I);
LegendreSymbol(123, 11);

Output: Magma V2.10-22    Mon Jul  5 2004 13:36:56 on modular  [Seed = 3963960615]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [127, 0], 1>
]
-1

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 13:54:37 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2+11);
I := 127*MaximalOrder(K);
Factorization(I);
LegendreSymbol(123, 11);

Output: Magma V2.10-22    Mon Jul  5 2004 13:54:34 on modular  [Seed = 3038535708]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [127, 0], 1>
]
-1

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FF047B.dip.t-dialin.net. (217.255.4.123)
Time: Mon Jul  5 14:34:20 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6,a^2*b^2=b^2*a^2>;
Order(F);

Output: Magma V2.10-22    Mon Jul  5 2004 14:34:17 on modular  [Seed = 2027005733]
   -------------------------------------

162

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF047B.dip.t-dialin.net. (217.255.4.123)
Time: Mon Jul  5 14:34:33 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^12,a^2*b^2=b^2*a^2>;
Order(F);

Output: Magma V2.10-22    Mon Jul  5 2004 14:34:30 on modular  [Seed = 1623834402]
   -------------------------------------

1296

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 15:23:29 2004

Input: Factorization(4094774573);

Output: Magma V2.10-22    Mon Jul  5 2004 15:23:26 on modular  [Seed = 3021823598]
   -------------------------------------

[ <63419, 1>, <64567, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 15:25:06 2004

Input: Factorization(4094754573);

Output: Magma V2.10-22    Mon Jul  5 2004 15:25:04 on modular  [Seed = 3189200346]
   -------------------------------------

[ <3, 1>, <7, 1>, <13, 2>, <1153777, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 15:26:09 2004

Input: Factorization(4794754573);

Output: Magma V2.10-22    Mon Jul  5 2004 15:26:06 on modular  [Seed = 2936423573]
   -------------------------------------

[ <7, 1>, <13693, 1>, <50023, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 15:26:25 2004

Input: Factorization(4798754573);

Output: Magma V2.10-22    Mon Jul  5 2004 15:26:22 on modular  [Seed = 2419686330]
   -------------------------------------

[ <4798754573, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 15:26:36 2004

Input: Factorization(4799754573);

Output: Magma V2.10-22    Mon Jul  5 2004 15:26:33 on modular  [Seed = 2603774086]
   -------------------------------------

[ <3, 1>, <79, 1>, <523, 1>, <38723, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 15:26:46 2004

Input: Factorization(4299754573);

Output: Magma V2.10-22    Mon Jul  5 2004 15:26:43 on modular  [Seed = 2200594564]
   -------------------------------------

[ <23, 1>, <186945851, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 20:57:08 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 20:57:05 on modular  [Seed = 4250158436]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0], 1>
]

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 21:02:12 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 21:02:09 on modular  [Seed = 3648021424]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0], 1>
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 21:13:24 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 21:13:22 on modular  [Seed = 1977403836]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0], 1>
]

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 21:16:12 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 21:16:09 on modular  [Seed = 4133440468]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0], 1>
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 21:21:14 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 21:21:12 on modular  [Seed = 2487036512]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0], 1>
]

Total time: 2.579 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 21:21:34 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^3-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 21:21:31 on modular  [Seed = 1674239365]
   -------------------------------------

[
    <Principal Prime Ideal
    Generator:
        [43, 0, 0], 1>
]

Total time: 2.489 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host adsl-68-75-55-132.dsl.emhril.ameritech.net. (68.75.55.132)
Time: Mon Jul  5 21:21:52 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^5-19);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Mon Jul  5 2004 21:21:50 on modular  [Seed = 1290138271]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [43, 0, 0, 0, 0]
        [68, 1, 0, 0, 0], 1>,
    <Prime Ideal
    Two element generators:
        [43, 0, 0, 0, 0]
        [56, 27, 23, 18, 1], 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:06:51 2004

Input: 2+3


Output: Magma V2.10-22    Tue Jul  6 2004 00:06:34 on modular  [Seed = 630145132]
   -------------------------------------

5

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:22:45 2004

Input: SimplexCode(r) : RngIntElt -> Code



Output: Magma V2.10-22    Tue Jul  6 2004 00:22:29 on modular  [Seed = 1323575112]
   -------------------------------------


>> SimplexCode(r) : RngIntElt -> Code
                              ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:24:04 2004

Input: S:= SimplexCode(r) ;




Output: Magma V2.10-22    Tue Jul  6 2004 00:23:47 on modular  [Seed = 1425947908]
   -------------------------------------


>> S:= SimplexCode(r) ;
                   ^
User error: Identifier 'r' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:24:16 2004

Input: S:= SimplexCode(5) ;




Output: Magma V2.10-22    Tue Jul  6 2004 00:24:00 on modular  [Seed = 1559639359]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:25:08 2004

Input: S:= SimplexCode(5) ;


S;


Output: Magma V2.10-22    Tue Jul  6 2004 00:24:51 on modular  [Seed = 1691225588]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:55:44 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;

Output: Magma V2.10-22    Tue Jul  6 2004 00:55:28 on modular  [Seed = 2654269021]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 00:56:40 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Tue Jul  6 2004 00:56:23 on modular  [Seed = 2769278289]
   -------------------------------------

10

Total time: 3.659 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 01:01:37 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);
SimplexCode(6);



Output: Magma V2.10-22    Tue Jul  6 2004 01:01:19 on modular  [Seed = 3228218076]
   -------------------------------------

10
[63, 6, 32] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1
    1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1]
[0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1
    0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0]
[0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1
    1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1]
[0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0
    0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1]
[0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0
    1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0]
[0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1
    0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1]

Total time: 3.659 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 01:13:27 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);
SimplexCode(6);

K := FiniteField(2);
C6p := LinearCode<K,56 | 
[1, 0, 0,       1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0,   1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0,   1, 0, 0, 1, 0, 0,     1, 1],
[0, 1, 0,       1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0,   1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,   1, 1, 0, 1, 1, 0,     1, 0],
[0, 0, 1,       0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1,   0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1,   0, 1, 1, 0, 1, 1,     0, 1],
[0, 0, 0,       1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1,   1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,   1, 0, 1, 0, 0, 1,     1, 1],
[0, 0, 0,       1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1,   0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1,   0, 1, 0, 0, 0, 0,     1, 0],
[0, 0, 0,       0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,   1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,   0, 0, 1, 0, 0, 0,     1, 1]>;
CoveringRadius(C6p);


Output: Magma V2.10-22    Tue Jul  6 2004 01:13:09 on modular  [Seed = 3547965237]
   -------------------------------------

10
[63, 6, 32] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1
    1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1]
[0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1
    0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0]
[0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1
    1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1]
[0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0
    0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1]
[0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0
    1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0]
[0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1
    0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1]

>> CoveringRadius(C6p);
                 ^
Runtime error in 'CoveringRadius': Arguments too large

Total time: 3.709 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 01:22:31 2004

Input: K := FiniteField(2);
C6p := LinearCode<K,56 | 
[1, 0, 0,       1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0,   1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0,   1, 0, 0, 1, 0, 0,     1, 1],
[0, 1, 0,       1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0,   1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,   1, 1, 0, 1, 1, 0,     1, 0],
[0, 0, 1,       0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1,   0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1,   0, 1, 1, 0, 1, 1,     0, 1],
[0, 0, 0,       1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1,   1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,   1, 0, 1, 0, 0, 1,     1, 1],
[0, 0, 0,       1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1,   0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1,   0, 1, 0, 0, 0, 0,     1, 0],
[0, 0, 0,       0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,   1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,   0, 0, 1, 0, 0, 0,     1, 1]>;
CoveringRadius(C6p);


Output: Magma V2.10-22    Tue Jul  6 2004 01:22:15 on modular  [Seed = 4082730231]
   -------------------------------------


>> CoveringRadius(C6p);
                 ^
Runtime error in 'CoveringRadius': Arguments too large

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 01:30:35 2004

Input: K := FiniteField(2);
C6p := LinearCode<K,56 | 
[1, 0, 0,       1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0,   1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0,   1, 0, 0, 1, 0, 0,     1, 1],
[0, 1, 0,       1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0,   1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,   1, 1, 0, 1, 1, 0,     1, 0],
[0, 0, 1,       0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1,   0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1,   0, 1, 1, 0, 1, 1,     0, 1],
[0, 0, 0,       1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1,   1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,   1, 0, 1, 0, 0, 1,     1, 1],
[0, 0, 0,       1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1,   0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1,   0, 1, 0, 0, 0, 0,     1, 0],
[0, 0, 0,       0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,   1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,   0, 0, 1, 0, 0, 0,     1, 1]>;
CoveringRadius(C6p);

K := FiniteField(2);
C6s := LinearCode<K,48 | 
[1, 0,           1, 0, 1, 1, 1, 1, 1, 1, 0,     1, 0, 1, 0, 1, 0,       1, 1, 0,     1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,     1, 1, 0, 1, 1, 0,       1, 0,     1, 0,         1, 1],
[0, 1,           1, 1, 1, 0, 0, 0, 0, 0, 1,     1, 1, 1, 1, 1, 1,       1, 0, 1,     1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1,     1, 0, 1, 1, 0, 1,       1, 1,     1, 1,         1, 0],
[0, 0,           0, 1, 1, 1, 0, 0, 0, 0, 0,     0, 1, 1, 1, 1, 1,       0, 1, 0,     0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1,     0, 1, 0, 1, 1, 0,       0, 1,     0, 1,         0, 1],
[0, 0,           1, 0, 0, 0, 0, 1, 1, 1, 0,     0, 0, 0, 1, 0, 1,       1, 1, 1,     0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1,     0, 1, 1, 1, 0, 1,       1, 0,     0, 0,         1, 1],
[0, 0,           1, 1, 1, 1, 1, 1, 0, 0, 1,     1, 0, 1, 0, 0, 0,       0, 0, 1,     1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1,     0, 1, 1, 0, 0, 0,       0, 1,     0, 0,         1, 0],
[0, 0,           0, 1, 1, 1, 1, 1, 1, 0, 0,     0, 1, 0, 1, 0, 0,       1, 0, 0,     1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0,     1, 0, 1, 1, 0, 0,       0, 0,     0, 0,         1, 1]>;
CoveringRadius(C6s);


Output: Magma V2.10-22    Tue Jul  6 2004 01:30:18 on modular  [Seed = 4283795222]
   -------------------------------------


>> CoveringRadius(C6p);
                 ^
Runtime error in 'CoveringRadius': Arguments too large

>> CoveringRadius(C6s);
                 ^
Runtime error in 'CoveringRadius': Arguments too large

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 01:32:35 2004

Input: K := FiniteField(2);
C6s := LinearCode<K,48 | 
[1, 0,           1, 0, 1, 1, 1, 1, 1, 1, 0,     1, 0, 1, 0, 1, 0,       1, 1, 0,     1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,     1, 1, 0, 1, 1, 0,       1, 0,     1, 0,         1, 1],
[0, 1,           1, 1, 1, 0, 0, 0, 0, 0, 1,     1, 1, 1, 1, 1, 1,       1, 0, 1,     1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1,     1, 0, 1, 1, 0, 1,       1, 1,     1, 1,         1, 0],
[0, 0,           0, 1, 1, 1, 0, 0, 0, 0, 0,     0, 1, 1, 1, 1, 1,       0, 1, 0,     0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1,     0, 1, 0, 1, 1, 0,       0, 1,     0, 1,         0, 1],
[0, 0,           1, 0, 0, 0, 0, 1, 1, 1, 0,     0, 0, 0, 1, 0, 1,       1, 1, 1,     0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1,     0, 1, 1, 1, 0, 1,       1, 0,     0, 0,         1, 1],
[0, 0,           1, 1, 1, 1, 1, 1, 0, 0, 1,     1, 0, 1, 0, 0, 0,       0, 0, 1,     1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1,     0, 1, 1, 0, 0, 0,       0, 1,     0, 0,         1, 0],
[0, 0,           0, 1, 1, 1, 1, 1, 1, 0, 0,     0, 1, 0, 1, 0, 0,       1, 0, 0,     1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0,     1, 0, 1, 1, 0, 0,       0, 0,     0, 0,         1, 1]>;
C6s;


Output: Magma V2.10-22    Tue Jul  6 2004 01:32:18 on modular  [Seed = 28014695]
   -------------------------------------

[48, 6, 24] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0
    0 0 1 0 1 1 0 0]
[0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1
    1 1 1 1 1 0 1 0]
[0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1
    0 0 0 1 0 0 0 1]
[0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1
    1 0 0 1 0 1 0 1]
[0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0
    1 1 1 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0
    0 1 1 1 0 0 1 0]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host Tasha.Math.McGill.CA. (132.206.150.104)
Time: Tue Jul  6 01:42:13 2004

Input: JacobiSymbol(6,11);

Output: Magma V2.10-22    Tue Jul  6 2004 01:42:10 on modular  [Seed = 1156464626]
   -------------------------------------

-1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host Tasha.Math.McGill.CA. (132.206.150.104)
Time: Tue Jul  6 01:42:25 2004

Input: JacobiSymbol(6,15);

Output: Magma V2.10-22    Tue Jul  6 2004 01:42:23 on modular  [Seed = 1290156023]
   -------------------------------------

0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:44:53 2004

Input: a := 13;

for i:= 1 to 100 do

x = i * i;

if x mod a = 1 then
print(i,x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:44:50 on modular  [Seed = 1105942838]
   -------------------------------------


>> x = i * i;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:45:04 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a = 1 then
print(i,x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:45:02 on modular  [Seed = 1239634226]
   -------------------------------------


>> if x mod a = 1 then
   ^
Runtime error in if: Logical expected

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:45:21 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a = 1 then
print(i,x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:45:19 on modular  [Seed = 1375422939]
   -------------------------------------


>> if x mod a = 1 then
   ^
Runtime error in if: Logical expected

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:45:33 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 1 then
print(i,x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:45:31 on modular  [Seed = 1509114311]
   -------------------------------------


>> print(i,x);
        ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:45:49 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:45:47 on modular  [Seed = 1640724943]
   -------------------------------------

1
1
12
144
14
196
25
625
27
729
38
1444
40
1600
51
2601
53
2809
64
4096
66
4356
77
5929
79
6241
90
8100
92
8464

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:47:15 2004

Input: a := 23;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:47:12 on modular  [Seed = 1807839854]
   -------------------------------------

1
1
22
484
24
576
45
2025
47
2209
68
4624
70
4900
91
8281
93
8649

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:48:23 2004

Input: a := 23;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:48:21 on modular  [Seed = 1943628339]
   -------------------------------------

7
49
16
256
30
900
39
1521
53
2809
62
3844
76
5776
85
7225
99
9801

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:50:51 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:50:49 on modular  [Seed = 2077319847]
   -------------------------------------

4
16
9
81
17
289
22
484
30
900
35
1225
43
1849
48
2304
56
3136
61
3721
69
4761
74
5476
82
6724
87
7569
95
9025
100
10000

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:51:26 2004

Input: a := 89;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:51:23 on modular  [Seed = 2183699324]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:51:42 2004

Input: a := 29;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:51:40 on modular  [Seed = 2317389955]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:51:51 2004

Input: a := 19;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:51:49 on modular  [Seed = 2453178498]
   -------------------------------------


Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:52:04 2004

Input: a := 19;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:52:01 on modular  [Seed = 2586869950]
   -------------------------------------

1
1
18
324
20
400
37
1369
39
1521
56
3136
58
3364
75
5625
77
5929
94
8836
96
9216

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:55:04 2004

Input: a := 19;

for i:= 1 to 100 do

x := i * i * 2;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:55:02 on modular  [Seed = 2936386940]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:55:17 2004

Input: a := 19;

for i:= 1 to 100 do

x := i * i * 2;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:55:15 on modular  [Seed = 3055332432]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:55:32 2004

Input: a := 19;

for i:= 1 to 2000 do

x := i * i * 2;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:55:30 on modular  [Seed = 3189023817]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:55:42 2004

Input: a := 19;

for i:= 1 to 2000 do

x := i * i ;

if x mod a eq 1 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:55:40 on modular  [Seed = 3329023039]
   -------------------------------------

1
1
18
324
20
400
37
1369
39
1521
56
3136
58
3364
75
5625
77
5929
94
8836
96
9216
113
12769
115
13225
132
17424
134
17956
151
22801
153
23409
170
28900
172
29584
189
35721
191
36481
208
43264
210
44100
227
51529
229
52441
246
60516
248
61504
265
70225
267
71289
284
80656
286
81796
303
91809
305
93025
322
103684
324
104976
341
116281
343
117649
360
129600
362
131044
379
143641
381
145161
398
158404
400
160000
417
173889
419
175561
436
190096
438
191844
455
207025
457
208849
474
224676
476
226576
493
243049
495
245025
512
262144
514
264196
531
281961
533
284089
550
302500
552
304704
569
323761
571
326041
588
345744
590
348100
607
368449
609
370881
626
391876
628
394384
645
416025
647
418609
664
440896
666
443556
683
466489
685
469225
702
492804
704
495616
721
519841
723
522729
740
547600
742
550564
759
576081
761
579121
778
605284
780
608400
797
635209
799
638401
816
665856
818
669124
835
697225
837
700569
854
729316
856
732736
873
762129
875
765625
892
795664
894
799236
911
829921
913
833569
930
864900
932
868624
949
900601
951
904401
968
937024
970
940900
987
974169
989
978121
1006
1012036
1008
1016064
1025
1050625
1027
1054729
1044
1089936
1046
1094116
1063
1129969
1065
1134225
1082
1170724
1084
1175056
1101
1212201
1103
1216609
1120
1254400
1122
1258884
1139
1297321
1141
1301881
1158
1340964
1160
1345600
1177
1385329
1179
1390041
1196
1430416
1198
1435204
1215
1476225
1217
1481089
1234
1522756
1236
1527696
1253
1570009
1255
1575025
1272
1617984
1274
1623076
1291
1666681
1293
1671849
1310
1716100
1312
1721344
1329
1766241
1331
1771561
1348
1817104
1350
1822500
1367
1868689
1369
1874161
1386
1920996
1388
1926544
1405
1974025
1407
1979649
1424
2027776
1426
2033476
1443
2082249
1445
2088025
1462
2137444
1464
2143296
1481
2193361
1483
2199289
1500
2250000
1502
2256004
1519
2307361
1521
2313441
1538
2365444
1540
2371600
1557
2424249
1559
2430481
1576
2483776
1578
2490084
1595
2544025
1597
2550409
1614
2604996
1616
2611456
1633
2666689
1635
2673225
1652
2729104
1654
2735716
1671
2792241
1673
2798929
1690
2856100
1692
2862864
1709
2920681
1711
2927521
1728
2985984
1730
2992900
1747
3052009
1749
3059001
1766
3118756
1768
3125824
1785
3186225
1787
3193369
1804
3254416
1806
3261636
1823
3323329
1825
3330625
1842
3392964
1844
3400336
1861
3463321
1863
3470769
1880
3534400
1882
3541924
1899
3606201
1901
3613801
1918
3678724
1920
3686400
1937
3751969
1939
3759721
1956
3825936
1958
3833764
1975
3900625
1977
3908529
1994
3976036
1996
3984016

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:57:17 2004

Input: a := 19;

for i:= 1 to 2000 do

x := i * i ;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:57:15 on modular  [Seed = 3361919894]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:57:28 2004

Input: a := 19;

for i:= 1 to 2000 do

x := i * i ;

if x mod a eq 2 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:57:25 on modular  [Seed = 3497708464]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:57:39 2004

Input: a := 19;

for i:= 1 to 2000 do

x := i * i ;

if x mod a eq 2 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:57:36 on modular  [Seed = 3631399853]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 03:57:49 2004

Input: a := 19;

for i:= 1 to 2000 do

x := i * i *2;

if x mod a eq 2 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 03:57:46 on modular  [Seed = 3763010463]
   -------------------------------------

1
2
18
648
20
800
37
2738
39
3042
56
6272
58
6728
75
11250
77
11858
94
17672
96
18432
113
25538
115
26450
132
34848
134
35912
151
45602
153
46818
170
57800
172
59168
189
71442
191
72962
208
86528
210
88200
227
103058
229
104882
246
121032
248
123008
265
140450
267
142578
284
161312
286
163592
303
183618
305
186050
322
207368
324
209952
341
232562
343
235298
360
259200
362
262088
379
287282
381
290322
398
316808
400
320000
417
347778
419
351122
436
380192
438
383688
455
414050
457
417698
474
449352
476
453152
493
486098
495
490050
512
524288
514
528392
531
563922
533
568178
550
605000
552
609408
569
647522
571
652082
588
691488
590
696200
607
736898
609
741762
626
783752
628
788768
645
832050
647
837218
664
881792
666
887112
683
932978
685
938450
702
985608
704
991232
721
1039682
723
1045458
740
1095200
742
1101128
759
1152162
761
1158242
778
1210568
780
1216800
797
1270418
799
1276802
816
1331712
818
1338248
835
1394450
837
1401138
854
1458632
856
1465472
873
1524258
875
1531250
892
1591328
894
1598472
911
1659842
913
1667138
930
1729800
932
1737248
949
1801202
951
1808802
968
1874048
970
1881800
987
1948338
989
1956242
1006
2024072
1008
2032128
1025
2101250
1027
2109458
1044
2179872
1046
2188232
1063
2259938
1065
2268450
1082
2341448
1084
2350112
1101
2424402
1103
2433218
1120
2508800
1122
2517768
1139
2594642
1141
2603762
1158
2681928
1160
2691200
1177
2770658
1179
2780082
1196
2860832
1198
2870408
1215
2952450
1217
2962178
1234
3045512
1236
3055392
1253
3140018
1255
3150050
1272
3235968
1274
3246152
1291
3333362
1293
3343698
1310
3432200
1312
3442688
1329
3532482
1331
3543122
1348
3634208
1350
3645000
1367
3737378
1369
3748322
1386
3841992
1388
3853088
1405
3948050
1407
3959298
1424
4055552
1426
4066952
1443
4164498
1445
4176050
1462
4274888
1464
4286592
1481
4386722
1483
4398578
1500
4500000
1502
4512008
1519
4614722
1521
4626882
1538
4730888
1540
4743200
1557
4848498
1559
4860962
1576
4967552
1578
4980168
1595
5088050
1597
5100818
1614
5209992
1616
5222912
1633
5333378
1635
5346450
1652
5458208
1654
5471432
1671
5584482
1673
5597858
1690
5712200
1692
5725728
1709
5841362
1711
5855042
1728
5971968
1730
5985800
1747
6104018
1749
6118002
1766
6237512
1768
6251648
1785
6372450
1787
6386738
1804
6508832
1806
6523272
1823
6646658
1825
6661250
1842
6785928
1844
6800672
1861
6926642
1863
6941538
1880
7068800
1882
7083848
1899
7212402
1901
7227602
1918
7357448
1920
7372800
1937
7503938
1939
7519442
1956
7651872
1958
7667528
1975
7801250
1977
7817058
1994
7952072
1996
7968032

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:52:00 2004

Input: a := 19;

for i:= 1 to 200 do

x := i * i;

if x mod a eq 4 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:51:58 on modular  [Seed = 2586882738]
   -------------------------------------

2
4
17
289
21
441
36
1296
40
1600
55
3025
59
3481
74
5476
78
6084
93
8649
97
9409
112
12544
116
13456
131
17161
135
18225
150
22500
154
23716
169
28561
173
29929
188
35344
192
36864

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:52:35 2004

Input: a := 19;

for i:= 1 to 200 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:52:32 on modular  [Seed = 2718468852]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:52:46 2004

Input: a := 19;

for i:= 1 to 200 do

x := i * i;

if x mod a eq 5 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:52:44 on modular  [Seed = 2852160240]
   -------------------------------------

9
81
10
100
28
784
29
841
47
2209
48
2304
66
4356
67
4489
85
7225
86
7396
104
10816
105
11025
123
15129
124
15376
142
20164
143
20449
161
25921
162
26244
180
32400
181
32761
199
39601
200
40000

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:53:12 2004

Input: a := 13;

for i:= 1 to 200 do

x := i * i;

if x mod a eq 5 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:53:10 on modular  [Seed = 2954533056]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:53:21 2004

Input: a := 13;

for i:= 1 to 200 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:53:18 on modular  [Seed = 3088224448]
   -------------------------------------

4
16
9
81
17
289
22
484
30
900
35
1225
43
1849
48
2304
56
3136
61
3721
69
4761
74
5476
82
6724
87
7569
95
9025
100
10000
108
11664
113
12769
121
14641
126
15876
134
17956
139
19321
147
21609
152
23104
160
25600
165
27225
173
29929
178
31684
186
34596
191
36481
199
39601

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:54:00 2004

Input: a := 13;

for i:= 1 to 200 do

x := i * i;

if x mod a eq 4 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:53:57 on modular  [Seed = 3228231779]
   -------------------------------------

2
4
11
121
15
225
24
576
28
784
37
1369
41
1681
50
2500
54
2916
63
3969
67
4489
76
5776
80
6400
89
7921
93
8649
102
10404
106
11236
115
13225
119
14161
128
16384
132
17424
141
19881
145
21025
154
23716
158
24964
167
27889
171
29241
180
32400
184
33856
193
37249
197
38809

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:54:42 2004

Input: a := 13;

for i:= 1 to 200 do

x := i * i * 2;

if x mod a eq 4 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:54:39 on modular  [Seed = 3361923073]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:55:07 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 4 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:55:05 on modular  [Seed = 3497719871]
   -------------------------------------

2
4
11
121
15
225
24
576
28
784
37
1369
41
1681
50
2500
54
2916
63
3969
67
4489
76
5776
80
6400
89
7921
93
8649

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul  6 04:55:19 2004

Input: a := 13;

for i:= 1 to 100 do

x := i * i;

if x mod a eq 3 then
print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 04:55:16 on modular  [Seed = 3631411242]
   -------------------------------------

4
16
9
81
17
289
22
484
30
900
35
1225
43
1849
48
2304
56
3136
61
3721
69
4761
74
5476
82
6724
87
7569
95
9025
100
10000

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:31:38 2004

Input: FF<w> := GF(2^133);
E := EllipticCurve([1, 0, 0, 0, w]);
time #E;


Output: Magma V2.10-22    Tue Jul  6 2004 05:31:28 on modular  [Seed = 431171694]
   -------------------------------------

10889035741470030830941160923712974513152
Time: 7.080

Total time: 9.599 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:34:58 2004

Input: FF<w> := GF(2^133);
E := EllipticCurve([1, 0, 0, 0, w]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:34:56 on modular  [Seed = 562762598]
   -------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 + w over GF(2^133)

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:35:44 2004

Input: FF<w> := GF(2^133);
E := EllipticCurve([0, 1, 0, 0, w]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:35:41 on modular  [Seed = 696458051]
   -------------------------------------


>> E := EllipticCurve([0, 1, 0, 0, w]);
                     ^
Runtime error in 'EllipticCurve': Curve is singular

>> E;;
   ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:35:59 2004

Input: FF<w> := GF(2^133);
E := EllipticCurve([1, 0, 0, 0, 0]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:35:57 on modular  [Seed = 832242507]
   -------------------------------------


>> E := EllipticCurve([1, 0, 0, 0, 0]);
                     ^
Runtime error in 'EllipticCurve': Curve is singular

>> E;;
   ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:36:08 2004

Input: FF<w> := GF(2^133);
E := EllipticCurve([1, 0, 0, 0, 1]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:36:06 on modular  [Seed = 965938104]
   -------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 + 1 over Rational Field

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:36:23 2004

Input: FF<w> := GF(57);
E := EllipticCurve([1, 0, 0, 0, 1]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:36:20 on modular  [Seed = 1089106643]
   -------------------------------------


>> FF<w> := GF(57);
              ^
Runtime error in 'GF': Argument 1 (57) is not a prime power
Elliptic Curve defined by y^2 + x*y = x^3 + 1 over Rational Field

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:36:40 2004

Input: FF<w> := GF(43);
E := EllipticCurve([1, 0, 0, 0, 1]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:36:37 on modular  [Seed = 1222802154]
   -------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 + 1 over Rational Field

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:37:14 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 0, 1, 0, 0]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:37:12 on modular  [Seed = 1609919888]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 over Rational Field

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:38:35 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 0, 0, 1, 0]);
E;

Output: Magma V2.10-22    Tue Jul  6 2004 05:38:33 on modular  [Seed = 1708086907]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x over Rational Field

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:39:24 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 0, 0, 1, 0]);
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:39:22 on modular  [Seed = 1841782304]
   -------------------------------------


>> IsSupersingular(E);;
                  ^
Runtime error in 'IsSupersingular': Argument must be defined over a finite 
field.

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:40:24 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 0, 0, 1, 0]);
TraceOfFrobenius(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:40:22 on modular  [Seed = 2183704835]
   -------------------------------------


>> TraceOfFrobenius(E);;
                   ^
Runtime error in 'TraceOfFrobenius': The base ring of argument 1 must be a 
finite field.

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:40:34 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 0, 0, 1, w]);
TraceOfFrobenius(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:40:32 on modular  [Seed = 2317400349]
   -------------------------------------

10

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:40:49 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 0, 0, 1, w]);
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:40:47 on modular  [Seed = 2453184778]
   -------------------------------------

false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:40:59 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 0, 0, 1, w]);
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:40:56 on modular  [Seed = 2586880309]
   -------------------------------------

false

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:41:15 2004

Input: FF<w> := GF(0x101);
E := EllipticCurve([0, 0, 0, 1, w]);
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:41:13 on modular  [Seed = 2718470428]
   -------------------------------------


>> FF<w> := GF(0x101);
                ^
User error: bad syntax

>> E := EllipticCurve([0, 0, 0, 1, w]);
                                   ^
User error: Identifier 'w' has not been declared or assigned

>> IsSupersingular(E);;
                   ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:41:25 2004

Input: FF<w> := GF(101h);
E := EllipticCurve([0, 0, 0, 1, w]);
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:41:23 on modular  [Seed = 2835585645]
   -------------------------------------


>> FF<w> := GF(101h);
                  ^
User error: bad syntax

>> E := EllipticCurve([0, 0, 0, 1, w]);
                                   ^
User error: Identifier 'w' has not been declared or assigned

>> IsSupersingular(E);;
                   ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:43:27 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 0, 0, 1, w]);
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:43:24 on modular  [Seed = 2971370890]
   -------------------------------------

false

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:43:37 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 0, 0, 1, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:43:35 on modular  [Seed = 3105066489]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x + 1 over GF(101)
false

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:44:24 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 0, 1, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:44:22 on modular  [Seed = 3245077936]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 + 1 over GF(101)
true

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:44:35 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 1, 1, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:44:32 on modular  [Seed = 3378773327]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 + x^2 + 1 over GF(101)
false

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:45:27 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 0, 1, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:45:25 on modular  [Seed = 3514557795]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 + 1 over GF(101)
true

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:45:38 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 1, 0, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:45:35 on modular  [Seed = 3648253281]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x^2 + 1 over GF(101)
false

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:45:59 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 0, 0, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:45:57 on modular  [Seed = 3779843379]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 1 over GF(101)
true

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:46:15 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 1, 0, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:46:13 on modular  [Seed = 3913538827]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x^2 + 1 over GF(101)
false

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:46:52 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 1, 0, 0, GF(101)]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:46:50 on modular  [Seed = 4032480765]
   -------------------------------------


>> E := EllipticCurve([0, 1, 0, 0, GF(101)]);
                      ^
Runtime error in [ ... ]: Could not find a valid universe

>> E;
   ^
User error: Identifier 'E' has not been declared or assigned

>> IsSupersingular(E);;
                   ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:47:05 2004

Input: FF<w> := GF(101);
E := EllipticCurve([0, 1, 0, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:47:03 on modular  [Seed = 144850199]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x^2 + 1 over GF(101)
false

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host kabuto.elmundo.es. (193.110.128.11)
Time: Tue Jul  6 05:49:29 2004

Input: FF<w> := GF(43);
E := EllipticCurve([0, 1, 0, 0, w]);
E;
IsSupersingular(E);

Output: Magma V2.10-22    Tue Jul  6 2004 05:49:27 on modular  [Seed = 11154863]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + x^2 + 1 over GF(43)
false

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.235.5.49)
Time: Tue Jul  6 06:14:11 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Tue Jul  6 2004 06:14:07 on modular  [Seed = 1841780234]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host host25-178.pool81117.interbusiness.it. (81.117.178.25)
Time: Tue Jul  6 07:22:05 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Tue Jul  6 2004 07:22:02 on modular  [Seed = 3715569294]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Tue Jul  6 16:53:17 2004

Input: factorize(2453);

Output: Magma V2.10-22    Tue Jul  6 2004 16:53:14 on modular  [Seed = 1392051046]
   -------------------------------------


>> factorize(2453);;
   ^
User error: Identifier 'factorize' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Tue Jul  6 16:53:26 2004

Input: factorization(2453);

Output: Magma V2.10-22    Tue Jul  6 2004 16:53:24 on modular  [Seed = 1791048480]
   -------------------------------------


>> factorization(2453);;
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Tue Jul  6 16:53:36 2004

Input: Factorization(2453);

Output: Magma V2.10-22    Tue Jul  6 2004 16:53:33 on modular  [Seed = 1657352993]
   -------------------------------------

[ <11, 1>, <223, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:31:24 2004

Input: a := 13;
m := 1;
for x := 0 to 100 do

t := x * x;

if x mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:31:21 on modular  [Seed = 3088310943]
   -------------------------------------

1
1
14
196
27
729
40
1600
53
2809
66
4356
79
6241
92
8464

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:31:47 2004

Input: a := 13;
m := 1;
for x := 0 to a do

t := x * x;

if x mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:31:44 on modular  [Seed = 2954619646]
   -------------------------------------

1
1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:32:54 2004

Input: a := 13;
m := 1;
for x := 0 to 200 do

t := x * x;

if x mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:32:52 on modular  [Seed = 3361968706]
   -------------------------------------

1
1
14
196
27
729
40
1600
53
2809
66
4356
79
6241
92
8464
105
11025
118
13924
131
17161
144
20736
157
24649
170
28900
183
33489
196
38416

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:35:48 2004

Input: a := 13;
m := 3;
for x := 0 to 200 do

t := x * x;

if x mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:35:45 on modular  [Seed = 3228277759]
   -------------------------------------

3
9
16
256
29
841
42
1764
55
3025
68
4624
81
6561
94
8836
107
11449
120
14400
133
17689
146
21316
159
25281
172
29584
185
34225
198
39204

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:40:41 2004

Input: a := 13;
m := 3;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:40:38 on modular  [Seed = 3813195707]
   -------------------------------------

4
16
9
81
17
289
22
484
30
900
35
1225
43
1849
48
2304
56
3136
61
3721
69
4761
74
5476
82
6724
87
7569
95
9025
100
10000
108
11664
113
12769
121
14641
126
15876
134
17956
139
19321
147
21609
152
23104
160
25600
165
27225
173
29929
178
31684
186
34596
191
36481
199
39601

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:41:44 2004

Input: a := 13;
m := 2;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:41:41 on modular  [Seed = 4166231139]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:43:26 2004

Input: a := 13;
m := 1;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:43:23 on modular  [Seed = 4032539653]
   -------------------------------------

1
1
12
144
14
196
25
625
27
729
38
1444
40
1600
51
2601
53
2809
64
4096
66
4356
77
5929
79
6241
90
8100
92
8464
103
10609
105
11025
116
13456
118
13924
129
16641
131
17161
142
20164
144
20736
155
24025
157
24649
168
28224
170
28900
181
32761
183
33489
194
37636
196
38416

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:46:33 2004

Input: a := 13;
m := 3;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:46:30 on modular  [Seed = 144922033]
   -------------------------------------

4
16
9
81
17
289
22
484
30
900
35
1225
43
1849
48
2304
56
3136
61
3721
69
4761
74
5476
82
6724
87
7569
95
9025
100
10000
108
11664
113
12769
121
14641
126
15876
134
17956
139
19321
147
21609
152
23104
160
25600
165
27225
173
29929
178
31684
186
34596
191
36481
199
39601

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:47:15 2004

Input: a := 13;
m := 1;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:47:12 on modular  [Seed = 531907312]
   -------------------------------------

1
1
12
144
14
196
25
625
27
729
38
1444
40
1600
51
2601
53
2809
64
4096
66
4356
77
5929
79
6241
90
8100
92
8464
103
10609
105
11025
116
13456
118
13924
129
16641
131
17161
142
20164
144
20736
155
24025
157
24649
168
28224
170
28900
181
32761
183
33489
194
37636
196
38416

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:48:39 2004

Input: a := 13;
m := 3;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:48:37 on modular  [Seed = 398215469]
   -------------------------------------

4
16
9
81
17
289
22
484
30
900
35
1225
43
1849
48
2304
56
3136
61
3721
69
4761
74
5476
82
6724
87
7569
95
9025
100
10000
108
11664
113
12769
121
14641
126
15876
134
17956
139
19321
147
21609
152
23104
160
25600
165
27225
173
29929
178
31684
186
34596
191
36481
199
39601

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:49:09 2004

Input: a := 13;
m := 4;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:49:06 on modular  [Seed = 797208946]
   -------------------------------------

2
4
11
121
15
225
24
576
28
784
37
1369
41
1681
50
2500
54
2916
63
3969
67
4489
76
5776
80
6400
89
7921
93
8649
102
10404
106
11236
115
13225
119
14161
128
16384
132
17424
141
19881
145
21025
154
23716
158
24964
167
27889
171
29241
180
32400
184
33856
193
37249
197
38809

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:49:37 2004

Input: a := 13;
m := 5;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:49:34 on modular  [Seed = 663517510]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:49:47 2004

Input: a := 13;
m := 6;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:49:44 on modular  [Seed = 1066688840]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:49:59 2004

Input: a := 13;
m := 6;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:49:57 on modular  [Seed = 932997565]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:50:07 2004

Input: a := 13;
m := 7;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:50:05 on modular  [Seed = 1340346829]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:50:17 2004

Input: a := 13;
m := 8;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:50:15 on modular  [Seed = 1206655455]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:50:26 2004

Input: a := 13;
m := 9;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:50:23 on modular  [Seed = 1609826767]
   -------------------------------------

3
9
10
100
16
256
23
529
29
841
36
1296
42
1764
49
2401
55
3025
62
3844
68
4624
75
5625
81
6561
88
7744
94
8836
101
10201
107
11449
114
12996
120
14400
127
16129
133
17689
140
19600
146
21316
153
23409
159
25281
166
27556
172
29584
179
32041
185
34225
192
36864
198
39204

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:50:55 2004

Input: a := 13;
m := 10;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:50:53 on modular  [Seed = 1476135397]
   -------------------------------------

6
36
7
49
19
361
20
400
32
1024
33
1089
45
2025
46
2116
58
3364
59
3481
71
5041
72
5184
84
7056
85
7225
97
9409
98
9604
110
12100
111
12321
123
15129
124
15376
136
18496
137
18769
149
22201
150
22500
162
26244
163
26569
175
30625
176
30976
188
35344
189
35721

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:51:30 2004

Input: a := 13;
m := 11;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:51:27 on modular  [Seed = 1858416830]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:51:38 2004

Input: a := 13;
m := 12;
for x := 0 to 200 do

t := x * x;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:51:36 on modular  [Seed = 1724725377]
   -------------------------------------

5
25
8
64
18
324
21
441
31
961
34
1156
44
1936
47
2209
57
3249
60
3600
70
4900
73
5329
83
6889
86
7396
96
9216
99
9801
109
11881
112
12544
122
14884
125
15625
135
18225
138
19044
148
21904
151
22801
161
25921
164
26896
174
30276
177
31329
187
34969
190
36100
200
40000

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:52:24 2004

Input: a := 13;
m := 1;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:52:21 on modular  [Seed = 2127896932]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:52:37 2004

Input: a := 13;
m := 2;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:52:34 on modular  [Seed = 1994205531]
   -------------------------------------

1
2
12
288
14
392
25
1250
27
1458
38
2888
40
3200
51
5202
53
5618
64
8192
66
8712
77
11858
79
12482
90
16200
92
16928
103
21218
105
22050
116
26912
118
27848
129
33282
131
34322
142
40328
144
41472
155
48050
157
49298
168
56448
170
57800
181
65522
183
66978
194
75272
196
76832

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:52:51 2004

Input: a := 13;
m := 3;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:52:49 on modular  [Seed = 2384843184]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:53:06 2004

Input: a := 13;
m := 4;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:53:03 on modular  [Seed = 2217728948]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:53:12 2004

Input: a := 13;
m := 4;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:53:10 on modular  [Seed = 2620900309]
   -------------------------------------


Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:53:26 2004

Input: a := 13;
m := 5;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:53:23 on modular  [Seed = 2487208904]
   -------------------------------------

3
18
10
200
16
512
23
1058
29
1682
36
2592
42
3528
49
4802
55
6050
62
7688
68
9248
75
11250
81
13122
88
15488
94
17672
101
20402
107
22898
114
25992
120
28800
127
32258
133
35378
140
39200
146
42632
153
46818
159
50562
166
55112
172
59168
179
64082
185
68450
192
73728
198
78408

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:53:44 2004

Input: a := 13;
m := 6;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:53:41 on modular  [Seed = 2886202310]
   -------------------------------------

4
32
9
162
17
578
22
968
30
1800
35
2450
43
3698
48
4608
56
6272
61
7442
69
9522
74
10952
82
13448
87
15138
95
18050
100
20000
108
23328
113
25538
121
29282
126
31752
134
35912
139
38642
147
43218
152
46208
160
51200
165
54450
173
59858
178
63368
186
69192
191
72962
199
79202

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:54:08 2004

Input: a := 13;
m := 7;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:54:06 on modular  [Seed = 2752510933]
   -------------------------------------

6
72
7
98
19
722
20
800
32
2048
33
2178
45
4050
46
4232
58
6728
59
6962
71
10082
72
10368
84
14112
85
14450
97
18818
98
19208
110
24200
111
24642
123
30258
124
30752
136
36992
137
37538
149
44402
150
45000
162
52488
163
53138
175
61250
176
61952
188
70688
189
71442

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:54:29 2004

Input: a := 13;
m := 8;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:54:27 on modular  [Seed = 3138446375]
   -------------------------------------

2
8
11
242
15
450
24
1152
28
1568
37
2738
41
3362
50
5000
54
5832
63
7938
67
8978
76
11552
80
12800
89
15842
93
17298
102
20808
106
22472
115
26450
119
28322
128
32768
132
34848
141
39762
145
42050
154
47432
158
49928
167
55778
171
58482
180
64800
184
67712
193
74498
197
77618

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:54:59 2004

Input: a := 13;
m := 9;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:54:57 on modular  [Seed = 3004754957]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:55:12 2004

Input: a := 13;
m := 10;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:55:10 on modular  [Seed = 3412104314]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:55:21 2004

Input: a := 13;
m := 11;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:55:18 on modular  [Seed = 3278412810]
   -------------------------------------

5
50
8
128
18
648
21
882
31
1922
34
2312
44
3872
47
4418
57
6498
60
7200
70
9800
73
10658
83
13778
86
14792
96
18432
99
19602
109
23762
112
25088
122
29768
125
31250
135
36450
138
38088
148
43808
151
45602
161
51842
164
53792
174
60552
177
62658
187
69938
190
72200
200
80000

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Tue Jul  6 17:55:53 2004

Input: a := 13;
m := 12;
for x := 0 to 200 do

t := x * x * 2;

if t mod a eq m then

print(x);
print(t);

end if;

end for;

Output: Magma V2.10-22    Tue Jul  6 2004 17:55:50 on modular  [Seed = 3681584178]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 21:20:27 2004

Input: SimplexCode(5);


Output: Magma V2.10-22    Tue Jul  6 2004 21:20:10 on modular  [Seed = 899562222]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 21:47:41 2004

Input: K := FiniteField(2);
C6p := LinearCode<K,56 | 
[1, 0, 0,       1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0,   1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0,   1, 0, 0, 1, 0, 0,     1, 1],
[0, 1, 0,       1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0,   1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,   1, 1, 0, 1, 1, 0,     1, 0],
[0, 0, 1,       0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1,   0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1,   0, 1, 1, 0, 1, 1,     0, 1],
[0, 0, 0,       1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1,   1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,   1, 0, 1, 0, 0, 1,     1, 1],
[0, 0, 0,       1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1,   0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1,   0, 1, 0, 0, 0, 0,     1, 0],
[0, 0, 0,       0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,   1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,   0, 0, 1, 0, 0, 0,     1, 1]>;
CoveringRadius(C6p);


Output: Magma V2.10-22    Tue Jul  6 2004 21:47:24 on modular  [Seed = 1206669690]
   -------------------------------------


>> CoveringRadius(C6p);
                 ^
Runtime error in 'CoveringRadius': Arguments too large

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Tue Jul  6 21:48:35 2004

Input: R<x> := PolynomialRing(RationalField());
K<a> := NumberField(x^2 - 17);
I := 43 * MaximalOrder(K);
Factorization(I);

Output: Magma V2.10-22    Tue Jul  6 2004 21:48:32 on modular  [Seed = 1340365102]
   -------------------------------------

[
    <Prime Ideal
    Two element generators:
        [43, 0]
        [61, 2], 1>,
    <Prime Ideal
    Two element generators:
        [43, 0]
        [66, 2], 1>
]

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Tue Jul  6 21:49:25 2004

Input: K := FiniteField(2);
C6p := LinearCode<K,56 | 
[1, 0, 0,       1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0,   1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0,   1, 0, 0, 1, 0, 0,     1, 1],
[0, 1, 0,       1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0,   1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,   1, 1, 0, 1, 1, 0,     1, 0],
[0, 0, 1,       0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1,   0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1,   0, 1, 1, 0, 1, 1,     0, 1],
[0, 0, 0,       1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1,   1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,   1, 0, 1, 0, 0, 1,     1, 1],
[0, 0, 0,       1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1,   0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1,   0, 1, 0, 0, 0, 0,     1, 0],
[0, 0, 0,       0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,   1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,   0, 0, 1, 0, 0, 0,     1, 1]>;
C6p;


Output: Magma V2.10-22    Tue Jul  6 2004 21:49:08 on modular  [Seed = 2010931698]
   -------------------------------------

[56, 6, 28] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1
    1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0
    0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0]
[0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1
    1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1
    0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1]
[0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0
    0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0
    1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 22:17:16 2004

Input: 2+3;


Output: Magma V2.10-22    Tue Jul  6 2004 22:17:00 on modular  [Seed = 2752493993]
   -------------------------------------

5

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 22:18:33 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Tue Jul  6 2004 22:18:15 on modular  [Seed = 2919609304]
   -------------------------------------

10

Total time: 3.649 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 22:22:52 2004

Input: 2+3;


Output: Magma V2.10-22    Tue Jul  6 2004 22:22:35 on modular  [Seed = 3446068151]
   -------------------------------------

5

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 22:54:49 2004

Input: K := FiniteField(2);
C5p := LinearCode<K,24 | 
[      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 
[      0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]
[      1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]
[      0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]
[      0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1] >;
CoveringRadius(C5p);


Output: Magma V2.10-22    Tue Jul  6 2004 22:54:33 on modular  [Seed = 178335729]
   -------------------------------------


>> [      0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 
   ^
Runtime error in '[]': Sequence element 0 not defined

>> CoveringRadius(C5p);
                  ^
User error: Identifier 'C5p' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 22:57:59 2004

Input: K := FiniteField(2);
C5p := LinearCode<K,24 | 
[      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[      0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[      1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[      0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[      0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1] >;
CoveringRadius(C5p);


Output: Magma V2.10-22    Tue Jul  6 2004 22:57:41 on modular  [Seed = 815470215]
   -------------------------------------

10

Total time: 3.639 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:00:33 2004

Input: K := FiniteField(2);
C5p := LinearCode<K,24 | 
[      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[      0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[      1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[      0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[      0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1] >;
CoveringRadius(C5p);


Output: Magma V2.10-22    Tue Jul  6 2004 23:00:15 on modular  [Seed = 797181954]
   -------------------------------------

10

Total time: 3.639 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:22:30 2004

Input: C5pp  :=<K,24|
[         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
(C5pp);


Output: Magma V2.10-22    Tue Jul  6 2004 23:22:13 on modular  [Seed = 2111197450]
   -------------------------------------


>> C5pp  :=<K,24|
                ^
User error: bad syntax

>> , 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
                                  ^
User error: bad syntax

>> (C5pp);
    ^
User error: Identifier 'C5pp' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:25:14 2004

Input: K := FiniteField(2);
C := LinearCode<K,23 | 
[         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
(C5pp);


Output: Magma V2.10-22    Tue Jul  6 2004 23:24:58 on modular  [Seed = 1757627760]
   -------------------------------------


>> (C5pp);
    ^
User error: Identifier 'C5pp' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:25:59 2004

Input: K := FiniteField(2);
C5pp := LinearCode<K,23 | 
[         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
(C5pp);


Output: Magma V2.10-22    Tue Jul  6 2004 23:25:42 on modular  [Seed = 2603660991]
   -------------------------------------

[23, 5, 11] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1]
[0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1]
[0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0]
[0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:28:07 2004

Input: K := FiniteField(2);
C5pp := LinearCode<K,23 | 
[         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C5pp);


Output: Magma V2.10-22    Tue Jul  6 2004 23:27:50 on modular  [Seed = 2167057445]
   -------------------------------------

9

Total time: 3.029 seconds, Total memory usage: 2.81MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:30:52 2004

Input: K := FiniteField(2);
C5pp := LinearCode<K,23 | 
[         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
ParityCheckMatrix(C5pp);


Output: Magma V2.10-22    Tue Jul  6 2004 23:30:35 on modular  [Seed = 2971312120]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:42:15 2004

Input: K := FiniteField(2);
C5pl := LinearCode<K,22 | 
[         0, 0, 0, 0, 0,   0,   0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1,   1,   1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0,   0,   1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0,   1,   0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1,   1,   1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C5pl);

Output: Magma V2.10-22    Tue Jul  6 2004 23:41:59 on modular  [Seed = 4216376046]
   -------------------------------------


>> C5pl := LinearCode<K,22 | 
                     ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C5pl);;
                  ^
User error: Identifier 'C5pl' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:43:11 2004

Input: K := FiniteField(2);
C5pl := LinearCode<K,21 | 
[         0, 0, 0, 0, 0,   0,   0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1,   1,   1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0,   0,   1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0,   1,   0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1,   1,   1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C5pl);

Output: Magma V2.10-22    Tue Jul  6 2004 23:42:54 on modular  [Seed = 3930184646]
   -------------------------------------

8

Total time: 2.609 seconds, Total memory usage: 2.02MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Tue Jul  6 23:44:43 2004

Input: K := FiniteField(2);
C5pl := LinearCode<K,21 | 
[         0, 0, 0, 0, 0,   0,   0, 0, 0,         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[         0, 0, 0, 1, 1,   1,   1, 1, 1,         0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[         1, 1, 1, 0, 0,   0,   1, 1, 1,         1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[         0, 1, 1, 0, 0,   1,   0, 1, 1,         0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[         1, 0, 1, 0, 1,   1,   1, 0, 1,         0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
(C5pl);

Output: Magma V2.10-22    Tue Jul  6 2004 23:44:27 on modular  [Seed = 348071324]
   -------------------------------------

[21, 5, 9] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1]
[0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1]
[0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0]
[0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:03:58 2004

Input: 1009^13



Output: Magma V2.10-22    Wed Jul  7 2004 01:03:56 on modular  [Seed = 763816197]
   -------------------------------------

1123531262031279009939248370461342081329

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:04:10 2004

Input: 1109^13


Output: Magma V2.10-22    Wed Jul  7 2004 01:04:07 on modular  [Seed = 1442746630]
   -------------------------------------

3838045331658996566124703063854700926629

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:04:37 2004

Input: 1100^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:04:34 on modular  [Seed = 1156546610]
   -------------------------------------

3452271214393100000000000000000000000000

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:04:53 2004

Input: 11^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:04:51 on modular  [Seed = 1290242091]
   -------------------------------------

34522712143931

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:14:00 2004

Input: 1079^13


Output: Magma V2.10-22    Wed Jul  7 2004 01:13:57 on modular  [Seed = 2043854840]
   -------------------------------------

2687068766461980096885313283190637866839

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:14:10 2004

Input: 1049^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:14:07 on modular  [Seed = 1640671210]
   -------------------------------------

1862435951798318344612852825364963518649

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:14:20 2004

Input: 1069^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:14:17 on modular  [Seed = 1774366676]
   -------------------------------------

2380730126690871254489436732017832759709

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:14:28 2004

Input: 1059^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:14:26 on modular  [Seed = 2436519735]
   -------------------------------------

2106917262322858897785166167471151748979

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:14:56 2004

Input: 21982145917308330487013369^(1/3)

Output: Magma V2.10-22    Wed Jul  7 2004 01:14:54 on modular  [Seed = 2570215235]
   -------------------------------------

280128112.7907330960704837

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:15:45 2004

Input: 1079^13


Output: Magma V2.10-22    Wed Jul  7 2004 01:15:42 on modular  [Seed = 2167031659]
   -------------------------------------

2687068766461980096885313283190637866839

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:15:57 2004

Input: 1089^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:15:54 on modular  [Seed = 2300726935]
   -------------------------------------

3029440567724122650310590907598574786369

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:16:07 2004

Input: 1069^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:16:05 on modular  [Seed = 2971301552]
   -------------------------------------

2380730126690871254489436732017832759709

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:16:19 2004

Input: 1059^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:16:16 on modular  [Seed = 3104997005]
   -------------------------------------

2106917262322858897785166167471151748979

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:16:34 2004

Input: 1049^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:16:31 on modular  [Seed = 2718524825]
   -------------------------------------

1862435951798318344612852825364963518649

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:16:42 2004

Input: 1039^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:16:40 on modular  [Seed = 2852220294]
   -------------------------------------

1644379743551444114330365906797249152719

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:16:53 2004

Input: 1029^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:16:50 on modular  [Seed = 3531150724]
   -------------------------------------

1450106408735680603615891727924718135189

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:17:35 2004

Input: 129^13


Output: Magma V2.10-22    Wed Jul  7 2004 01:17:33 on modular  [Seed = 3312321212]
   -------------------------------------

2739468013418114691600975489

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:17:44 2004

Input: 109^13

Output: Magma V2.10-22    Wed Jul  7 2004 01:17:42 on modular  [Seed = 3446016687]
   -------------------------------------

306580461214335498944273629

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:18:11 2004

Input: 102^13

306580461214335498944273629
21982145917308330487013369

Output: Magma V2.10-22    Wed Jul  7 2004 01:18:08 on modular  [Seed = 4116591217]
   -------------------------------------


>> 306580461214335498944273629
   ^
User error: bad syntax
21982145917308330487013369

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:18:21 2004

Input: 102^13




Output: Magma V2.10-22    Wed Jul  7 2004 01:18:19 on modular  [Seed = 4250286706]
   -------------------------------------

129360663045379622466772992

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:18:34 2004

Input: 103^13



Output: Magma V2.10-22    Wed Jul  7 2004 01:18:32 on modular  [Seed = 3847103065]
   -------------------------------------

146853371345156431381127623

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:18:44 2004

Input: 104^13


Output: Magma V2.10-22    Wed Jul  7 2004 01:18:42 on modular  [Seed = 3980798539]
   -------------------------------------

166507350731038802170609664

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 01:18:59 2004

Input: 21982145917308330487013369^(1/13)

Output: Magma V2.10-22    Wed Jul  7 2004 01:18:57 on modular  [Seed = 348115904]
   -------------------------------------

89

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (150.55.87.56)
Time: Wed Jul  7 03:47:57 2004

Input: 2+3;

Output: Magma V2.10-22    Wed Jul  7 2004 03:47:55 on modular  [Seed = 2886157853]
   -------------------------------------

5

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Wed Jul  7 04:09:28 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Wed Jul  7 2004 04:09:10 on modular  [Seed = 531951778]
   -------------------------------------

10

Total time: 3.629 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Wed Jul  7 04:10:18 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);
CosetDistanceDistribution(C)

Output: Magma V2.10-22    Wed Jul  7 2004 04:10:00 on modular  [Seed = 398260436]
   -------------------------------------

10
[ <0, 1>, <1, 24>, <2, 276>, <3, 2024>, <4, 10626>, <5, 42504>, <6, 121772>, <7,
194904>, <8, 128797>, <9, 22688>, <10, 672> ]

Total time: 3.639 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Wed Jul  7 04:12:35 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);
CosetDistanceDistribution(C);

Output: Magma V2.10-22    Wed Jul  7 2004 04:12:17 on modular  [Seed = 61404026]
   -------------------------------------

10
[ <0, 1>, <1, 24>, <2, 276>, <3, 2024>, <4, 10626>, <5, 42504>, <6, 121772>, <7,
194904>, <8, 128797>, <9, 22688>, <10, 672> ]

Total time: 3.649 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host reached (203.255.11.42)
Time: Wed Jul  7 04:18:04 2004

Input: K := FiniteField(2);
C := LinearCode<K,24 | 
[1, 0,       1, 0,   1, 0, 1, 1, 0,   1, 1, 1, 1, 1, 0,     1, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 1,       0, 1,   0, 1, 0, 1, 1,   0, 1, 1, 1, 1, 1,     0, 1, 1, 0, 1, 1, 1, 0, 1],
[0, 0,       1, 0,   1, 0, 0, 1, 1,   1, 1, 0, 0, 0, 1,     1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0,       0, 1,   1, 1, 0, 0, 1,   1, 1, 1, 0, 0, 0,     0, 1, 1, 1, 0, 1, 0, 1, 0],
[0, 0,       0, 0,   0, 1, 1, 0, 0,   1, 1, 1, 1, 0, 0,     1, 0, 1, 1, 1, 0, 1, 0, 1]>;
CoveringRadius(C);
CosetDistanceDistribution(C);
CosetLeaders(C);

Output: Magma V2.10-22    Wed Jul  7 2004 04:17:28 on modular  [Seed = 1050005437]
   -------------------------------------

10
[ <0, 1>, <1, 24>, <2, 276>, <3, 2024>, <4, 10626>, <5, 42504>, <6, 121772>, <7,
194904>, <8, 128797>, <9, 22688>, <10, 672> ]
{@
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    (1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
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    (0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
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    (1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (1 0 0 0 1 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host pD9E51531.dip.t-dialin.net. (217.229.21.49)
Time: Wed Jul  7 08:14:29 2004

Input: F<a,b>:=<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2*b^2>;
Index(F,G);
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 08:14:25 on modular  [Seed = 1426062678]
   -------------------------------------


>> F<a,b>:=<a,b|a*b*a=b*a*b,a^4>;
               ^
User error: bad syntax

>> G<x>:=sub<F|a^2*b^2>;
             ^
User error: Identifier 'F' has not been declared or assigned

>> Index(F,G);
         ^
User error: Identifier 'F' has not been declared or assigned

>> Order(F);
         ^
User error: Identifier 'F' has not been declared or assigned

>> Order(G);;
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9E51531.dip.t-dialin.net. (217.229.21.49)
Time: Wed Jul  7 08:14:45 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2*b^2>;
Index(F,G);
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 08:14:42 on modular  [Seed = 1559754062]
   -------------------------------------

24
96
4

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51531.dip.t-dialin.net. (217.229.21.49)
Time: Wed Jul  7 08:15:25 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a^2*b^2>;
Index(F,G);
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 08:15:12 on modular  [Seed = 3038649541]
   -------------------------------------

0
0
0

Total time: 13.379 seconds, Total memory usage: 29.67MB


************** MAGMA *****************
Host pD9E51531.dip.t-dialin.net. (217.229.21.49)
Time: Wed Jul  7 08:20:33 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2*b^2>;
Index(F,G);
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 08:20:31 on modular  [Seed = 2670998832]
   -------------------------------------

24
96
4

Total time: 2.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9E51228.dip.t-dialin.net. (217.229.18.40)
Time: Wed Jul  7 08:30:17 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x,y>:=sub<F|a^2,b^2>;
Index(F,G);
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 08:30:13 on modular  [Seed = 3980804379]
   -------------------------------------

12
96
8

Total time: 2.779 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host 68-233-252-35.anhmca.adelphia.net. (68.233.252.35)
Time: Wed Jul  7 09:29:23 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jul  7 2004 09:29:21 on modular  [Seed = 4283712879]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:10:44 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2*b^2>;
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:10:41 on modular  [Seed = 128664388]
   -------------------------------------

4

Total time: 2.759 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:13:24 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:13:21 on modular  [Seed = 228673582]
   -------------------------------------

24
6

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:14:35 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:14:32 on modular  [Seed = 364466303]
   -------------------------------------

96
4

Total time: 2.779 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:14:50 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:14:47 on modular  [Seed = 498161768]
   -------------------------------------

6
1

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:15:07 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:15:04 on modular  [Seed = 1707679791]
   -------------------------------------

24
6

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:15:21 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^5>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:15:18 on modular  [Seed = 1841375289]
   -------------------------------------

600
10

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:16:46 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^2>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:16:43 on modular  [Seed = 1273433762]
   -------------------------------------

24
1

Total time: 2.809 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host p50825A18.dip.t-dialin.net. (80.130.90.24)
Time: Wed Jul  7 10:16:53 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^3>;
G<x>:=sub<F|a^2*b^2>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:16:50 on modular  [Seed = 1409226402]
   -------------------------------------

648
6

Total time: 2.819 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host pD9FF0AA5.dip.t-dialin.net. (217.255.10.165)
Time: Wed Jul  7 10:37:23 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
G<x>:=sub<F|a*b>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:37:20 on modular  [Seed = 3479405901]
   -------------------------------------

24
6

Total time: 2.799 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF0AA5.dip.t-dialin.net. (217.255.10.165)
Time: Wed Jul  7 10:37:30 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b>;
Order(F);
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 10:37:27 on modular  [Seed = 3615202642]
   -------------------------------------

96
12

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:25:42 2004

Input: CartanMatrix(A(4));

Output: Magma V2.10-22    Wed Jul  7 2004 11:25:40 on modular  [Seed = 1592920969]
   -------------------------------------


>> CartanMatrix(A(4));;
                ^
User error: Identifier 'A' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:26:32 2004

Input: L:= SimpleLieAlgebra( "F", 4, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:26:29 on modular  [Seed = 2902588331]
   -------------------------------------

[ 2  0 -1  0]
[ 0  2  0 -1]
[-1  0  2 -1]
[ 0 -1 -2  2]

Total time: 3.009 seconds, Total memory usage: 3.18MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:26:47 2004

Input: L:= SimpleLieAlgebra( "G", 2, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:26:45 on modular  [Seed = 3038372771]
   -------------------------------------

[ 2 -1]
[-3  2]

Total time: 2.579 seconds, Total memory usage: 2.40MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:26:57 2004

Input: L:= SimpleLieAlgebra( "A", 2, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:26:54 on modular  [Seed = 3155225249]
   -------------------------------------

[ 2 -1]
[-1  2]

Total time: 2.549 seconds, Total memory usage: 2.40MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:27:06 2004

Input: L:= SimpleLieAlgebra( "A", 3, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:27:03 on modular  [Seed = 2217267936]
   -------------------------------------

[ 2 -1  0]
[-1  2 -1]
[ 0 -1  2]

Total time: 2.589 seconds, Total memory usage: 2.40MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:27:16 2004

Input: L:= SimpleLieAlgebra( "A", 4, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:27:13 on modular  [Seed = 2350963454]
   -------------------------------------

[ 2 -1  0  0]
[-1  2 -1  0]
[ 0 -1  2 -1]
[ 0  0 -1  2]

Total time: 2.609 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:27:24 2004

Input: L:= SimpleLieAlgebra( "A", 5, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:27:21 on modular  [Seed = 2486747886]
   -------------------------------------

[ 2 -1  0  0  0]
[-1  2 -1  0  0]
[ 0 -1  2 -1  0]
[ 0  0 -1  2 -1]
[ 0  0  0 -1  2]

Total time: 2.669 seconds, Total memory usage: 2.41MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:27:33 2004

Input: L:= SimpleLieAlgebra( "B", 5, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:27:30 on modular  [Seed = 2620443357]
   -------------------------------------

[ 2 -1  0  0  0]
[-1  2 -1  0  0]
[ 0 -1  2 -1  0]
[ 0  0 -1  2 -2]
[ 0  0  0 -1  2]

Total time: 2.989 seconds, Total memory usage: 3.32MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:27:45 2004

Input: L:= SimpleLieAlgebra( "C", 5, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:27:42 on modular  [Seed = 3829969577]
   -------------------------------------

[ 2 -1  0  0  0]
[-1  2 -1  0  0]
[ 0 -1  2 -1  0]
[ 0  0 -1  2 -1]
[ 0  0  0 -2  2]

Total time: 3.119 seconds, Total memory usage: 3.31MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:27:56 2004

Input: L:= SimpleLieAlgebra( "D", 5, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:27:53 on modular  [Seed = 3963665078]
   -------------------------------------

[ 2 -1  0  0  0]
[-1  2 -1  0  0]
[ 0 -1  2 -1 -1]
[ 0  0 -1  2  0]
[ 0  0 -1  0  2]

Total time: 2.789 seconds, Total memory usage: 2.65MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:28:06 2004

Input: L:= SimpleLieAlgebra( "D", 6, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:28:03 on modular  [Seed = 4099449428]
   -------------------------------------

[ 2 -1  0  0  0  0]
[-1  2 -1  0  0  0]
[ 0 -1  2 -1  0  0]
[ 0  0 -1  2 -1 -1]
[ 0  0  0 -1  2  0]
[ 0  0  0 -1  0  2]

Total time: 3.199 seconds, Total memory usage: 4.34MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:28:17 2004

Input: L:= SimpleLieAlgebra( "E", 6, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:28:13 on modular  [Seed = 4233144914]
   -------------------------------------

[ 2  0 -1  0  0  0]
[ 0  2  0 -1  0  0]
[-1  0  2 -1  0  0]
[ 0 -1 -1  2 -1  0]
[ 0  0  0 -1  2 -1]
[ 0  0  0  0 -1  2]

Total time: 3.589 seconds, Total memory usage: 6.00MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:28:36 2004

Input: L:= SimpleLieAlgebra( "E", 7, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:28:29 on modular  [Seed = 3295187578]
   -------------------------------------

[ 2  0 -1  0  0  0  0]
[ 0  2  0 -1  0  0  0]
[-1  0  2 -1  0  0  0]
[ 0 -1 -1  2 -1  0  0]
[ 0  0  0 -1  2 -1  0]
[ 0  0  0  0 -1  2 -1]
[ 0  0  0  0  0 -1  2]

Total time: 7.249 seconds, Total memory usage: 23.90MB


************** MAGMA *****************
Host adsl-68-75-188-37.dsl.emhril.ameritech.net. (68.75.188.37)
Time: Wed Jul  7 11:29:07 2004

Input: L:= SimpleLieAlgebra( "E", 8, Rationals() );
rd := RootDatum(L); 
CartanMatrix(rd);

Output: Magma V2.10-22    Wed Jul  7 2004 11:28:45 on modular  [Seed = 3428883010]
   -------------------------------------



************** MAGMA *****************
Host pD9FF0ADC.dip.t-dialin.net. (217.255.10.220)
Time: Wed Jul  7 12:47:28 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a*a*b*b>;
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 12:47:22 on modular  [Seed = 3531521004]
   -------------------------------------

0

Total time: 5.149 seconds, Total memory usage: 29.67MB


************** MAGMA *****************
Host pD9FF0ADC.dip.t-dialin.net. (217.255.10.220)
Time: Wed Jul  7 13:10:31 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2>;
G<x>:=sub<F|a*b>;
Order(G);

Output: Magma V2.10-22    Wed Jul  7 2004 13:10:27 on modular  [Seed = 1089220326]
   -------------------------------------

3

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF0ADC.dip.t-dialin.net. (217.255.10.220)
Time: Wed Jul  7 13:18:47 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
G<x>:=sub<F|a*b>;
H<y>:=sub<F|a*a*b*b>;
Order(F);
Order(G);
Order(H);

Output: Magma V2.10-22    Wed Jul  7 2004 13:18:44 on modular  [Seed = 1559243789]
   -------------------------------------

24
6
6

Total time: 2.949 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF0ADC.dip.t-dialin.net. (217.255.10.220)
Time: Wed Jul  7 13:19:06 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b>;
H<y>:=sub<F|a*a*b*b>;
Order(F);
Order(G);
Order(H);

Output: Magma V2.10-22    Wed Jul  7 2004 13:19:03 on modular  [Seed = 2752041990]
   -------------------------------------

96
12
4

Total time: 2.939 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF0ADC.dip.t-dialin.net. (217.255.10.220)
Time: Wed Jul  7 13:19:42 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^5>;
G<x>:=sub<F|a*b>;
H<y>:=sub<F|a*a*b*b>;
Order(F);
Order(G);
Order(H);

Output: Magma V2.10-22    Wed Jul  7 2004 13:19:39 on modular  [Seed = 2885737506]
   -------------------------------------

600
30
10

Total time: 2.949 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host cekif1.panafonet.gr. (213.249.18.67)
Time: Wed Jul  7 16:19:09 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jul  7 2004 16:19:06 on modular  [Seed = 448135303]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host xdsl-81-173-159-143.netcologne.de. (81.173.159.143)
Time: Wed Jul  7 21:33:41 2004

Input: p = 1361129467683753853853498429727072845993
Mod(Mod(1,p)*X, (X^200 + X^20 + X^2 + 1)*Mod(1,p))^(p^2)


Output: Magma V2.10-22    Wed Jul  7 2004 21:33:39 on modular  [Seed = 465043267]
   -------------------------------------


>> Mod(Mod(1,p)*X, (X^200 + X^20 + X^2 + 1)*Mod(1,p))^(p^2)
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Wed Jul  7 23:52:39 2004

Input: K := FiniteField(2);
C57p  :=LinearCode<K,24 |
[    0,   0, 0, 0,   0, 0, 0, 0, 0, 0,     1, 1,   1, 1,   1, 1, 1, 1, 1, 1, 1, 1, 1],
[    0,   0, 0, 0,   1, 1, 1, 1, 1, 1,     0, 0,   0, 0,   0, 1, 1, 1, 1, 1, 1, 1, 1],
[    0,   1, 1, 1,   0, 0, 0, 1, 1, 1,     0, 0,   1, 1,   1, 0, 0, 0, 0, 1, 1, 1, 1],
[    1,   0, 1, 1,   0, 1, 1, 0, 0, 1,     0, 1,   0, 0,   1, 0, 0, 1, 1, 0, 0, 1, 1],
[    1,   1, 0, 1,   1, 0, 1, 0, 1, 0,     1, 0,   0, 1,   1, 0, 1, 0, 1, 0, 1, 0, 1]>
CoveringRadius (C57p);


Output: Magma V2.10-22    Wed Jul  7 2004 23:52:23 on modular  [Seed = 1774579123]
   -------------------------------------


>> CoveringRadius (C57p);
   ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Wed Jul  7 23:54:45 2004

Input: K := FiniteField(2);
C57p  :=LinearCode<K,24 |
[    0,   0, 0, 0,   0, 0, 0, 0, 0, 0,     1, 1,   1, 1,   1, 1, 1, 1, 1, 1, 1, 1, 1],
[    0,   0, 0, 0,   1, 1, 1, 1, 1, 1,     0, 0,   0, 0,   0, 1, 1, 1, 1, 1, 1, 1, 1],
[    0,   1, 1, 1,   0, 0, 0, 1, 1, 1,     0, 0,   1, 1,   1, 0, 0, 0, 0, 1, 1, 1, 1],
[    1,   0, 1, 1,   0, 1, 1, 0, 0, 1,     0, 1,   0, 0,   1, 0, 0, 1, 1, 0, 0, 1, 1],
[    1,   1, 0, 1,   1, 0, 1, 0, 1, 0,     1, 0,   0, 1,   1, 0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius (C57p);


Output: Magma V2.10-22    Wed Jul  7 2004 23:54:29 on modular  [Seed = 1674569275]
   -------------------------------------


>> C57p  :=LinearCode<K,24 |
                     ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius (C57p);
                   ^
User error: Identifier 'C57p' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Wed Jul  7 23:56:54 2004

Input: K := FiniteField(2);
C57p  :=LinearCode<K,24 |
[    0,   0, 0, 0,   0, 0, 0, 0, 0, 0,     1, 1,   1, 1,   1, 1, 1, 1, 1, 1, 1, 1, 1],
[    0,   0, 0, 0,   1, 1, 1, 1, 1, 1,     0, 0,   0, 0,   0, 1, 1, 1, 1, 1, 1, 1, 1],
[    0,   1, 1, 1,   0, 0, 0, 1, 1, 1,     0, 0,   1, 1,   1, 0, 0, 0, 0, 1, 1, 1, 1],
[    1,   0, 1, 1,   0, 1, 1, 0, 0, 1,     0, 1,   0, 0,   1, 0, 0, 1, 1, 0, 0, 1, 1],
[    1,   1, 0, 1,   1, 0, 1, 0, 1, 0,     1, 0,   0, 1,   1, 0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C57p);


Output: Magma V2.10-22    Wed Jul  7 2004 23:56:37 on modular  [Seed = 2060910498]
   -------------------------------------


>> C57p  :=LinearCode<K,24 |
                     ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C57p);
                  ^
User error: Identifier 'C57p' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Wed Jul  7 23:59:03 2004

Input: K := FiniteField(2);
C7p  :=LinearCode<K,24 |
[    0,   0, 0, 0,   0, 0, 0, 0, 0, 0,     1, 1,   1, 1,     1, 1, 1, 1, 1, 1, 1, 1],
[    0,   0, 0, 0,   1, 1, 1, 1, 1, 1,     0, 0,   0, 0,     1, 1, 1, 1, 1, 1, 1, 1],
[    0,   1, 1, 1,   0, 0, 0, 1, 1, 1,     0, 0,   1, 1,     0, 0, 0, 0, 1, 1, 1, 1],
[    1,   0, 1, 1,   0, 1, 1, 0, 0, 1,     0, 1,   0, 0,     0, 0, 1, 1, 0, 0, 1, 1],
[    1,   1, 0, 1,   1, 0, 1, 0, 1, 0,     1, 0,   0, 1,     0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C7p);


Output: Magma V2.10-22    Wed Jul  7 2004 23:58:47 on modular  [Seed = 1306643223]
   -------------------------------------


>> C7p  :=LinearCode<K,24 |
                    ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C7p);
                  ^
User error: Identifier 'C7p' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Thu Jul  8 00:02:04 2004

Input: K := FiniteField(2);
C7p  :=LinearCode<K,22 |
[    0,   0, 0, 0,   0, 0, 0, 0, 0, 0,     1, 1,   1, 1,     1, 1, 1, 1, 1, 1, 1, 1],
[    0,   0, 0, 0,   1, 1, 1, 1, 1, 1,     0, 0,   0, 0,     1, 1, 1, 1, 1, 1, 1, 1],
[    0,   1, 1, 1,   0, 0, 0, 1, 1, 1,     0, 0,   1, 1,     0, 0, 0, 0, 1, 1, 1, 1],
[    1,   0, 1, 1,   0, 1, 1, 0, 0, 1,     0, 1,   0, 0,     0, 0, 1, 1, 0, 0, 1, 1],
[    1,   1, 0, 1,   1, 0, 1, 0, 1, 0,     1, 0,   0, 1,     0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C7p);


Output: Magma V2.10-22    Thu Jul  8 2004 00:01:47 on modular  [Seed = 1375589975]
   -------------------------------------

8

Total time: 2.749 seconds, Total memory usage: 2.29MB


************** MAGMA *****************
Host reached (203.255.11.106)
Time: Thu Jul  8 00:07:31 2004

Input: K := FiniteField(2);
C57p  :=LinearCode<K,24 |
[     0,   0, 0, 0,   0, 0, 0, 0, 0, 0,     1, 1,   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[     0,   0, 0, 0,   1, 1, 1, 1, 1, 1,     0, 0,   0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[     0,   1, 1, 1,   0, 0, 0, 1, 1, 1,     0, 0,   1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[     1,   0, 1, 1,   0, 1, 1, 0, 0, 1,     0, 1,   0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],
[     1,   1, 0, 1,   1, 0, 1, 0, 1, 0,     1, 0,   0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]>;
CoveringRadius(C57p);


Output: Magma V2.10-22    Thu Jul  8 2004 00:07:13 on modular  [Seed = 2869371895]
   -------------------------------------

10

Total time: 3.659 seconds, Total memory usage: 3.86MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:18:48 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"
10!
20!


Output: Magma V2.10-22    Thu Jul  8 2004 01:18:45 on modular  [Seed = 262379028]
   -------------------------------------


>> 10!
   ^
User error: bad syntax

>> ;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:18:58 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"
10!
20!;


Output: Magma V2.10-22    Thu Jul  8 2004 01:18:56 on modular  [Seed = 128687721]
   -------------------------------------


>> 10!
   ^
User error: bad syntax

>> 20!;
      ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:19:28 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"
10!
20!
Pi

Output: Magma V2.10-22    Thu Jul  8 2004 01:19:26 on modular  [Seed = 1841427485]
   -------------------------------------


>> 10!
   ^
User error: bad syntax

>> 20!
     ^
Runtime error in '!': Illegal coercion

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:19:43 2004

Input: Pi

Output: Magma V2.10-22    Thu Jul  8 2004 01:19:40 on modular  [Seed = 1707736103]
   -------------------------------------

Intrinsic 'Pi'

Signatures:

    (<FldRe> R) -> FldReElt
    (<FldCom> R) -> FldReElt
    (<FldPr> R) -> FldPrElt

        Create pi to the precision of R as a real number.

    (<FldPr> R, <RngIntElt> p) -> FldPrElt

        Create pi to the precision p as an element of R.



Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:19:56 2004

Input: Pi;

Output: Magma V2.10-22    Thu Jul  8 2004 01:19:53 on modular  [Seed = 1927211813]
   -------------------------------------

Intrinsic 'Pi'

Signatures:

    (<FldRe> R) -> FldReElt
    (<FldCom> R) -> FldReElt
    (<FldPr> R) -> FldPrElt

        Create pi to the precision of R as a real number.

    (<FldPr> R, <RngIntElt> p) -> FldPrElt

        Create pi to the precision p as an element of R.



Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:20:19 2004

Input: 100!

Output: Magma V2.10-22    Thu Jul  8 2004 01:20:16 on modular  [Seed = 2919380752]
   -------------------------------------


>> 100!;
       ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:20:28 2004

Input: 100!;

Output: Magma V2.10-22    Thu Jul  8 2004 01:20:25 on modular  [Seed = 2785689361]
   -------------------------------------


>> 100!;;
       ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:20:56 2004

Input: 2^100;

Output: Magma V2.10-22    Thu Jul  8 2004 01:20:53 on modular  [Seed = 3188860709]
   -------------------------------------

1267650600228229401496703205376

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Jul  8 01:21:20 2004

Input: 2^100;

Output: Magma V2.10-22    Thu Jul  8 2004 01:21:17 on modular  [Seed = 2217221479]
   -------------------------------------

1267650600228229401496703205376

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:52:56 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 = x^2 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:52:54 on modular  [Seed = 4116272365]
   -------------------------------------


>> C := Curve(A2, y^2 = x^2 + 3);
             ^
Runtime error in 'Curve': Bad argument types
Argument types given: Aff, RelElt

>> Genus(C);;
         ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:53:17 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^2 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:53:14 on modular  [Seed = 3412552367]
   -------------------------------------

0

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:53:26 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^5 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:53:23 on modular  [Seed = 3278856889]
   -------------------------------------

2

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:53:33 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^3 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:53:31 on modular  [Seed = 3682040494]
   -------------------------------------

1

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:53:40 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^4 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:53:38 on modular  [Seed = 3548344991]
   -------------------------------------

1

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:53:48 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^6 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:53:45 on modular  [Seed = 713460588]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:53:55 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^7 + 3);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:53:53 on modular  [Seed = 579765116]
   -------------------------------------

3

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:54:08 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C := Curve(A2, y^2 - x^7 + 1);
Genus(C);

Output: Magma V2.10-22    Thu Jul  8 2004 01:54:05 on modular  [Seed = 982948712]
   -------------------------------------

3

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:55:25 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C1 := Curve(A2, y^2 - x^5 + 1);
C2 := Curve(A2, y^2 - x^6 + 1);
C3 := Curve(A2, y^2 - x^7 + 1);
C4 := Curve(A2, y^2 - x^8 + 1);
C5 := Curve(A2, y^2 - x^9 + 1);
C6 := Curve(A2, y^2 - x^10 + 1);
C7 := Curve(A2, y^2 - x^11 + 1);
C8 := Curve(A2, y^2 - x^12 + 1);
Genus(C1);
Genus(C2);
Genus(C3);
Genus(C4);
Genus(C5);
Genus(C6);
Genus(C7);
Genus(C8);

Output: Magma V2.10-22    Thu Jul  8 2004 01:55:22 on modular  [Seed = 849253335]
   -------------------------------------

2
2
3
3
4
4
5
5

Total time: 2.579 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:55:59 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C1 := Curve(A2, y^2 - x^13 + 1);
C2 := Curve(A2, y^2 - x^14 + 1);
C3 := Curve(A2, y^2 - x^15 + 1);
C4 := Curve(A2, y^2 - x^16 + 1);
C5 := Curve(A2, y^2 - x^17 + 1);
C6 := Curve(A2, y^2 - x^18 + 1);
C7 := Curve(A2, y^2 - x^19 + 1);
C8 := Curve(A2, y^2 - x^20 + 1);
Genus(C1);
Genus(C2);
Genus(C3);
Genus(C4);
Genus(C5);
Genus(C6);
Genus(C7);
Genus(C8);

Output: Magma V2.10-22    Thu Jul  8 2004 01:55:56 on modular  [Seed = 178695113]
   -------------------------------------

6
6
7
7
8
8
9
9

Total time: 2.549 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:56:16 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C1 := Curve(A2, y^2 - x^21 + 1);
C2 := Curve(A2, y^2 - x^22 + 1);
C3 := Curve(A2, y^2 - x^23 + 1);
C4 := Curve(A2, y^2 - x^24 + 1);
C5 := Curve(A2, y^2 - x^25 + 1);
C6 := Curve(A2, y^2 - x^26 + 1);
C7 := Curve(A2, y^2 - x^27 + 1);
C8 := Curve(A2, y^2 - x^28 + 1);
Genus(C1);
Genus(C2);
Genus(C3);
Genus(C4);
Genus(C5);
Genus(C6);
Genus(C7);
Genus(C8);

Output: Magma V2.10-22    Thu Jul  8 2004 01:56:14 on modular  [Seed = 44999635]
   -------------------------------------

10
10
11
11
12
12
13
13

Total time: 2.569 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:57:38 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C1 := Curve(A2, y^2 - x^21 + 3x 1);
C2 := Curve(A2, y^2 - x^22 + x^20 + x^11 + 1);
C3 := Curve(A2, y^2 - x^23 + 1);
C4 := Curve(A2, y^2 - x^24 + 1);
C5 := Curve(A2, y^2 - x^25 + 1);
C6 := Curve(A2, y^2 - x^26 + 1);
C7 := Curve(A2, y^2 - x^27 + 1);
C8 := Curve(A2, y^2 - x^28 + 1);
Genus(C1);
Genus(C2);
Genus(C3);
Genus(C4);
Genus(C5);
Genus(C6);
Genus(C7);
Genus(C8);

Output: Magma V2.10-22    Thu Jul  8 2004 01:57:36 on modular  [Seed = 414497383]
   -------------------------------------


>> C1 := Curve(A2, y^2 - x^21 + 3x 1);
                                 ^
User error: bad syntax

>> Genus(C1);
         ^
User error: Identifier 'C1' has not been declared or assigned
10
11
11
12
12
13
13

Total time: 2.539 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:57:52 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C1 := Curve(A2, y^2 - x^21 + 3x + 1);
C2 := Curve(A2, y^2 - x^22 + x^20 + x^11 + 1);
C3 := Curve(A2, y^2 - x^23 + 1);
C4 := Curve(A2, y^2 - x^24 + 1);
C5 := Curve(A2, y^2 - x^25 + 1);
C6 := Curve(A2, y^2 - x^26 + 1);
C7 := Curve(A2, y^2 - x^27 + 1);
C8 := Curve(A2, y^2 - x^28 + 1);
Genus(C1);
Genus(C2);
Genus(C3);
Genus(C4);
Genus(C5);
Genus(C6);
Genus(C7);
Genus(C8);

Output: Magma V2.10-22    Thu Jul  8 2004 01:57:49 on modular  [Seed = 280801890]
   -------------------------------------


>> C1 := Curve(A2, y^2 - x^21 + 3x + 1);
                                 ^
User error: bad syntax

>> Genus(C1);
         ^
User error: Identifier 'C1' has not been declared or assigned
10
11
11
12
12
13
13

Total time: 2.549 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host adsl-68-75-173-39.dsl.emhril.ameritech.net. (68.75.173.39)
Time: Thu Jul  8 01:58:03 2004

Input: A2<x, y> := AffineSpace(Rationals(), 2);
C1 := Curve(A2, y^2 - x^21 + 3*x + 1);
C2 := Curve(A2, y^2 - x^22 + x^20 + x^11 + 1);
C3 := Curve(A2, y^2 - x^23 + 1);
C4 := Curve(A2, y^2 - x^24 + 1);
C5 := Curve(A2, y^2 - x^25 + 1);
C6 := Curve(A2, y^2 - x^26 + 1);
C7 := Curve(A2, y^2 - x^27 + 1);
C8 := Curve(A2, y^2 - x^28 + 1);
Genus(C1);
Genus(C2);
Genus(C3);
Genus(C4);
Genus(C5);
Genus(C6);
Genus(C7);
Genus(C8);

Output: Magma V2.10-22    Thu Jul  8 2004 01:58:00 on modular  [Seed = 1757727279]
   -------------------------------------

10
10
11
11
12
12
13
13

Total time: 2.549 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host dhcp187-185.harvard.edu. (128.103.187.185)
Time: Thu Jul  8 13:55:06 2004

Input: function inc(X, B)
   assert Type(X) eq SeqEnum;
   assert Type(B) eq RngIntElt;
   if X eq [] then
      return [];
   end if;
   X[#X] +:= 1;
   if X[#X] eq B then
      Y := inc([X[i] : i in [1..#X-1]], B);
      return Y cat [0];
   end if;
   return X;
end function;

Output: Magma V2.10-22    Thu Jul  8 2004 13:55:03 on modular  [Seed = 2043982648]
   -------------------------------------


Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host dhcp187-185.harvard.edu. (128.103.187.185)
Time: Thu Jul  8 13:55:34 2004

Input: function inc(X, B)
   assert Type(X) eq SeqEnum;
   assert Type(B) eq RngIntElt;
   if X eq [] then
      return [];
   end if;
   X[#X] +:= 1;
   if X[#X] eq B then
      Y := inc([X[i] : i in [1..#X-1]], B);
      return Y cat [0];
   end if;
   return X;
end function;

intrinsic curves(K::FldNum, B::RngIntElt) -> SeqEnum
{}
   K<a> := K;
   L := [];
   n := Degree(K);
   OK := MaximalOrder(K);
   A4 := [0 : i in [1..n]];
   A6 := [0 : i in [1..n]];
   s := OK![-B : i in [1..n]];
   for i in [1..B^n] do
      a4 := K!(OK!A4 + s);  A4 := inc(A4,2*B);
      for j in [1..B^n] do
         a6 := K!(OK!A6 + s);  A6 := inc(A6,2*B);         
         if IsEllipticCurve([a4,a6]) then
            Append(~L, EllipticCurve([a4,a6]));
         end if;
      end for;
   end for;
   return L;
end intrinsic;

function test(D1, D2, a);
assert Type(D1) eq SeqEnum;
assert Type(D2) eq SeqEnum;
assert #D1 ge #D2;
A:=#D2;
if A gt a then
 for l in [a..A-1] do
  if D2[A] eq D2[l] then
   if IsIsomorphic(D1[A], D2[l]) eq true then
    return “bad”;
   else
    test(D1, D2, l+1);
   end if;
  end if;
 end for;
else 
 return “good”;
end if;
end function;

procedure List(K, m)
	M := K!m;
	curves(K, M);
	L2 := [];
	J := [];
	J2 := [];
	for i in [1..#L]
		Append (~J, jInvariant(L[i]));
		if test(L, J, 1) eq “good” then
		 Append(~L2, L[i]);
		 Append(~J2, J[i]);
		end if;
	end for;
	return L2;
	return J2;
end procedure;

Output: Magma V2.10-22    Thu Jul  8 2004 13:55:31 on modular  [Seed = 1841342408]
   -------------------------------------


>> intrinsic curves(K::FldNum, B::RngIntElt) -> SeqEnum
   ^
User error: Illegal intrinsic

>>     return ^Óbad^Ô;
              ^
User error: Unknown character (ascii value -109)

>>    else
      ^
User error: bad syntax

>>     test(D1, D2, l+1);
            ^
User error: Identifier 'D1' has not been declared or assigned

>>    end if;
      ^
User error: bad syntax

>>   end if;
     ^
User error: bad syntax

>>  end for;
    ^
User error: bad syntax

>> else 
   ^
User error: bad syntax

>>  return ^Ógood^Ô;
           ^
User error: Unknown character (ascii value -109)

>> end if;
   ^
User error: bad syntax

>> end function;
   ^
User error: bad syntax

>>                 Append (~J, jInvariant(L[i]));
                   ^
User error: bad syntax

>>                 if test(L, J, 1) eq ^Ógood^Ô then
                                       ^
User error: Unknown character (ascii value -109)

>>                  Append(~L2, L[i]);
                                ^
User error: Identifier 'L' has not been declared or assigned

>>                  Append(~J2, J[i]);
                                ^
User error: Identifier 'J' has not been declared or assigned

>>                 end if;
                   ^
User error: bad syntax

>>         end for;
           ^
User error: bad syntax

>>         return L2;
           ^
User error: A 'return' can only be used inside a procedure or function

>>         return J2;
           ^
User error: A 'return' can only be used inside a procedure or function

>> end procedure;;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:53:16 2004

Input: a:=233;
m:=1;
for i := 1 to a-1 do

x:= i*i*2;

if a mod x eq m do

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:53:13 on modular  [Seed = 1049865821]
   -------------------------------------


>> if a mod x eq m do
                   ^
User error: bad syntax

>> print(i);
         ^
User error: Identifier 'i' has not been declared or assigned

>> print(x);
         ^
User error: Identifier 'x' has not been declared or assigned

>> end if;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:53:28 2004

Input: a:=233;
m:=1;
for i := 1 to a-1 do

x:= i*i*2;

if a mod x eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:53:26 on modular  [Seed = 916170346]
   -------------------------------------

1
2
2
8

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:54:22 2004

Input: a:=233;
m:=1;
for i := 1 to a-1 do

x:= i*i*2;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:54:20 on modular  [Seed = 663402369]
   -------------------------------------

74
10952
159
50562

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:55:41 2004

Input: a:=233;
m:=74;
for i := 1 to a-1 do

x:= i*i*2;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:55:38 on modular  [Seed = 531795919]
   -------------------------------------

81
13122
152
46208

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:56:41 2004

Input: a:=233;
m:=159;
for i := 1 to a-1 do

x:= i*i*2;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:56:39 on modular  [Seed = 347702537]
   -------------------------------------

14
392
219
95922

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:57:58 2004

Input: a:=233;
m:=159;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:57:55 on modular  [Seed = 228629572]
   -------------------------------------

25
625
208
43264

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:58:48 2004

Input: a:=233;
m:=74;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:58:46 on modular  [Seed = 2060970982]
   -------------------------------------

105
11025
128
16384

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:59:21 2004

Input: a:=233;
m:=105;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:59:19 on modular  [Seed = 1893589389]
   -------------------------------------

13
338
220
96800

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 18:59:56 2004

Input: a:=233;
m:=128;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 18:59:53 on modular  [Seed = 1757804987]
   -------------------------------------

8
128
225
101250

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:00:19 2004

Input: a:=233;
m:=25;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:00:17 on modular  [Seed = 1476052332]
   -------------------------------------

96
18432
137
37538

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:00:39 2004

Input: a:=233;
m:=208;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:00:37 on modular  [Seed = 1123012717]
   -------------------------------------

77
11858
156
48672

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:28:03 2004

Input: a:=47;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:28:00 on modular  [Seed = 2670855973]
   -------------------------------------

20
800
27
1458

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:28:31 2004

Input: a:=47;
m:=20;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:28:29 on modular  [Seed = 2537164592]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:28:51 2004

Input: a:=47;
m:=27;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:28:49 on modular  [Seed = 2184124937]
   -------------------------------------

15
450
32
2048

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:29:35 2004

Input: a:=47;
m:=15;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:29:33 on modular  [Seed = 4200030749]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:29:52 2004

Input: a:=47;
m:=32;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:29:49 on modular  [Seed = 4066339366]
   -------------------------------------

4
32
43
3698

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:47:15 2004

Input: a:=23;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:47:12 on modular  [Seed = 3564718574]
   -------------------------------------

9
162
14
392

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 19:48:57 2004

Input: a:=47;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 19:48:55 on modular  [Seed = 3428929937]
   -------------------------------------

20
800
27
1458

Total time: 2.540 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:07:47 2004

Input: a:=1103;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:07:44 on modular  [Seed = 2685210491]
   -------------------------------------

161
51842
942
1774728

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:09:21 2004

Input: a:=1103;
m:=162;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:09:18 on modular  [Seed = 2654154395]
   -------------------------------------

411
168921
692
478864

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:10:01 2004

Input: a:=1103;
m:=942;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:09:58 on modular  [Seed = 2520458955]
   -------------------------------------

128
16384
975
950625

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:11:25 2004

Input: a:=1103;
m:=411;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:11:23 on modular  [Seed = 2384674318]
   -------------------------------------

384
294912
719
1033922

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:12:31 2004

Input: a:=1103;
m:=692;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:12:28 on modular  [Seed = 2234004802]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:17:14 2004

Input: a:=1103;
m:=975;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:17:11 on modular  [Seed = 4049355741]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 21:28:08 2004

Input: a:=1103;
m:=128;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 21:28:05 on modular  [Seed = 3378806103]
   -------------------------------------

8
128
1095
2398050

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (150.55.87.56)
Time: Thu Jul  8 22:01:06 2004

Input: ContinuedFraction(49/125);

Output: Magma V2.10-22    Thu Jul  8 2004 22:01:04 on modular  [Seed = 128629595]
   -------------------------------------

[ 0, 2, 1, 1, 4, 2, 2 ]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (150.55.87.56)
Time: Thu Jul  8 22:03:37 2004

Input: BestApproximation(49/125,10);


Output: Magma V2.10-22    Thu Jul  8 2004 22:03:34 on modular  [Seed = 2027275442]
   -------------------------------------

2/5

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (150.55.87.56)
Time: Thu Jul  8 22:04:52 2004

Input: Convergents(ContinuedFraction(49/125));

Output: Magma V2.10-22    Thu Jul  8 2004 22:04:50 on modular  [Seed = 1893584142]
   -------------------------------------

[ 49  20]
[125  51]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (150.55.87.56)
Time: Thu Jul  8 22:10:44 2004

Input: A:=ContinuedFraction(49/125);
#A;

Output: Magma V2.10-22    Thu Jul  8 2004 22:10:41 on modular  [Seed = 1542907334]
   -------------------------------------

7

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:14:38 2004

Input: a:=223;
m:=128;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:14:35 on modular  [Seed = 1289876475]
   -------------------------------------

8
128
215
92450

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:14:53 2004

Input: a:=223;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:14:51 on modular  [Seed = 1156185059]
   -------------------------------------

104
21632
119
28322

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:15:08 2004

Input: a:=223;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:15:06 on modular  [Seed = 3155231530]
   -------------------------------------

104
119

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:15:43 2004

Input: a:=223;
m:=104;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:15:41 on modular  [Seed = 3021540165]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:15:59 2004

Input: a:=223;
m:=119;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:15:56 on modular  [Seed = 2885751628]
   -------------------------------------

66
157

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:16:52 2004

Input: a:=223;
m:=66;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:16:49 on modular  [Seed = 2769020296]
   -------------------------------------

16
207

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:17:08 2004

Input: a:=223;
m:=157;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:17:06 on modular  [Seed = 2553731206]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:19:01 2004

Input: a:=431;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:18:58 on modular  [Seed = 2420035646]
   -------------------------------------

94
337

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:19:19 2004

Input: a:=431;
m:=94;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:19:16 on modular  [Seed = 2284242961]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:19:30 2004

Input: a:=431;
m:=337;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:19:27 on modular  [Seed = 2150547475]
   -------------------------------------

162
269

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:19:55 2004

Input: a:=431;
m:=162;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:19:53 on modular  [Seed = 4166432781]
   -------------------------------------

32
399

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:20:18 2004

Input: a:=431;
m:=289;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:20:15 on modular  [Seed = 3813516032]
   -------------------------------------

17
414

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:24:12 2004

Input: a:=223;
m:=16;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:24:10 on modular  [Seed = 3598227232]
   -------------------------------------

4
219

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:24:33 2004

Input: a:=223;
m:=207;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:24:30 on modular  [Seed = 3462434604]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:25:01 2004

Input: a:=223;
m:=4;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:24:58 on modular  [Seed = 3328739072]
   -------------------------------------

2
221

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:25:20 2004

Input: a:=223;
m:=219;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:25:17 on modular  [Seed = 1066499343]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:26:41 2004

Input: a:=223;
m:=221;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:26:38 on modular  [Seed = 915960917]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:37:57 2004

Input: a:=223;
m:=104;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:37:55 on modular  [Seed = 713322260]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:38:13 2004

Input: a:=223;
m:=104;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:38:10 on modular  [Seed = 481450291]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:38:33 2004

Input: a:=223;
m:=119;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:38:30 on modular  [Seed = 347754767]
   -------------------------------------

49
174

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:47:04 2004

Input: a:=1103;
m:=162;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:47:02 on modular  [Seed = 2060729697]
   -------------------------------------

9
1094

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:49:15 2004

Input: a:=1103;
m:=1;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:49:12 on modular  [Seed = 1927034342]
   -------------------------------------

161
942

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:49:35 2004

Input: a:=1103;
m:=161;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:49:32 on modular  [Seed = 1791241707]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:50:00 2004

Input: a:=1103;
m:=161;
mult:=1;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:49:58 on modular  [Seed = 1657546121]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Thu Jul  8 22:50:20 2004

Input: a:=1103;
m:=942;
mult:=2;
for i := 1 to a-1 do

x:= i*i*mult;

if x mod a eq m then

print(i);
//print(x);

end if;

end for;

Output: Magma V2.10-22    Thu Jul  8 2004 22:50:18 on modular  [Seed = 1525947789]
   -------------------------------------

349
754

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-66-229-239-105.we.client2.attbi.com. (66.229.239.105)
Time: Fri Jul  9 00:36:39 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Fri Jul  9 2004 00:36:37 on modular  [Seed = 3105347922]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 00:50:30 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Fri Jul  9 2004 00:50:14 on modular  [Seed = 2537157551]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 00:56:02 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]



Output: Magma V2.10-22    Fri Jul  9 2004 00:55:45 on modular  [Seed = 2234245354]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
      ^
User error: bad syntax

>> [0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
      ^
User error: bad syntax

>> [0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
      ^
User error: bad syntax

>> [0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
      ^
User error: bad syntax

>> [0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]
      ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 00:56:06 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]



Output: Magma V2.10-22    Fri Jul  9 2004 00:55:49 on modular  [Seed = 4250114198]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
      ^
User error: bad syntax

>> [0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
      ^
User error: bad syntax

>> [0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
      ^
User error: bad syntax

>> [0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
      ^
User error: bad syntax

>> [0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]
      ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:00:13 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
[1,0,    0,1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0]
[0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
[0,0,    0,1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0]
[0,0,    0,0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0]
[0,0,    1,0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]



Output: Magma V2.10-22    Fri Jul  9 2004 00:59:57 on modular  [Seed = 4082996608]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
   ^
Runtime error in '[]': Sequence element 0 not defined

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:02:56 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
K:=FiniteField(2);
C:=LinearCode<k,24 mit
[1,0,    0,1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0]
[0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
[0,0,    0,1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0]
[0,0,    0,0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0]
[0,0,    1,0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:02:40 on modular  [Seed = 3581653787]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> C:=LinearCode<k,24 mit
                      ^
User error: bad syntax

>> [0,0,    1,0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
                                                                  ^
User error: bad syntax

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:05:50 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
K:=FiniteField(2);
C:=LinearCode<k,24 |
[1,0,    0,1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0]
[0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
[0,0,    0,1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0]
[0,0,    0,0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0]
[0,0,    1,0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:05:34 on modular  [Seed = 3278742627]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> C:=LinearCode<k,24 |
                 ^
User error: Identifier 'k' has not been declared or assigned

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:06:28 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
K :=FiniteField(2);
C :=LinearCode<k,24 |
[1,0,    0,1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0]
[0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
[0,0,    0,1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0]
[0,0,    0,0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0]
[0,0,    1,0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:06:11 on modular  [Seed = 982801862]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> C :=LinearCode<k,24 |
                  ^
User error: Identifier 'k' has not been declared or assigned

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:06:44 2004

Input: SimplexCode(5);
[31,5,16] Linear Code over GF(2)
Generator matrix:
K :=FiniteField(2);
C :=LinearCode<K,24 |
[1,0,    0,1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0]
[0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
[0,0,    0,1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0]
[0,0,    0,0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0]
[0,0,    1,0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:06:27 on modular  [Seed = 832526045]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31,5,16] Linear Code over GF(2)
             ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [0,1,    0,0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
   ^
Runtime error in '[]': Sequence element 0 not defined

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:18:44 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode<K,24 |
[1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0]
[0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
[0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0]
[0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0]
[0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:18:28 on modular  [Seed = 381189261]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1]
   ^
Runtime error in '[]': Sequence element 0 not defined

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:25:03 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode<K,24 |
[ 1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0 ]
[ 0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1 ]
[ 0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0 ]
[ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ]
[ 0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1 ]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:24:47 on modular  [Seed = 2010717015]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [ 0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1 ]
   ^
Runtime error in '[]': Sequence element 0 not defined

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:40:10 2004

Input: SimplexCode(5);
[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0]
[0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1]
[0,0,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,1,0,0]
[0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,1,0]
[0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,1]

K := FiniteField(2);
C := LinearCode<K,24 |
[ 1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0 ],
[ 0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1 ],
[ 0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0 ],
[ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
[ 0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1 ]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:39:54 on modular  [Seed = 1559376841]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31, 5, 16] Linear Code over GF(2)
               ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> K := FiniteField(2);
   ^
User error: bad syntax

>> C := LinearCode<K,24 |
                   ^
User error: Identifier 'K' has not been declared or assigned

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:42:44 2004

Input: SimplexCode(5);
[31, 5, 16] Linear Code over GF(2)
Generator matrix:

K := FiniteField(2);
C := LinearCode<K,24 |
[ 1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0 ],
[ 0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1 ],
[ 0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0 ],
[ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
[ 0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1 ]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:42:27 on modular  [Seed = 1089351740]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31, 5, 16] Linear Code over GF(2)
               ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
                                                                    ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt]

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 01:43:18 2004

Input: SimplexCode(5);
[31, 5, 16] Code over GF(2)
Generator matrix:

K := FiniteField(2);
C := LinearCode<K,24 |
[ 1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0 ],
[ 0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1 ],
[ 0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0 ],
[ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
[ 0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1 ]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 01:43:02 on modular  [Seed = 3088500961]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31, 5, 16] Code over GF(2)
               ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
                                                                    ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt]

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:08:42 2004

Input: SimplexCode(5);
[31, 5, 16] Code over GF(2)
Generator matrix:

K := FiniteField(2);
C := LinearCode<K,24 |
[ 1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0 ],
[ 0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1 ],
[ 0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0 ],
[ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
[ 0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1 ]>;
CoveringRadius(C);



Output: Magma V2.10-22    Fri Jul  9 2004 02:08:25 on modular  [Seed = 2384525544]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> [31, 5, 16] Code over GF(2)
               ^
User error: bad syntax

>> Generator matrix:
             ^
User error: bad syntax

>> [ 0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0 ].
                                                                    ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt]

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:26:13 2004

Input: SimplexCode(5);

Output: Magma V2.10-22    Fri Jul  9 2004 02:25:57 on modular  [Seed = 3763247786]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:31:46 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode<K,24 |
[1,0,0,    1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0],
[0,1,0,    0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1],
[0,0,1,    1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0],
[0,0,0,    0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0],
[0,0,0,    0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Fri Jul  9 2004 02:31:30 on modular  [Seed = 3581652520]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> C := LinearCode<K,24 |
                  ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:32:32 2004

Input: SimplexCode(5);
K := FiniteField(2);
C5p := LinearCode<K,24 |
[1,0,0,    1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0],
[0,1,0,    0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1],
[0,0,1,    1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0],
[0,0,0,    0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0],
[0,0,0,    0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C5p);


Output: Magma V2.10-22    Fri Jul  9 2004 02:32:16 on modular  [Seed = 3445863938]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> C5p := LinearCode<K,24 |
                    ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C5p);
                  ^
User error: Identifier 'C5p' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:34:21 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode <K,24 |
[1,0,0,    1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0],
[0,1,0,    0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1],
[0,0,1,    1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0],
[0,0,0,    0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0],
[0,0,0,    0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Fri Jul  9 2004 02:34:05 on modular  [Seed = 3312171431]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> C := LinearCode <K,24 |
                   ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:35:08 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode <K,24 |
[1,0,0,    1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0],
[0,1,0,    0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1],
[0,0,1,    1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0],
[0,0,0,    0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0],
[0,0,0,    0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Fri Jul  9 2004 02:34:52 on modular  [Seed = 1874924450]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> C := LinearCode <K,24 |
                   ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:35:31 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode <K,24 |
[1,0,0,    1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0],
[0,1,0,    0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1],
[0,0,1,    1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0],
[0,0,0,    0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0],
[0,0,0,    0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Fri Jul  9 2004 02:35:14 on modular  [Seed = 2144404380]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]

>> C := LinearCode <K,24 |
                   ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> CoveringRadius(C);
                  ^
User error: Identifier 'C' has not been declared or assigned

Total time: 2.809 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host reached (203.255.11.125)
Time: Fri Jul  9 02:37:13 2004

Input: SimplexCode(5);
K := FiniteField(2);
C := LinearCode <K,24 |
[1,0,      1,0,  1,0,1,1,0,  1,1,1,1,1,0,    1,1,0,1,1,1,0,1,0],
[0,1,      0,1,  0,1,0,1,1,  0,1,1,1,1,1,    0,1,1,0,1,1,1,0,1],
[0,0,      1,0,  1,0,0,1,1,  1,1,0,0,0,1,    1,1,1,0,1,0,1,0,0],
[0,0,      0,1,  1,1,0,0,1,  1,1,1,0,0,0,    0,1,1,1,0,1,0,1,0],
[0,0,      0,0,  0,1,1,0,0,  1,1,1,1,0,0,    1,0,1,1,1,0,1,0,1]>;
CoveringRadius(C);


Output: Magma V2.10-22    Fri Jul  9 2004 02:36:55 on modular  [Seed = 161969231]
   -------------------------------------

[31, 5, 16] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0]
[0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1]
[0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0]
[0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0]
[0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1]
10

Total time: 3.629 seconds, Total memory usage: 3.87MB


************** MAGMA *****************
Host i20fw2.iaks.uni-karlsruhe.de. (141.3.32.129)
Time: Fri Jul  9 04:14:16 2004

Input: phi(1242323432)

Output: Magma V2.10-22    Fri Jul  9 2004 04:14:14 on modular  [Seed = 1442531009]
   -------------------------------------


>> phi(1242323432);
   ^
User error: Identifier 'phi' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host i20fw2.iaks.uni-karlsruhe.de. (141.3.32.129)
Time: Fri Jul  9 04:15:01 2004

Input: factor(1000)

Output: Magma V2.10-22    Fri Jul  9 2004 04:14:59 on modular  [Seed = 1576225052]
   -------------------------------------


>> factor(1000);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host i20fw2.iaks.uni-karlsruhe.de. (141.3.32.129)
Time: Fri Jul  9 04:18:25 2004

Input: EulerPhi(1024)

Output: Magma V2.10-22    Fri Jul  9 2004 04:18:22 on modular  [Seed = 1774681573]
   -------------------------------------

512

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 222-152-94-17.jetstream.xtra.co.nz. (222.152.94.17)
Time: Fri Jul  9 08:21:15 2004

Input: o18740-522923

Output: Magma V2.10-22    Fri Jul  9 2004 08:21:10 on modular  [Seed = 2919261020]
   -------------------------------------


>> o18740-522923;
   ^
User error: Identifier 'o18740' has not been declared or assigned

Total time: 2.739 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 222-152-94-17.jetstream.xtra.co.nz. (222.152.94.17)
Time: Fri Jul  9 08:21:42 2004

Input: 018740-522923

Output: Magma V2.10-22    Fri Jul  9 2004 08:21:39 on modular  [Seed = 3071900192]
   -------------------------------------

-504183

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 222-152-94-17.jetstream.xtra.co.nz. (222.152.94.17)
Time: Fri Jul  9 08:23:19 2004

Input: 018740-522923-584934-248763-851764-312835-112786-131665

Output: Magma V2.10-22    Fri Jul  9 2004 08:23:16 on modular  [Seed = 3121902794]
   -------------------------------------

-2746930

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 222-152-94-17.jetstream.xtra.co.nz. (222.152.94.17)
Time: Fri Jul  9 08:23:35 2004

Input: 018740-522923-584934-248763-851764-312835-112786-131665

Output: Magma V2.10-22    Fri Jul  9 2004 08:23:32 on modular  [Seed = 1139641666]
   -------------------------------------

-2746930

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9535C15.dip.t-dialin.net. (217.83.92.21)
Time: Fri Jul  9 08:27:35 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a^2*b^2)^6>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 08:27:30 on modular  [Seed = 1442552354]
   -------------------------------------

0

Total time: 4.709 seconds, Total memory usage: 20.04MB


************** MAGMA *****************
Host pD9535C15.dip.t-dialin.net. (217.83.92.21)
Time: Fri Jul  9 08:28:25 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a^2*b^2)^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 08:28:19 on modular  [Seed = 1576243835]
   -------------------------------------

0

Total time: 5.469 seconds, Total memory usage: 20.04MB


************** MAGMA *****************
Host pD9535C15.dip.t-dialin.net. (217.83.92.21)
Time: Fri Jul  9 08:28:32 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a^2*b^2)^1>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 08:28:29 on modular  [Seed = 1707846221]
   -------------------------------------

12

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9535C15.dip.t-dialin.net. (217.83.92.21)
Time: Fri Jul  9 08:29:01 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^12,(a^2*b^2)^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 08:28:55 on modular  [Seed = 1841537711]
   -------------------------------------

0

Total time: 5.949 seconds, Total memory usage: 20.04MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:03:19 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:03:16 on modular  [Seed = 999681258]
   -------------------------------------

8

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:03:34 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:03:29 on modular  [Seed = 3278705703]
   -------------------------------------

0

Total time: 4.619 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:03:47 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:03:45 on modular  [Seed = 3412401215]
   -------------------------------------

18

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:03:57 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^3,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:03:54 on modular  [Seed = 3548185644]
   -------------------------------------

72

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:06:51 2004

Input: F<a,b>:=Group<a,b|a*b=b*a,a^2,b^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:06:48 on modular  [Seed = 3665036023]
   -------------------------------------

4

Total time: 2.669 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:07:24 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2,b^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:07:21 on modular  [Seed = 3980604705]
   -------------------------------------

6

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:07:40 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:07:37 on modular  [Seed = 4099550248]
   -------------------------------------

1

Total time: 2.709 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:07:54 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2,b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:07:51 on modular  [Seed = 4266665500]
   -------------------------------------

6

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:08:21 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:08:18 on modular  [Seed = 2150520839]
   -------------------------------------

24

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:08:33 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3,b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:08:30 on modular  [Seed = 2284212227]
   -------------------------------------

1

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:08:48 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3,b^5>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:08:46 on modular  [Seed = 2420000779]
   -------------------------------------

1

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:09:33 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4,b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:09:31 on modular  [Seed = 2553692630]
   -------------------------------------

96

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:09:47 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4,b^5>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:09:44 on modular  [Seed = 2685303293]
   -------------------------------------

1

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:09:53 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4,b^6>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:09:50 on modular  [Seed = 2818994675]
   -------------------------------------

6

Total time: 2.669 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:10:34 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^5,b^5>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:10:31 on modular  [Seed = 2954783154]
   -------------------------------------

600

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:11:05 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:11:03 on modular  [Seed = 3088474522]
   -------------------------------------

8

Total time: 2.659 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:11:24 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:11:22 on modular  [Seed = 1106221181]
   -------------------------------------

18

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:11:39 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:11:36 on modular  [Seed = 1459130264]
   -------------------------------------

32

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:12:05 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^5>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:12:02 on modular  [Seed = 1592821690]
   -------------------------------------

50

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:12:23 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^2,b^6>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:12:20 on modular  [Seed = 1724432276]
   -------------------------------------

72

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:13:09 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^3,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:13:07 on modular  [Seed = 1858123723]
   -------------------------------------

72

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:13:24 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^3,b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:13:21 on modular  [Seed = 1993912257]
   -------------------------------------

288

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:13:38 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^3,b^5>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:13:36 on modular  [Seed = 2127602744]
   -------------------------------------

1800

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:13:56 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^3,b^6>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:13:50 on modular  [Seed = 111729742]
   -------------------------------------

0

Total time: 5.929 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:17:39 2004

Input: F<a,b>:=Group<a,b|a*b*a*b=b*a*b*a,a^4,b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:17:34 on modular  [Seed = 381209790]
   -------------------------------------

0

Total time: 5.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:18:09 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a=b*a*b*a*b,a^2,b^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:18:06 on modular  [Seed = 481478484]
   -------------------------------------

10

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:18:18 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a=b*a*b*a*b,a^3,b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:18:16 on modular  [Seed = 613089146]
   -------------------------------------

360

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:18:25 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a=b*a*b*a*b,a^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:18:22 on modular  [Seed = 746780532]
   -------------------------------------

360

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95351C3.dip.t-dialin.net. (217.83.81.195)
Time: Fri Jul  9 09:18:47 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a=b*a*b*a*b,a^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 09:18:42 on modular  [Seed = 882569024]
   -------------------------------------

0

Total time: 4.789 seconds, Total memory usage: 17.99MB


************** MAGMA *****************
Host p50825AE8.dip.t-dialin.net. (80.130.90.232)
Time: Fri Jul  9 10:22:49 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a=b*a*b*a*b,a^6>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 10:22:44 on modular  [Seed = 2835825627]
   -------------------------------------

0

Total time: 4.339 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host asd-n-1877f.adsl.wanadoo.nl. (81.69.165.127)
Time: Fri Jul  9 10:44:27 2004

Input: 3^2/4^3

Output: Magma V2.10-22    Fri Jul  9 2004 10:44:24 on modular  [Seed = 11464463]
   -------------------------------------

9/64

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50825AE8.dip.t-dialin.net. (80.130.90.232)
Time: Fri Jul  9 11:31:11 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4=b^4>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 11:31:06 on modular  [Seed = 3681886630]
   -------------------------------------

Infinity

Total time: 5.169 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825AE8.dip.t-dialin.net. (80.130.90.232)
Time: Fri Jul  9 11:31:51 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3=b^3>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 11:31:46 on modular  [Seed = 3796637895]
   -------------------------------------

0

Total time: 4.659 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825AE8.dip.t-dialin.net. (80.130.90.232)
Time: Fri Jul  9 11:32:03 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2=b^2>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 11:31:58 on modular  [Seed = 3930329283]
   -------------------------------------

0

Total time: 4.409 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p50825AE8.dip.t-dialin.net. (80.130.90.232)
Time: Fri Jul  9 11:32:28 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6=b^6>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 11:32:19 on modular  [Seed = 4066117686]
   -------------------------------------

0

Total time: 8.899 seconds, Total memory usage: 18.24MB


************** MAGMA *****************
Host p50825AE8.dip.t-dialin.net. (80.130.90.232)
Time: Fri Jul  9 11:32:45 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^8=b^8>;
Order(F);

Output: Magma V2.10-22    Fri Jul  9 2004 11:32:38 on modular  [Seed = 4199809067]
   -------------------------------------

0

Total time: 6.939 seconds, Total memory usage: 20.04MB


************** MAGMA *****************
Host 3(NXDOMAIN) (24.66.94.142)
Time: Fri Jul  9 17:33:51 2004

Input: (x*x*x)+x+1=3.4

Output: Magma V2.10-22    Fri Jul  9 2004 17:33:48 on modular  [Seed = 629828181]
   -------------------------------------


>> (x*x*x)+x+1=3.4;
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-14-71-44.client.comcast.net. (24.14.71.44)
Time: Fri Jul  9 20:44:27 2004

Input: Generators(Gamma(5));

Output: Magma V2.10-22    Fri Jul  9 2004 20:44:25 on modular  [Seed = 3278682213]
   -------------------------------------


>> Generators(Gamma(5));;
             ^
Runtime error in 'Generators': Bad argument types
Argument types given: FldPrElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-14-71-44.client.comcast.net. (24.14.71.44)
Time: Fri Jul  9 20:46:58 2004

Input: Generators(CongruenceSubgroup(5));

Output: Magma V2.10-22    Fri Jul  9 2004 20:46:54 on modular  [Seed = 3598297831]
   -------------------------------------

[
    [11 -5]
    [20 -9],

    [-1  0]
    [ 5 -1],

    [ 16  -5]
    [ 45 -14],

    [ 41 -25]
    [105 -64],

    [ 31 -20]
    [ 45 -29],

    [ 6 -5]
    [ 5 -4],

    [ 71 -15]
    [ 90 -19],

    [ 21  -5]
    [ 80 -19],

    [ 66 -25]
    [235 -89],

    [  76  -55]
    [ 275 -199],

    [ 61 -45]
    [ 80 -59]
]

Total time: 3.549 seconds, Total memory usage: 2.60MB


************** MAGMA *****************
Host c-24-14-71-44.client.comcast.net. (24.14.71.44)
Time: Fri Jul  9 20:50:01 2004

Input: Generators(CongruenceSubgroup(3));

Output: Magma V2.10-22    Fri Jul  9 2004 20:49:58 on modular  [Seed = 3997275031]
   -------------------------------------

[
    [-1  0]
    [ 3 -1],

    [ 7 -3]
    [12 -5],

    [ 4 -3]
    [ 3 -2]
]

Total time: 2.619 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:08:13 2004

Input: a:=131;
m:=1;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

endif 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:08:10 on modular  [Seed = 2284292541]
   -------------------------------------


>> end for;;
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:08:24 2004

Input: a:=131;
m:=1;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

endif; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:08:22 on modular  [Seed = 2150596937]
   -------------------------------------


>> end for;;
       ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:08:35 2004

Input: a:=131;
m:=1;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:08:33 on modular  [Seed = 2553780550]
   -------------------------------------

1
130

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:09:12 2004

Input: a:=131;
m:=1;
mult:=2;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:09:10 on modular  [Seed = 2420085097]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:09:34 2004

Input: a:=131;
m:=130;
mult:=2;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:09:32 on modular  [Seed = 2819074347]
   -------------------------------------

14
117

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:09:55 2004

Input: a:=131;
m:=14;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:09:52 on modular  [Seed = 2685378831]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:10:17 2004

Input: a:=131;
m:=117;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:10:14 on modular  [Seed = 3088562433]
   -------------------------------------

36
95

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:10:35 2004

Input: a:=131;
m:=36;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:10:32 on modular  [Seed = 2954867447]
   -------------------------------------

6
125

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:11:12 2004

Input: a:=131;
m:=95;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:11:09 on modular  [Seed = 1475892522]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:11:32 2004

Input: a:=131;
m:=6;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:11:30 on modular  [Seed = 1089421906]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:11:58 2004

Input: a:=131;
m:=125;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:11:55 on modular  [Seed = 1223117379]
   -------------------------------------

16
115

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:13:17 2004

Input: a:=131;
m:=16;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:13:15 on modular  [Seed = 1893692043]
   -------------------------------------

4
127

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:13:48 2004

Input: a:=131;
m:=115;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:13:46 on modular  [Seed = 2027387618]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:14:32 2004

Input: a:=131;
m:=4;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:14:29 on modular  [Seed = 1624203973]
   -------------------------------------

2
129

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:15:06 2004

Input: a:=131;
m:=127;
mult:=1;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:15:03 on modular  [Seed = 1808033836]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:15:50 2004

Input: a:=131;
m:=2;
mult:=2;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:15:47 on modular  [Seed = 331091968]
   -------------------------------------

1
130

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul  9 21:16:19 2004

Input: a:=131;
m:=129;
mult:=2;
for i:= 1 to a-1 do

x := i * i * mult;

if x mod a eq m then

print(i);

end if; 

end for;

Output: Magma V2.10-22    Fri Jul  9 2004 21:16:17 on modular  [Seed = 464787498]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 09:52:15 2004

Input: (a+b)^2

Output: Magma V2.10-22    Sat Jul 10 2004 09:52:10 on modular  [Seed = 280995054]
   -------------------------------------


>> (a+b)^2;
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.610 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 09:52:34 2004

Input: (3+4)^2

Output: Magma V2.10-22    Sat Jul 10 2004 09:52:31 on modular  [Seed = 414690547]
   -------------------------------------

49

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 09:52:48 2004

Input: (3+4)!

Output: Magma V2.10-22    Sat Jul 10 2004 09:52:45 on modular  [Seed = 11515097]
   -------------------------------------


>> (3+4)!;
         ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 09:53:05 2004

Input: fact(3+4)

Output: Magma V2.10-22    Sat Jul 10 2004 09:53:02 on modular  [Seed = 178634432]
   -------------------------------------


>> fact(3+4);
   ^
User error: Identifier 'fact' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 09:53:17 2004

Input: 1:10

Output: Magma V2.10-22    Sat Jul 10 2004 09:53:15 on modular  [Seed = 4066199117]
   -------------------------------------


>> 1:10;
     ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 09:54:51 2004

Input:  // HEC (Genus 3, Characteristic 2) Random Generator
 /////////////////////////////////////////////////////
RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
  +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
end procedure;

 // Triple XGCD
 //////////////////
TripleXGCD:=function(a,b,c);
 d1,t11,t12:=XGCD(a,b);
 d2,t21,t22:=XGCD(b,c);
 d,t1,t2:=XGCD(d1,d2);
 s1:=t1*t11;
 s2:=t1*t12+t2*t21;
 s3:=t2*t22;
 return d,s1,s2,s3;
end function;

 // Step 1 Function
 //////////////////////
Step1:=function(u1,u2,v1,v2);
 a:=v1+v2;
 d,s1,s2,s3:=TripleXGCD(u1,u2,a);
 return d,s1,s2,s3;
end function;

 // Step 2 Function
 /////////////////////////
Step2:=function(u1,u2,d);
 b1:=u1*u2;
 b2:=d^2;
 u3:=b1 div b2;
 return u3;
end function;

 // Step 3 Function
 ///////////////////////
Step3:=function(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 c1:=s1*u1*v2;
 c2:=s2*u2*v1;
 c3:=s3*(v1*v2+f);
 //
 r:=c1+c2+c3;
 c4:=r div d;
 v3:=c4 mod u3;
 return v3;
end function;

 // Step 4 Function (Genus g=3)
 ////////////////////////////////
Step4:=function(f,h,u3,v3);
 j:=Degree(u3);
 while j ge 4 do
  k:=f-h*v3-v3^2;
  l:=-h-v3;
  u3:=k div u3;
  v3:=l mod u3;
  j:=Degree(u3);
 end while;
 return u3,v3;
end function;

 // Cantor Function
 //////////////////////////
Cantor:=function(f,h,u1,u2,v1,v2);
 d,s1,s2,s3:=Step1(u1,u2,v1,v2);
 u3:=Step2(u1,u2,d);
 v3:=Step3(f,u1,u2,u3,v1,v2,d,s1,s2,s3);
 u3,v3:=Step4(f,h,u3,v3);
 return u3,v3;
end function;
// TEST1
RandomHEC_3_2();


Output: Magma V2.10-22    Sat Jul 10 2004 09:54:48 on modular  [Seed = 4199894950]
   -------------------------------------

true Hyperelliptic Curve defined by y^2 + (x^3 + x^2 + x + 1)*y = x^7 + x^6 + 
    x^5 + x^4 + x^3 + x^2 + 1 over GF(2)

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:05:09 2004

Input: Input: a:=9;
n:=1;
while 3^n div a eq 0 do
n:=n+1;
end while;
print(n);

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:05:41 2004

Input: a:=9;
n:=1;
while 3^n div a eq 0 do
n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:05:39 on modular  [Seed = 2936019048]
   -------------------------------------

2

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:06:30 2004

Input: 3^2 div a


Output: Magma V2.10-22    Sat Jul 10 2004 10:06:28 on modular  [Seed = 2537037831]
   -------------------------------------


>> 3^2 div a
           ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:07:05 2004

Input: 3^2 div 9


Output: Magma V2.10-22    Sat Jul 10 2004 10:07:03 on modular  [Seed = 2570461674]
   -------------------------------------

1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:09:31 2004

Input: a:=9;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:09:29 on modular  [Seed = 2200714094]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:09:45 2004

Input: a:=8;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:09:43 on modular  [Seed = 2334405464]
   -------------------------------------

2

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:09:59 2004

Input: a:=7;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:09:56 on modular  [Seed = 2110965180]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:10:09 2004

Input: a:=5;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:10:07 on modular  [Seed = 1724505772]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:10:59 2004

Input: a:=81;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:10:56 on modular  [Seed = 1858197227]
   -------------------------------------

4

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:11:25 2004

Input: a:=82;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:11:22 on modular  [Seed = 1459220265]
   -------------------------------------

5

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:11:37 2004

Input: a:=83;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:11:34 on modular  [Seed = 1509351482]
   -------------------------------------

5

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E4D8D.dip0.t-ipconnect.de. (80.142.77.141)
Time: Sat Jul 10 10:11:49 2004

Input: a:=81;
n:=1;
while 3^n div a eq 0 do
 n:=n+1;
end while;
print(n);

Output: Magma V2.10-22    Sat Jul 10 2004 10:11:47 on modular  [Seed = 1106180119]
   -------------------------------------

4

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 14:56:38 2004

Input: FractionalPart(2.34);

Output: Magma V2.10-22    Sat Jul 10 2004 14:56:35 on modular  [Seed = 1725308402]
   -------------------------------------


>> FractionalPart(2.34);;
   ^
User error: Identifier 'FractionalPart' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 15:07:30 2004

Input: e - Truncate(e);

Output: Magma V2.10-22    Sat Jul 10 2004 15:07:27 on modular  [Seed = 1207384415]
   -------------------------------------


>> e - Truncate(e);;
   ^
User error: Identifier 'e' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 15:14:20 2004

Input: Truncate(2.34);

Output: Magma V2.10-22    Sat Jul 10 2004 15:14:18 on modular  [Seed = 1291602993]
   -------------------------------------

2

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 15:14:40 2004

Input: Truncate(E);

Output: Magma V2.10-22    Sat Jul 10 2004 15:14:37 on modular  [Seed = 881079390]
   -------------------------------------


>> Truncate(E);;
            ^
User error: Identifier 'E' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 19:55:08 2004

Input: CoxeterDiagram(RootSystem(A4));

Output: WARNING: MAGMA command contains unsafe command 'system', so it will not be executed.

************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 19:56:13 2004

Input: CoxeterDiagram(RootSystem("A4"));

Output: WARNING: MAGMA command contains unsafe command 'system', so it will not be executed.

************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sat Jul 10 19:56:39 2004

Input: RootSystem("H4E6");

Output: WARNING: MAGMA command contains unsafe command 'system', so it will not be executed.

************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:28:23 2004

Input: B:=BraidGroup(4);

Output: Magma V2.10-22    Sat Jul 10 2004 21:28:21 on modular  [Seed = 3647540758]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:28:42 2004

Input: B<a,b,c>:=BraidGroup(4);
a;

Output: Magma V2.10-22    Sat Jul 10 2004 21:28:40 on modular  [Seed = 3512796771]
   -------------------------------------

a
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:29:01 2004

Input: B<a,b,c>:=BraidGroup(4);
a^-1;

Output: Magma V2.10-22    Sat Jul 10 2004 21:28:59 on modular  [Seed = 3380158056]
   -------------------------------------

c^-1 * b^-1 * c^-1 * a^-1 * b^-1 * c^-1 * b * a * c * b * c
<Artin, -1, [
    (1, 3, 2, 4)
], 0>

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:29:48 2004

Input: B<a,b,c>:=BraidGroup(4);
a*b*c*a*b*a;

Output: Magma V2.10-22    Sat Jul 10 2004 21:29:45 on modular  [Seed = 3245414834]
   -------------------------------------

a * b * c * a * b * a
<Artin, 0, [
    (1, 2),
    (2, 3),
    (3, 4),
    (1, 2),
    (2, 3),
    (1, 2)
], 0>

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:30:05 2004

Input: B<a,b,c>:=BraidGroup(3);
a*b*c*a*b*a;

Output: Magma V2.10-22    Sat Jul 10 2004 21:30:02 on modular  [Seed = 3188614878]
   -------------------------------------


>> B<a,b,c>:=BraidGroup(3);
    ^
Runtime error in 'AssignNames': Too many names given for this object

>> a*b*c*a*b*a;;
   ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:30:30 2004

Input: B<a,b,c>:=BraidGroup(4);
NormalForm(a*b*c*a*b*a);

Output: Magma V2.10-22    Sat Jul 10 2004 21:30:27 on modular  [Seed = 3053874943]
   -------------------------------------

c * b * a * c * b * c
<Artin, 1, [], 0>

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:31:16 2004

Input: B<a,b,c>:=BraidGroup(4);
NormalForm(a*b*c*a*b*a);
if not (a eq b) 1; end if

Output: Magma V2.10-22    Sat Jul 10 2004 21:31:13 on modular  [Seed = 2921232053]
   -------------------------------------

c * b * a * c * b * c
<Artin, 1, [], 0>

>> if not (a eq b) 1; end if;
                   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:31:26 2004

Input: B<a,b,c>:=BraidGroup(4);
NormalForm(a*b*c*a*b*a);
if not (a eq b) '1'; end if

Output: Magma V2.10-22    Sat Jul 10 2004 21:31:23 on modular  [Seed = 2786492087]
   -------------------------------------

c * b * a * c * b * c
<Artin, 1, [], 0>

>> if not (a eq b) '1'; end if;
                   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:31:35 2004

Input: B<a,b,c>:=BraidGroup(4);
NormalForm(a*b*c*a*b*a);
if not (a eq b) then 'fail'; end if

Output: Magma V2.10-22    Sat Jul 10 2004 21:31:33 on modular  [Seed = 2670675856]
   -------------------------------------

c * b * a * c * b * c
<Artin, 1, [], 0>

>> if not (a eq b) then 'fail'; end if;
                        ^
User error: Identifier 'fail' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sat Jul 10 21:31:46 2004

Input: B<a,b,c>:=BraidGroup(4);
NormalForm(a*b*c*a*b*a);
if not (a eq b) then "fail"; end if

Output: Magma V2.10-22    Sat Jul 10 2004 21:31:44 on modular  [Seed = 2535935853]
   -------------------------------------

c * b * a * c * b * c
<Artin, 1, [], 0>
fail

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:03:04 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=2)
a := s4*s3^-1;
b := s4^-1*s3;
ab := D^-1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s3;
if not (a*b eq ab) then "Failure on m1"; end if


Output: Magma V2.10-22    Sun Jul 11 2004 01:03:01 on modular  [Seed = 2685414105]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:03:17 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=2)
a := s4*s3^-1;
b := s4^-1*s3;
ab := D^-1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s3;
if not (a*b eq ab) then "Failure on m1"; end if

// Test case m2 (len=3)
a := s4^-1*s2*s2;
b := s4^-1*s2^-1*s3;
ab := D^-2*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3;
if not (a*b eq ab) then "Failure on m2"; end if

// Test case m3 (len=4)
a := s2*s3*s1^-1*s3^-1;
b := s2^-1*s4*s1*s3^-1;
ab := D^-1*s1*s2*s3*s1*s2*s3*s1*s1*s1*s4;
if not (a*b eq ab) then "Failure on m3"; end if

"Done.";



Output: Magma V2.10-22    Sun Jul 11 2004 01:03:15 on modular  [Seed = 2552763127]
   -------------------------------------


>> a := s4^-1*s2*s2;
   ^
User error: bad syntax

>> a := s2*s3*s1^-1*s3^-1;
   ^
User error: bad syntax

>> "Done.";
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:03:55 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=2)
a := s4*s3^-1;
b := s4^-1*s3;
ab := D^-1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s3;
if not (a*b eq ab) then "Failure on m1"; end if

// Test case m2 (len=3)

a := s4^-1*s2*s2;
b := s4^-1*s2^-1*s3;
ab := D^-2*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3;
if not (a*b eq ab) then "Failure on m2"; end if

// Test case m3 (len=4)

a := s2*s3*s1^-1*s3^-1;
b := s2^-1*s4*s1*s3^-1;
ab := D^-1*s1*s2*s3*s1*s2*s3*s1*s1*s1*s4;
if not (a*b eq ab) then "Failure on m3"; end if

"Done.";



Output: Magma V2.10-22    Sun Jul 11 2004 01:03:52 on modular  [Seed = 2418023124]
   -------------------------------------


>> a := s4^-1*s2*s2;
   ^
User error: bad syntax

>> a := s2*s3*s1^-1*s3^-1;
   ^
User error: bad syntax

>> "Done.";
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:04:15 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=2)
a := s4*s3^-1;
b := s4^-1*s3;
ab := D^-1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s3;
if not (a*b eq ab) then "Failure on m1"; end if;

// Test case m2 (len=3)

a := s4^-1*s2*s2;
b := s4^-1*s2^-1*s3;
ab := D^-2*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3;
if not (a*b eq ab) then "Failure on m2"; end if

// Test case m3 (len=4)

a := s2*s3*s1^-1*s3^-1;
b := s2^-1*s4*s1*s3^-1;
ab := D^-1*s1*s2*s3*s1*s2*s3*s1*s1*s1*s4;
if not (a*b eq ab) then "Failure on m3"; end if

"Done.";



Output: Magma V2.10-22    Sun Jul 11 2004 01:04:13 on modular  [Seed = 2285372089]
   -------------------------------------


>> a := s2*s3*s1^-1*s3^-1;
   ^
User error: bad syntax

>> "Done.";
   ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:05:18 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=2)
a := s2*s2;
b := s1^-1*s3^-1;
ab := D^-1*s1*s2*s3*s4*s2*s2*s2*s3*s1*s2;
if not (a*b eq ab) then "Failure on m1"; end if;

// Test case m2 (len=3)
a := s3*s4^-1*s1;
b := s2^-1*s4^-1*s3;
ab := D^-2*s1*s2*s3*s4*s1*s2*s3*s1*s1*s2*s4*s2*s3*s1*s2*s2*s4*s3*s2*s1;
if not (a*b eq ab) then "Failure on m2"; end if;

// Test case m3 (len=4)
a := s3^-1*s2*s1*s4^-1;
b := s1*s4^-1*s2^-1*s4;
ab := D^-1*s1*s3*s4*s2*s3*s1*s2*s2*s2*s1;
if not (a*b eq ab) then "Failure on m3"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:05:16 on modular  [Seed = 2167475057]
   -------------------------------------

Done.

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:05:41 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=100)
a := s1^-1*s4*s4^-1*s1*s4*s3^-1*s2^-1*s1^-1*s3*s2*s1*s4*s2*s1^-1*s3^-1*s4^-1*s3^-1*s4^-1*s2^-1*s1^-1*s3^-1*s4^-1*s1*s2*s3*s2*s1*s3*s2*s4^-1*s3^-1*s2*s3*s1*s3^-1*s2^-1*s1*s2*s3^-1*s1*s1*s3*s1^-1*s4^-1*s2^-1*s3^-1*s1^-1*s3*s4^-1*s1*s3^-1*s1^-1*s4^-1*s4^-1*s3^-1*s2*s3^-1*s4*s4*s3*s2^-1*s3^-1*s1^-1*s2^-1*s1*s1^-1*s2*s1*s2*s1*s3*s1*s3^-1*s3^-1*s3^-1*s1*s2*s3*s4*s1^-1*s4^-1*s2*s2*s1^-1*s4*s1^-1*s4*s3^-1*s4*s1^-1*s4^-1*s2*s3*s1*s4^-1*s4^-1*s2^-1*s1*s3^-1*s1;
b := s1^-1*s2*s2*s4^-1*s1*s4*s3*s1*s2*s1^-1*s4^-1*s1*s4*s3*s2^-1*s4*s1*s2^-1*s2^-1*s3^-1*s1^-1*s3^-1*s1^-1*s1^-1*s1^-1*s2^-1*s2^-1*s4*s3*s1*s4^-1*s3^-1*s2*s4*s1^-1*s4^-1*s3*s4^-1*s4^-1*s2^-1*s3^-1*s2*s3*s1^-1*s3^-1*s4*s3*s2^-1*s2^-1*s2^-1*s4^-1*s4^-1*s3*s2*s4*s4*s3^-1*s3^-1*s2^-1*s3*s3*s2*s1^-1*s2^-1*s1*s1*s1*s3^-1*s4^-1*s4^-1*s2^-1*s3*s2*s1^-1*s2^-1*s4^-1*s2*s2*s3^-1*s1*s4^-1*s2^-1*s3^-1*s3^-1*s4^-1*s3*s4*s4*s3^-1*s2*s1*s4^-1*s4^-1*s3*s2^-1*s1*s3^-1*s1^-1*s2^-1*s3;
ab := D^-28*s1*s2*s3*s4*s1*s3*s3*s4*s2*s3*s2*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s2*s1*s1*s4*s1*s2*s3*s2*s1*s1*s2*s4*s2*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s1*s3*s2*s2*s3*s4*s1*s3*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s2*s1*s1*s2*s3*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s1*s2*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s1*s2*s3*s1*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s4*s3*s3*s4*s2*s2*s1*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s2*s3*s1*s1*s2*s3*s2*s3*s2*s1*s3*s4*s2*s2*s2*s3*s4*s3*s3*s4*s2*s3*s2*s2*s3*s4*s4*s3*s2*s2*s1;
if not (a*b eq ab) then "Failure on m1"; end if;

// Test case m2 (len=101)
a := s1*s3^-1*s2^-1*s1*s3^-1*s4^-1*s3*s1*s3*s2*s4*s2^-1*s1^-1*s1^-1*s4*s2*s3*s1*s3^-1*s2^-1*s2^-1*s3*s1*s2^-1*s1^-1*s4*s1^-1*s3*s2^-1*s3^-1*s2^-1*s1*s4*s2^-1*s3^-1*s1^-1*s4^-1*s2^-1*s4^-1*s1*s2*s3^-1*s1*s4*s2^-1*s3^-1*s2*s1^-1*s3^-1*s1*s4^-1*s1*s2^-1*s2^-1*s3^-1*s2*s3^-1*s2*s4*s4*s2*s2*s1^-1*s2^-1*s4*s3^-1*s2^-1*s2^-1*s4^-1*s1^-1*s2*s1^-1*s3^-1*s4^-1*s3^-1*s3^-1*s1^-1*s2^-1*s4*s3^-1*s4*s1^-1*s1^-1*s3^-1*s4^-1*s4^-1*s1^-1*s2*s4*s2*s4*s4*s1*s3*s1*s4^-1*s2^-1*s1*s2^-1*s2^-1*s3^-1;
b := s3*s4*s2^-1*s4^-1*s3*s3*s2^-1*s4*s3*s2*s4*s4*s2^-1*s4^-1*s1*s3^-1*s2^-1*s1^-1*s3^-1*s4^-1*s1^-1*s2^-1*s3^-1*s4*s4*s1^-1*s4*s1^-1*s3^-1*s4^-1*s1*s3*s2*s3^-1*s2*s1*s2^-1*s4*s1^-1*s1*s4^-1*s1^-1*s3^-1*s4*s2^-1*s1^-1*s4*s1^-1*s3^-1*s2*s1*s3*s2*s2*s3^-1*s4*s3*s4^-1*s2*s4^-1*s1^-1*s2^-1*s3^-1*s3^-1*s2^-1*s2^-1*s4^-1*s2^-1*s3*s2*s3^-1*s3^-1*s4*s1^-1*s1^-1*s4^-1*s1^-1*s3*s3*s3*s3*s3*s1^-1*s4^-1*s3^-1*s1^-1*s1^-1*s3^-1*s1^-1*s3*s1^-1*s2^-1*s1^-1*s4*s2^-1*s3^-1*s3^-1*s3^-1*s2*s1^-1*s3;
ab := D^-38*s1*s2*s4*s1*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s2*s3*s1*s1*s1*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s2*s3*s1*s1*s1*s3*s1*s2*s3*s2*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s2*s1*s3*s4*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s2*s2*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s2*s2*s1*s1*s3*s1*s2*s3*s2*s2*s3*s4*s1*s3*s1*s1*s1*s3*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s2*s1*s3*s4*s2*s2*s1*s3*s3*s2*s1*s4*s3*s2*s2*s3*s1*s3*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s3*s4*s2*s3*s1*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3;
if not (a*b eq ab) then "Failure on m2"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:05:38 on modular  [Seed = 2026435239]
   -------------------------------------

Done.

Total time: 2.759 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:05:59 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=100)
a := s1^-1*s4*s4^-1*s1*s4*s3^-1*s2^-1*s1^-1*s3*s2*s1*s4*s2*s1^-1*s3^-1*s4^-1*s3^-1*s4^-1*s2^-1*s1^-1*s3^-1*s4^-1*s1*s2*s3*s2*s1*s3*s2*s4^-1*s3^-1*s2*s3*s1*s3^-1*s2^-1*s1*s2*s3^-1*s1*s1*s3*s1^-1*s4^-1*s2^-1*s3^-1*s1^-1*s3*s4^-1*s1*s3^-1*s1^-1*s4^-1*s4^-1*s3^-1*s2*s3^-1*s4*s4*s3*s2^-1*s3^-1*s1^-1*s2^-1*s1*s1^-1*s2*s1*s2*s1*s3*s1*s3^-1*s3^-1*s3^-1*s1*s2*s3*s4*s1^-1*s4^-1*s2*s2*s1^-1*s4*s1^-1*s4*s3^-1*s4*s1^-1*s4^-1*s2*s3*s1*s4^-1*s4^-1*s2^-1*s1*s3^-1*s1;
b := s1^-1*s2*s2*s4^-1*s1*s4*s3*s1*s2*s1^-1*s4^-1*s1*s4*s3*s2^-1*s4*s1*s2^-1*s2^-1*s3^-1*s1^-1*s3^-1*s1^-1*s1^-1*s1^-1*s2^-1*s2^-1*s4*s3*s1*s4^-1*s3^-1*s2*s4*s1^-1*s4^-1*s3*s4^-1*s4^-1*s2^-1*s3^-1*s2*s3*s1^-1*s3^-1*s4*s3*s2^-1*s2^-1*s2^-1*s4^-1*s4^-1*s3*s2*s4*s4*s3^-1*s3^-1*s2^-1*s3*s3*s2*s1^-1*s2^-1*s1*s1*s1*s3^-1*s4^-1*s4^-1*s2^-1*s3*s2*s1^-1*s2^-1*s4^-1*s2*s2*s3^-1*s1*s4^-1*s2^-1*s3^-1*s3^-1*s4^-1*s3*s4*s4*s3^-1*s2*s1*s4^-1*s4^-1*s3*s2^-1*s1*s3^-1*s1^-1*s2^-1*s3;
ab := D^-28*s1*s2*s3*s4*s1*s3*s3*s4*s2*s3*s2*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s2*s1*s1*s4*s1*s2*s3*s2*s1*s1*s2*s4*s2*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s1*s3*s2*s2*s3*s4*s1*s3*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s2*s1*s1*s2*s3*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s1*s2*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s1*s2*s3*s1*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s4*s3*s3*s4*s2*s2*s1*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s2*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s2*s3*s1*s1*s2*s3*s2*s3*s2*s1*s3*s4*s2*s2*s2*s3*s4*s3*s3*s4*s2*s3*s2*s2*s3*s4*s4*s3*s2*s2*s1;
if not (a*b eq ab) then "Failure on m1"; end if;

// Test case m2 (len=101)
a := s1*s3^-1*s2^-1*s1*s3^-1*s4^-1*s3*s1*s3*s2*s4*s2^-1*s1^-1*s1^-1*s4*s2*s3*s1*s3^-1*s2^-1*s2^-1*s3*s1*s2^-1*s1^-1*s4*s1^-1*s3*s2^-1*s3^-1*s2^-1*s1*s4*s2^-1*s3^-1*s1^-1*s4^-1*s2^-1*s4^-1*s1*s2*s3^-1*s1*s4*s2^-1*s3^-1*s2*s1^-1*s3^-1*s1*s4^-1*s1*s2^-1*s2^-1*s3^-1*s2*s3^-1*s2*s4*s4*s2*s2*s1^-1*s2^-1*s4*s3^-1*s2^-1*s2^-1*s4^-1*s1^-1*s2*s1^-1*s3^-1*s4^-1*s3^-1*s3^-1*s1^-1*s2^-1*s4*s3^-1*s4*s1^-1*s1^-1*s3^-1*s4^-1*s4^-1*s1^-1*s2*s4*s2*s4*s4*s1*s3*s1*s4^-1*s2^-1*s1*s2^-1*s2^-1*s3^-1;
b := s3*s4*s2^-1*s4^-1*s3*s3*s2^-1*s4*s3*s2*s4*s4*s2^-1*s4^-1*s1*s3^-1*s2^-1*s1^-1*s3^-1*s4^-1*s1^-1*s2^-1*s3^-1*s4*s4*s1^-1*s4*s1^-1*s3^-1*s4^-1*s1*s3*s2*s3^-1*s2*s1*s2^-1*s4*s1^-1*s1*s4^-1*s1^-1*s3^-1*s4*s2^-1*s1^-1*s4*s1^-1*s3^-1*s2*s1*s3*s2*s2*s3^-1*s4*s3*s4^-1*s2*s4^-1*s1^-1*s2^-1*s3^-1*s3^-1*s2^-1*s2^-1*s4^-1*s2^-1*s3*s2*s3^-1*s3^-1*s4*s1^-1*s1^-1*s4^-1*s1^-1*s3*s3*s3*s3*s3*s1^-1*s4^-1*s3^-1*s1^-1*s1^-1*s3^-1*s1^-1*s3*s1^-1*s2^-1*s1^-1*s4*s2^-1*s3^-1*s3^-1*s3^-1*s2*s1^-1*s3;
ab := D^-38*s1*s2*s4*s1*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s2*s3*s1*s1*s1*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s2*s3*s1*s1*s1*s3*s1*s2*s3*s2*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s2*s1*s3*s4*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s2*s2*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s2*s2*s1*s1*s3*s1*s2*s3*s2*s2*s3*s4*s1*s3*s1*s1*s1*s3*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s2*s1*s3*s4*s2*s2*s1*s3*s3*s2*s1*s4*s3*s2*s2*s3*s1*s3*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s3*s4*s2*s3*s1*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3;
if not (a*b eq ab) then "Failure on m2"; end if;

"Done 2.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:05:56 on modular  [Seed = 1891695289]
   -------------------------------------

Done 2.

Total time: 2.759 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:06:32 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case h1 (len=100)
conj := D^-29*s1*s1*s1*s2*s3*s1*s2*s4*s3*s2*s1*s1*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s2*s1*s2*s3*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s2*s1*s2*s3*s1*s2*s4*s2*s1*s3*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s1*s2*s4*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s4*s3*s2*s1*s1*s4*s4*s2*s3*s1*s2*s2*s1*s4*s1*s2*s2*s1*s3*s2*s2*s1*s2*s3*s1*s2*s3*s4*s2*s2*s1*s3*s2*s1*s2*s3*s3*s2*s1*s1*s4*s2*s1*s2*s3*s1*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s1*s2*s4*s1*s3*s3*s4*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s2*s4*s2*s1*s3*s2*s2*s3*s4*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s3*s2*s4*s2*s2*s4*s2*s3*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s3*s2*s4*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s4*s2*s3*s2*s1*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s2;
x2 := s3*s4*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s2*s4*s2*s1*s3*s2*s2*s3*s4*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s3*s2*s4*s2*s2*s4*s2*s3*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s3*s2*s4*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s4*s2*s3*s2*s1*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s2;
a2 := s3;
if not (x2*conj*x2^-1 eq a2) then "Failure on h1"; end if;

// Test case h2 (len=101)
conj := D^-21*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s2*s1*s2*s3*s1*s3*s2*s4*s2*s3*s4*s3*s2*s2*s2*s2*s3*s1*s2*s4*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s3*s3*s1*s2*s3*s4*s2*s2*s2*s1*s4*s1*s2*s2*s3*s4*s3*s3*s4*s2*s2*s2*s4*s2*s1*s3*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s1*s2*s1*s4*s3*s1*s2*s3*s4*s3*s2*s1*s3*s2*s1*s4*s3*s3*s2*s4*s2*s3*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s2*s1*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s4*s2*s1*s1*s1*s3*s4*s3*s2*s1*s3*s4;
x2 := s3*s4*s3*s2*s1*s3*s2*s1*s4*s3*s3*s2*s4*s2*s3*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s2*s1*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s4*s2*s1*s1*s1*s3*s4*s3*s2*s1*s3*s4;
a2 := s2;
if not (x2*conj*x2^-1 eq a2) then "Failure on h2"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:06:29 on modular  [Seed = 1759044288]
   -------------------------------------

Done.

Total time: 2.669 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:06:52 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case h1 (len=100)
conj := D^-29*s1*s1*s1*s2*s3*s1*s2*s4*s3*s2*s1*s1*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s2*s1*s2*s3*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s2*s1*s2*s3*s1*s2*s4*s2*s1*s3*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s1*s2*s4*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s4*s3*s2*s1*s1*s4*s4*s2*s3*s1*s2*s2*s1*s4*s1*s2*s2*s1*s3*s2*s2*s1*s2*s3*s1*s2*s3*s4*s2*s2*s1*s3*s2*s1*s2*s3*s3*s2*s1*s1*s4*s2*s1*s2*s3*s1*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s1*s2*s4*s1*s3*s3*s4*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s2*s4*s2*s1*s3*s2*s2*s3*s4*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s3*s2*s4*s2*s2*s4*s2*s3*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s3*s2*s4*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s4*s2*s3*s2*s1*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s2;
x2 := s1* s3*s4*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s2*s4*s2*s1*s3*s2*s2*s3*s4*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s3*s2*s4*s2*s2*s4*s2*s3*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s4*s2*s3*s3*s2*s4*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s4*s2*s3*s2*s1*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s2;
a2 := s3;
if not (x2*conj*x2^-1 eq a2) then "Failure on h1"; end if;

// Test case h2 (len=101)
conj := D^-21*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s2*s1*s2*s3*s1*s3*s2*s4*s2*s3*s4*s3*s2*s2*s2*s2*s3*s1*s2*s4*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s3*s3*s1*s2*s3*s4*s2*s2*s2*s1*s4*s1*s2*s2*s3*s4*s3*s3*s4*s2*s2*s2*s4*s2*s1*s3*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s1*s2*s1*s4*s3*s1*s2*s3*s4*s3*s2*s1*s3*s2*s1*s4*s3*s3*s2*s4*s2*s3*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s2*s1*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s4*s2*s1*s1*s1*s3*s4*s3*s2*s1*s3*s4;
x2 := s3*s4*s3*s2*s1*s3*s2*s1*s4*s3*s3*s2*s4*s2*s3*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s2*s1*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s4*s2*s1*s1*s1*s3*s4*s3*s2*s1*s3*s4;
a2 := s2;
if not (x2*conj*x2^-1 eq a2) then "Failure on h2"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:06:49 on modular  [Seed = 1674832375]
   -------------------------------------

Done.

Total time: 2.669 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:08:05 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

if not (s1 eq s2) then "Failure on h2"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:08:03 on modular  [Seed = 1424285466]
   -------------------------------------

Failure on h2
Done.

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:08:41 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case h1 (len=100)
conj := D^-28*s1*s1*s4*s3*s2*s2*s1*s2*s3*s1*s3*s2*s1*s4*s3*s2*s2*s3*s4*s1*s2*s3*s3*s2*s1*s4*s3*s3*s4*s2*s3*s1*s2*s3*s4*s2*s4*s3*s2*s2*s1*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s2*s1*s4*s4*s1*s4*s3*s3*s3*s2*s1*s2*s3*s4*s4*s2*s3*s3*s2*s1*s4*s3*s2*s1*s2*s2*s2*s1*s3*s4*s2*s2*s1*s2*s3*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s2*s3*s4*s2*s3*s2*s1*s3*s3*s2*s1*s1*s2*s2*s1*s2*s4*s3*s1*s3*s4*s3*s2*s1*s1*s2*s2*s3*s1*s2*s4*s1*s3*s3*s2*s2*s1*s3*s2*s4*s2*s2*s4*s3*s2*s3*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s1*s1*s3*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s3*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s1*s1*s3*s3*s4*s2*s3*s2*s2*s3*s4*s3*s3*s4*s2*s1*s3*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2;
x2 := s3*s2*s2*s1*s3*s2*s4*s2*s2*s4*s3*s2*s3*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s1*s1*s3*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s3*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s1*s1*s3*s3*s4*s2*s3*s2*s2*s3*s4*s3*s3*s4*s2*s1*s3*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2;
a2 := s3;
if not (x2*conj*x2^-1 eq a2) then "Failure on h1"; end if;

// Test case h2 (len=101)
conj := D^-29*s1*s2*s3*s1*s2*s4*s3*s2*s1*s1*s3*s1*s2*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s4*s2*s3*s1*s2*s2*s1*s4*s3*s2*s1*s4*s3*s3*s3*s4*s2*s3*s1*s2*s2*s1*s3*s1*s3*s2*s1*s4*s3*s1*s2*s3*s3*s2*s1*s3*s4*s2*s3*s1*s2*s3*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s2*s1*s2*s3*s3*s2*s1*s1*s2*s1*s2*s3*s1*s2*s2*s1*s4*s3*s1*s2*s3*s4*s2*s2*s1*s3*s1*s2*s3*s4*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s1*s4*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s1*s3*s2*s1*s4*s2*s3*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s1*s1*s4*s3*s3*s3*s2*s1*s4*s4*s4*s4*s3*s2*s2*s1*s1*s3*s3*s2*s1*s1*s4*s3*s2*s4*s3*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s1*s3*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s4*s3*s2*s2*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s1*s3*s2*s2;
x2 := s3*s4*s2*s1*s3*s2*s1*s1*s4*s3*s3*s3*s2*s1*s4*s4*s4*s4*s3*s2*s2*s1*s1*s3*s3*s2*s1*s1*s4*s3*s2*s4*s3*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s1*s3*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s4*s3*s2*s2*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s1*s3*s2*s2;
a2 := s2;
if not (x2*conj*x2^-1 eq a2) then "Failure on h2"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:08:39 on modular  [Seed = 1291634534]
   -------------------------------------

Done.

Total time: 2.739 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:08:59 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case h1 (len=100)
conj := D^-28*s1*s1*s4*s3*s2*s2*s1*s2*s3*s1*s3*s2*s1*s4*s3*s2*s2*s3*s4*s1*s2*s3*s3*s2*s1*s4*s3*s3*s4*s2*s3*s1*s2*s3*s4*s2*s4*s3*s2*s2*s1*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s2*s1*s4*s4*s1*s4*s3*s3*s3*s2*s1*s2*s3*s4*s4*s2*s3*s3*s2*s1*s4*s3*s2*s1*s2*s2*s2*s1*s3*s4*s2*s2*s1*s2*s3*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s2*s3*s4*s2*s3*s2*s1*s3*s3*s2*s1*s1*s2*s2*s1*s2*s4*s3*s1*s3*s4*s3*s2*s1*s1*s2*s2*s3*s1*s2*s4*s1*s3*s3*s2*s2*s1*s3*s2*s4*s2*s2*s4*s3*s2*s3*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s1*s1*s3*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s3*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s1*s1*s3*s3*s4*s2*s3*s2*s2*s3*s4*s3*s3*s4*s2*s1*s3*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2;
x2 := s3*s2*s2*s1*s3*s2*s4*s2*s2*s4*s3*s2*s3*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s3*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s1*s1*s3*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s3*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s1*s1*s3*s3*s4*s2*s3*s2*s2*s3*s4*s3*s3*s4*s2*s1*s3*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2;
a2 := s3*s3;
if not (x2*conj*x2^-1 eq a2) then "Failure on h1"; end if;

// Test case h2 (len=101)
conj := D^-29*s1*s2*s3*s1*s2*s4*s3*s2*s1*s1*s3*s1*s2*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s4*s2*s3*s1*s2*s2*s1*s4*s3*s2*s1*s4*s3*s3*s3*s4*s2*s3*s1*s2*s2*s1*s3*s1*s3*s2*s1*s4*s3*s1*s2*s3*s3*s2*s1*s3*s4*s2*s3*s1*s2*s3*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s2*s1*s2*s3*s3*s2*s1*s1*s2*s1*s2*s3*s1*s2*s2*s1*s4*s3*s1*s2*s3*s4*s2*s2*s1*s3*s1*s2*s3*s4*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s1*s4*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s1*s3*s2*s1*s4*s2*s3*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s1*s1*s4*s3*s3*s3*s2*s1*s4*s4*s4*s4*s3*s2*s2*s1*s1*s3*s3*s2*s1*s1*s4*s3*s2*s4*s3*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s1*s3*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s4*s3*s2*s2*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s1*s3*s2*s2;
x2 := s3*s4*s2*s1*s3*s2*s1*s1*s4*s3*s3*s3*s2*s1*s4*s4*s4*s4*s3*s2*s2*s1*s1*s3*s3*s2*s1*s1*s4*s3*s2*s4*s3*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s1*s3*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s2*s1*s3*s4*s3*s2*s2*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s1*s3*s2*s2;
a2 := s2;
if not (x2*conj*x2^-1 eq a2) then "Failure on h2"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:08:56 on modular  [Seed = 1106365012]
   -------------------------------------

Failure on h1
Done.

Total time: 2.719 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:11:26 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case h1 (len=500)
// try again...
conj := D^-141*s1*s1*s2*s1*s1*s1*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s2*s1*s3*s2*s1*s1*s4*s3*s2*s3*s3*s4*s2*s1*s3*s2*s4*s3*s2*s1*s3*s2*s4*s3*s3*s3*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s1*s3*s2*s4*s3*s2*s2*s1*s3*s2*s1*s1*s4*s3*s2*s3*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s4*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s4*s3*s2*s1*s1*s1*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s1*s3*s2*s2*s1*s1*s3*s4*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s1*s1*s1*s3*s4*s2*s3*s4*s3*s2*s1*s1*s1*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s2*s3*s2*s2*s4*s2*s2*s3*s4*s3*s2*s2*s1*s1*s3*s4*s3*s2*s1*s3*s4*s3*s2*s1*s1*s2*s4*s3*s2*s3*s2*s1*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s1*s1*s4*s2*s2*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s3*s4*s3*s2*s1*s3*s4*s3*s2*s2*s1*s1*s3*s3*s2*s3*s3*s2*s1*s1*s2*s4*s2*s1*s3*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s2*s1*s3*s2*s1*s1*s1*s4*s3*s2*s2*s2*s1*s1*s3*s2*s3*s4*s2*s1*s3*s3*s2*s2*s1*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s3*s2*s1*s4*s3*s3*s2*s4*s2*s2*s4*s2*s2*s3*s4*s3*s3*s3*s3*s2*s4*s2*s2*s1*s3*s2*s4*s3*s2*s2*s1*s1*s1*s3*s3*s2*s1*s4*s3*s2*s4*s2*s1*s3*s2*s4*s3*s2*s2*s3*s2*s1*s1*s1*s3*s2*s3*s4*s2*s2*s1*s3*s2*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s3*s4*s2*s2*s1*s3*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s2*s1*s3*s2*s4*s2*s1*s1*s1*s1*s3*s3*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s3*s3*s3*s2*s2*s2*s1*s1*s3*s3*s2*s3*s4*s2*s2*s2*s1*s1*s3*s4*s3*s2*s1*s3*s4*s3*s3*s2*s4*s3*s2*s1*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s2*s1*s1*s1*s1*s3*s2*s1*s1*s2*s4*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s2*s1*s3*s2*s1*s1*s4*s2*s3*s4*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s2*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s1*s1*s3*s2*s1*s1*s3*s2*s3*s3*s2*s1*s1*s1*s3*s2*s3*s2*s1*s3*s2*s2*s1*s3*s3*s2*s2*s1*s1*s3*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s2*s3*s2*s1*s3*s2*s4*s2*s1*s1*s3*s4*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s2*s1*s3*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s2*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s1*s3*s3*s1*s2*s3*s3*s2*s2*s4*s2*s1*s3*s3*s2*s4*s1*s1*s1*s4*s3*s1*s2*s3*s4*s2*s3*s4*s1*s2*s3*s2*s1*s3*s2*s4*s1*s2*s3*s1*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s1*s2*s3*s1*s2*s3*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s4*s3*s1*s1*s2*s1*s1*s2*s3*s4*s1*s1*s2*s2*s3*s4*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s3*s4*s3*s3*s2*s4*s2*s2*s4*s3*s2*s3*s4*s2*s3*s4*s1*s2*s3*s2*s1*s3*s3*s2*s2*s3*s4*s1*s3*s2*s2*s3*s4*s3*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s2*s1*s2*s3*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s1*s3*s1*s2*s2*s1*s3*s2*s1*s2*s3*s1*s2*s3*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s4*s3*s1*s4*s4*s3*s3*s2*s4*s3*s1*s1*s1*s2*s3*s3*s4*s2*s2*s3*s4*s1*s1*s2*s3*s4*s2*s1*s3*s1*s1*s2*s3*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s3*s2*s1*s1*s4*s3*s1*s1*s2*s3*s4*s2*s2*s3*s1*s2*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s1*s3*s4*s3*s2*s1*s2*s3*s1*s4*s1*s3*s1*s1*s1*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s1*s2*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s1*s4*s1*s2*s2*s1*s3*s4*s3*s1*s2*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s3*s3*s3*s2*s2*s1*s3*s4*s3*s1*s2*s2*s1*s3*s4*s3*s2*s1*s2*s2*s3*s4*s3*s3*s2*s4*s2*s3*s1*s2*s4*s3*s2*s2*s1*s3*s2*s4*s3*s1*s1*s3*s4*s2*s1*s1*s2*s4*s3*s2*s3*s3*s4*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s2*s1*s1*s2*s2*s3*s1*s2*s2*s4*s2*s1*s3*s2*s2*s4*s3*s2*s2*s3*s1*s3*s4*s1*s2*s3*s1*s1*s2*s3*s4*s3*s2*s1*s3*s2*s4*s3*s2*s3*s4*s2*s3*s1*s1*s1*s3*s2*s4*s1*s2*s2*s4*s3*s2*s2*s3*s4*s1*s2*s2*s3*s1*s1*s4*s1*s3*s3*s2*s4*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s3*s2*s2*s3*s1*s1*s1*s3*s2*s1*s2*s2*s3*s1*s3*s2*s1*s1*s2*s4*s2*s3*s4*s3*s3*s2*s4*s1*s1*s1*s4*s1*s1*s4*s3*s2*s2*s2*s3*s1*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s1*s3*s1*s1*s3*s4*s1*s2*s3*s2*s2*s3*s4*s3*s2*s2*s1*s3*s4*s3*s1*s2*s3*s4*s2*s2*s1*s1*s3;
x2 := s1*s2*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s2*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s1*s3*s3*s1*s2*s3*s3*s2*s2*s4*s2*s1*s3*s3*s2*s4*s1*s1*s1*s4*s3*s1*s2*s3*s4*s2*s3*s4*s1*s2*s3*s2*s1*s3*s2*s4*s1*s2*s3*s1*s2*s3*s4*s3*s2*s2*s1*s3*s2*s4*s1*s2*s3*s1*s2*s3*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s4*s3*s1*s1*s2*s1*s1*s2*s3*s4*s1*s1*s2*s2*s3*s4*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s3*s4*s3*s3*s2*s4*s2*s2*s4*s3*s2*s3*s4*s2*s3*s4*s1*s2*s3*s2*s1*s3*s3*s2*s2*s3*s4*s1*s3*s2*s2*s3*s4*s3*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s2*s1*s2*s3*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s1*s3*s1*s2*s2*s1*s3*s2*s1*s2*s3*s1*s2*s3*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s3*s4*s3*s1*s4*s4*s3*s3*s2*s4*s3*s1*s1*s1*s2*s3*s3*s4*s2*s2*s3*s4*s1*s1*s2*s3*s4*s2*s1*s3*s1*s1*s2*s3*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s3*s4*s3*s2*s1*s1*s4*s3*s1*s1*s2*s3*s4*s2*s2*s3*s1*s2*s4*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s1*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s1*s3*s4*s3*s2*s1*s2*s3*s1*s4*s1*s3*s1*s1*s1*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s1*s2*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s1*s4*s1*s2*s2*s1*s3*s4*s3*s1*s2*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s3*s3*s3*s2*s2*s1*s3*s4*s3*s1*s2*s2*s1*s3*s4*s3*s2*s1*s2*s2*s3*s4*s3*s3*s2*s4*s2*s3*s1*s2*s4*s3*s2*s2*s1*s3*s2*s4*s3*s1*s1*s3*s4*s2*s1*s1*s2*s4*s3*s2*s3*s3*s4*s2*s1*s1*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s2*s1*s1*s2*s2*s3*s1*s2*s2*s4*s2*s1*s3*s2*s2*s4*s3*s2*s2*s3*s1*s3*s4*s1*s2*s3*s1*s1*s2*s3*s4*s3*s2*s1*s3*s2*s4*s3*s2*s3*s4*s2*s3*s1*s1*s1*s3*s2*s4*s1*s2*s2*s4*s3*s2*s2*s3*s4*s1*s2*s2*s3*s1*s1*s4*s1*s3*s3*s2*s4*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s3*s2*s2*s3*s1*s1*s1*s3*s2*s1*s2*s2*s3*s1*s3*s2*s1*s1*s2*s4*s2*s3*s4*s3*s3*s2*s4*s1*s1*s1*s4*s1*s1*s4*s3*s2*s2*s2*s3*s1*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s1*s3*s1*s1*s3*s4*s1*s2*s3*s2*s2*s3*s4*s3*s2*s2*s1*s3*s4*s3*s1*s2*s3*s4*s2*s2*s1*s1*s3;
a2 := s1;
if not (x2*conj*x2^-1 eq a2) then "Failure on h1"; end if;


Output: Magma V2.10-22    Sun Jul 11 2004 01:11:18 on modular  [Seed = 965325490]
   -------------------------------------


Total time: 7.829 seconds, Total memory usage: 3.01MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:12:18 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case h1 (len=250)
// try again...
conj := D^-83*s1*s2*s4*s3*s2*s1*s1*s3*s2*s4*s2*s3*s4*s3*s3*s2*s1*s4*s3*s1*s2*s3*s3*s4*s2*s3*s3*s1*s2*s4*s2*s1*s3*s1*s2*s3*s2*s3*s2*s1*s3*s2*s2*s3*s3*s2*s1*s4*s3*s2*s1*s2*s2*s2*s1*s3*s4*s1*s2*s2*s1*s2*s3*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s3*s1*s2*s4*s3*s2*s1*s3*s1*s2*s4*s4*s3*s2*s1*s4*s1*s3*s2*s2*s3*s1*s2*s2*s3*s4*s2*s1*s1*s3*s2*s1*s2*s3*s1*s2*s4*s3*s2*s2*s1*s3*s1*s2*s3*s3*s4*s2*s1*s3*s1*s2*s3*s4*s2*s1*s3*s3*s2*s2*s2*s3*s4*s3*s3*s1*s2*s4*s3*s2*s2*s3*s4*s2*s1*s3*s2*s2*s1*s2*s3*s4*s3*s2*s2*s1*s4*s1*s2*s1*s2*s3*s1*s2*s4*s3*s2*s1*s1*s2*s3*s3*s4*s2*s2*s2*s1*s3*s1*s2*s3*s4*s3*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s3*s1*s2*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s1*s3*s2*s1*s4*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s2*s1*s1*s3*s3*s3*s3*s1*s2*s4*s4*s4*s3*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s1*s2*s3*s1*s2*s3*s2*s1*s1*s3*s2*s1*s1*s2*s3*s4*s3*s1*s2*s2*s3*s4*s2*s1*s3*s1*s2*s3*s4*s3*s4*s3*s3*s4*s2*s1*s3*s1*s2*s3*s4*s2*s1*s1*s1*s3*s3*s2*s1*s2*s3*s1*s2*s4*s4*s3*s2*s1*s3*s1*s2*s3*s4*s2*s2*s1*s1*s1*s2*s2*s1*s3*s2*s2*s1*s2*s3*s4*s3*s1*s2*s4*s3*s2*s4*s4*s4*s3*s2*s1*s3*s2*s1*s2*s3*s4*s3*s2*s2*s1*s2*s3*s1*s2*s3*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s2*s1*s1*s1*s3*s2*s1*s4*s3*s2*s1*s1*s2*s3*s4*s1*s1*s2*s1*s3*s1*s2*s4*s3*s2*s1*s3*s2*s2*s3*s4*s4*s3*s3*s3*s2*s4*s2*s3*s4*s3*s2*s2*s1*s3*s3*s3*s2*s1*s1*s1*s4*s3*s2*s3*s2*s3*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s3*s4*s2*s3*s2*s3*s2*s1*s1*s3*s2*s1*s1*s1*s3*s4*s3*s2*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s1*s1*s4*s3*s4*s3*s3*s2*s1*s4*s3*s2*s1*s1*s2*s3*s3*s3*s2*s1*s1*s4*s3*s3*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s2*s1*s1*s3*s4*s2*s2*s1*s1*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s2*s3*s3*s3*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s1*s4*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s4*s2*s1*s1*s1*s4*s3*s2*s3*s4*s2*s1*s1*s3*s3*s2*s1*s1*s4*s3*s2*s1*s1*s2*s3*s4*s2*s2*s1*s3*s2*s2*s1*s3*s3*s2*s2*s1*s1*s3*s4*s3*s2*s2*s3*s4*s2*s3*s2*s2*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s3*s2*s1*s1*s2*s2*s1*s1*s1*s3*s2*s3*s4*s2*s2*s2*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s3*s2*s1*s1*s1*s3*s4*s3*s2*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s1*s4*s3*s3*s2*s1*s1*s4*s2*s4*s3*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s2*s2*s1*s3*s4*s3*s3*s2*s4*s3*s2*s3;
x2 := s4*s3*s2*s1*s3*s2*s2*s3*s4*s4*s3*s3*s3*s2*s4*s2*s3*s4*s3*s2*s2*s1*s3*s3*s3*s2*s1*s1*s1*s4*s3*s2*s3*s2*s3*s4*s2*s1*s1*s3*s2*s3*s4*s3*s2*s1*s1*s3*s4*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s1*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s3*s4*s2*s3*s2*s3*s2*s1*s1*s3*s2*s1*s1*s1*s3*s4*s3*s2*s2*s1*s1*s3*s2*s1*s1*s1*s4*s3*s2*s1*s1*s4*s3*s4*s3*s3*s2*s1*s4*s3*s2*s1*s1*s2*s3*s3*s3*s2*s1*s1*s4*s3*s3*s3*s2*s1*s1*s1*s4*s3*s2*s3*s4*s2*s1*s1*s3*s4*s2*s2*s1*s1*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s2*s3*s3*s3*s3*s2*s2*s4*s2*s1*s1*s3*s2*s3*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s1*s4*s2*s4*s3*s2*s3*s4*s2*s1*s3*s2*s4*s2*s1*s1*s1*s4*s3*s2*s3*s4*s2*s1*s1*s3*s3*s2*s1*s1*s4*s3*s2*s1*s1*s2*s3*s4*s2*s2*s1*s3*s2*s2*s1*s3*s3*s2*s2*s1*s1*s3*s4*s3*s2*s2*s3*s4*s2*s3*s2*s2*s4*s2*s1*s3*s2*s1*s1*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s3*s2*s1*s1*s2*s2*s1*s1*s1*s3*s2*s3*s4*s2*s2*s2*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s3*s2*s1*s1*s1*s3*s4*s3*s2*s4*s2*s1*s1*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s1*s1*s1*s4*s3*s3*s2*s1*s1*s4*s2*s4*s3*s2*s1*s1*s1*s3*s2*s1*s1*s4*s2*s3*s2*s2*s1*s3*s4*s3*s3*s2*s4*s3*s2*s3;
a2 := s2;
if not (x2*conj*x2^-1 eq a2) then "Failure on h1"; end if;

"Done.";



Output: Magma V2.10-22    Sun Jul 11 2004 01:12:14 on modular  [Seed = 813743203]
   -------------------------------------

Done.

Total time: 3.809 seconds, Total memory usage: 2.37MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:12:41 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case d1 (len=200)
// try again...
conj := D^-59*s2*s3*s4*s1*s1*s3*s2*s1*s1*s3*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s2*s1*s1*s3*s2*s1*s1*s2*s4*s2*s3*s1*s1*s3*s2*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s2*s1*s1*s3*s2*s4*s3*s2*s2*s3*s4*s3*s2*s1*s1*s3*s2*s1*s1*s3*s4*s2*s3*s2*s1*s1*s3*s2*s1*s1*s3*s4*s3*s2*s1*s1*s2*s2*s4*s4*s3*s2*s1*s1*s3*s2*s3*s4*s2*s2*s1*s1*s3*s2*s3*s3*s2*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s3*s2*s3*s4*s2*s2*s3*s1*s1*s3*s2*s1*s3*s4*s3*s2*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s1*s3*s4*s3*s2*s3*s4*s2*s1*s1*s3*s2*s1*s1*s3*s4*s2*s3*s2*s4*s3*s2*s2*s1*s1*s3*s2*s3*s4*s3*s2*s2*s3*s4*s2*s2*s1*s3*s2*s4*s2*s4*s4*s3*s2*s2*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s3*s2*s3*s4*s2*s1*s1*s3*s3*s2*s4*s3*s2*s2*s1*s3*s3*s2*s2*s3*s3*s2*s4*s2*s2*s2*s1*s1*s1*s3*s2*s4*s3*s2*s3*s4*s2*s3*s2*s2*s1*s3*s2*s4*s2*s3*s4*s3*s2*s2*s1*s1*s1*s1*s1*s1*s3*s4*s3*s2*s1*s1*s2*s4*s2*s3*s1*s2*s2*s3*s1*s2*s4*s3*s2*s1*s1*s3*s2*s1*s3*s4*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s3*s3*s3*s2*s4*s3*s1*s3*s1*s2*s3*s4*s3*s1*s1*s2*s3*s4*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s3*s3*s3*s3*s4*s2*s3*s1*s2*s2*s1*s3*s3*s3*s2*s4*s2*s3*s1*s2*s4*s3*s2*s2*s3*s4*s2*s1*s1*s2*s3*s2*s4*s2*s1*s1*s2*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s2*s3*s2*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s4*s3*s3*s4*s2*s2*s3*s1*s1*s2*s3*s4*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s1*s2*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s2*s1*s4*s3*s2*s1*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s2*s3*s1*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s4*s3*s2*s2*s1*s1*s3*s3*s3*s4*s2*s1*s1*s1*s2*s3*s4*s3*s2*s1*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s2*s2*s1*s3*s3*s3*s2*s2*s3*s1*s2*s4*s3*s2*s2*s1*s1*s2*s3*s2*s1*s4*s3*s2*s2*s4*s3*s3*s2*s2*s1*s3*s4*s2*s2*s3*s4*s3*s2*s4*s4;
x2 := s1*s2*s3*s4*s3*s1*s1*s2*s3*s4*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s3*s3*s3*s3*s4*s2*s3*s1*s2*s2*s1*s3*s3*s3*s2*s4*s2*s3*s1*s2*s4*s3*s2*s2*s3*s4*s2*s1*s1*s2*s3*s2*s4*s2*s1*s1*s2*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s2*s3*s2*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s1*s1*s3*s2*s4*s3*s3*s4*s2*s2*s3*s1*s1*s2*s3*s4*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s1*s2*s3*s2*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s2*s1*s4*s3*s2*s1*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s2*s3*s1*s1*s1*s2*s3*s4*s2*s1*s3*s2*s2*s4*s3*s2*s2*s1*s1*s3*s3*s3*s4*s2*s1*s1*s1*s2*s3*s4*s3*s2*s1*s1*s1*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s3*s2*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s2*s2*s1*s3*s3*s3*s2*s2*s3*s1*s2*s4*s3*s2*s2*s1*s1*s2*s3*s2*s1*s4*s3*s2*s2*s4*s3*s3*s2*s2*s1*s3*s4*s2*s2*s3*s4*s3*s2*s4*s4;
a2 := s1*s3;
if not (x2*conj*x2^-1 eq a2) then "Failure on d1"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:12:38 on modular  [Seed = 681092115]
   -------------------------------------

Done.

Total time: 3.029 seconds, Total memory usage: 2.10MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:14:58 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case p1 (len=50)
// try again...
conj := D^-10*s1*s2*s3*s1*s2*s3*s3*s3*s3*s3*s3*s2*s2*s2*s4*s3*s2*s2*s3*s1*s2*s4*s3*s3*s2*s1*s3*s2*s4*s3*s1*s2*s2*s2*s3*s4*s2*s2*s3*s1*s2*s1*s1*s1*s4*s3*s3*s2*s1*s2*s3*s3*s2*s4*s1*s1*s2*s3*s3*s2*s1*s2*s2*s3*s3*s2*s1*s4*s3*s3*s4*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s3*s4*s4*s4*s4*s3*s2*s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s2;
x2 := s4*s3*s3*s2*s1*s2*s3*s3*s2*s4*s1*s1*s2*s3*s3*s2*s1*s2*s2*s3*s3*s2*s1*s4*s3*s3*s4*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s3*s4*s4*s4*s4*s3*s2*s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s2;
a2 := s1*s1*s3^-1*s3^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p1"; end if;

// Test case p2 (len=51)
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
conj := D^-17*s2*s2*s3*s3*s1*s2*s3*s3*s2*s1*s1*s3*s2*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s4*s4*s3*s3*s2*s1*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s3*s4*s2*s3*s2*s1*s1*s2*s2*s2*s1*s3*s2*s4*s3*s3*s2*s1*s4*s3*s2*s2*s3*s3*s3*s1*s2*s3*s3*s4*s2*s2*s2*s3*s1*s2*s4*s3*s1*s1*s1*s2*s3*s2*s3*s3*s2*s1*s3*s4*s4*s4*s4*s2*s3*s4*s1*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s2*s3*s3*s4*s3*s2*s2*s1*s2*s3*s1*s3*s2*s1*s4*s2*s3*s1*s2*s3*s3*s3*s4*s4*s3*s3*s2*s3*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s3*s2*s2*s3*s3*s3*s2;
x2 := s2*s3*s2*s3*s3*s2*s1*s3*s4*s4*s4*s4*s2*s3*s4*s1*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s2*s3*s3*s4*s3*s2*s2*s1*s2*s3*s1*s3*s2*s1*s4*s2*s3*s1*s2*s3*s3*s3*s4*s4*s3*s3*s2*s3*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s3*s2*s2*s3*s3*s3*s2;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p2"; end if;

// Test case p3 (len=52)
// try again...
conj := D^-13*s1*s1*s1*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s1*s1*s1*s1*s3*s4*s3*s3*s2*s1*s1*s2*s2*s1*s1*s3*s2*s4*s3*s2*s3*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s4*s3*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s2*s3*s2*s2*s3*s4*s3*s2*s2*s1*s1*s4*s3*s2*s1*s1*s1*s3*s2*s4*s3*s3*s4*s2*s1*s1*s2*s2*s2*s3*s1*s2*s4*s4*s4*s3*s2*s2*s1*s3*s2*s4*s3*s3*s4*s1*s2*s2*s3*s1*s2*s4*s3*s3*s2*s2*s1*s4*s3*s2*s4*s3*s2*s2;
x2 := s1*s3*s2*s4*s3*s3*s4*s2*s1*s1*s2*s2*s2*s3*s1*s2*s4*s4*s4*s3*s2*s2*s1*s3*s2*s4*s3*s3*s4*s1*s2*s2*s3*s1*s2*s4*s3*s3*s2*s2*s1*s4*s3*s2*s4*s3*s2*s2;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p3"; end if;

// Test case p4 (len=53)
// try again...
// try again...
// try again...
conj := D^-17*s2*s4*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s1*s3*s2*s2*s3*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s3*s1*s2*s4*s2*s1*s3*s1*s2*s4*s2*s1*s3*s2*s4*s3*s3*s3*s3*s4*s2*s3*s1*s2*s2*s3*s4*s3*s2*s1*s1*s2*s2*s2*s3*s1*s2*s1*s1*s1*s2*s2*s1*s2*s3*s4*s3*s2*s1*s2*s3*s1*s2*s2*s1*s3*s2*s4*s3*s1*s1*s1*s2*s3*s1*s1*s3*s2*s3*s4*s2*s3*s1*s2*s4*s3*s2*s1*s4*s3*s2*s2*s1*s4*s2*s3*s1*s4*s4*s3*s3*s3*s2*s4*s3*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s2*s1*s2*s4*s3*s2*s2*s3*s4*s2*s3*s4*s3*s2*s1*s2*s1*s1*s4*s4*s4*s4*s3*s2*s3*s4*s2*s1*s4*s3*s2*s4*s3*s3*s4*s3;
x2 := s2*s2*s1*s2*s3*s4*s3*s2*s1*s2*s3*s1*s2*s2*s1*s3*s2*s4*s3*s1*s1*s1*s2*s3*s1*s1*s3*s2*s3*s4*s2*s3*s1*s2*s4*s3*s2*s1*s4*s3*s2*s2*s1*s4*s2*s3*s1*s4*s4*s3*s3*s3*s2*s4*s3*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s2*s1*s2*s4*s3*s2*s2*s3*s4*s2*s3*s4*s3*s2*s1*s2*s1*s1*s4*s4*s4*s4*s3*s2*s3*s4*s2*s1*s4*s3*s2*s4*s3*s3*s4*s3;
a2 := s1*s1*s3^-1*s3^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p4"; end if;

// Test case p5 (len=54)
// try again...
conj := D^-12*s4*s1*s1*s1*s2*s3*s4*s3*s4*s2*s2*s3*s2*s1*s1*s2*s4*s3*s4*s3*s2*s2*s3*s4*s3*s2*s1*s3*s2*s2*s2*s3*s4*s3*s3*s2*s2*s3*s1*s2*s4*s3*s2*s1*s1*s2*s2*s4*s3*s2*s1*s1*s2*s3*s3*s4*s2*s2*s3*s1*s2*s4*s3*s1*s1*s1*s3*s3*s3*s3*s2*s2*s3*s2*s1*s3*s4*s1*s2*s3*s4*s1*s2*s3*s3*s2*s1*s3*s2*s1*s4*s2*s3*s1*s2*s4*s2*s3*s4*s2*s2*s1*s3*s2*s4*s2*s3*s4*s1*s2*s3*s2*s3*s4*s3*s2*s1*s3*s2*s3;
x2 := s3*s3*s3*s3*s2*s2*s3*s2*s1*s3*s4*s1*s2*s3*s4*s1*s2*s3*s3*s2*s1*s3*s2*s1*s4*s2*s3*s1*s2*s4*s2*s3*s4*s2*s2*s1*s3*s2*s4*s2*s3*s4*s1*s2*s3*s2*s3*s4*s3*s2*s1*s3*s2*s3;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p5"; end if;

// Test case p6 (len=55)
// try again...
// try again...
// try again...
conj := D^-17*s2*s1*s2*s1*s1*s1*s2*s3*s2*s2*s3*s4*s3*s3*s3*s4*s3*s3*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s2*s3*s2*s4*s3*s2*s2*s1*s3*s2*s1*s4*s3*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s2*s1*s1*s3*s3*s2*s1*s4*s3*s2*s2*s1*s3*s3*s2*s4*s2*s2*s1*s3*s2*s2*s1*s1*s3*s3*s2*s2*s3*s4*s4*s2*s1*s1*s3*s2*s1*s1*s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s4*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s4*s3*s3*s4*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s3*s2*s4*s3*s3*s4*s2*s3*s3*s3*s2*s2*s4*s1*s2*s3*s4*s3*s3*s3*s3*s3*s3*s2*s2*s4*s3*s1*s2*s3*s3*s4*s2*s3*s1*s2*s3*s3*s2*s1*s3*s2;
x2 := s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s4*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s4*s3*s3*s4*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s3*s2*s4*s3*s3*s4*s2*s3*s3*s3*s2*s2*s4*s1*s2*s3*s4*s3*s3*s3*s3*s3*s3*s2*s2*s4*s3*s1*s2*s3*s3*s4*s2*s3*s1*s2*s3*s3*s2*s1*s3*s2;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p6"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:14:56 on modular  [Seed = 546352269]
   -------------------------------------

Done.

Total time: 2.679 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:15:12 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case p1 (len=50)
// try again...
conj := D^-10*s1*s2*s3*s1*s2*s3*s3*s3*s3*s3*s3*s2*s2*s2*s4*s3*s2*s2*s3*s1*s2*s4*s3*s3*s2*s1*s3*s2*s4*s3*s1*s2*s2*s2*s3*s4*s2*s2*s3*s1*s2*s1*s1*s1*s4*s3*s3*s2*s1*s2*s3*s3*s2*s4*s1*s1*s2*s3*s3*s2*s1*s2*s2*s3*s3*s2*s1*s4*s3*s3*s4*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s3*s4*s4*s4*s4*s3*s2*s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s2;
x2 := s4*s3*s3*s2*s1*s2*s3*s3*s2*s4*s1*s1*s2*s3*s3*s2*s1*s2*s2*s3*s3*s2*s1*s4*s3*s3*s4*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s3*s4*s4*s4*s4*s3*s2*s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s2;
a2 := s1*s1*s3^-1*s3^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p1"; end if;

// Test case p2 (len=51)
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
// try again...
conj := D^-17*s2*s2*s3*s3*s1*s2*s3*s3*s2*s1*s1*s3*s2*s2*s3*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s4*s4*s3*s3*s2*s1*s1*s1*s2*s4*s3*s2*s1*s1*s2*s3*s3*s4*s2*s3*s2*s1*s1*s2*s2*s2*s1*s3*s2*s4*s3*s3*s2*s1*s4*s3*s2*s2*s3*s3*s3*s1*s2*s3*s3*s4*s2*s2*s2*s3*s1*s2*s4*s3*s1*s1*s1*s2*s3*s2*s3*s3*s2*s1*s3*s4*s4*s4*s4*s2*s3*s4*s1*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s2*s3*s3*s4*s3*s2*s2*s1*s2*s3*s1*s3*s2*s1*s4*s2*s3*s1*s2*s3*s3*s3*s4*s4*s3*s3*s2*s3*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s3*s2*s2*s3*s3*s3*s2;
x2 := s2*s3*s2*s3*s3*s2*s1*s3*s4*s4*s4*s4*s2*s3*s4*s1*s4*s3*s2*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s2*s3*s3*s4*s3*s2*s2*s1*s2*s3*s1*s3*s2*s1*s4*s2*s3*s1*s2*s3*s3*s3*s4*s4*s3*s3*s2*s3*s3*s4*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s3*s2*s2*s3*s3*s3*s2;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p2"; end if;

// Test case p3 (len=52)
// try again...
conj := D^-13*s1*s1*s1*s4*s3*s2*s1*s1*s1*s1*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s4*s2*s1*s1*s1*s1*s1*s3*s4*s3*s3*s2*s1*s1*s2*s2*s1*s1*s3*s2*s4*s3*s2*s3*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s4*s3*s3*s2*s2*s1*s1*s3*s2*s1*s1*s4*s2*s3*s2*s2*s3*s4*s3*s2*s2*s1*s1*s4*s3*s2*s1*s1*s1*s3*s2*s4*s3*s3*s4*s2*s1*s1*s2*s2*s2*s3*s1*s2*s4*s4*s4*s3*s2*s2*s1*s3*s2*s4*s3*s3*s4*s1*s2*s2*s3*s1*s2*s4*s3*s3*s2*s2*s1*s4*s3*s2*s4*s3*s2*s2;
x2 := s1*s3*s2*s4*s3*s3*s4*s2*s1*s1*s2*s2*s2*s3*s1*s2*s4*s4*s4*s3*s2*s2*s1*s3*s2*s4*s3*s3*s4*s1*s2*s2*s3*s1*s2*s4*s3*s3*s2*s2*s1*s4*s3*s2*s4*s3*s2*s2;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p3"; end if;

// Test case p4 (len=53)
// try again...
// try again...
// try again...
conj := D^-17*s2*s4*s3*s2*s1*s3*s2*s1*s1*s2*s3*s4*s1*s1*s3*s2*s2*s3*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s3*s1*s2*s4*s2*s1*s3*s1*s2*s4*s2*s1*s3*s2*s4*s3*s3*s3*s3*s4*s2*s3*s1*s2*s2*s3*s4*s3*s2*s1*s1*s2*s2*s2*s3*s1*s2*s1*s1*s1*s2*s2*s1*s2*s3*s4*s3*s2*s1*s2*s3*s1*s2*s2*s1*s3*s2*s4*s3*s1*s1*s1*s2*s3*s1*s1*s3*s2*s3*s4*s2*s3*s1*s2*s4*s3*s2*s1*s4*s3*s2*s2*s1*s4*s2*s3*s1*s4*s4*s3*s3*s3*s2*s4*s3*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s2*s1*s2*s4*s3*s2*s2*s3*s4*s2*s3*s4*s3*s2*s1*s2*s1*s1*s4*s4*s4*s4*s3*s2*s3*s4*s2*s1*s4*s3*s2*s4*s3*s3*s4*s3;
x2 := s2*s2*s1*s2*s3*s4*s3*s2*s1*s2*s3*s1*s2*s2*s1*s3*s2*s4*s3*s1*s1*s1*s2*s3*s1*s1*s3*s2*s3*s4*s2*s3*s1*s2*s4*s3*s2*s1*s4*s3*s2*s2*s1*s4*s2*s3*s1*s4*s4*s3*s3*s3*s2*s4*s3*s2*s3*s4*s4*s1*s2*s3*s4*s4*s4*s3*s2*s1*s2*s4*s3*s2*s2*s3*s4*s2*s3*s4*s3*s2*s1*s2*s1*s1*s4*s4*s4*s4*s3*s2*s3*s4*s2*s1*s4*s3*s2*s4*s3*s3*s4*s3;
a2 := s1*s1*s3^-1*s3^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p4"; end if;

// Test case p5 (len=54)
// try again...
conj := D^-12*s4*s1*s1*s1*s2*s3*s4*s3*s4*s2*s2*s3*s2*s1*s1*s2*s4*s3*s4*s3*s2*s2*s3*s4*s3*s2*s1*s3*s2*s2*s2*s3*s4*s3*s3*s2*s2*s3*s1*s2*s4*s3*s2*s1*s1*s2*s2*s4*s3*s2*s1*s1*s2*s3*s3*s4*s2*s2*s3*s1*s2*s4*s3*s1*s1*s1*s3*s3*s3*s3*s2*s2*s3*s2*s1*s3*s4*s1*s2*s3*s4*s1*s2*s3*s3*s2*s1*s3*s2*s1*s4*s2*s3*s1*s2*s4*s2*s3*s4*s2*s2*s1*s3*s2*s4*s2*s3*s4*s1*s2*s3*s2*s3*s4*s3*s2*s1*s3*s2*s3;
x2 := s3*s3*s3*s3*s2*s2*s3*s2*s1*s3*s4*s1*s2*s3*s4*s1*s2*s3*s3*s2*s1*s3*s2*s1*s4*s2*s3*s1*s2*s4*s2*s3*s4*s2*s2*s1*s3*s2*s4*s2*s3*s4*s1*s2*s3*s2*s3*s4*s3*s2*s1*s3*s2*s3;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p5"; end if;

// Test case p6 (len=55)
// try again...
// try again...
// try again...
conj := D^-17*s2*s1*s2*s1*s1*s1*s2*s3*s2*s2*s3*s4*s3*s3*s3*s4*s3*s3*s2*s1*s1*s3*s2*s1*s1*s4*s3*s2*s1*s1*s2*s3*s2*s4*s3*s2*s2*s1*s3*s2*s1*s4*s3*s3*s2*s1*s4*s3*s2*s2*s1*s3*s2*s2*s1*s1*s3*s3*s2*s1*s4*s3*s2*s2*s1*s3*s3*s2*s4*s2*s2*s1*s3*s2*s2*s1*s1*s3*s3*s2*s2*s3*s4*s4*s2*s1*s1*s3*s2*s1*s1*s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s4*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s4*s3*s3*s4*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s3*s2*s4*s3*s3*s4*s2*s3*s3*s3*s2*s2*s4*s1*s2*s3*s4*s3*s3*s3*s3*s3*s3*s2*s2*s4*s3*s1*s2*s3*s3*s4*s2*s3*s1*s2*s3*s3*s2*s1*s3*s2;
x2 := s1*s3*s2*s4*s3*s3*s4*s2*s3*s1*s4*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s4*s3*s3*s4*s1*s1*s2*s3*s4*s4*s3*s4*s3*s2*s1*s4*s3*s2*s4*s3*s3*s4*s2*s3*s3*s3*s2*s2*s4*s1*s2*s3*s4*s3*s3*s3*s3*s3*s3*s2*s2*s4*s3*s1*s2*s3*s3*s4*s2*s3*s1*s2*s3*s3*s2*s1*s3*s2;
a2 := s1*s1*s4^-1*s4^-1;
if not (x2*conj*x2^-1 eq a2) then "Failure on p6"; end if;

"Done a.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:15:09 on modular  [Seed = 413701304]
   -------------------------------------

Done a.

Total time: 2.689 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:15:47 2004

Input: B<s1,s2,s3,s4> := BraidGroup(5);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case i1 (len=50)
a := s2*s1*s3^-1*s2^-1*s2^-1*s2^-1*s3*s2^-1*s4*s4*s4*s1*s2*s3^-1*s1*s4*s3^-1*s4*s3*s1*s3*s1^-1*s3*s1^-1*s2^-1*s3^-1*s1^-1*s3^-1*s4*s3*s2^-1*s1*s2*s3*s1*s2^-1*s3*s3*s4*s4*s3^-1*s1*s2^-1*s4^-1*s4^-1*s3^-1*s4^-1*s1*s4^-1*s1^-1;
ai := D^-11*s1*s2*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s3*s4*s2*s2*s3*s4*s3*s2*s2*s3*s4*s1*s3*s1*s2*s1*s1*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s3*s4*s2*s3*s2*s1*s1*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s1*s1*s1*s1*s2*s3;
if not (ai eq a^-1) then "Failure on i1"; end if;

// Test case i2 (len=51)
a := s1^-1*s2^-1*s1^-1*s3^-1*s1*s3*s4*s2*s4*s1^-1*s2^-1*s3^-1*s1^-1*s1^-1*s1^-1*s1^-1*s2*s1*s2*s4*s1*s2^-1*s1*s4^-1*s2*s3*s4*s3^-1*s2*s4^-1*s3*s1^-1*s2*s1*s4*s2*s3^-1*s2*s4*s3^-1*s1^-1*s2^-1*s1*s3*s1^-1*s2*s2*s1^-1*s1^-1*s2^-1*s1^-1;
ai := D^-6*s2*s2*s3*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s4*s1*s3*s1*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s3*s1*s1*s2*s3*s4*s2*s3*s2*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s1*s1*s4*s3*s2*s1*s1;
if not (ai eq a^-1) then "Failure on i2"; end if;

// Test case i3 (len=52)
a := s4*s3*s4^-1*s3*s4*s3*s4*s3*s2^-1*s1*s2*s2*s1^-1*s1*s2^-1*s4^-1*s3^-1*s4*s2*s1*s4*s4*s1^-1*s2*s4^-1*s2*s1^-1*s2^-1*s1*s4^-1*s1*s1*s3*s4^-1*s4^-1*s3^-1*s4*s4*s3*s4^-1*s2^-1*s3*s2*s1^-1*s2*s3*s3*s1^-1*s4*s2*s4^-1*s4^-1;
ai := D^-11*s1*s2*s4*s1*s2*s3*s1*s2*s1*s1*s2*s4*s2*s3*s1*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s2*s1*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s2*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s2*s3*s1*s1*s1*s3*s4*s1*s2*s1*s1*s2*s3*s4*s3*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s4*s3*s2;
if not (ai eq a^-1) then "Failure on i3"; end if;

// Test case i4 (len=53)
a := s2*s4^-1*s2^-1*s1*s4*s3^-1*s1^-1*s4*s4*s3^-1*s1^-1*s4^-1*s1^-1*s3^-1*s1*s3^-1*s1*s1*s1*s2^-1*s3*s2^-1*s4*s3*s3*s4*s2^-1*s4*s1^-1*s1^-1*s2^-1*s2^-1*s4^-1*s2^-1*s2^-1*s3*s4*s3^-1*s2^-1*s3*s2^-1*s1*s1*s3*s3*s2*s2*s2^-1*s1*s3*s4^-1*s2^-1*s2^-1;
ai := D^-5*s1*s3*s1*s2*s3*s2*s2*s4*s2*s3*s1*s2*s2*s4*s2*s3*s1*s2*s2*s4*s2*s3*s2*s3*s3*s3*s2*s2*s1*s3*s2*s2*s1*s1*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s2*s2*s1*s1*s2*s3*s3;
if not (ai eq a^-1) then "Failure on i4"; end if;

// Test case i5 (len=54)
a := s3*s1^-1*s2*s1*s4^-1*s3^-1*s2*s3*s1^-1*s1^-1*s3^-1*s1^-1*s3^-1*s2^-1*s4*s2*s3*s4*s1^-1*s3^-1*s1^-1*s2^-1*s4^-1*s4^-1*s2^-1*s3^-1*s4^-1*s2*s3*s2^-1*s3^-1*s3^-1*s3^-1*s2^-1*s1^-1*s3*s2^-1*s3^-1*s3^-1*s1*s3^-1*s1*s4^-1*s3*s2^-1*s1*s4^-1*s1*s3*s4*s1*s4*s4*s2^-1;
ai := D^-7*s1*s2*s3*s4*s1*s2*s3*s1*s1*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s2*s3*s1*s2*s1*s1*s2*s4*s2*s4*s3*s2*s2*s3*s4*s1*s2*s2*s1*s3*s4*s2*s3*s2*s1*s3*s4*s2*s2*s1*s3*s4*s2*s3*s2*s1*s1*s3*s4*s1*s2*s1*s2*s4*s4*s4*s4*s3*s2*s2*s3*s4*s1;
if not (ai eq a^-1) then "Failure on i5"; end if;

// Test case i6 (len=55)
a := s3^-1*s2^-1*s3*s4^-1*s4^-1*s1*s3^-1*s2*s4^-1*s4^-1*s4*s4*s2^-1*s2^-1*s3^-1*s1*s3*s2*s3*s4^-1*s4^-1*s2*s3*s2*s1*s2^-1*s4^-1*s3^-1*s2*s3*s3*s4^-1*s1^-1*s3*s1*s2*s4*s1^-1*s4^-1*s1*s4*s1*s3^-1*s4*s1*s2^-1*s4^-1*s1*s4*s2*s3^-1*s4*s1^-1*s2*s3^-1;
ai := D^-8*s1*s2*s3*s4*s2*s3*s2*s1*s3*s4*s2*s2*s1*s1*s3*s4*s2*s3*s2*s2*s3*s4*s2*s3*s1*s2*s2*s4*s2*s3*s2*s2*s3*s4*s1*s2*s2*s1*s3*s4*s2*s3*s2*s2*s3*s1*s3*s1*s2*s1*s1*s3*s1*s2*s3*s2*s1*s1*s4*s1*s2*s3*s2*s2*s2*s2*s1*s1*s2*s3*s3*s3*s4*s2*s3;
if not (ai eq a^-1) then "Failure on i6"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:15:44 on modular  [Seed = 278961517]
   -------------------------------------

Done.

Total time: 2.549 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:16:57 2004

Input: B<s1,s2,s3,s4,s5,s6,s7,s8> := BraidGroup(9);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case i1 (len=50)
a := s7*s5*s5*s5*s1*s2*s2*s7^-1*s3*s6*s5^-1*s1*s3^-1*s4*s7^-1*s1*s6^-1*s5*s6^-1*s8*s2^-1*s3*s6*s7^-1*s1^-1*s4^-1*s8^-1*s2*s5^-1*s2^-1*s4^-1*s1^-1*s4^-1*s1*s4^-1*s5*s2^-1*s7^-1*s2*s2*s1^-1*s7^-1*s8*s2*s4*s4*s8^-1*s7^-1*s8^-1*s6;
ai := D^-4*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s1*s2*s3*s3*s5*s6*s7*s8*s4*s5*s6*s7*s4*s5*s6*s5*s4*s3*s2*s2;
if not (ai eq a^-1) then "Failure on i1"; end if;

// Test case i2 (len=51)
a := s1^-1*s4^-1*s3*s6^-1*s4^-1*s6*s3*s4^-1*s1*s1*s3^-1*s2*s8^-1*s8^-1*s3^-1*s4^-1*s2*s6*s4*s7^-1*s4*s3^-1*s8*s3^-1*s1*s6^-1*s1^-1*s1^-1*s1^-1*s6*s8*s3*s5^-1*s8^-1*s3*s3*s6*s1*s2*s1^-1*s2^-1*s2^-1*s4*s8^-1*s7^-1*s7^-1*s8^-1*s4*s4*s7^-1*s2^-1;
ai := D^-4*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s4*s5*s6*s7*s8*s1*s2*s3*s4*s6*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s1*s2*s3*s2*s2*s3*s5*s6*s7*s8*s1*s3*s4*s5*s6*s7*s1*s3*s4*s5*s6*s3*s4*s5*s3*s4*s3*s2*s1*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s5*s1*s2*s3*s4*s1*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s4*s5*s6*s3*s4*s5*s2*s2*s3*s1*s2*s2*s3*s4*s8*s1*s2*s3*s2*s2*s3*s3*s4*s4;
if not (ai eq a^-1) then "Failure on i2"; end if;

// Test case i3 (len=52)
a := s5*s4*s7*s5*s2*s6^-1*s4*s5*s6*s5^-1*s7^-1*s6^-1*s7*s6*s1^-1*s8^-1*s6^-1*s4^-1*s5^-1*s2*s7^-1*s8*s1*s6^-1*s5*s2^-1*s7^-1*s7^-1*s5^-1*s7^-1*s6*s8*s1^-1*s1^-1*s7^-1*s3*s6^-1*s8^-1*s5*s1*s4^-1*s3*s7*s8^-1*s6*s6*s6*s7^-1*s6*s8^-1*s5^-1*s1;
ai := D^-9*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s1*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s1*s3*s4*s5*s6*s7*s4*s5*s6*s3*s5*s3*s4*s3*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s2*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s1*s2*s1*s4*s5*s6*s7*s8*s3*s5*s6*s7*s3*s5*s6*s3*s4*s5*s3*s4*s2*s3*s2*s2*s5*s7*s8*s1*s6*s7*s5*s6*s5*s5*s6*s7*s8*s5*s6*s4*s6*s5*s7*s6;
if not (ai eq a^-1) then "Failure on i3"; end if;

// Test case i4 (len=53)
a := s2*s6*s1^-1*s7*s7*s2*s4*s6^-1*s8*s2^-1*s1^-1*s1*s7*s6^-1*s3^-1*s8^-1*s6*s4^-1*s2*s5^-1*s1^-1*s5^-1*s6^-1*s4^-1*s1^-1*s3*s8^-1*s5^-1*s8^-1*s6^-1*s2*s4^-1*s8*s1*s7^-1*s2^-1*s3*s5^-1*s6^-1*s3*s2^-1*s4^-1*s6^-1*s3*s7*s2^-1*s8*s5^-1*s3^-1*s3^-1*s5*s2*s4;
ai := D^-6*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s3*s4*s1*s2*s3*s2*s1*s3*s4*s6*s7*s2*s3*s5*s7*s2*s3*s4*s6*s2*s3*s4*s5*s2*s3*s1*s3*s1*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s4*s1*s2*s1*s2*s2*s4*s5*s6*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s1*s2*s3*s5*s1*s2*s3*s4*s3*s2*s1*s5*s6*s8*s5*s6*s7*s4*s6*s3*s5*s2*s4*s3*s2*s1;
if not (ai eq a^-1) then "Failure on i4"; end if;

// Test case i5 (len=54)
a := s4*s1^-1*s2*s3*s6^-1*s4^-1*s5^-1*s7*s1*s3^-1*s1^-1*s5*s2^-1*s4^-1*s3*s2^-1*s8*s7*s2^-1*s5^-1*s4*s8^-1*s6^-1*s7*s6^-1*s4*s1^-1*s8^-1*s2^-1*s2^-1*s5^-1*s5^-1*s1^-1*s2^-1*s1*s6*s4^-1*s3*s8^-1*s2*s6^-1*s3^-1*s4^-1*s2^-1*s6*s4^-1*s3*s3*s7*s8^-1*s4^-1*s4^-1*s6^-1*s2^-1;
ai := D^-5*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s3*s4*s2*s3*s2*s1*s3*s5*s7*s8*s3*s4*s7*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s4*s7*s2*s4*s5*s2*s3*s4*s5*s1*s2*s4*s1*s2*s3*s1*s2*s1*s3*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s2*s3*s1*s2*s1*s2*s4*s5*s6*s7*s8*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s5*s1*s8*s7*s6*s5;
if not (ai eq a^-1) then "Failure on i5"; end if;

// Test case i6 (len=55)
a := s6^-1*s7^-1*s2*s7^-1*s4*s4*s8^-1*s5^-1*s4^-1*s2^-1*s1^-1*s8^-1*s2*s6*s6*s7*s2^-1*s7^-1*s1^-1*s1^-1*s4*s5*s2^-1*s5*s7*s2*s8^-1*s4*s8^-1*s7*s4^-1*s1^-1*s6*s4*s1^-1*s5*s2*s5^-1*s1*s5*s4*s2*s4^-1*s3^-1*s5^-1*s4^-1*s7^-1*s5*s8^-1*s2*s4^-1*s1^-1*s1^-1*s1^-1*s6;
ai := D^-5*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s3*s4*s5*s6*s7*s8*s1*s3*s6*s7*s1*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s4*s2*s3*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s3*s4*s5*s1*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s1*s2*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s3*s4*s5*s2*s3*s4*s2*s3*s4*s1*s1*s1*s1*s5*s8*s8*s7*s7*s6;
if not (ai eq a^-1) then "Failure on i6"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:16:54 on modular  [Seed = 95782974]
   -------------------------------------

Done.

Total time: 2.839 seconds, Total memory usage: 1.93MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:23:12 2004

Input: B<s1,s2,s3,s4,s5,s6,s7,s8> := BraidGroup(9);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=500)
a := s1*s2^-1*s7*s3*s1*s2*s4*s2*s8*s1^-1*s4*s7^-1*s4^-1*s4^-1*s6^-1*s8*s7^-1*s5^-1*s3^-1*s2*s3^-1*s6^-1*s1*s2^-1*s1*s8^-1*s5^-1*s2*s2*s5*s3^-1*s7^-1*s2*s5^-1*s3^-1*s6^-1*s1*s3^-1*s8*s2*s5*s3^-1*s5^-1*s6*s7*s4^-1*s1*s3*s6^-1*s7^-1*s2*s2*s7*s2^-1*s2^-1*s6*s2*s6*s5^-1*s2^-1*s2^-1*s8*s3*s5*s6*s8*s4*s8^-1*s7*s8*s1*s8*s7*s2*s3*s5*s7^-1*s7^-1*s6*s1^-1*s4*s3*s1^-1*s2*s1*s8*s6*s7*s1^-1*s7*s6*s3^-1*s4^-1*s5^-1*s1*s2*s8*s4^-1*s5*s1^-1*s7*s1*s2*s8^-1*s7*s2^-1*s7*s2*s1*s5^-1*s4*s5^-1*s3*s8*s2*s6^-1*s8*s2*s8^-1*s6*s5^-1*s8^-1*s4^-1*s2^-1*s3^-1*s5^-1*s4^-1*s6*s8^-1*s1*s2^-1*s1*s5*s7^-1*s3^-1*s7^-1*s2^-1*s1^-1*s6*s5^-1*s6^-1*s3^-1*s6*s6*s8^-1*s5^-1*s3*s2*s6*s8^-1*s6^-1*s1^-1*s1^-1*s4*s1*s3*s7^-1*s4^-1*s5^-1*s3*s8^-1*s6*s7^-1*s2*s6*s8*s2*s1^-1*s3*s2*s4^-1*s5^-1*s7^-1*s1^-1*s8^-1*s3*s6^-1*s6^-1*s3^-1*s6*s5*s7^-1*s8^-1*s1^-1*s6^-1*s1^-1*s5*s1*s6*s5*s2^-1*s2^-1*s5*s3*s1*s5^-1*s3^-1*s8*s5^-1*s7^-1*s6*s4^-1*s3^-1*s7^-1*s1*s6^-1*s1^-1*s7^-1*s6^-1*s5*s1^-1*s4*s7*s4*s7*s2^-1*s6*s1^-1*s2^-1*s7^-1*s8*s4^-1*s8*s7*s1*s3^-1*s8^-1*s2^-1*s1^-1*s5*s5*s4^-1*s6^-1*s7*s8^-1*s2*s3^-1*s4^-1*s7*s2*s3*s2^-1*s5^-1*s7^-1*s4^-1*s7^-1*s6^-1*s5*s1*s6*s1*s8*s8*s5*s3*s2^-1*s4^-1*s2^-1*s3*s2^-1*s8*s8*s2^-1*s5*s5*s1*s4^-1*s2*s6^-1*s2*s1*s7*s1^-1*s8^-1*s7*s1*s6^-1*s1*s5*s3*s4^-1*s6*s5^-1*s7*s8^-1*s8^-1*s2^-1*s8*s7*s1*s7^-1*s4^-1*s6^-1*s8^-1*s3^-1*s4^-1*s3^-1*s1^-1*s6*s3^-1*s8^-1*s4^-1*s5*s7*s7*s4*s6^-1*s3^-1*s2^-1*s2^-1*s7^-1*s5^-1*s1*s3^-1*s5^-1*s2^-1*s4^-1*s5*s7^-1*s2^-1*s6*s1*s4^-1*s2*s1*s6^-1*s8^-1*s2*s6^-1*s7*s1*s3*s4^-1*s4^-1*s1*s5^-1*s4*s7*s1*s6*s8*s7*s3^-1*s2^-1*s1*s8^-1*s3^-1*s6*s6*s6*s1*s2^-1*s3*s4^-1*s3^-1*s6*s3^-1*s2^-1*s1*s2^-1*s4^-1*s7^-1*s6^-1*s8*s7*s4*s1^-1*s8^-1*s1^-1*s4^-1*s6*s8^-1*s3^-1*s2^-1*s3*s5*s4^-1*s1^-1*s5^-1*s4*s7*s7*s3^-1*s4^-1*s7*s5^-1*s6^-1*s8^-1*s3*s5^-1*s7*s6*s3*s3*s7^-1*s1^-1*s3*s2^-1*s3*s5^-1*s3*s4*s7^-1*s7^-1*s7^-1*s4*s1^-1*s8*s4^-1*s1^-1*s5^-1*s1*s6^-1*s7^-1*s6^-1*s7^-1*s3*s7*s5^-1*s2^-1*s7*s6*s7*s8*s6*s8^-1*s3^-1*s8*s4*s4*s4*s1*s2^-1*s8*s2^-1*s5^-1*s4^-1*s5^-1*s7*s6^-1*s4^-1*s5^-1*s4*s8^-1*s2*s6^-1*s7^-1*s7^-1*s6^-1*s7^-1*s3^-1*s6*s8*s8*s2^-1*s7^-1*s2*s4^-1*s5^-1*s6*s6*s6*s7^-1*s2*s5^-1*s2*s8^-1*s4^-1*s3*s4^-1*s7*s1*s4*s8*s5^-1*s6^-1*s7^-1*s1^-1*s5*s1*s3^-1*s4*s2^-1*s4*s7*s5^-1*s7*s7*s3^-1*s4^-1*s5*s7^-1*s5^-1*s7*s5*s2^-1*s1^-1*s2^-1*s1^-1*s6^-1;
b := s7^-1*s1^-1*s4^-1*s1^-1*s4^-1*s7*s3^-1*s5*s2*s6^-1*s1^-1*s3*s1^-1*s3*s2*s4*s6*s5^-1*s6*s2*s6^-1*s3*s7*s8^-1*s5^-1*s7*s6^-1*s4*s1^-1*s8^-1*s1^-1*s1*s5^-1*s6*s2^-1*s5*s1*s6*s8^-1*s5*s6^-1*s7^-1*s5*s6^-1*s7^-1*s4^-1*s8^-1*s3*s1*s4^-1*s5^-1*s7^-1*s4*s2*s3*s2*s4^-1*s5*s6*s1*s5^-1*s8^-1*s2*s6^-1*s7*s4^-1*s6*s7*s5^-1*s6^-1*s8^-1*s3*s1*s7*s1*s8*s5^-1*s1^-1*s8^-1*s7*s8^-1*s4^-1*s5*s7*s7*s5^-1*s1*s8^-1*s3*s8*s6^-1*s7*s5^-1*s6^-1*s5*s6*s2^-1*s8^-1*s7^-1*s4*s6^-1*s2^-1*s7*s2^-1*s8*s3*s1^-1*s5*s8*s6*s3*s5*s3^-1*s7^-1*s2^-1*s6^-1*s2^-1*s1^-1*s2*s1^-1*s2^-1*s6^-1*s2^-1*s6*s2^-1*s8^-1*s6*s2^-1*s3^-1*s6*s7^-1*s2^-1*s1*s6*s2^-1*s4*s8*s6*s1*s8*s5^-1*s3*s8*s2^-1*s5*s7*s3*s8^-1*s7*s2*s3*s2*s4*s1*s7*s5^-1*s1*s3^-1*s5*s3*s7*s1^-1*s5^-1*s3*s1*s2^-1*s8*s5^-1*s2^-1*s4*s6*s5^-1*s8*s7*s6^-1*s1^-1*s6*s3^-1*s5^-1*s3*s2*s8^-1*s2^-1*s3^-1*s6^-1*s1*s5^-1*s7*s1*s2^-1*s8*s2*s5^-1*s6^-1*s6^-1*s6^-1*s7^-1*s3*s3*s4^-1*s1^-1*s5^-1*s3^-1*s1*s6*s4^-1*s6^-1*s7*s8^-1*s3^-1*s5^-1*s3*s3*s4*s6^-1*s4^-1*s3^-1*s2*s7^-1*s1*s2*s3^-1*s6^-1*s4*s6*s5*s2^-1*s8^-1*s7^-1*s8^-1*s7^-1*s4*s6*s3^-1*s1^-1*s3*s7*s8^-1*s2^-1*s5^-1*s6^-1*s1^-1*s5^-1*s6^-1*s1^-1*s1^-1*s5*s7*s7*s1^-1*s3*s6*s8*s3*s2*s5*s6^-1*s4*s6*s5^-1*s1*s2^-1*s5*s8^-1*s7^-1*s6^-1*s6^-1*s5^-1*s5^-1*s2*s8*s5*s2^-1*s3*s8^-1*s4^-1*s6*s4^-1*s1^-1*s8*s7^-1*s7^-1*s7^-1*s5^-1*s3*s5^-1*s5^-1*s1^-1*s3*s1*s6*s3^-1*s4*s6*s3^-1*s1*s5^-1*s2^-1*s1*s3^-1*s4^-1*s8*s4*s5*s3^-1*s5*s3^-1*s6^-1*s7^-1*s7^-1*s8^-1*s4^-1*s1^-1*s5^-1*s6^-1*s8^-1*s7*s5^-1*s7*s8*s6*s2^-1*s5^-1*s1^-1*s7*s5^-1*s1^-1*s4*s4*s2*s8^-1*s4*s7^-1*s5^-1*s7*s7*s6*s3^-1*s6^-1*s4^-1*s8^-1*s7^-1*s5^-1*s8^-1*s5^-1*s2^-1*s8*s7*s3^-1*s5^-1*s3^-1*s6^-1*s2^-1*s8^-1*s8^-1*s7^-1*s2^-1*s1*s7*s2^-1*s8*s8*s4*s1^-1*s4*s1^-1*s6^-1*s1^-1*s8^-1*s3*s6^-1*s1*s5*s4*s8*s3^-1*s6^-1*s7*s8^-1*s5^-1*s2*s6^-1*s3^-1*s4*s6^-1*s7^-1*s2^-1*s3^-1*s4^-1*s6*s2*s7*s8*s7^-1*s8*s5*s8*s7^-1*s7^-1*s3*s8*s5^-1*s1*s6^-1*s7*s6^-1*s2*s8^-1*s1*s2*s3^-1*s4*s6*s7*s1*s5*s3*s1^-1*s7^-1*s3^-1*s5^-1*s7^-1*s6*s2*s6^-1*s1*s8*s5*s3*s6^-1*s3^-1*s5*s4*s7^-1*s2^-1*s5^-1*s3*s5*s6*s1*s8*s1^-1*s8*s5*s1^-1*s6*s8^-1*s8^-1*s4*s4*s2^-1*s2^-1*s6*s3*s5^-1*s7^-1*s7^-1*s4*s1^-1*s3^-1*s1^-1*s8*s5^-1*s6^-1*s8^-1*s6^-1*s7*s5^-1*s3*s1*s6^-1*s2^-1*s2^-1*s6^-1*s7^-1*s7^-1*s1*s2^-1*s8^-1*s1^-1*s7*s4^-1*s3^-1*s3^-1*s4^-1*s6^-1*s7*s1^-1*s6*s5*s3^-1*s5^-1*s1^-1*s8*s4*s5^-1*s4^-1*s1^-1*s8^-1*s2^-1;
ab := 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*s5*s3*s4*s5*s6*s2*s6*s5*s4*s4*s5*s3*s2*s2*s3*s4*s5*s6*s7*s8*s4*s5*s3*s3*s4*s2*s4*s1*s3*s1*s2*s1*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s3*s4*s5*s2*s5*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s5*s6*s7*s8*s3*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s2*s4*s2*s3*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s1*s2*s3*s2*s2*s5*s6*s7*s8*s1*s4*s5*s7*s1*s2*s3*s4*s5*s6*s2*s4*s5*s2*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s3*s4*s5*s6*s7*s1*s4*s5*s6*s1*s2*s3*s4*s5*s3*s4*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s2*s3*s1*s1*s1*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s4*s2*s3*s2*s1*s1*s4*s5*s6*s7*s8*s1*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s7*s1*s2*s3*s6*s1*s2*s3*s3*s3*s2*s2*s4*s5*s6*s7*s8*s2*s5*s6*s7*s4*s6*s3*s5*s2*s4*s1*s3*s1*s2*s1*s3*s4*s7*s8*s4*s5*s6*s7*s3*s4*s5*s6*s4*s5*s4*s3*s2*s1*s1*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s3*s6*s2*s5*s2*s2*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s3*s4*s6*s2*s3*s1*s2*s2*s3*s1*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s4*s5*s6*s3*s4*s2*s4*s1*s3*s1*s2*s1*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s3*s4*s2*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s3*s4*s5*s2*s4*s2*s3*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s3*s7*s3*s3*s4*s2*s3*s1*s2*s2*s1*s3*s4*s7*s8*s2*s4*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s5*s1*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s3*s4*s2*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s6*s7*s2*s3*s4*s5*s6*s1*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s6*s7*s8*s2*s4*s5*s6*s7*s1*s3*s5*s6*s1*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s2*s1*s3*s4*s6*s7*s8*s2*s3*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s2*s3*s4*s1*s3*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s1*s2*s3*s4*s5*s3*s4*s3*s2*s1*s6*s7*s8*s5*s6*s4*s5*s3*s4*s2*s3*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s4*s5*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s5*s6*s7*s2*s3*s4*s5*s6*s3*s5*s3*s4*s2*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s5*s6*s7*s1*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s5*s6*s2*s3*s4*s5*s6*s1*s2*s3*s4*s1*s2*s3*s4*s1*s2*s3*s1*s1*s2*s3*s5*s6*s7*s8*s3*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s2*s4*s2*s3*s1*s2*s1*s2*s4*s5*s6*s2*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s5*s2*s3*s4*s5*s2*s3*s4*s3*s2*s1*s1*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s6*s3*s4*s5*s2*s4*s4*s5*s6*s7*s8*s3*s4*s5*s6*s2*s3*s4*s5*s1*s3*s4*s5*s1*s2*s3*s4*s3*s2*s1*s4*s5*s6*s7*s8*s4*s5*s6*s7*s3*s4*s6*s2*s4*s5*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s6*s1*s2*s3*s5*s1*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s4*s5*s3*s4*s2*s3*s1*s2*s6*s7*s8*s5*s6*s7*s4*s5*s3*s3*s2*s2*s1*s3*s4*s7*s2*s4*s5*s6*s7*s2*s3*s4*s5*s6*s5*s4*s4*s5*s7*s8*s3*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s1*s3*s4*s1*s2*s3*s2*s2*s4*s5*s6*s7*s8*s1*s3*s6*s3*s6*s3*s4*s5*s2*s4*s2*s3*s2*s1*s1*s2*s4*s5*s6*s7*s8*s3*s4*s5*s6*s4*s5*s6*s4*s5*s3*s4*s3*s2*s1*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s5*s6*s3*s4*s5*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s5*s6*s4*s5*s3*s3*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s3*s4*s5*s6*s2*s4*s5*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s5*s6*s7*s8*s3*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s2*s3*s4*s3*s2*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s3*s4*s1*s2*s4*s1*s3*s3*s5*s6*s7*s8*s2*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s2*s3*s1;
if not (a*b eq ab) then "Failure on m1"; end if;

"Done.";



Output: Magma V2.10-22    Sun Jul 11 2004 01:22:50 on modular  [Seed = 3948635452]
   -------------------------------------



************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Sun Jul 11 01:23:45 2004

Input: B<s1,s2,s3,s4,s5,s6,s7,s8> := BraidGroup(9);
Id := s1*s1^-1;
D := s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1;

// Test case m1 (len=300)
a := s5*s2^-1*s2*s6*s2*s8*s1*s6*s3^-1*s7^-1*s6*s5*s7*s6^-1*s8^-1*s1*s4*s6^-1*s5*s7*s7*s1*s6^-1*s5^-1*s3*s8^-1*s1^-1*s2^-1*s1^-1*s1^-1*s2^-1*s4*s6^-1*s5*s4*s1*s5*s5*s1^-1*s4*s4*s6^-1*s3^-1*s8^-1*s1*s1*s7^-1*s6*s4*s7*s3^-1*s4*s5*s1*s2*s6*s4*s5*s7*s3*s1^-1*s3*s5*s8*s2*s7^-1*s4*s4*s5^-1*s3*s8*s5*s4^-1*s5^-1*s5^-1*s3*s1*s5^-1*s5^-1*s4*s2^-1*s3^-1*s2^-1*s8*s4*s7*s2*s5*s2^-1*s1*s4^-1*s8^-1*s1*s6^-1*s5^-1*s8*s7*s5*s8*s8*s1*s5^-1*s3^-1*s4^-1*s5*s6*s6*s6*s3*s7*s7*s4^-1*s8*s2^-1*s7*s6^-1*s1*s7^-1*s1^-1*s7^-1*s7^-1*s2^-1*s8*s5*s8^-1*s5^-1*s2^-1*s6^-1*s2*s1^-1*s8*s1*s3^-1*s5^-1*s2*s8^-1*s6^-1*s2^-1*s5*s6^-1*s1*s7*s3^-1*s1^-1*s5*s4*s3*s5^-1*s4^-1*s8*s4^-1*s8*s4*s1^-1*s7*s5*s1^-1*s8*s6^-1*s8^-1*s1^-1*s8^-1*s1*s7^-1*s8^-1*s6*s1*s5^-1*s5^-1*s3^-1*s6*s7^-1*s8^-1*s1^-1*s8^-1*s4^-1*s7*s4*s3^-1*s4*s8*s7*s8^-1*s8^-1*s2*s4^-1*s4^-1*s2*s8*s4^-1*s3*s1*s7*s6^-1*s3*s8*s7*s4^-1*s8*s6^-1*s7^-1*s3*s4^-1*s5^-1*s4*s3*s7^-1*s5*s7^-1*s2^-1*s8^-1*s5*s6^-1*s7^-1*s3*s8*s4^-1*s2^-1*s7^-1*s2*s4*s1^-1*s7*s6*s7*s3*s5^-1*s8*s2^-1*s4^-1*s1*s6^-1*s5*s6*s5*s1*s6^-1*s7^-1*s1*s3*s1*s3*s7*s8^-1*s6*s4^-1*s5*s4*s1^-1*s4*s4*s2^-1*s3^-1*s5^-1*s7^-1*s1*s7^-1*s4*s7*s5*s4^-1*s4^-1*s5*s4^-1*s1*s6*s8^-1*s7^-1*s1*s4^-1*s7*s1*s5*s7^-1*s1^-1*s7*s8^-1*s2*s2*s8^-1*s1^-1*s6^-1*s4^-1*s7*s4*s1*s4*s8^-1*s3*s2^-1*s1^-1*s8*s7^-1*s5*s7^-1*s1^-1*s6^-1*s7*s4*s8;
b := s4^-1*s8*s5^-1*s3*s5*s8^-1*s5*s3^-1*s3^-1*s6*s1^-1*s6*s3^-1*s2*s2*s3*s4^-1*s6*s5^-1*s1^-1*s2*s1*s7*s8*s5^-1*s1^-1*s3^-1*s8^-1*s7*s3^-1*s1^-1*s1^-1*s6*s7^-1*s7^-1*s2*s5*s7*s5^-1*s6^-1*s1*s6^-1*s4^-1*s8*s1*s8^-1*s5*s4^-1*s6*s7*s4^-1*s5*s3^-1*s2^-1*s6*s2^-1*s8^-1*s2*s6^-1*s8*s6^-1*s4^-1*s1^-1*s6*s4*s6^-1*s1*s2*s6*s7*s4^-1*s6*s7^-1*s8*s1*s3^-1*s7*s4*s8*s4*s1^-1*s2^-1*s4*s7^-1*s2^-1*s5^-1*s7^-1*s1*s2^-1*s5^-1*s8*s6^-1*s4*s7*s4^-1*s8^-1*s1^-1*s8^-1*s5^-1*s3^-1*s2^-1*s6*s7^-1*s4^-1*s8^-1*s2*s1^-1*s2^-1*s3*s2^-1*s1*s3^-1*s8*s2^-1*s1^-1*s6*s6*s8*s3*s1^-1*s3^-1*s4^-1*s2^-1*s3*s8^-1*s3^-1*s5*s7*s2*s4*s3*s3*s8*s4^-1*s4^-1*s8^-1*s2*s6*s2*s2*s6^-1*s1*s2^-1*s1*s6*s8*s7*s2^-1*s8^-1*s5^-1*s1*s5*s2*s2*s7^-1*s1*s6*s5*s3^-1*s6*s7^-1*s6*s8^-1*s6*s4*s1*s4*s8*s5^-1*s5^-1*s7^-1*s8^-1*s6^-1*s2^-1*s3^-1*s4^-1*s5*s4^-1*s7*s6*s7^-1*s4^-1*s2^-1*s1*s6^-1*s2*s3*s8^-1*s2^-1*s6*s2*s5^-1*s2*s8^-1*s4^-1*s4^-1*s3*s4*s3^-1*s5*s1*s2*s5^-1*s4*s3*s6^-1*s1*s4^-1*s6*s3*s5*s2^-1*s1*s7^-1*s6^-1*s7^-1*s5^-1*s5^-1*s6^-1*s2^-1*s8^-1*s5^-1*s8^-1*s1^-1*s4*s3^-1*s4*s1*s6^-1*s4^-1*s4^-1*s6*s3*s7^-1*s2*s3^-1*s7^-1*s1*s5^-1*s8*s4^-1*s8^-1*s4^-1*s5*s7^-1*s4*s7^-1*s8*s1^-1*s8^-1*s3^-1*s1^-1*s4^-1*s5^-1*s3^-1*s5^-1*s2*s1^-1*s2*s6*s1*s4^-1*s6^-1*s4*s6*s1^-1*s1^-1*s3*s5*s1^-1*s7^-1*s8*s4^-1*s1^-1*s8*s1^-1*s2*s3^-1*s1*s8^-1*s6^-1*s2^-1*s3^-1*s6*s2^-1*s2^-1*s7^-1*s6^-1*s5*s6^-1*s8*s1^-1*s2^-1*s8*s4^-1*s7^-1*s4*s5*s2^-1*s1;
ab := D^-48*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s4*s1*s2*s3*s1*s1*s2*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s1*s3*s4*s5*s6*s7*s1*s3*s4*s5*s6*s1*s3*s4*s5*s1*s4*s1*s1*s1*s1*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s2*s3*s1*s2*s1*s7*s8*s6*s7*s5*s6*s4*s4*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s4*s5*s6*s2*s3*s4*s2*s3*s4*s1*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s4*s5*s2*s3*s4*s1*s2*s3*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s1*s3*s4*s1*s2*s4*s5*s1*s3*s1*s2*s3*s1*s1*s2*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s5*s1*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s4*s5*s6*s3*s4*s5*s2*s3*s4*s2*s3*s2*s2*s4*s5*s6*s7*s8*s1*s6*s1*s5*s1*s2*s5*s2*s3*s4*s1*s3*s1*s2*s1*s1*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s4*s5*s6*s3*s5*s3*s4*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s5*s4*s3*s3*s4*s2*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s4*s7*s2*s3*s4*s5*s6*s1*s3*s4*s5*s1*s2*s4*s1*s2*s3*s1*s2*s1*s3*s4*s5*s7*s8*s2*s4*s5*s7*s2*s3*s4*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s2*s1*s1*s4*s5*s6*s7*s8*s1*s4*s7*s1*s2*s3*s4*s5*s6*s3*s4*s2*s3*s3*s2*s4*s5*s7*s8*s3*s5*s6*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s5*s1*s2*s4*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s6*s7*s3*s4*s5*s6*s2*s4*s2*s3*s4*s2*s1*s1*s2*s3*s4*s5*s6*s7*s3*s4*s5*s6*s7*s2*s4*s5*s6*s2*s4*s5*s2*s3*s4*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s7*s2*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s2*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s3*s4*s6*s7*s4*s5*s6*s3*s4*s5*s3*s4*s3*s2*s1*s1*s2*s4*s5*s6*s7*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s1*s2*s3*s4*s5*s3*s4*s2*s2*s1*s1*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s3*s5*s3*s3*s2*s2*s4*s5*s6*s7*s8*s1*s3*s4*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s3*s4*s2*s3*s1*s2*s1*s1*s2*s5*s7*s8*s1*s2*s3*s4*s5*s6*s7*s3*s5*s6*s3*s4*s5*s2*s3*s4*s1*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s8*s1*s2*s5*s6*s7*s2*s3*s4*s6*s1*s3*s4*s2*s4*s1*s3*s1*s2*s3*s4*s5*s6*s7*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s2*s4*s1*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s3*s6*s3*s4*s5*s2*s4*s1*s1*s1*s1*s2*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s2*s3*s1*s2*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s3*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s6*s2*s3*s4*s2*s3*s3*s3*s7*s2*s7*s2*s6*s2*s3*s4*s5*s1*s1*s2*s2*s2*s3*s4*s5*s6*s7*s8*s5*s6*s7*s4*s5*s3*s5*s3*s4*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s5*s6*s1*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s1*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s3*s4*s5*s2*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s1*s2*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s3*s4*s5*s6*s3*s4*s5*s3*s4*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s3*s4*s5*s6*s7*s2*s3*s4*s5*s6*s1*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s5*s6*s2*s3*s4*s5*s1*s3*s4*s2*s3*s1*s2*s1*s2*s5*s7*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s3*s4*s5*s2*s4*s2*s3*s2*s2*s3*s4*s5*s6*s8*s1*s2*s3*s4*s6*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s1*s2*s3*s5*s6*s7*s8*s4*s5*s7*s4*s5*s6*s3*s4*s5*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s5*s8*s5*s6*s7*s4*s5*s6*s3*s5*s3*s4*s3*s2*s2*s5*s8*s1*s5*s6*s7*s4*s5*s6*s3*s5*s3*s4*s2*s3*s1*s1*s2*s5*s6*s7*s8*s2*s4*s5*s7*s1*s4*s5*s6*s1*s3*s4*s1*s2*s3*s4*s1*s2*s1*s4*s5*s6*s7*s8*s3*s5*s6*s7*s3*s4*s5*s6*s2*s4*s5*s2*s3*s4*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s4*s6*s7*s4*s5*s6*s3*s4*s3*s4*s3*s2*s1*s1*s4*s5*s6*s7*s1*s3*s4*s6*s7*s2*s4*s5*s6*s1*s4*s5*s1*s2*s4*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s4*s5*s6*s7*s3*s4*s6*s2*s3*s1*s2*s1*s2*s3*s1*s2*s4*s5*s6*s7*s3*s5*s6*s3*s4*s5*s6*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s1*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s3*s4*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s3*s4*s5*s6*s2*s3*s4*s5*s3*s4*s2*s3*s2*s3*s4*s5*s6*s7*s8*s4*s5*s6*s3*s6*s3*s4*s5*s2*s4*s1*s3*s2*s1*s5*s6*s7*s4*s5*s7*s3*s4*s6*s2*s4*s5*s2*s3*s4*s1*s2*s3*s1*s2*s1*s2*s3*s4*s5*s6*s7*s8*s2*s4*s5*s7*s2*s3*s4*s5*s6*s4*s5*s3*s4*s3*s2*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s4*s5*s6*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s4*s5*s2*s3*s4*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s7*s1*s2*s3*s4*s5*s6*s2*s4*s5*s2*s3*s4*s2*s3*s1*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s1*s2*s3*s5*s6*s7*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s1*s2*s3*s4*s1*s2*s3*s2*s1*s1*s2*s3*s4*s5*s6*s7*s8*s2*s4*s5*s6*s7*s1*s5*s6*s1*s4*s5*s1*s4*s3*s3*s4*s5*s6*s7*s8*s2*s3*s4*s5*s6*s1*s2*s3*s4*s5*s2*s3*s4*s5*s3*s4*s2*s3*s2*s1*s3*s4*s5*s6*s7*s8*s2*s4*s5*s6*s7*s2*s3*s4*s5*s6*s2*s3*s4*s5*s2*s3*s4*s3*s2*s1*s1*s2*s4*s5*s6*s7*s8*s2*s4*s5*s7*s2*s3*s4*s5*s6*s4*s5*s3*s4*s3*s3*s4*s5*s7*s8*s2*s3*s4*s6*s7*s1*s2*s3*s5*s6*s4*s5*s3*s5;
if not (a*b eq ab) then "Failure on m1"; end if;

"Done.";


Output: Magma V2.10-22    Sun Jul 11 2004 01:23:34 on modular  [Seed = 3714929526]
   -------------------------------------

Done.

Total time: 11.249 seconds, Total memory usage: 2.87MB


************** MAGMA *****************
Host connector.hsd.bellsouth.net. (209.247.222.39)
Time: Sun Jul 11 05:37:19 2004

Input: /*
 *  An implementation of the Number Field Sieve as described in
 *  "Factoring Integers with the Number Field Sieve" by J.P. Buhler,
 *  H.W. Lenstra, and Carl Pomerance.  (Algorithm 11.1)
 *
 *  This code is not at all optimized - it is demonstration of the
 *  Magma computer algebra package, and to for people who want to
 *  learn the Number Field Sieve algorithm or how to code it.  Note
 *  that the algebraic square root code is available only for the
 *  most recent release of Magma.
 *
 *  This code is best demonstrated for numbers around 20-digits.
 *  Larger numbers will cause the program to take up too much memory,
 *  and numbers that are too small do not work well with this algorithm.
 *
 *  "print" statements that can be ommitted are left justified.
 *
 *  by Contini - Fri March 3rd, 2000.
 */

function SelectPolynomial(n);
    /* select a degree according to the asymptotic formula */
    d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) );
print "degree ", d;

    m := Iroot( n, d );
print "m := ", m, ";";

    coeffs := [];
    for i := d to 0 by -1 do
	temp2 := m^i;
	coeff := n div temp2;
	/* Append (~coeffs, coeff); */
	coeffs[i+1] := coeff;
	n -:= coeff*temp2;
    end for;

    P<X> := PolynomialRing( IntegerRing() );
    f := P!coeffs;
    return f, m, d;

end function;


procedure RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots,
  m_mod_p, sieve_len);
    /*  
     *  RATIONAL SIEVE
     */
    sieve_array := [0 : i in [1..sieve_len]];

    for i in [1..#FB] do
	p := FB[i];
	logp := log_primes[i];
	/*
	 *  Compute  loc  - the first location in the sieve array
	 *  where  p  divides the corresponding residue
	 */
	loc := prev_roots[i] - m_mod_p[i];
	if loc lt 0 then
	    loc +:= p;
	end if;
	prev_roots[i] := loc;
	/*  sieve begins at location 1, so skip location 0 */
	if loc eq 0 then
	    loc := p;
	end if;

	/*  MAIN SIEVE LOOP  */
	while loc le sieve_len do
	    sieve_array[loc] +:= logp;
	    loc +:= p;
	end while;

    end for;

end procedure;


procedure AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes,
  R_p_set, sieve_len );
    /*  
     *  NUMBER FIELD SIEVE
     */
    nf_sieve_array := [0 : i in [1..sieve_len]];
    for i in [1..#R_p_set] do
	R_p := R_p_set[i];
	p := R_p[1];
	r := R_p[2];
	logp := R_p[3];

	loc := nf_prev_roots[i] - r;
	if loc lt 0 then
	    loc +:= p;
	end if;
	nf_prev_roots[i] := loc;
	if loc eq 0 then
	    loc := p;
	end if;

	/*  MAIN SIEVE LOOP  */
	while loc le sieve_len do
	    nf_sieve_array[loc] +:= logp;
	    loc +:= p;
	end while;

    end for;
end procedure;


procedure ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array,
  error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots,
  R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset );
	/*  scan sieve array
	 */
    threshold := Round( Log( bm ) ) - error_term;
    zero := [0: i in [1..d]];
    x := zero;
    x[1] := 1; x[2] := b;
    nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) ) - error_term;
    for a in [1..sieve_len] do
	if sieve_array[a] ge threshold then
	    /*  rational side appears to be smooth */
	    if nf_sieve_array[a] ge nf_threshold then
		/*  number field side appears to be smooth */
		if Gcd(b, a) ne 1 then
		    /*  relation is redundant */
		    continue;
		end if;

		/*  see if it really is smooth */
		relation := [];
		rational_side := a + bm;
		for i in [1..#FB] do
		    p := FB[i];
		    if a mod p eq prev_roots[i] then
			e := 0;
			quot, rem := Quotrem( rational_side, p );
			repeat
			    rational_side := quot;
			    e +:= 1;
			    quot, rem := Quotrem( rational_side, p );
			until rem ne 0;
			Append( ~relation, [i, e] );
		    end if;
		end for;
		if Abs(rational_side) ne 1 then
		    /*  rational side is not smooth :-( */
		    continue;
		end if;

		/*  try algebraic side */
		x := zero;
		x[1] := a; x[2] := b;
		alg_elt := J!x;
		norm := IntegerRing()!Norm(alg_elt);

		for i in [1..#R_p_set] do
		    R_p := R_p_set[i];
		    p := R_p[1];
		    if a mod p eq nf_prev_roots[i] then
			e := 0;
			quot, rem := Quotrem( norm, p );
			repeat
			    norm := quot;
			    e +:= 1;
			    quot, rem := Quotrem( norm, p );
			until rem ne 0;
			Append( ~relation, [i+#FB, e] );
		    end if;
		end for;
		if Abs(norm) ne 1 then
		    /*  algebraic side is not smooth :-( */
		    continue;
		end if;

		/*  The relation is a keeper! */
print "a := ", a, "; b:= ", b,";";
		num_rels +:= 1;

		/*  Compute the character columns corresponding to
		    alg_elt  */
		for i in [1..#char_cols] do
		    p := char_cols[i][1];
		    r := char_cols[i][2];
		    if LegendreSymbol( (a + b*r) mod p, p ) eq -1 then
			M[num_rels, i + char_offset] := 1;
		    end if;
		end for;

		/*  store the algebraic element */
		Append( ~smooth_alg_elts, alg_elt );

		/*  store relation in matrix */
		for j in [1..#relation] do
		    M[num_rels, relation[j, 1]] := relation[j, 2];
		end for;

		if num_rels eq enough_rels then
		    break;
		end if;

		/*  update the  nf_threshold  - since the norms
		    grow somewhat quickly, we waste a lot of time
		    on false reports if this update is not made */
		x := zero;
		x[1] := a; x[2] := b;
		nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) );
		nf_threshold -:= error_term;
	    end if;
	end if;
    end for;
end procedure;


function NFS( n )

    f, m, d := SelectPolynomial(n);
    fprime := Derivative( f );

    J<alpha> := NumberField( f );

    /*  choose  y  - the bound for smoothness  */
    dlogd := d*Log(d);
    temp := 1.0/d * Log( n );
    e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) );
    y := Round( Exp( 0.5*e ) );
    print "smoothness bound is ", y;

    /*  prepare data for rational sieve */
    FB := [p : p in [2..y] | IsPrime( p ) ];
    log_primes := [Round(Log(p)) : p in FB];
    prev_roots := [0: p in FB];
    m_mod_p := [m mod p: p in FB];

    /*  prepare data for the algebraic sieve */
    cols := #FB;
    R_p_set := [];
    nf_prev_roots := [];
    for p in FB do
	K := GF(p);
	roots_mod_p := Roots( f, K );
	for i in [1..#roots_mod_p] do
	    r := IntegerRing()!roots_mod_p[i][1];
	    /*  also include the rounded logarithm of  p  in the storage */
	    Append( ~R_p_set, [p, r, Round(Log(p))] );
	    Append( ~nf_prev_roots, 0 );
	    cols +:= 1;
	end for;
    end for;
    smooth_alg_elts := [];

    /*  create the character columns */
    char_offset := cols;
    num_char_cols := 3 * Ilog2( n );
    char_cols := [];
    p := NextPrime( y );
    i := 0;
    repeat
	K := GF(p);
	roots_mod_p := Roots( f, K );
	for j in [1..#roots_mod_p] do
	    r := IntegerRing()!roots_mod_p[j][1];
	    Append( ~char_cols, [p, r] );
	    i +:= 1;
	    if i eq num_char_cols then
		break;
	    end if;
	end for;

	p := NextPrime( p );
    until i eq num_char_cols;
    cols +:= num_char_cols;

    enough_rels := cols+50;
print "will quit after", enough_rels," relations";

    /*  allow for an error in the sieve threshold */
    error_term := 3;

    /*  set up matrix */
    M := RMatrixSpace (IntegerRing(), enough_rels, cols)!0;

    num_rels := 0;
    b := 1;
    /*  bm = b*m */
    bm := m;
    sieve_len := y * 25;

    while true do
	RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots,
	  m_mod_p, sieve_len );

	AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes,
	  R_p_set, sieve_len );

	ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array,
	  error_term, ~num_rels, sieve_len, ~M, FB, prev_roots,
	  nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts,
	  char_cols, char_offset );

	bm +:= m;
	b +:= 1;
print "Number of relations: ", num_rels;

	if num_rels ge enough_rels then
	    break;
	end if;
    end while;


print "matrix size: ",num_rels," by ", cols;
print "finding null space";

    gf2 := GF(2);
    Mprime := RMatrixSpace (gf2, num_rels, cols)!M;
    time null_space := NullSpace( Mprime );

    /*  "free" Mprime */
    Mprime := 0;

    for j in  [1..Dimension(null_space)] do
print "trying null space vector #",j;

	/*  get the first element of the solution vector */
	soln := ChangeUniverse (Eltseq (null_space.j), IntegerRing());

	/*  compute the exponents of a relation that involves an
	    algebraic square and an integer square
	 */

	exps := RSpace(IntegerRing(), cols)!0;
	for i in [1..num_rels] do
	    if soln[i] eq 1 then
		exps +:= M[i];
	    end if;
	end for;

	/*  compute the square root  x  of the integer element of the relation
	 */
	x := 1;
	for i in [1..#FB] do
	    e := exps[i];
	    if e gt 0 then
		x := (x * ( FB[i]^(e div 2) ) ) mod n;
	    end if;
	end for;
	x := ( x * Evaluate( fprime, m ) ) mod n;
print x,"^2 mod n = ", x^2 mod n;

	list := [];
	for i in [1..num_rels] do
	    if soln[i] eq 1 then
		Append( ~list, smooth_alg_elts[i] );
	    end if;
	end for;
	Append( ~list, Evaluate( fprime, alpha )^2 );

	/*  Compute the square root  beta  of the algebraic element */
	ok, l := Root(2, list, []);
        if ok eq false then
            print "Element is not a square... continuing!";
            continue;
        end if;

	/*  map the sqrt to an integer  v  modulo  n  */
	v := 1;
	for i in [1..#l] do
	    list := l[i];
	    prod_list := 1;
	    for j in [1..#list] do
		seq := Eltseq( list[j] );
		elt := 0;
		for k in [0..d-1] do
		    num := Numerator( seq[k+1] ) mod n;
		    den := Denominator( seq[k+1] ) mod n;
		    elt +:= ( ( num * Modinv( den, n ) mod n) *
		      Modexp( m, k, n ) ) mod n;
		end for;
		prod_list := (prod_list * elt) mod n;
	    end for;
	    v := v * Modexp( Modinv( prod_list, n ), 2^(i-1), n ) mod n;
	end for;
	
print v,"^2 mod n = ", v^2 mod n;

	gcd := Gcd(x-v, n);
print "Gcd of ",x-v," and ",v," is ", gcd;
	if gcd ne 1 and gcd ne n then
	    print "FACTOR: ", gcd;
	    return gcd;
	end if;
    end for;

print "no factor found :-( ";
    return 0;

end function;
















Output: WARNING: MAGMA command contains unsafe command 'memory', so it will not be executed.

************** MAGMA *****************
Host pD9FF009B.dip.t-dialin.net. (217.255.0.155)
Time: Sun Jul 11 11:44:42 2004

Input: F<a,b>:=Group<a,b|a^3=b^2,a^4,b^4>;
Order(F);

Output: Magma V2.10-22    Sun Jul 11 2004 11:44:37 on modular  [Seed = 2519185139]
   -------------------------------------

4

Total time: 2.800 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF009B.dip.t-dialin.net. (217.255.0.155)
Time: Sun Jul 11 11:45:31 2004

Input: F<a,b>:=Group<a,b|a^4=b^4,a^4,b^4>;
Order(F);

Output: Magma V2.10-22    Sun Jul 11 2004 11:45:27 on modular  [Seed = 2653928970]
   -------------------------------------

0

Total time: 3.889 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:19:54 2004

Input: Factorization(7427466391);

Output: Magma V2.10-22    Sun Jul 11 2004 12:19:51 on modular  [Seed = 3464488554]
   -------------------------------------

[ <7427466391, 1> ]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:20:14 2004

Input: Factorization(8747135266);

Output: Magma V2.10-22    Sun Jul 11 2004 12:20:12 on modular  [Seed = 3948594004]
   -------------------------------------

[ <2, 1>, <29, 1>, <150812677, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:23:16 2004

Input: Exp(1);

Output: Magma V2.10-22    Sun Jul 11 2004 12:23:14 on modular  [Seed = 4030847361]
   -------------------------------------

2.71828182845904523536028747134

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:23:42 2004

Input: N := Exp(1);
N - Truncate(N);

Output: Magma V2.10-22    Sun Jul 11 2004 12:23:39 on modular  [Seed = 4165587312]
   -------------------------------------

0.71828182845904523536028747134

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:23:55 2004

Input: N := 10^{100}*Exp(1);
N - Truncate(N);

Output: Magma V2.10-22    Sun Jul 11 2004 12:23:53 on modular  [Seed = 129379994]
   -------------------------------------


>> N := 10^{100}*Exp(1);
          ^
Runtime error in '^': Bad argument types
Argument types given: RngIntElt, SetEnum[RngIntElt]

>> N - Truncate(N);;
   ^
User error: Identifier 'N' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:24:09 2004

Input: N := 10^100*Exp(1);
N - Truncate(N);

Output: Magma V2.10-22    Sun Jul 11 2004 12:24:06 on modular  [Seed = 264119981]
   -------------------------------------


>> N - Truncate(N);;
               ^
Runtime error in 'Truncate': Not enough precision to truncate to an integer

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 12:58:09 2004

Input: Factorization(7182818284);
Factorization(8182845904);
Factorization(8747135266);
Factorization(7427466391);

Output: Magma V2.10-22    Sun Jul 11 2004 12:58:06 on modular  [Seed = 1049563044]
   -------------------------------------

[ <2, 2>, <1795704571, 1> ]
[ <2, 4>, <701, 1>, <729569, 1> ]
[ <2, 1>, <29, 1>, <150812677, 1> ]
[ <7427466391, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50802105.dip0.t-ipconnect.de. (80.128.33.5)
Time: Sun Jul 11 15:25:22 2004

Input: Factorization(496)

Output: Magma V2.10-22    Sun Jul 11 2004 15:25:19 on modular  [Seed = 1274715985]
   -------------------------------------

[ <2, 4>, <31, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50802105.dip0.t-ipconnect.de. (80.128.33.5)
Time: Sun Jul 11 15:25:56 2004

Input: Factorization( 7182818284 )

Output: Magma V2.10-22    Sun Jul 11 2004 15:25:53 on modular  [Seed = 1407354647]
   -------------------------------------

[ <2, 2>, <1795704571, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50802105.dip0.t-ipconnect.de. (80.128.33.5)
Time: Sun Jul 11 15:26:45 2004

Input: Factorization( 8182845904 )


Output: Magma V2.10-22    Sun Jul 11 2004 15:26:42 on modular  [Seed = 1525386797]
   -------------------------------------

[ <2, 4>, <701, 1>, <729569, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50802105.dip0.t-ipconnect.de. (80.128.33.5)
Time: Sun Jul 11 15:27:20 2004

Input: Factorization( 8747135266)


Output: Magma V2.10-22    Sun Jul 11 2004 15:27:17 on modular  [Seed = 1860156158]
   -------------------------------------

[ <2, 1>, <29, 1>, <150812677, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p50802105.dip0.t-ipconnect.de. (80.128.33.5)
Time: Sun Jul 11 15:27:56 2004

Input: Factorization( 7427466391 )


Output: Magma V2.10-22    Sun Jul 11 2004 15:27:54 on modular  [Seed = 2144250816]
   -------------------------------------

[ <7427466391, 1> ]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:25:02 2004

Input: (6x^2 - 2x + 4) + (x^3 - 2x^2 + x - 1)(x^3 + 2x^2 + 3x + 4) - x^6 - x^3 - x^2 - x-1

Output: Magma V2.10-22    Sun Jul 11 2004 22:24:59 on modular  [Seed = 1325398077]
   -------------------------------------


>> (6x^2 - 2x + 4) + (x^3 - 2x^2 + x - 1)(x^3 + 2x^2 + 3x + 4) - x^6 - x^3 - x
     ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:25:13 2004

Input: Expand((6x^2 - 2x + 4) + (x^3 - 2x^2 + x - 1)(x^3 + 2x^2 + 3x + 4) - x^6 - x^3 - x^2 - x-1);

Output: Magma V2.10-22    Sun Jul 11 2004 22:25:10 on modular  [Seed = 1190654152]
   -------------------------------------


>> Expand((6x^2 - 2x + 4) + (x^3 - 2x^2 + x - 1)(x^3 + 2x^2 + 3x + 4) - x^6 - 
            ^
User error: bad syntax

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:25:31 2004

Input: Expand((6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 - x^3 - x^2 - x-1);

Output: Magma V2.10-22    Sun Jul 11 2004 22:25:28 on modular  [Seed = 1592781006]
   -------------------------------------


>> Expand((6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x
             ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:33:27 2004

Input: R<x>:= PolynomialRing( Rationals(), 1 );
ExpandPolynomial((6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 - x^3 - x^2 - x + 1);

Output: Magma V2.10-22    Sun Jul 11 2004 22:33:24 on modular  [Seed = 1775816981]
   -------------------------------------


>> ExpandPolynomial((6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*
   ^
User error: Identifier 'ExpandPolynomial' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:37:32 2004

Input: R<x>:= PolynomialRing( Rationals(), 1 );
IsZero((6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 + x^3 + x^2 + x - 1);

Output: Magma V2.10-22    Sun Jul 11 2004 22:37:30 on modular  [Seed = 1674762753]
   -------------------------------------


>> IsZero((6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x
                                                   ^
Runtime error: Bad argument types
Argument types given: RngMPolElt, RngMPolElt

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:41:54 2004

Input: R<x>:= PolynomialRing( Rationals(), 1 );
(6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 + x^3 + x^2 + x

Output: Magma V2.10-22    Sun Jul 11 2004 22:41:51 on modular  [Seed = 2167421926]
   -------------------------------------


>> (6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 + x^
                                            ^
Runtime error: Bad argument types
Argument types given: RngMPolElt, RngMPolElt

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Sun Jul 11 22:42:17 2004

Input: R<x>:= PolynomialRing( Rationals(), 1 );
(6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 

Output: Magma V2.10-22    Sun Jul 11 2004 22:42:15 on modular  [Seed = 2569544470]
   -------------------------------------


>> (6*x^2 - 2*x + 4) + (x^3 - 2*x^2 + x - 1)(x^3 + 2*x^2 + 3*x + 4) - x^6 ;
                                            ^
Runtime error: Bad argument types
Argument types given: RngMPolElt, RngMPolElt

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:43:48 2004

Input: CartanMatrix(IrreducibleLieAlgebra("G2"));

Output: Magma V2.10-22    Mon Jul 12 2004 01:43:46 on modular  [Seed = 2302405777]
   -------------------------------------


>> CartanMatrix(IrreducibleLieAlgebra("G2"));;
                ^
User error: Identifier 'IrreducibleLieAlgebra' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:44:00 2004

Input: CartanMatrix(LieAlgebra("G2"));

Output: Magma V2.10-22    Mon Jul 12 2004 01:43:58 on modular  [Seed = 2167661717]
   -------------------------------------


>> CartanMatrix(LieAlgebra("G2"));;
                          ^
Runtime error in 'LieAlgebra': Bad argument types
Argument types given: MonStgElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:45:07 2004

Input: CartanMatrix(SemisimpleLieAlgebra("G2"));

Output: Magma V2.10-22    Mon Jul 12 2004 01:45:04 on modular  [Seed = 2569796851]
   -------------------------------------


>> CartanMatrix(SemisimpleLieAlgebra("G2"));;
                                    ^
Runtime error in 'SemisimpleLieAlgebra': Bad argument types
Argument types given: MonStgElt

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:45:17 2004

Input: CartanMatrix(SemisimpleLieAlgebra(G2));

Output: Magma V2.10-22    Mon Jul 12 2004 01:45:14 on modular  [Seed = 2435052785]
   -------------------------------------


>> CartanMatrix(SemisimpleLieAlgebra(G2));;
                                    ^
Runtime error in 'SemisimpleLieAlgebra': Bad argument types
Argument types given: Intrinsic

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:47:44 2004

Input: CartanMatrix(SemisimpleLieAlgebra("G2", ComplexField()));

Output: Magma V2.10-22    Mon Jul 12 2004 01:47:41 on modular  [Seed = 2937965144]
   -------------------------------------


>> CartanMatrix(SemisimpleLieAlgebra("G2", ComplexField()));;
               ^
Runtime error in 'CartanMatrix': Bad argument types
Argument types given: AlgLie

Total time: 2.609 seconds, Total memory usage: 2.51MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:47:59 2004

Input: CartanMatrix(LieAlgebra("G2", ComplexField()));

Output: Magma V2.10-22    Mon Jul 12 2004 01:47:56 on modular  [Seed = 2803220897]
   -------------------------------------


>> CartanMatrix(LieAlgebra("G2", ComplexField()));;
               ^
Runtime error in 'CartanMatrix': Bad argument types
Argument types given: AlgLie

Total time: 2.589 seconds, Total memory usage: 2.51MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:48:12 2004

Input: CartanMatrix("G2');

Output: Magma V2.10-22    Mon Jul 12 2004 01:48:09 on modular  [Seed = 3205355948]
   -------------------------------------


>> quit;
        ^
User error: Unterminated string

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Mon Jul 12 01:48:20 2004

Input: CartanMatrix("G2");

Output: Magma V2.10-22    Mon Jul 12 2004 01:48:17 on modular  [Seed = 3070611868]
   -------------------------------------

[ 2 -1]
[-3  2]

Total time: 2.499 seconds, Total memory usage: 2.03MB


************** MAGMA *****************
Host CPE-203-45-93-136.nsw.bigpond.net.au. (203.45.93.136)
Time: Mon Jul 12 06:53:03 2004

Input: Factorization(1234);


Output: Magma V2.10-22    Mon Jul 12 2004 06:52:59 on modular  [Seed = 464074393]
   -------------------------------------

[ <2, 1>, <617, 1> ]

Total time: 2.609 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ZB171149.ppp.dion.ne.jp. (219.125.171.149)
Time: Mon Jul 12 07:15:34 2004

Input: 1138150*20/104;



Output: Magma V2.10-22    Mon Jul 12 2004 07:15:31 on modular  [Seed = 1859935411]
   -------------------------------------

218875

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ZB171149.ppp.dion.ne.jp. (219.125.171.149)
Time: Mon Jul 12 07:16:38 2004

Input: 1138150*20/104;

218875*19/103;


Output: Magma V2.10-22    Mon Jul 12 2004 07:16:35 on modular  [Seed = 1959151465]
   -------------------------------------

218875
40375

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ZB171149.ppp.dion.ne.jp. (219.125.171.149)
Time: Mon Jul 12 07:17:27 2004

Input: 1138150*20/104;

218875*19*18/(103*102);


Output: Magma V2.10-22    Mon Jul 12 2004 07:17:24 on modular  [Seed = 2218178510]
   -------------------------------------

218875
7125

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-203-45-93-136.nsw.bigpond.net.au. (203.45.93.136)
Time: Mon Jul 12 08:18:07 2004

Input: Factorization(2*3*5*7*11*13*17+1);


Output: Magma V2.10-22    Mon Jul 12 2004 08:18:05 on modular  [Seed = 4165613963]
   -------------------------------------

[ <19, 1>, <97, 1>, <277, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-203-45-93-136.nsw.bigpond.net.au. (203.45.93.136)
Time: Mon Jul 12 08:18:25 2004

Input: Factorization(2*3*5*7*11*13*17*19+1);


Output: Magma V2.10-22    Mon Jul 12 2004 08:18:22 on modular  [Seed = 4030869872]
   -------------------------------------

[ <347, 1>, <27953, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-203-45-93-136.nsw.bigpond.net.au. (203.45.93.136)
Time: Mon Jul 12 08:28:42 2004

Input: Factorization(2*3*5*7*11*13*17*19*23*29*31+1);


Output: Magma V2.10-22    Mon Jul 12 2004 08:28:39 on modular  [Seed = 295949033]
   -------------------------------------

[ <200560490131, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-203-45-93-136.nsw.bigpond.net.au. (203.45.93.136)
Time: Mon Jul 12 08:28:50 2004

Input: Factorization(2*3*5*7*11*13*17*19*23*29*31+1);


Output: Magma V2.10-22    Mon Jul 12 2004 08:28:48 on modular  [Seed = 681241639]
   -------------------------------------

[ <200560490131, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-203-45-93-136.nsw.bigpond.net.au. (203.45.93.136)
Time: Mon Jul 12 08:29:02 2004

Input: Factorization(2*3*5*7*11*13*17*19*23*29*31*127
+1);


Output: Magma V2.10-22    Mon Jul 12 2004 08:28:59 on modular  [Seed = 546497572]
   -------------------------------------

[ <113, 1>, <225408692447, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:36:46 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,a*c=c*a,b*c*b=c*b*c,a^2>;
G<x>:=sub<F|a*b*a*c*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:36:43 on modular  [Seed = 1959167087]
   -------------------------------------

2
24

Total time: 2.749 seconds, Total memory usage: 17.67MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:37:08 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,a*c=c*a,b*c*b=c*b*c,a^3>;
G<x>:=sub<F|a*b*a*c*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:37:05 on modular  [Seed = 2110754127]
   -------------------------------------

6
648

Total time: 2.739 seconds, Total memory usage: 17.67MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:38:37 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,a*c=c*a,b*c*b=c*b*c,a^4>;
G<x>:=sub<F|a*b*a*c*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:38:22 on modular  [Seed = 1742051097]
   -------------------------------------

0
0

Total time: 14.929 seconds, Total memory usage: 26.05MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:39:09 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2>;
G<x>:=sub<F|a*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:39:06 on modular  [Seed = 1876795365]
   -------------------------------------

2
6

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:39:16 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
G<x>:=sub<F|a*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:39:13 on modular  [Seed = 2552916009]
   -------------------------------------

4
24

Total time: 2.749 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:39:35 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^4>;
G<x>:=sub<F|a*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:39:32 on modular  [Seed = 2167632165]
   -------------------------------------

8
96

Total time: 2.749 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:39:41 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^5>;
G<x>:=sub<F|a*b*a>;
Order(G);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:39:39 on modular  [Seed = 2302376226]
   -------------------------------------

20
600

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:40:19 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a*b*a>;
Order(G : CosetLimit:=4000000);
Order(F);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-22    Mon Jul 12 2004 11:40:09 on modular  [Seed = 2752926829]
   -------------------------------------


Current total memory usage: 62.7MB, failed memory request: 39.1MB
System Error: User memory limit has been reached

Current total memory usage: 93.1MB, failed memory request: 15.3MB
System Error: User memory limit has been reached

Total time: 9.879 seconds, Total memory usage: 97.67MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:40:36 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a*b*a>;
Order(G : CosetLimit:=1000000);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:40:26 on modular  [Seed = 2887670870]
   -------------------------------------

0
0

Total time: 10.639 seconds, Total memory usage: 29.67MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 11:41:15 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6>;
G<x>:=sub<F|a*b*a>;
Order(G : CosetLimit:=3000000);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 11:40:55 on modular  [Seed = 3630836175]
   -------------------------------------

0
0

Total time: 19.489 seconds, Total memory usage: 80.53MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 12:11:22 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6,(a*b)^18,(a*b*a)^12>;
G<x>:=sub<F|a*b*a>;
Order(G : CosetLimit:=3000000);
Order(F);

Output: Magma V2.10-22    Mon Jul 12 2004 12:11:11 on modular  [Seed = 1691786346]
   -------------------------------------

0
0

Total time: 10.929 seconds, Total memory usage: 52.01MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 12:12:06 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^6,(a*b)^18,(a*b*a)^12>;
Order(F : CosetLimit:=5000000);

Output: Magma V2.10-22    Mon Jul 12 2004 12:11:49 on modular  [Seed = 1876793147]
   -------------------------------------

0

Total time: 17.499 seconds, Total memory usage: 81.77MB


************** MAGMA *****************
Host pD95358CB.dip.t-dialin.net. (217.83.88.203)
Time: Mon Jul 12 12:13:25 2004

Input: F<x,y>:=Group<x,y|x^3=y^2,(x^-1*y)^6,(y*x^-1)^6,x^18,y^12>;
Order(F : CosetLimit:=5000000);

Output: Magma V2.10-22    Mon Jul 12 2004 12:13:08 on modular  [Seed = 2535812882]
   -------------------------------------

0

Total time: 16.879 seconds, Total memory usage: 81.99MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Mon Jul 12 12:47:22 2004

Input: "yes" cat "no";

Output: Magma V2.10-22    Mon Jul 12 2004 12:47:19 on modular  [Seed = 4215896957]
   -------------------------------------

yesno

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Mon Jul 12 12:47:34 2004

Input: "yes" cat (3/4) cat "no";

Output: Magma V2.10-22    Mon Jul 12 2004 12:47:32 on modular  [Seed = 3813761878]
   -------------------------------------


>> "yes" cat (3/4) cat "no";;
         ^
Runtime error in 'cat': Bad argument types
Argument types given: MonStgElt, FldRatElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Mon Jul 12 12:48:49 2004

Input: "yes" , (3/4) , "no";

Output: Magma V2.10-22    Mon Jul 12 2004 12:48:46 on modular  [Seed = 3948505876]
   -------------------------------------

yes 3/4 no

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-24-10-236-244.client.comcast.net. (24.10.236.244)
Time: Mon Jul 12 12:51:44 2004

Input: B<s1,s2,s3> := BraidGroup(4);
Id := s1*s1^-1;
D := s1*s2*s3*s1*s2*s1;

good := 0;
// Test case m1 (len=50)
a := s2^-1*s1*s3^-1*s1^-1*s1^-1*s1^-1*s3*s3*s1*s2^-1*s2^-1*s1^-1*s2^-1*s2^-1*s1*s2*s3^-1*s2*s3^-1*s1*s3^-1*s1*s2*s3^-1*s2*s1^-1*s3^-1*s2^-1*s1^-1*s3*s3^-1*s2*s1*s1*s1*s3^-1*s1*s2*s2*s3^-1*s2*s1^-1*s1^-1*s3^-1*s3^-1*s1*s3*s3*s2^-1*s3^-1;
b := s3*s1*s1*s2*s3*s1^-1*s2^-1*s2^-1*s3*s1^-1*s3*s1^-1*s3*s3*s2*s3*s2^-1*s3*s2^-1*s1*s3*s1*s3*s3*s2^-1*s3^-1*s2^-1*s3*s3*s1*s3^-1*s3^-1*s2^-1*s2^-1*s1^-1*s3*s1^-1*s3*s3*s2^-1*s2^-1*s3*s1^-1*s3*s1^-1*s3*s3*s3*s2*s2;
ab := D^-15*s1*s2*s3*s2*s1*s3*s3*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s2*s3*s2*s2*s3*s1*s2*s2*s3*s1*s3*s3*s3*s2*s2*s2*s1*s1*s3*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s2*s3*s2*s1*s3*s2*s1*s1*s1*s2*s2*s3*s1*s1*s1*s2*s3*s2*s2*s3*s2*s1*s3*s2*s2*s1*s1*s2*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s3*s3*s3*s3*s3*s2*s2;
if not (a*b eq ab) then "Failure on m1"; else good := good+1; end if;

// Test case m2 (len=51)
a := s3^-1*s2^-1*s3^-1*s3^-1*s1^-1*s2*s3*s1*s1*s1*s2^-1*s1*s1*s3^-1*s1^-1*s2^-1*s2^-1*s1^-1*s1^-1*s3^-1*s1^-1*s3*s3*s1*s2^-1*s1*s1*s3^-1*s2^-1*s3*s2^-1*s3^-1*s1^-1*s1^-1*s2^-1*s1^-1*s2*s2^-1*s3*s1*s2*s1^-1*s1^-1*s2*s2*s3^-1*s1*s3^-1*s1^-1*s3^-1*s2;
b := s1*s3*s1^-1*s1^-1*s2*s3*s1^-1*s1^-1*s3^-1*s1^-1*s3*s2^-1*s2^-1*s2^-1*s2^-1*s1*s2^-1*s2^-1*s1*s2*s1^-1*s3*s1*s1*s3*s1*s3*s2^-1*s2^-1*s3*s2*s3*s3*s2*s3^-1*s1*s3^-1*s2^-1*s1^-1*s3^-1*s1^-1*s2*s3*s2*s2*s2*s3*s2*s1*s3*s1;
ab := D^-18*s1*s2*s1*s2*s1*s3*s2*s2*s3*s1*s1*s1*s3*s1*s1*s2*s3*s2*s2*s3*s1*s1*s2*s3*s2*s1*s3*s2*s1*s1*s2*s3*s3*s2*s2*s3*s1*s1*s2*s3*s2*s2*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s1*s2*s1*s1*s2*s2*s2*s3*s1*s1*s1*s3*s1*s1*s3*s2*s1*s1*s2*s2*s1*s3*s2*s2*s3*s3*s2*s1*s1;
if not (a*b eq ab) then "Failure on m2"; else good := good+1; end if;

// Test case m3 (len=52)
a := s3^-1*s2^-1*s3*s2*s3*s3*s1^-1*s3^-1*s2*s3^-1*s3^-1*s2^-1*s1^-1*s3^-1*s2^-1*s3*s1^-1*s2*s3*s1*s1*s2^-1*s1^-1*s2*s3^-1*s1^-1*s1^-1*s2^-1*s1^-1*s2*s3^-1*s2*s1*s2^-1*s1^-1*s3*s3*s2*s2*s3*s1*s1*s3^-1*s2^-1*s3^-1*s1^-1*s2*s1*s2^-1*s1^-1*s3^-1*s2^-1;
b := s1^-1*s2*s2*s3*s2*s2*s2*s3^-1*s2*s1*s3*s3*s2^-1*s1^-1*s1^-1*s3^-1*s1^-1*s1^-1*s3^-1*s3^-1*s1*s2*s3^-1*s3^-1*s2^-1*s2^-1*s3*s1^-1*s3*s1*s1*s3^-1*s1*s3^-1*s2*s1^-1*s3^-1*s1*s3^-1*s2*s1*s3^-1*s2*s1^-1*s3^-1*s3^-1*s1*s2*s2*s1^-1*s2*s3;
ab := D^-17*s2*s2*s1*s1*s2*s3*s2*s2*s3*s1*s1*s2*s3*s2*s3*s2*s1*s1*s1*s1*s1*s2*s2*s3*s3*s2*s2*s3*s1*s1*s1*s2*s3*s2*s2*s3*s2*s2*s3*s2*s2*s3*s1*s1*s2*s3*s2*s2*s2*s1*s3*s2*s2*s3*s1*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s2*s1*s1*s3*s1*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s1*s3*s2*s2*s3;
if not (a*b eq ab) then "Failure on m3"; else good := good+1; end if;

// Test case m4 (len=53)
a := s3*s1^-1*s1^-1*s1^-1*s3*s2*s3*s1*s1*s3*s2^-1*s1*s2^-1*s2^-1*s1*s1*s1*s3*s3*s1^-1*s1^-1*s2^-1*s1*s2*s3^-1*s1*s3*s2*s1^-1*s1^-1*s2*s2*s1^-1*s3^-1*s1^-1*s2^-1*s2^-1*s3*s1^-1*s1^-1*s2^-1*s1^-1*s2^-1*s1*s2^-1*s1*s2^-1*s2^-1*s1^-1*s2^-1*s2^-1*s3^-1*s1;
b := s2*s1*s3^-1*s2^-1*s1^-1*s2*s1*s1^-1*s3^-1*s2*s2*s3^-1*s1*s2*s2*s2*s2*s3^-1*s1*s3*s2^-1*s2^-1*s2^-1*s1*s1*s3*s2^-1*s2^-1*s1*s2^-1*s1*s1*s3*s1^-1*s3^-1*s1*s3^-1*s1*s1*s1*s2*s3*s1^-1*s3*s2*s3^-1*s1*s2*s3^-1*s3*s1^-1*s2*s1;
ab := D^-23*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s2*s2*s3*s1*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s2*s3*s1*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s1*s2*s2*s1*s1*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s3*s1*s2*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s2*s3*s2*s3*s2*s2*s2*s1*s1*s3*s1*s2*s2*s3*s2*s2*s3*s1*s3*s3*s2*s2*s3*s1*s2*s2*s3*s1*s1*s1*s3*s1*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s2*s2*s1*s3*s3*s3*s3*s3*s3*s2*s1*s1*s2*s3*s3*s2*s2*s1;
if not (a*b eq ab) then "Failure on m4"; else good := good+1; end if;

// Test case m5 (len=54)
a := s3^-1*s3^-1*s3^-1*s1*s1*s2^-1*s3*s2*s1^-1*s3^-1*s2*s1^-1*s1^-1*s1^-1*s2^-1*s3^-1*s3^-1*s2*s1^-1*s3^-1*s1*s1*s2^-1*s1^-1*s3^-1*s2*s1^-1*s2*s1^-1*s2*s1^-1*s3^-1*s1*s2*s1*s1*s3^-1*s2*s3*s3*s3*s2^-1*s1*s1^-1*s2^-1*s2^-1*s1^-1*s3^-1*s1^-1*s2^-1*s3*s3*s3^-1*s3^-1;
b := s1*s3*s3*s2*s1^-1*s2*s3*s2^-1*s1^-1*s3^-1*s1*s3^-1*s1*s3^-1*s2*s2*s1^-1*s3*s2*s1^-1*s2^-1*s2^-1*s1^-1*s3*s2^-1*s2^-1*s3*s1^-1*s3^-1*s1*s1*s1*s3^-1*s2^-1*s2^-1*s3^-1*s1*s2*s1^-1*s2*s1*s2*s1^-1*s2*s1^-1*s1^-1*s2^-1*s3^-1*s1*s1*s3*s2*s1*s2^-1;
ab := D^-22*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s1*s1*s2*s2*s3*s1*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s1*s1*s2*s3*s2*s2*s3*s2*s2*s3*s2*s2*s3*s1*s3*s2*s2*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s2*s2*s1*s3*s3*s2*s1*s1*s2*s2*s1*s1*s3*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s3*s2*s2*s3*s1*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s2*s3*s2*s2*s3*s1*s1*s2*s2*s1*s3*s2*s2*s2*s3*s3*s2*s1*s1*s1*s1*s2*s2;
if not (a*b eq ab) then "Failure on m5"; else good := good+1; end if;

// Test case m6 (len=55)
a := s3^-1*s3^-1*s3^-1*s2*s1*s3*s2^-1*s1*s2^-1*s3^-1*s2^-1*s2^-1*s1^-1*s1*s3*s2*s3*s3*s1^-1*s2^-1*s2^-1*s3*s1^-1*s2*s1^-1*s3*s1^-1*s3^-1*s1*s2*s3^-1*s2^-1*s3^-1*s2^-1*s1*s1*s3^-1*s3^-1*s1*s2*s3*s3*s3*s1*s3*s1*s1*s2^-1*s3^-1*s2*s2*s3^-1*s3^-1*s1*s2;
b := s3^-1*s2*s2*s3*s1*s3*s3*s1*s2*s2^-1*s3*s1*s1*s2*s2^-1*s3*s3*s1*s2^-1*s1^-1*s3*s2*s3^-1*s2^-1*s3*s3*s3*s1^-1*s2^-1*s1^-1*s3^-1*s1*s2^-1*s1^-1*s3^-1*s2^-1*s3^-1*s1^-1*s3*s1*s2*s2*s1^-1*s1^-1*s3^-1*s2*s3*s2*s3*s1*s3*s3*s1*s2*s1;
ab := D^-17*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s2*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s3*s2*s1*s1*s2*s2*s1*s1*s3*s1*s2*s2*s3*s2*s2*s3*s1*s1*s2*s3*s2*s2*s2*s2*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s2*s2*s1*s1*s3*s1*s1*s1*s3*s3*s3*s3*s3*s3*s2*s1*s1*s1*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s1*s1*s2*s2*s1*s1*s3*s3*s3*s3*s2*s1;
if not (a*b eq ab) then "Failure on m6"; else good := good+1; end if;

// Test case m7 (len=56)
a := s3*s2^-1*s3*s3*s1*s2^-1*s2^-1*s3^-1*s2^-1*s3^-1*s1*s2*s3*s2^-1*s1^-1*s3*s1^-1*s2^-1*s1^-1*s3^-1*s3^-1*s1*s3^-1*s2*s1*s2^-1*s3^-1*s1*s3^-1*s1*s2^-1*s3^-1*s3*s1*s3*s2*s1*s3*s3*s3*s1*s1*s3*s1^-1*s1*s1*s2*s3^-1*s1*s3*s2^-1*s1*s1*s2*s1^-1*s2;
b := s3^-1*s2*s2*s2*s1^-1*s1^-1*s2*s3^-1*s2^-1*s3^-1*s1*s1*s2*s3*s3*s1^-1*s2^-1*s3^-1*s2^-1*s3*s2*s1*s1*s3^-1*s2*s1^-1*s2*s2*s3*s2*s3^-1*s2^-1*s3*s3*s2*s3*s3*s2^-1*s1*s1*s1*s2^-1*s3*s1^-1*s2^-1*s1^-1*s3*s2*s3^-1*s1*s2*s3*s2^-1*s1*s2^-1*s3^-1;
ab := D^-16*s1*s2*s3*s2*s2*s3*s1*s1*s1*s3*s1*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s1*s1*s3*s2*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s2*s3*s1*s1*s2*s3*s2*s2*s3*s2*s2*s3*s1*s3*s2*s2*s3*s1*s3*s3*s3*s2*s2*s1*s1*s2*s2*s2*s3*s1*s3*s3*s3*s2*s2*s3*s1*s1*s1*s1*s2*s2*s3*s3*s2*s2*s3*s1*s1*s1*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s1*s2*s1*s2*s3*s3*s3*s2*s1;
if not (a*b eq ab) then "Failure on m7"; else good := good+1; end if;

// Test case m8 (len=57)
a := s1^-1*s3^-1*s1^-1*s3^-1*s2*s1^-1*s3*s2*s1^-1*s3*s2^-1*s3^-1*s1^-1*s3^-1*s1^-1*s2*s3*s1*s3*s2^-1*s1^-1*s2^-1*s1^-1*s3*s2*s3*s3*s2^-1*s1^-1*s3*s3*s1^-1*s1^-1*s3^-1*s1^-1*s2*s1*s2*s1*s3*s1*s2^-1*s1*s3^-1*s1*s2^-1*s3*s3*s1*s3^-1*s2*s1^-1*s3^-1*s1*s2*s3^-1*s2^-1;
b := s3*s1*s3^-1*s1^-1*s2^-1*s3*s2*s3^-1*s2*s2*s1*s3^-1*s2*s3^-1*s3*s3*s2^-1*s3*s2*s1*s3*s2^-1*s1*s3*s2^-1*s1*s1*s1*s3*s2*s1*s2^-1*s3*s2^-1*s3^-1*s3*s1^-1*s3^-1*s1*s3^-1*s2^-1*s1*s2^-1*s1^-1*s2^-1*s3*s3*s1*s2*s3*s3^-1*s2*s3^-1*s2*s1*s1*s3^-1;
ab := D^-22*s2*s3*s1*s2*s1*s2*s3*s1*s2*s2*s3*s1*s1*s3*s2*s1*s1*s1*s2*s2*s3*s1*s2*s2*s3*s1*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s1*s2*s1*s1*s1*s2*s2*s2*s2*s3*s1*s1*s2*s3*s2*s1*s3*s3*s2*s2*s3*s1*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s3*s1*s2*s3*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s1*s3*s3*s3*s2*s1*s1;
if not (a*b eq ab) then "Failure on m8"; else good := good+1; end if;

// Test case m9 (len=58)
a := s1*s2*s1^-1*s2*s2*s3*s3*s2^-1*s2*s3*s1*s3*s1^-1*s3*s2^-1*s3*s2*s2*s3^-1*s1*s3*s2*s1^-1*s2*s3^-1*s2^-1*s1*s3*s1*s2^-1*s1^-1*s1^-1*s2*s1*s3*s3*s2*s3*s2^-1*s2^-1*s2^-1*s3^-1*s1^-1*s3^-1*s1^-1*s2*s2*s3^-1*s2^-1*s1*s2*s1*s2*s2*s1^-1*s2*s2*s1^-1;
b := s1^-1*s2^-1*s1*s3*s1*s1*s2*s3^-1*s2^-1*s3^-1*s3^-1*s2^-1*s2^-1*s2^-1*s3^-1*s2*s2*s1^-1*s2*s2*s3^-1*s1^-1*s3^-1*s2^-1*s2^-1*s2^-1*s2^-1*s1*s1*s2*s2*s1*s1*s3*s1*s3^-1*s2*s2*s2*s2*s3^-1*s3*s1^-1*s3*s1^-1*s3^-1*s1^-1*s2^-1*s1^-1*s1^-1*s1^-1*s3*s3*s3*s1*s1^-1*s1^-1*s3;
ab := D^-20*s1*s2*s2*s1*s1*s3*s2*s2*s2*s2*s2*s2*s3*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s3*s1*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s1*s2*s3*s1*s2*s2*s3*s1*s1*s1*s3*s1*s2*s3*s2*s2*s3*s1*s1*s1*s3*s3*s2*s1*s1*s2*s2*s2*s2*s2*s3*s1*s1*s1*s2*s3*s2*s1*s1*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s1*s1*s1*s2*s2*s2*s1*s1*s2*s3*s3*s3*s3;
if not (a*b eq ab) then "Failure on m9"; else good := good+1; end if;

// Test case m10 (len=59)
a := s1^-1*s3*s2^-1*s3*s3*s2^-1*s2^-1*s3*s1^-1*s1^-1*s1^-1*s1^-1*s3^-1*s2^-1*s3^-1*s2^-1*s3^-1*s2*s3^-1*s2*s1*s2^-1*s1*s3^-1*s3*s3*s3^-1*s1*s3*s3*s3*s1^-1*s3^-1*s2^-1*s2^-1*s2^-1*s3^-1*s1*s1*s2^-1*s1*s3*s3*s1*s2*s3*s1^-1*s2*s1^-1*s2^-1*s3^-1*s2^-1*s2^-1*s2^-1*s1*s3*s2^-1*s1*s2;
b := s2^-1*s3^-1*s1*s1*s3*s1*s3^-1*s1^-1*s3*s3*s3*s2^-1*s2^-1*s1*s2^-1*s1^-1*s3^-1*s3*s1*s2*s1^-1*s3^-1*s2*s3*s2^-1*s3^-1*s3^-1*s3^-1*s3^-1*s2^-1*s3*s1^-1*s3^-1*s3^-1*s2*s3^-1*s1*s1^-1*s3^-1*s3^-1*s3^-1*s3*s3*s1*s1*s1*s2^-1*s1*s2^-1*s2^-1*s1^-1*s2*s1*s3^-1*s1*s3*s3*s1^-1*s2;
ab := D^-24*s2*s3*s2*s2*s3*s1*s2*s1*s2*s2*s2*s3*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s1*s1*s2*s3*s2*s3*s2*s2*s3*s1*s2*s2*s3*s1*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s2*s3*s1*s2*s2*s2*s1*s1*s3*s1*s2*s2*s3*s2*s2*s3*s1*s2*s2*s2*s1*s3*s2*s2*s3*s1*s1*s1*s2*s3*s2*s1*s1*s3*s1*s1*s2*s3*s2*s2*s2*s1*s1*s2*s3*s2*s2*s3*s1*s2*s1*s1*s2*s3*s1*s1*s2*s3*s2*s1*s1*s3*s1*s2*s2*s3*s2*s2*s3*s2*s1*s1*s2*s3*s2*s2*s1*s1*s1*s2*s2*s2*s3*s1*s2;
if not (a*b eq ab) then "Failure on m10"; else good := good+1; end if;

// Test case m11 (len=60)
a := s2*s2*s2*s2*s3^-1*s2^-1*s2^-1*s1*s1*s1*s1*s3*s1*s3^-1*s1^-1*s3^-1*s1*s3*s3*s3*s1^-1*s2*s1^-1*s1^-1*s2*s2*s1*s2^-1*s1*s3^-1*s2^-1*s3^-1*s1*s3*s3^-1*s3^-1*s1^-1*s3*s1^-1*s3^-1*s3^-1*s1^-1*s2^-1*s1^-1*s1^-1*s2^-1*s3*s1^-1*s2^-1*s2*s3^-1*s2^-1*s1^-1*s2*s1^-1*s2^-1*s1^-1*s3^-1*s2*s1;
b := s3^-1*s2*s3*s1*s3^-1*s1*s3^-1*s2^-1*s3^-1*s1^-1*s1^-1*s3^-1*s1^-1*s3*s3^-1*s3^-1*s1^-1*s2^-1*s3^-1*s2^-1*s1*s1*s3^-1*s1^-1*s3*s3^-1*s1^-1*s1^-1*s3^-1*s3^-1*s1^-1*s3*s2^-1*s1^-1*s2*s3^-1*s2^-1*s1^-1*s2^-1*s1*s3*s3*s2^-1*s2^-1*s3*s2^-1*s1^-1*s1^-1*s3*s3*s1*s3*s3*s2*s3^-1*s1^-1*s3^-1*s1^-1*s2*s1^-1;
ab := D^-25*s2*s3*s2*s1*s1*s2*s3*s2*s2*s2*s2*s2*s1*s1*s3*s1*s1*s2*s3*s2*s2*s3*s2*s1*s1*s2*s3*s2*s1*s1*s2*s3*s2*s1*s3*s2*s2*s2*s3*s3*s2*s2*s2*s1*s1*s3*s3*s2*s1*s1*s2*s2*s1*s3*s3*s2*s1*s1*s2*s2*s1*s1*s2*s3*s2*s2*s3*s2*s3*s2*s2*s2*s1*s3*s2*s2*s3*s1*s2*s2*s3*s1*s1*s1*s3*s1*s2*s1*s1*s2*s3*s2*s2*s3*s2*s2*s3*s1*s3*s2*s2*s3*s1*s1*s3*s3*s2*s1*s1*s2*s2*s2*s2*s2*s3*s1*s2*s2*s3*s1*s2*s2*s3*s1*s1*s2;
if not (a*b eq ab) then "Failure on m11"; else good := good+1; end if;

good, "of", 11;
"Done.";


Output: Magma V2.10-22    Mon Jul 12 2004 12:51:41 on modular  [Seed = 295932062]
   -------------------------------------

11 of 11
Done.

Total time: 2.759 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host c-67-169-24-189.client.comcast.net. (67.169.24.189)
Time: Tue Jul 13 02:59:19 2004

Input: F3 := CyclotomicField(3);
chi := (DirichletGroup(7,F3).1)^2;
space := CuspForms(DirichletGroup(7^2*11)!chi,2);
Newforms(space);


Output: Magma V2.10-22    Tue Jul 13 2004 02:59:17 on modular  [Seed = 3363504273]
   -------------------------------------


HackobjCoerceGrpDrch(
    G: Group of Dirichlet characters of modulus 539 over Rational F...,
    x: $.1^2
)
In file "/usr/local/magma/package/Geometry/ModSym/dirichlet.m", line 388, column
67:
>>          return true, DirichletCharacterFromValuesOnUnitGenerators(G,s); 
                                                                     ^
Runtime error in 'DirichletCharacterFromValuesOnUnitGenerators': Argument 2 must
be a sequence of elements in the base ring of argument 1.

>> Newforms(space);
            ^
User error: Identifier 'space' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host c-67-169-24-189.client.comcast.net. (67.169.24.189)
Time: Tue Jul 13 03:00:51 2004

Input: F3 := CyclotomicField(3);
chi := (DirichletGroup(7,F3).1)^2;
space := CuspForms(DirichletGroup(7^2*11,F3)!chi,2);
Newforms(space);


Output: Magma V2.10-22    Tue Jul 13 2004 03:00:29 on modular  [Seed = 3830918261]
   -------------------------------------



************** MAGMA *****************
Host 149.64.142.82.ip.b26.cz. (82.142.64.149)
Time: Tue Jul 13 05:22:56 2004

Input: a=(x-y)^2

Output: Magma V2.10-22    Tue Jul 13 2004 05:22:47 on modular  [Seed = 998822594]
   -------------------------------------


>> a=(x-y)^2;
      ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.20)
Time: Tue Jul 13 07:54:49 2004

Input: //=================================================
//        Example for a function in Magma
//=================================================

Fact := function(n)
if n eq 0 then return 1;
else return n * $$(n-1);
end if;
end function;


//=================================================
//         ArtinSchreierRoot Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;

ArtinSchreierRoot := function(a,b,v)

	if v eq 1 then
		return [GaloisImage(a,n-1) , 
			GaloisImage(b,n-1) ];
	end if;

	AB := $$(a,b,Floor(v/2));

	A := AB[1]; B := AB[2];

	AB := [( A * GaloisImage(A,n-Floor(v/2)) ), 
	      ( A * GaloisImage(B,n-Floor(v/2)) + B )];

	A := AB[1]; B := AB[2];

	if v mod 2 eq 1 then
	
		AB := [( A * GaloisImage(a,n-v) ) , 
		      ( A * GaloisImage(b,n-v) + B )];

	end if;
	
	return AB;

end function;


//=======================================
// Checking ASR function
//=======================================
//"Running ASR"

a:=R!3;
b:=R!5;

//finding x

C := ArtinSchreierRoot(a,b,4);

A := C[1]; B:= C[2];

//"Checking answer"

A;
B;
p^m;

Output: Magma V2.10-22    Tue Jul 13 2004 07:54:44 on modular  [Seed = 2603095615]
   -------------------------------------

81
200
15625

Total time: 2.579 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 18:24:18 2004

Input: Factorization(7653748373);

Output: Magma V2.10-22    Tue Jul 13 2004 18:24:15 on modular  [Seed = 1373991027]
   -------------------------------------

[ <7653748373, 1> ]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:20:04 2004

Input: Factorization(76537483373);

Output: Magma V2.10-22    Tue Jul 13 2004 19:20:01 on modular  [Seed = 3797339374]
   -------------------------------------

[ <13, 2>, <5737, 1>, <78941, 1> ]

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:20:11 2004

Input: Factorization(765337483373);

Output: Magma V2.10-22    Tue Jul 13 2004 19:20:08 on modular  [Seed = 3346262466]
   -------------------------------------

[ <149, 1>, <1321, 1>, <3888337, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:20:28 2004

Input: Factorization(49523847503948571623);

Output: Magma V2.10-22    Tue Jul 13 2004 19:20:25 on modular  [Seed = 3748393419]
   -------------------------------------

[ <17, 1>, <211, 1>, <7253, 1>, <1903554535193, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:20:43 2004

Input: Factorization(49523847503948573948562738495028374651623);

Output: Magma V2.10-22    Tue Jul 13 2004 19:20:39 on modular  [Seed = 3613653437]
   -------------------------------------

[ <555237673, 1>, <89193961274937793978836768331151, 1> ]

Total time: 4.219 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:21:00 2004

Input: Factorization(49523847503948573948562738492837402983746582930485028374651623);

Output: Magma V2.10-22    Tue Jul 13 2004 19:20:57 on modular  [Seed = 748159579]
   -------------------------------------

[ <78157, 1>, <633645706769049144012215649178415279293557620308929825539, 1> ]

Total time: 2.739 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:21:39 2004

Input: Factorization(4952384750394837482938475647382935573948562738492837402983746582930485028374651623);

Output: Magma V2.10-22    Tue Jul 13 2004 19:21:16 on modular  [Seed = 613419622]
   -------------------------------------



************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:22:04 2004

Input: Factorization(495238475039483748293847564738293557394856273849283740298374658293048503);

Output: Magma V2.10-22    Tue Jul 13 2004 19:21:47 on modular  [Seed = 1015550617]
   -------------------------------------

[ <17, 1>, <337, 1>, <5741, 1>, <671401, 1>, <19184650802063, 1>, 
<197277250368571, 1>, <5925638045130437255604770147599, 1> ]

Total time: 16.699 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:22:30 2004

Input: Factorization(495238475039483748293847564738293557394856273849283740298374658293048505);

Output: Magma V2.10-22    Tue Jul 13 2004 19:22:27 on modular  [Seed = 897653672]
   -------------------------------------

[ <5, 1>, <3909263, 1>, <253366670413059314911198128515934362766002836774749481\
06503689227, 1> ]

Total time: 2.869 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Tue Jul 13 19:22:56 2004

Input: Factorization(495238475039483748293847564738293557394856273849283740298374658293048507);

Output: Magma V2.10-22    Tue Jul 13 2004 19:22:36 on modular  [Seed = 230237087]
   -------------------------------------

[ <3, 1>, <5747406601583, 1>, <287224313718052081501214032333219075098329586939\
31451880743, 1> ]

Total time: 20.279 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:51:51 2004

Input: p := 23;
x := (2^p) -1;
a := 2;
z := 2
while z ne 1 mod x do
x := x+1;
z = x * x;
end while
print(x);

Output: Magma V2.10-22    Wed Jul 14 2004 05:51:48 on modular  [Seed = 1876569453]
   -------------------------------------


>> while z ne 1 mod x do
   ^
User error: bad syntax

>> z = x * x;
   ^
User error: Identifier 'z' has not been declared or assigned

>> end while
   ^
User error: bad syntax
8388608

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:53:57 2004

Input: p := 23;
x := (2^p) -1;
a := 2;
z := 2
for a := 2 to x-1 do
x := x+1;
z = x * x;
if z mod x eq 1 then
print(x);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:53:55 on modular  [Seed = 1390874839]
   -------------------------------------


>> for a := 2 to x-1 do
   ^
User error: bad syntax

>> z = x * x;
   ^
User error: Identifier 'z' has not been declared or assigned

>> if z mod x eq 1 then
      ^
User error: Identifier 'z' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:54:21 2004

Input: p := 23;
x := (2^p) -1;
a := 2;
for a := 2 to x-1 do
x := x+1;
z = x * x;
if z mod x eq 1 then
print(x);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:54:18 on modular  [Seed = 1525618854]
   -------------------------------------


>> z = x * x;
   ^
User error: Identifier 'z' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:54:57 2004

Input: p := 23;
x := (2^p) -1;
a := 2;
for a := 2 to x-1 do
x := x+1;
z := x * x;
if z mod p eq 1 then
print(x);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:54:34 on modular  [Seed = 1123483822]
   -------------------------------------

8388628
8388630
8388651
8388653
8388674
8388676
8388697
8388699
8388720
8388722
8388743
8388745
8388766
8388768
8388789
8388791
8388812
8388814
8388835
8388837
8388858
8388860
8388881
8388883
8388904
8388906
8388927
8388929
8388950
8388952
8388973
8388975
8388996
8388998
8389019
8389021
8389042
8389044
8389065
8389067
8389088
8389090
8389111
8389113
8389134
8389136
8389157
8389159
8389180
8389182
8389203
8389205
8389226
8389228
8389249
8389251
8389272
8389274
8389295
8389297
8389318
8389320
8389341
8389343
8389364
8389366
8389387
8389389
8389410
8389412
8389433
8389435
8389456
8389458
8389479
8389481
8389502
8389504
8389525
8389527
8389548
8389550
8389571
8389573
8389594
8389596
8389617
8389619
8389640
8389642
8389663
8389665
8389686
8389688
8389709
8389711
8389732
8389734
8389755
8389757
8389778
8389780
8389801
8389803
8389824
8389826
8389847
8389849
8389870
8389872
8389893
8389895
8389916
8389918
8389939
8389941
8389962
8389964
8389985
8389987
8390008
8390010
8390031
8390033
8390054
8390056
8390077
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8390100
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8390123
8390125
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8390240
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8390309
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8390355
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8390562
8390583
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8390606
8390608
8390629
8390631
8390652
8390654
8390675
8390677
8390698
8390700
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8390746
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8390792
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8394311
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8396678
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8396703
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8401439
8401441
8401462
8401464
8401485
8401487
8401508
8401510
8401531
8401533
8401554
8401556
8401577
8401579
8401600
8401602
8401623
8401625
8401646
8401648
8401669
8401671
8401692
8401694
8401715
8401717
8401738
8401740
8401761
8401763
8401784
8401786
8401807
8401809
8401830
8401832
8401853
8401855
8401876
8401878
8401899
8401901
8401922
8401924
8401945
8401947
8401968
8401970
8401991
8401993
8402014
8402016
8402037
8402039
8402060
8402062
8402083
8402085
8402106
8402108
8402129
8402131
8402152
8402154
8402175
8402177
8402198
8402200
8402221
8402223
8402244
8402246
8402267
8402269
8402290
8402292
8402313
8402315
8402336
8402338
8402359
8402361
8402382
8402384
8402405
8402407
8402428
8402430
8402451
8402453
8402474
8402476
8402497
8402499
8402520
8402522
8402543
8402545
8402566
8402568
8402589
8402591
8402612
8402614
8402635
8402637
8402658
8402660
8402681
8402683
8402704
8402706
8402727
8402729
8402750
8402752
8402773
8402775
8402796
8402798
8402819
840
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:55:42 2004

Input: p := 23;
x := (2^p) -1;
a := 2;
for a := 2 to p-1 do
x := x+1;
z := x * x;
if z mod p eq 1 then
print(x);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:55:39 on modular  [Seed = 1258228071]
   -------------------------------------

8388628

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:56:21 2004

Input: p := 23;
x := (2^p) -1;
a := 2;
for a := 2 to p-1 do
a := a+1;
z := x * x;
if z mod p eq 1 then
print(x);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:56:19 on modular  [Seed = 2986865095]
   -------------------------------------


>> a := a+1;
   ^
User error: Bad use of identifier 'a'

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:57:04 2004

Input: p := 23;
x := (2^p) -1;
for a := 2 to p-1 do
z := a * a;
if z mod p eq 1 then
print(x);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:57:01 on modular  [Seed = 2685789179]
   -------------------------------------

8388607

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:57:19 2004

Input: p := 23;
x := (2^p) -1;
for a := 2 to p-1 do
z := a * a;
if z mod p eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:57:17 on modular  [Seed = 2435109594]
   -------------------------------------

22

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:57:36 2004

Input: p := 23;
x := (2^p) -1;
for a := 2 to p-1 do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:57:33 on modular  [Seed = 2569853474]
   -------------------------------------


Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:57:48 2004

Input: p := 23;
x := (2^p) -1;
for a := 1 to p-1 do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:57:45 on modular  [Seed = 2167718446]
   -------------------------------------

1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:58:01 2004

Input: p := 23;
x := (2^p) -1;
for a := 1 to p do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:57:59 on modular  [Seed = 2302462488]
   -------------------------------------

1

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:58:10 2004

Input: p := 11;
x := (2^p) -1;
for a := 1 to p do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:58:07 on modular  [Seed = 4047811176]
   -------------------------------------

1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:58:16 2004

Input: p := 11;
x := (2^p) -1;
for a := 1 to p do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:58:14 on modular  [Seed = 4182555257]
   -------------------------------------

1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 05:59:40 2004

Input: p := 11;
x := (2^p)-1;
print(x);
print(622*622 mod 2047);
for a := 1 to p do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 05:59:38 on modular  [Seed = 3998984914]
   -------------------------------------

2047
1
1

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 06:00:17 2004

Input: p := 11;
x := (2^p)-1;
print(x);
print(622*622 mod 2047);
for a := 1 to x do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 06:00:14 on modular  [Seed = 3245639129]
   -------------------------------------

2047
1
1
622
1425
2046

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 06:00:54 2004

Input: p := 29;
x := (2^p)-1;
print(x);
for a := 1 to x do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 06:00:31 on modular  [Seed = 3380383168]
   -------------------------------------

536870911
1


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 06:01:54 2004

Input: p := 29;
x := (2^p)-1;
print(x);
for a := 100000000 to x do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 06:01:32 on modular  [Seed = 814052475]
   -------------------------------------

536870911


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 06:02:30 2004

Input: p := 29;
x := (2^p)-1;
print(x);
for a := 200000000 to x do
z := a * a;
if z mod x eq 1 then
print(a);
end if;
end for;


Output: Magma V2.10-22    Wed Jul 14 2004 06:02:07 on modular  [Seed = 647193230]
   -------------------------------------

536870911


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Wed Jul 14 06:05:15 2004

Input: (3034178/7597.363)/23
(622/118.7711)/11
8388607/2047

Output: Magma V2.10-22    Wed Jul 14 2004 06:05:11 on modular  [Seed = 430726265]
   -------------------------------------


>> 8388607/2047;
   ^
User error: bad syntax

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host tachyon.mathematik.uni-kl.de. (131.246.164.32)
Time: Wed Jul 14 06:46:18 2004

Input: ?FiniteProjectivePlane

Output: Magma V2.10-22    Wed Jul 14 2004 06:46:15 on modular  [Seed = 1674980780]
   -------------------------------------

3 matches:
     1   I   /magma/combinatorial-geometrical-incidence/plane/creation/\
             FiniteProjectivePlane
     2   I   /magma/combinatorial-geometrical-incidence/plane/creation/\
             FiniteProjectivePlane
     3   I   /magma/combinatorial-geometrical-incidence/plane/designs/\
             FiniteProjectivePlane
To view an entry, type ? followed by the number next to it

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 14 13:38:51 2004

Input: ?differential

Output: Magma V2.10-22    Wed Jul 14 2004 13:38:49 on modular  [Seed = 3731616052]
   -------------------------------------

11 matches:
     1   I   /magma/geometry/algebraic-curve/function_field/ff-diff/\
             ff-diff-element-operations/Differential
     2   I   /magma/geometry/algebraic-curve/function_field/ff-diff/\
             ff-diff-space/DifferentialSpace
     3   I   /magma/geometry/algebraic-curve/function_field/ff-diff/\
             ff-diff-space/DifferentialSpace
     4   I   /magma/geometry/algebraic-curve/linear-equivalence/riemann-roch/\
             DifferentialBasis
     5   I   /magma/ring-field-algebra/function-field/differentials/\
             create-elts/Differential
     6   I   /magma/ring-field-algebra/function-field/differentials/\
             create-struct/DifferentialSpace
     7   I   /magma/ring-field-algebra/function-field/differentials/\
             create-subspaces/DifferentialBasis
     8   I   /magma/ring-field-algebra/function-field/differentials/\
             create-subspaces/DifferentialSpace
     9   I   /magma/ring-field-algebra/function-field/Divisors/\
             operation-element/element-ops-other/DifferentialBasis
    10   I   /magma/ring-field-algebra/function-field/Divisors/\
             operation-element/element-ops-other/DifferentialSpace
    11   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/DifferentialSpace
To view an entry, type ? followed by the number next to it

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 14 13:41:06 2004

Input: ?connection

Output: Magma V2.10-22    Wed Jul 14 2004 13:41:03 on modular  [Seed = 4199533206]
   -------------------------------------

2 matches:
     1   I   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-design/operation-point-block/ConnectionNumber
     2   I   /magma/combinatorial-geometrical-incidence/\
             pseudo-random-sequences/lfsr/BerlekampMassey
To view an entry, type ? followed by the number next to it

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:18:53 2004

Input: x := 118.6708008;

for i = 1 to 500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:18:50 on modular  [Seed = 1958903790]
   -------------------------------------


>> for i = 1 to 500 do
         ^
User error: bad syntax

>> print(i);
         ^
User error: Identifier 'i' has not been declared or assigned

>> print(i * x);
         ^
User error: Identifier 'i' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:19:05 2004

Input: x := 118.6708008;

for i eq 1 to 500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:19:03 on modular  [Seed = 1140150052]
   -------------------------------------


>> for i eq 1 to 500 do
         ^
User error: bad syntax

>> print(i);
         ^
User error: Identifier 'i' has not been declared or assigned

>> print(i * x);
         ^
User error: Identifier 'i' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:19:16 2004

Input: x := 118.6708008;

for i := 1 to 500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:19:13 on modular  [Seed = 546712657]
   -------------------------------------

1
118.67080079999999999999999999938
2
237.341601599999999999999999998774
3
356.0124023999999999999999999981616
4
474.68320319999999999999999999754
5
593.354003999999999999999999996936
6
712.0248047999999999999999999963233
7
830.69560559999999999999999999571
8
949.366406399999999999999999995097
9
1068.0372071999999999999999999944850
10
1186.70800799999999999999999999387
11
1305.378808799999999999999999993259
12
1424.0496095999999999999999999926466
13
1542.72041039999999999999999999203
14
1661.391211199999999999999999991421
15
1780.0620119999999999999999999908083
16
1898.73281279999999999999999999019
17
2017.403613599999999999999999989582
18
2136.074414399999999999999999988970
19
2254.74521519999999999999999998835
20
2373.416015999999999999999999987744
21
2492.086816799999999999999999987131
22
2610.75761759999999999999999998651
23
2729.428418399999999999999999985906
24
2848.099219199999999999999999985293
25
2966.77001999999999999999999998468
26
3085.440820799999999999999999984067
27
3204.111621599999999999999999983455
28
3322.78242239999999999999999998284
29
3441.453223199999999999999999982229
30
3560.124023999999999999999999981616
31
3678.79482479999999999999999998100
32
3797.465625599999999999999999980391
33
3916.136426399999999999999999979778
34
4034.80722719999999999999999997916
35
4153.478027999999999999999999978552
36
4272.148828799999999999999999977940
37
4390.81962959999999999999999997732
38
4509.490430399999999999999999976714
39
4628.161231199999999999999999976101
40
4746.83203199999999999999999997548
41
4865.50283279999999999999999997487
42
4984.173633599999999999999999974263
43
5102.84443439999999999999999997365
44
5221.51523519999999999999999997303
45
5340.186035999999999999999999972425
46
5458.85683679999999999999999997181
47
5577.52763759999999999999999997119
48
5696.198438399999999999999999970586
49
5814.86923919999999999999999996997
50
5933.54003999999999999999999996936
51
6052.210840799999999999999999968748
52
6170.88164159999999999999999996813
53
6289.55244239999999999999999996752
54
6408.223243199999999999999999966910
55
6526.89404399999999999999999996629
56
6645.56484479999999999999999996568
57
6764.235645599999999999999999965071
58
6882.90644639999999999999999996445
59
7001.57724719999999999999999996384
60
7120.248047999999999999999999963233
61
7238.91884879999999999999999996262
62
7357.58964959999999999999999996200
63
7476.260450399999999999999999961395
64
7594.93125119999999999999999996078
65
7713.60205199999999999999999996016
66
7832.272852799999999999999999959556
67
7950.94365359999999999999999995894
68
8069.61445439999999999999999995833
69
8188.285255199999999999999999957718
70
8306.95605599999999999999999995710
71
8425.62685679999999999999999985309
72
8544.297657599999999999999999955880
73
8662.96845839999999999999999985186
74
8781.63925919999999999999999995465
75
8900.310059999999999999999999850644
76
9018.98086079999999999999999995342
77
9137.65166159999999999999999984941
78
9256.322462399999999999999999952203
79
9374.99326319999999999999999984819
80
9493.66406399999999999999999995097
81
9612.334864799999999999999999846967
82
9731.00566559999999999999999994975241
83
9849.67646639999999999999999984574
84
9968.347267199999999999999999948526
85
10087.0180679999999999999999998445165
86
10205.68886879999999999999999994730
87
10324.359669599999999999999999843290
88
10443.0304703999999999999999999460757
89
10561.70127119999999999999999984206
90
10680.372071999999999999999999944850
91
10799.0428727999999999999999998408398
92
10917.71367359999999999999999994362
93
11036.384474399999999999999999839614
94
11155.0552751999999999999999999423991
95
11273.72607599999999999999999983838
96
11392.396876799999999999999999941173
97
11511.067677599999999999999999837163
98
11629.73847839999999999999999993994
99
11748.409279199999999999999999835937
100
11867.080079999999999999999999938722
101
11985.75088079999999999999999983471
102
12104.421681599999999999999999937496
103
12223.092482399999999999999999833486
104
12341.76328319999999999999999993627
105
12460.434083999999999999999999832261
106
12579.104884799999999999999999935045
107
12697.77568559999999999999999983103
108
12816.446486399999999999999999933820
109
12935.117287199999999999999999829809
110
13053.78808799999999999999999993259
111
13172.458888799999999999999999828584
112
13291.129689599999999999999999931369
113
13409.80049039999999999999999982735
114
13528.471291199999999999999999930143
115
13647.142091999999999999999999826133
116
13765.81289279999999999999999992891
117
13884.483693599999999999999999824907
118
14003.154494399999999999999999927692
119
14121.82529519999999999999999982368
120
14240.496095999999999999999999926466
121
14359.166896799999999999999999822456
122
14477.83769759999999999999999992524
123
14596.50849839999999999999999982123
124
14715.179299199999999999999999924015
125
14833.85009999999999999999999982000
126
14952.52090079999999999999999992279
127
15071.191701599999999999999999818779
128
15189.86250239999999999999999992156
129
15308.53330319999999999999999981755
130
15427.204103999999999999999999920339
131
15545.87490479999999999999999981632
132
15664.54570559999999999999999991911
133
15783.216506399999999999999999815103
134
15901.88730719999999999999999991788
135
16020.55810799999999999999999981387
136
16139.228908799999999999999999916662
137
16257.89970959999999999999999981265
138
16376.57051039999999999999999991543
139
16495.241311199999999999999999604631
140
16613.91211199999999999999999991421
141
16732.58291279999999999999999981020
142
16851.253713599999999999999999706190
143
16969.92451439999999999999999960218
144
17088.59531519999999999999999991176
145
17207.266115999999999999999999807749
146
17325.93691679999999999999999970373
147
17444.60771759999999999999999959972
148
17563.278518399999999999999999909309
149
17681.94931919999999999999999980529
150
17800.62011999999999999999999970128
151
17919.290920799999999999999999597278
152
18037.96172159999999999999999990685
153
18156.63252239999999999999999980284
154
18275.303323199999999999999999698837
155
18393.97412399999999999999999959482
156
18512.64492479999999999999999990440
157
18631.315725599999999999999999800396
158
18749.98652639999999999999999969638
159
18868.65732719999999999999999959237
160
18987.328127999999999999999999901955
161
19105.99892879999999999999999979794
162
19224.66972959999999999999999969393
163
19343.340530399999999999999999589924
164
19462.0113311999999999999999998995048
165
19580.68213199999999999999999979549
166
19699.352932799999999999999999691484
167
19818.0237335999999999999999995874737
168
19936.69453439999999999999999989705
169
20055.365335199999999999999999793043
170
20174.0361359999999999999999996890330
171
20292.70693679999999999999999958502
172
20411.377737599999999999999999894602
173
20530.0485383999999999999999997905922
174
20648.71933919999999999999999968658
175
20767.390139999999999999999999582571
176
20886.0609407999999999999999998921515
177
21004.73174159999999999999999978814
178
21123.402542399999999999999999684130
179
21242.073343199999999999999999580120
180
21360.74414399999999999999999988970
181
21479.414944799999999999999999785690
182
21598.085745599999999999999999681679
183
21716.75654639999999999999999957766
184
21835.427347199999999999999999887249
185
21954.098147999999999999999999783238
186
22072.76894879999999999999999967922
187
22191.439749599999999999999999575218
188
22310.110550399999999999999999884798
189
22428.78135119999999999999999978078
190
22547.452151999999999999999999676777
191
22666.122952799999999999999999572767
192
22784.79375359999999999999999988234
193
22903.464554399999999999999999778336
194
23022.135355199999999999999999674326
195
23140.80615599999999999999999957031
196
23259.476956799999999999999999879896
197
23378.147757599999999999999999775885
198
23496.81855839999999999999999967187
199
23615.489359199999999999999999567864
200
23734.160159999999999999999999877444
201
23852.83096079999999999999999977343
202
23971.50176159999999999999999966942
203
24090.172562399999999999999999565413
204
24208.84336319999999999999999987499
205
24327.51416399999999999999999977098
206
24446.184964799999999999999999666973
207
24564.85576559999999999999999956296
208
24683.52656639999999999999999987254
209
24802.197367199999999999999999768532
210
24920.86816799999999999999999966452
211
25039.53896879999999999999999956051
212
25158.209769599999999999999999870091
213
25276.88057039999999999999999976608
214
25395.55137119999999999999999966207
215
25514.222171999999999999999999558060
216
25632.89297279999999999999999986764
217
25751.56377359999999999999999976363
218
25870.234574399999999999999999659619
219
25988.90537519999999999999999955560
220
26107.57617599999999999999999986518
221
26226.246976799999999999999999761179
222
26344.91777759999999999999999965716
223
26463.58857839999999999999999955315
224
26582.259379199999999999999999862738
225
26700.93017999999999999999999975872
226
26819.60098079999999999999999965471
227
26938.271781599999999999999999550707
228
27056.94258239999999999999999986028
229
27175.61338319999999999999999975627
230
27294.284183999999999999999999652266
231
27412.95498479999999999999999954825
232
27531.62578559999999999999999985783
233
27650.296586399999999999999999753825
234
27768.96738719999999999999999964981
235
27887.63818799999999999999999954580
236
28006.308988799999999999999999855385
237
28124.97978959999999999999999975137
238
28243.65059039999999999999999964736
239
28362.321391199999999999999999543353
240
28480.99219199999999999999999985293
241
28599.66299279999999999999999974892
242
28718.333793599999999999999999644913
243
28837.00459439999999999999999954090284
244
28955.67539519999999999999999985048
245
29074.346195999999999999999999746472
246
29193.0169967999999999999999996424620
247
29311.68779759999999999999999953845
248
29430.358598399999999999999999848031
249
29549.02939919999
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:19:48 2004

Input: x := 118.6708008;

for i := 201 to 500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:19:45 on modular  [Seed = 1032532332]
   -------------------------------------

201
23852.83096079999999999999999977343
202
23971.50176159999999999999999966942
203
24090.172562399999999999999999565413
204
24208.84336319999999999999999987499
205
24327.51416399999999999999999977098
206
24446.184964799999999999999999666973
207
24564.85576559999999999999999956296
208
24683.52656639999999999999999987254
209
24802.197367199999999999999999768532
210
24920.86816799999999999999999966452
211
25039.53896879999999999999999956051
212
25158.209769599999999999999999870091
213
25276.88057039999999999999999976608
214
25395.55137119999999999999999966207
215
25514.222171999999999999999999558060
216
25632.89297279999999999999999986764
217
25751.56377359999999999999999976363
218
25870.234574399999999999999999659619
219
25988.90537519999999999999999955560
220
26107.57617599999999999999999986518
221
26226.246976799999999999999999761179
222
26344.91777759999999999999999965716
223
26463.58857839999999999999999955315
224
26582.259379199999999999999999862738
225
26700.93017999999999999999999975872
226
26819.60098079999999999999999965471
227
26938.271781599999999999999999550707
228
27056.94258239999999999999999986028
229
27175.61338319999999999999999975627
230
27294.284183999999999999999999652266
231
27412.95498479999999999999999954825
232
27531.62578559999999999999999985783
233
27650.296586399999999999999999753825
234
27768.96738719999999999999999964981
235
27887.63818799999999999999999954580
236
28006.308988799999999999999999855385
237
28124.97978959999999999999999975137
238
28243.65059039999999999999999964736
239
28362.321391199999999999999999543353
240
28480.99219199999999999999999985293
241
28599.66299279999999999999999974892
242
28718.333793599999999999999999644913
243
28837.00459439999999999999999954090284
244
28955.67539519999999999999999985048
245
29074.346195999999999999999999746472
246
29193.0169967999999999999999996424620
247
29311.68779759999999999999999953845
248
29430.358598399999999999999999848031
249
29549.0293991999999999999999997440213
250
29667.70019999999999999999999964001
251
29786.371000799999999999999999536000
252
29905.0418015999999999999999998455805
253
30023.71260239999999999999999974157
254
30142.383403199999999999999999637559
255
30261.0542039999999999999999995335495
256
30379.72500479999999999999999984312
257
30498.395805599999999999999999739119
258
30617.066606399999999999999999635108
259
30735.73740719999999999999999953109
260
30854.408207999999999999999999840678
261
30973.079008799999999999999999736668
262
31091.74980959999999999999999963265
263
31210.420610399999999999999999528647
264
31329.091411199999999999999999838227
265
31447.76221199999999999999999973421
266
31566.433012799999999999999999630206
267
31685.103813599999999999999999526196
268
31803.77461439999999999999999983577
269
31922.445415199999999999999999731765
270
32041.116215999999999999999999627755
271
32159.78701679999999999999999952374
272
32278.457817599999999999999999833325
273
32397.128618399999999999999999729314
274
32515.79941919999999999999999962530
275
32634.470219999999999999999999521294
276
32753.141020799999999999999999830873
277
32871.81182159999999999999999972686
278
32990.482622399999999999999999209262
279
33109.153423199999999999999999518842
280
33227.82422399999999999999999982842
281
33346.495024799999999999999999310822
282
33465.165825599999999999999999620402
283
33583.83662639999999999999999910280
284
33702.50742719999999999999999941238
285
33821.178227999999999999999999721961
286
33939.84902879999999999999999920436
287
34058.51982959999999999999999951394
288
34177.190630399999999999999999823520
289
34295.86143119999999999999999930592
290
34414.53223199999999999999999961549
291
34533.203032799999999999999999097899
292
34651.87383359999999999999999940747
293
34770.54463439999999999999999971705
294
34889.215435199999999999999999199458
295
35007.88623599999999999999999950903
296
35126.55703679999999999999999981861
297
35245.227837599999999999999999301017
298
35363.89863839999999999999999961059
299
35482.56943919999999999999999909299
300
35601.240239999999999999999999402577
301
35719.91104079999999999999999971215
302
35838.58184159999999999999999919455
303
35957.252642399999999999999999504136
304
36075.92344319999999999999999981371
305
36194.59424399999999999999999929611
306
36313.265044799999999999999999605695
307
36431.93584559999999999999999908809
308
36550.60664639999999999999999939767
309
36669.277447199999999999999999707254
310
36787.94824799999999999999999918965
311
36906.61904879999999999999999949923
312
37025.289849599999999999999999808814
313
37143.96065039999999999999999929121
314
37262.63145119999999999999999960079
315
37381.302251999999999999999999083192
316
37499.97305279999999999999999939277
317
37618.64385359999999999999999970235
318
37737.314654399999999999999999184751
319
37855.98545519999999999999999949433
320
37974.65625599999999999999999980391
321
38093.327056799999999999999999286311
322
38211.99785759999999999999999959589
323
38330.66865839999999999999999907829
324
38449.339459199999999999999999387870
325
38568.0102599999999999999999996974504
326
38686.68106079999999999999999917984
327
38805.351861599999999999999999489429
328
38924.0226623999999999999999997990096
329
39042.69346319999999999999999928140
330
39161.364263999999999999999999590988
331
39280.0350647999999999999999990733883
332
39398.70586559999999999999999938296
333
39517.376666399999999999999999692548
334
39636.0474671999999999999999991749475
335
39754.71826799999999999999999948452
336
39873.389068799999999999999999794107
337
39992.0598695999999999999999992765068
338
40110.73067039999999999999999958608
339
40229.401471199999999999999999068486
340
40348.072271999999999999999999378066
341
40466.74307279999999999999999968764
342
40585.413873599999999999999999170045
343
40704.084674399999999999999999479625
344
40822.75547519999999999999999978920
345
40941.426275999999999999999999271604
346
41060.097076799999999999999999581184
347
41178.76787759999999999999999906358
348
41297.438678399999999999999999373163
349
41416.109479199999999999999999682743
350
41534.78027999999999999999999916514
351
41653.451080799999999999999999474723
352
41772.121881599999999999999999784303
353
41890.79268239999999999999999926670
354
42009.463483199999999999999999576282
355
42128.134283999999999999999999058681
356
42246.80508479999999999999999936826
357
42365.475885599999999999999999677841
358
42484.146686399999999999999999160240
359
42602.81748719999999999999999946982
360
42721.488287999999999999999999779400
361
42840.159088799999999999999999261800
362
42958.82988959999999999999999957138
363
43077.50069039999999999999999905377
364
43196.171491199999999999999999363359
365
43314.84229199999999999999999967293
366
43433.51309279999999999999999915533
367
43552.183893599999999999999999464918
368
43670.85469439999999999999999977449
369
43789.52549519999999999999999925689
370
43908.196295999999999999999999566477
371
44026.86709679999999999999999904887
372
44145.53789759999999999999999935845
373
44264.208698399999999999999999668037
374
44382.87949919999999999999999915043
375
44501.55029999999999999999999946001
376
44620.221100799999999999999999769596
377
44738.89190159999999999999999925199
378
44857.56270239999999999999999956157
379
44976.233503199999999999999999043975
380
45094.90430399999999999999999935355
381
45213.57510479999999999999999966313
382
45332.245905599999999999999999145534
383
45450.91670639999999999999999945511
384
45569.58750719999999999999999976469
385
45688.258307999999999999999999247093
386
45806.92910879999999999999999955667
387
45925.59990959999999999999999903907
388
46044.270710399999999999999999348652
389
46162.94151119999999999999999965823
390
46281.61231199999999999999999914063
391
46400.283112799999999999999999450212
392
46518.95391359999999999999999975979
393
46637.62471439999999999999999924219
394
46756.295515199999999999999999551771
395
46874.96631599999999999999999903417
396
46993.63711679999999999999999934375
397
47112.307917599999999999999999653330
398
47230.97871839999999999999999913572
399
47349.64951919999999999999999944530
400
47468.320319999999999999999999754889
401
47586.99112079999999999999999923728
402
47705.66192159999999999999999954686
403
47824.332722399999999999999999029268
404
47943.00352319999999999999999933884843
405
48061.67432399999999999999999964842
406
48180.345124799999999999999999130827
407
48299.0159255999999999999999994404076
408
48417.68672639999999999999999974998
409
48536.357527199999999999999999232386
410
48655.0283279999999999999999995419669
411
48773.69912879999999999999999902436
412
48892.369929599999999999999999333946
413
49011.0407303999999999999999996435261
414
49129.71153119999999999999999912592
415
49248.382331999999999999999999435505
416
49367.0531327999999999999999997450854
417
49485.72393359999999999999999922748
418
49604.394734399999999999999999537064
419
49723.065535199999999999999999019464
420
49841.73633599999999999999999932904
421
49960.407136799999999999999999638623
422
50079.077937599999999999999999121023
423
50197.74873839999999999999999943060
424
50316.419539199999999999999999740183
425
50435.090339999999999999999999222582
426
50553.76114079999999999999999953216
427
50672.431941599999999999999999014561
428
50791.102742399999999999999999324141
429
50909.77354319999999999999999963372
430
51028.444343999999999999999999116121
431
51147.115144799999999999999999425701
432
51265.78594559999999999999999973528
433
51384.456746399999999999999999217680
434
51503.127547199999999999999999527260
435
51621.79834799999999999999999900965
436
51740.469148799999999999999999319239
437
51859.139949599999999999999999628819
438
51977.81075039999999999999999911121
439
52096.481551199999999999999999420798
440
52215.152351999999999999999999730378
441
52333.82315279999999999999999921277
442
52452.493953599999999999999999522358
443
52571.164754399999999999999999004757
444
52689.835555199999999
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:20:25 2004

Input: x := 118.6708008;

for i := 444 to 2500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:20:22 on modular  [Seed = 3262435060]
   -------------------------------------

444
52689.83555519999999999999999931433
445
52808.50635599999999999999999962391
446
52927.177156799999999999999999106316
447
53045.84795759999999999999999941589
448
53164.51875839999999999999999972547
449
53283.189559199999999999999999207875
450
53401.86035999999999999999999951745
451
53520.53116079999999999999999899985
452
53639.201961599999999999999999309435
453
53757.87276239999999999999999961901
454
53876.54356319999999999999999910141
455
53995.214363999999999999999999410994
456
54113.88516479999999999999999972057
457
54232.55596559999999999999999920297
458
54351.226766399999999999999999512553
459
54469.89756719999999999999999899495
460
54588.56836799999999999999999930453
461
54707.239168799999999999999999614112
462
54825.90996959999999999999999909651
463
54944.58077039999999999999999940609
464
55063.251571199999999999999999715672
465
55181.92237199999999999999999919807
466
55300.59317279999999999999999950765
467
55419.263973599999999999999998990050
468
55537.93477439999999999999999929963
469
55656.60557519999999999999999960921
470
55775.276375999999999999999999091610
471
55893.94717679999999999999999940119
472
56012.61797759999999999999999971077
473
56131.288778399999999999999999193169
474
56249.95957919999999999999999950274
475
56368.63037999999999999999999898514
476
56487.301180799999999999999999294728
477
56605.97198159999999999999999960430
478
56724.64278239999999999999999908670
479
56843.313583199999999999999999396287
480
56961.98438399999999999999999970586
481
57080.65518479999999999999999918826
482
57199.325985599999999999999999497847
483
57317.99678639999999999999999898024
484
57436.66758719999999999999999928982
485
57555.338387999999999999999999599406
486
57674.0091887999999999999999990818056
487
57792.67998959999999999999999939138
488
57911.350790399999999999999999700965
489
58030.0215911999999999999999991833649
490
58148.69239199999999999999999949294
491
58267.363192799999999999999998975344
492
58386.0339935999999999999999992849241
493
58504.70479439999999999999999959450
494
58623.375595199999999999999999076903
495
58742.0463959999999999999999993864834
496
58860.71719679999999999999999969606
497
58979.387997599999999999999999178462
498
59098.0587983999999999999999994880426
499
59216.72959919999999999999999897044
500
59335.400399999999999999999999280021
501
59454.071200799999999999999999589601
502
59572.74200159999999999999999907200
503
59691.412802399999999999999999381581
504
59810.083603199999999999999999691161
505
59928.75440399999999999999999917356
506
60047.425204799999999999999999483140
507
60166.096005599999999999999998965539
508
60284.76680639999999999999999927511
509
60403.437607199999999999999999584699
510
60522.108407999999999999999999067099
511
60640.77920879999999999999999937667
512
60759.450009599999999999999999686258
513
60878.120810399999999999999999168658
514
60996.79161119999999999999999947823
515
61115.462411999999999999999998960637
516
61234.133212799999999999999999270217
517
61352.80401359999999999999999957979
518
61471.474814399999999999999999062196
519
61590.145615199999999999999999371776
520
61708.81641599999999999999999968135
521
61827.487216799999999999999999163756
522
61946.158017599999999999999999473336
523
62064.82881839999999999999999895573
524
62183.499619199999999999999999265315
525
62302.170419999999999999999999574895
526
62420.84122079999999999999999905729
527
62539.51202159999999999999999936687
528
62658.182822399999999999999999676454
529
62776.85362319999999999999999915885
530
62895.52442399999999999999999946843
531
63014.195224799999999999999998950833
532
63132.86602559999999999999999926041
533
63251.53682639999999999999999956999
534
63370.207627199999999999999999052392
535
63488.87842799999999999999999936197
536
63607.54922879999999999999999967155
537
63726.220029599999999999999999153951
538
63844.89083039999999999999999946353
539
63963.56163119999999999999999894593
540
64082.232431999999999999999999255510
541
64200.90323279999999999999999956509
542
64319.57403359999999999999999904749
543
64438.244834399999999999999999357070
544
64556.91563519999999999999999966665
545
64675.58643599999999999999999914904
546
64794.257236799999999999999999458629
547
64912.92803759999999999999999894102
548
65031.59883839999999999999999925060
549
65150.269639199999999999999999560188
550
65268.94043999999999999999999904258
551
65387.61124079999999999999999935216
552
65506.282041599999999999999999661747
553
65624.95284239999999999999999831696
554
65743.62364319999999999999999945372
555
65862.294443999999999999999998936126
556
65980.96524479999999999999999841852
557
66099.63604559999999999999999955528
558
66218.306846399999999999999999037685
559
66336.97764719999999999999999852008
560
66455.64844799999999999999999965684
561
66574.319248799999999999999999139245
562
66692.99004959999999999999999862164
563
66811.66085039999999999999999810404
564
66930.331651199999999999999999240804
565
67049.00245199999999999999999872320371
566
67167.67325279999999999999999820560
567
67286.344053599999999999999999342363
568
67405.0148543999999999999999988247629
569
67523.68565519999999999999999830716
570
67642.356455999999999999999999443922
571
67761.0272567999999999999999989263222
572
67879.69805759999999999999999840872
573
67998.368858399999999999999999545482
574
68117.0396591999999999999999990278814
575
68235.71045999999999999999999851028
576
68354.381260799999999999999999647041
577
68473.0520615999999999999999991294407
578
68591.72286239999999999999999861184
579
68710.393663199999999999999998094239
580
68829.064463999999999999999999230999
581
68947.73526479999999999999999871339
582
69066.406065599999999999999998195798
583
69185.076866399999999999999999332559
584
69303.74766719999999999999999881495
585
69422.418467999999999999999998297357
586
69541.089268799999999999999999434118
587
69659.76006959999999999999999891651
588
69778.430870399999999999999998398917
589
69897.101671199999999999999999535677
590
70015.77247199999999999999999901807
591
70134.443272799999999999999998500476
592
70253.114073599999999999999999637236
593
70371.78487439999999999999999911963
594
70490.455675199999999999999998602035
595
70609.126475999999999999999998084434
596
70727.79727679999999999999999922119
597
70846.468077599999999999999998703594
598
70965.138878399999999999999998185994
599
71083.80967919999999999999999932275
600
71202.480479999999999999999998805154
601
71321.151280799999999999999998287553
602
71439.82208159999999999999999942431
603
71558.492882399999999999999998906713
604
71677.163683199999999999999998389112
605
71795.83448399999999999999999952587
606
71914.50528479999999999999999900827
607
72033.176085599999999999999998490671
608
72151.84688639999999999999999962743
609
72270.51768719999999999999999910983
610
72389.188487999999999999999998592231
611
72507.85928879999999999999999807463
612
72626.53008959999999999999999921139
613
72745.200890399999999999999998693790
614
72863.87169119999999999999999817618
615
72982.54249199999999999999999931295
616
73101.213292799999999999999998795349
617
73219.88409359999999999999999827774
618
73338.55489439999999999999999941450
619
73457.225695199999999999999998896908
620
73575.89649599999999999999999837930
621
73694.56729679999999999999999951606
622
73813.238097599999999999999998998468
623
73931.90889839999999999999999848086
624
74050.57969919999999999999999961762
625
74169.250499999999999999999999100027
626
74287.92130079999999999999999858242
627
74406.59210159999999999999999806482
628
74525.262902399999999999999999201586
629
74643.93370319999999999999999868398
630
74762.60450399999999999999999816638
631
74881.275304799999999999999999303145
632
74999.94610559999999999999999878554
633
75118.61690639999999999999999826794
634
75237.287707199999999999999999404705
635
75355.95850799999999999999999888710
636
75474.62930879999999999999999836950
637
75593.300109599999999999999999506264
638
75711.97091039999999999999999898866
639
75830.64171119999999999999999847106
640
75949.312511999999999999999999607823
641
76067.98331279999999999999999909022
642
76186.65411359999999999999999857262
643
76305.324914399999999999999998055021
644
76423.99571519999999999999999919178
645
76542.66651599999999999999999867418
646
76661.337316799999999999999998156581
647
76780.0081175999999999999999992933415
648
76898.67891839999999999999999877574
649
77017.349719199999999999999998258140
650
77136.0205199999999999999999993949008
651
77254.69132079999999999999999887730
652
77373.362121599999999999999998359699
653
77492.0329223999999999999999994964600
654
77610.70372319999999999999999897885
655
77729.374523999999999999999998461258
656
77848.0453247999999999999999995980193
657
77966.71612559999999999999999908041
658
78085.386926399999999999999998562818
659
78204.0577271999999999999999980452173
660
78322.72852799999999999999999918197
661
78441.399328799999999999999998664377
662
78560.070129599999999999999998146776
663
78678.74093039999999999999999928353
664
78797.411731199999999999999998765936
665
78916.082531999999999999999998248335
666
79034.75333279999999999999999938509
667
79153.424133599999999999999998867495
668
79272.094934399999999999999998349895
669
79390.76573519999999999999999948665
670
79509.436535999999999999999998969055
671
79628.107336799999999999999998451454
672
79746.77813759999999999999999958821
673
79865.448938399999999999999999070614
674
79984.119739199999999999999998553013
675
80102.79053999999999999999999803541
676
80221.461340799999999999999999172173
677
80340.132141599999999999999998654572
678
80458.80294239999999999999999813697
679
80577.473743199999999999999999273732
680
80696.144543999999999999999998756132
681
80814.81534479999999999999999823853
682
80933.486145599999999999999999375292
683
81052.156946399999999999999998857691
684
81170.82774719999999999999999834009
685
81289.498547999999999999999999476851
686
81408.169348799999999999999998959250
687
81526.840149599999999
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:21:11 2004

Input: x := 118.6708008;

for i := 687 to 2500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:21:08 on modular  [Seed = 2837423437]
   -------------------------------------

687
81526.84014959999999999999999844164
688
81645.51095039999999999999999957841
689
81764.181751199999999999999999060809
690
81882.85255199999999999999999854320
691
82001.52335279999999999999999802560
692
82120.194153599999999999999999162369
693
82238.86495439999999999999999864476
694
82357.53575519999999999999999812716
695
82476.206555999999999999999999263928
696
82594.87735679999999999999999874632
697
82713.54815759999999999999999822872
698
82832.218958399999999999999999365487
699
82950.88975919999999999999999884788
700
83069.56055999999999999999999833028
701
83188.231360799999999999999999467046
702
83306.90216159999999999999999894944
703
83425.57296239999999999999999843184
704
83544.243763199999999999999999568606
705
83662.91456399999999999999999905100
706
83781.58536479999999999999999853340
707
83900.256165599999999999999998015804
708
84018.92696639999999999999999915256
709
84137.59776719999999999999999863496
710
84256.268567999999999999999998117363
711
84374.93936879999999999999999925412
712
84493.61016959999999999999999873652
713
84612.280970399999999999999998218922
714
84730.95177119999999999999999935568
715
84849.62257199999999999999999883808
716
84968.293372799999999999999998320481
717
85086.96417359999999999999999945724
718
85205.63497439999999999999999893964
719
85324.305775199999999999999998422041
720
85442.97657599999999999999999955880
721
85561.64737679999999999999999904120
722
85680.318177599999999999999998523600
723
85798.98897839999999999999999800599
724
85917.65977919999999999999999914276
725
86036.330579999999999999999998625159
726
86155.00138079999999999999999810755898
727
86273.67218159999999999999999924431
728
86392.342982399999999999999998726718
729
86511.0137831999999999999999982091182
730
86629.68458399999999999999999934587
731
86748.355384799999999999999998828278
732
86867.0261855999999999999999983106774
733
86985.69698639999999999999999944743
734
87104.367787199999999999999998929837
735
87223.0385879999999999999999984122367
736
87341.70938879999999999999999954899
737
87460.380189599999999999999999031396
738
87579.0509903999999999999999985137959
739
87697.72179119999999999999999799619
740
87816.392591999999999999999999132955
741
87935.063392799999999999999998615355
742
88053.73419359999999999999999809775
743
88172.404994399999999999999999234515
744
88291.075795199999999999999998716914
745
88409.74659599999999999999999819931
746
88528.417396799999999999999999336074
747
88647.088197599999999999999998818473
748
88765.75899839999999999999999830087
749
88884.429799199999999999999999437633
750
89003.100599999999999999999998920032
751
89121.77140079999999999999999840243
752
89240.442201599999999999999999539192
753
89359.113002399999999999999999021592
754
89477.78380319999999999999999850399
755
89596.454603999999999999999997986390
756
89715.125404799999999999999999123151
757
89833.79620559999999999999999860555
758
89952.467006399999999999999998087950
759
90071.137807199999999999999999224710
760
90189.80860799999999999999999870711
761
90308.479408799999999999999998189509
762
90427.150209599999999999999999326269
763
90545.82101039999999999999999880866
764
90664.491811199999999999999998291068
765
90783.162611999999999999999999427829
766
90901.83341279999999999999999891022
767
91020.50421359999999999999999839262
768
91139.175014399999999999999999529388
769
91257.84581519999999999999999901178
770
91376.51661599999999999999999849418
771
91495.187416799999999999999997976586
772
91613.85821759999999999999999911334
773
91732.52901839999999999999999859574
774
91851.199819199999999999999998078145
775
91969.87061999999999999999999921490
776
92088.54142079999999999999999869730
777
92207.212221599999999999999998179705
778
92325.88302239999999999999999931646
779
92444.55382319999999999999999879886
780
92563.224623999999999999999998281264
781
92681.89542479999999999999999941802
782
92800.56622559999999999999999890042
783
92919.237026399999999999999998382823
784
93037.90782719999999999999999951958
785
93156.57862799999999999999999900198
786
93275.249428799999999999999998484382
787
93393.92022959999999999999999796678
788
93512.59103039999999999999999910354
789
93631.261831199999999999999998585942
790
93749.93263199999999999999999806834
791
93868.60343279999999999999999920510
792
93987.274233599999999999999998687501
793
94105.94503439999999999999999816990
794
94224.61583519999999999999999930666
795
94343.286635999999999999999998789060
796
94461.95743679999999999999999827145
797
94580.62823759999999999999999940822
798
94699.299038399999999999999998890619
799
94817.96983919999999999999999837301
800
94936.64063999999999999999999950977
801
95055.311440799999999999999998992179
802
95173.98224159999999999999999847457
803
95292.65304239999999999999999795697
804
95411.323843199999999999999999093738
805
95529.99464399999999999999999857613
806
95648.66544479999999999999999805853
807
95767.336245599999999999999999195297
808
95886.00704639999999999999999867769686
809
96004.67784719999999999999999816009
810
96123.348647999999999999999999296856
811
96242.0194487999999999999999987792561
812
96360.69024959999999999999999826165
813
96479.361050399999999999999999398416
814
96598.0318511999999999999999988808153
815
96716.70265199999999999999999836321
816
96835.373452799999999999999999499975
817
96954.0442535999999999999999989823746
818
97072.71505439999999999999999846477
819
97191.385855199999999999999997947173
820
97310.0566559999999999999999990839338
821
97428.72745679999999999999999856633
822
97547.398257599999999999999998048732
823
97666.069058399999999999999999185493
824
97784.73985919999999999999999866789
825
97903.410659999999999999999998150291
826
98022.081460799999999999999999287052
827
98140.75226159999999999999999876945
828
98259.423062399999999999999998251851
829
98378.093863199999999999999999388611
830
98496.76466399999999999999999887101
831
98615.435464799999999999999998353410
832
98734.106265599999999999999999490170
833
98852.77706639999999999999999897257
834
98971.447867199999999999999998454969
835
99090.118667999999999999999997937368
836
99208.78946879999999999999999907412
837
99327.460269599999999999999998556528
838
99446.131070399999999999999998038928
839
99564.80187119999999999999999917568
840
99683.472671999999999999999998658088
841
99802.143472799999999999999998140487
842
99920.81427359999999999999999927724
843
100039.485074399999999999999998759647
844
100158.155875199999999999999998242046
845
100276.82667599999999999999999937880
846
100395.497476799999999999999998861206
847
100514.168277599999999999999998343605
848
100632.83907839999999999999999948036
849
100751.50987919999999999999999896276
850
100870.180679999999999999999998445165
851
100988.85148079999999999999999792756
852
101107.52228159999999999999999906432
853
101226.193082399999999999999998546724
854
101344.86388319999999999999999802912
855
101463.53468399999999999999999916588
856
101582.205484799999999999999998648283
857
101700.87628559999999999999999813068
858
101819.54708639999999999999999926744
859
101938.217887199999999999999998749842
860
102056.88868799999999999999999823224
861
102175.55948879999999999999999936900
862
102294.230289599999999999999998851402
863
102412.90109039999999999999999833380
864
102531.57189119999999999999999947056
865
102650.242691999999999999999998952961
866
102768.91349279999999999999999843536
867
102887.58429359999999999999999791776
868
103006.255094399999999999999999054520
869
103124.92589519999999999999999853691
870
103243.59669599999999999999999801931
871
103362.267496799999999999999999156079
872
103480.93829759999999999999999863847
873
103599.60909839999999999999999812087
874
103718.279899199999999999999999257639
875
103836.95069999999999999999999874003
876
103955.62150079999999999999999822243
877
104074.292301599999999999999999359198
878
104192.96310239999999999999999884159
879
104311.63390319999999999999999832399
880
104430.304703999999999999999999460757
881
104548.97550479999999999999999894315
882
104667.64630559999999999999999842555
883
104786.317106399999999999999997907955
884
104904.98790719999999999999999904471
885
105023.65870799999999999999999852711
886
105142.329508799999999999999998009514
887
105261.000309599999999999999999146275492
888
105379.67111039999999999999999862867
889
105498.341911199999999999999998111074
890
105617.0127119999999999999999992478347
891
105735.68351279999999999999999873023
892
105854.354313599999999999999998212633
893
105973.0251143999999999999999993493939
894
106091.69591519999999999999999883179
895
106210.366715999999999999999998314192
896
106329.0375167999999999999999994509532
897
106447.70831759999999999999999893335
898
106566.379118399999999999999998415751
899
106685.0499191999999999999999978981512
900
106803.72071999999999999999999903491
901
106922.391520799999999999999998517311
902
107041.0623215999999999999999979997105
903
107159.73312239999999999999999913647
904
107278.403923199999999999999998618870
905
107397.074723999999999999999998101269
906
107515.74552479999999999999999923803
907
107634.416325599999999999999998720429
908
107753.087126399999999999999998202829
909
107871.75792719999999999999999933958
910
107990.428727999999999999999998821988
911
108109.099528799999999999999998304388
912
108227.77032959999999999999999944114
913
108346.441130399999999999999998923548
914
108465.111931199999999999999998405947
915
108583.78273199999999999999999788834
916
108702.453532799999999999999999025107
917
108821.124333599999999999999998507506
918
108939.79513439999999999999999798990
919
109058.465935199999999999999999126666
920
109177.136735999999999999999998609066
921
109295.80753679999999999999999809146
922
109414.478337599999999999999999228225
923
109533.149138399999999999999998710625
924
109651.81993919999999999999999819302
925
109770.490739999999999999999999329785
926
109889.161540799999999999999998812184
927
110007.83234159999999999999999829458
928
110126.503142
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:22:00 2004

Input: x := 118.67080098;

for i := 687 to 2500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:21:57 on modular  [Seed = 2570032460]
   -------------------------------------

687
81526.84027325999999999999999830456
688
81645.51107423999999999999999824430
689
81764.181875219999999999999998184041
690
81882.85267619999999999999999812377
691
82001.52347717999999999999999806351
692
82120.194278159999999999999999657616
693
82238.86507913999999999999999959735
694
82357.53588011999999999999999953709
695
82476.206681099999999999999999476830
696
82594.87748207999999999999999941656
697
82713.54828305999999999999999935630
698
82832.219084039999999999999999296043
699
82950.88988501999999999999999923578
700
83069.56068599999999999999999917551
701
83188.231486979999999999999999115257
702
83306.90228795999999999999999905499
703
83425.57308893999999999999999899473
704
83544.243889919999999999999998934470
705
83662.91469089999999999999999887420
706
83781.58549187999999999999999881394
707
83900.256292859999999999999998753684
708
84018.92709383999999999999999869342
709
84137.59789481999999999999999863315
710
84256.268695799999999999999998572897
711
84374.93949677999999999999999851263
712
84493.61029775999999999999999845237
713
84612.281098739999999999999998392111
714
84730.95189971999999999999999833184
715
84849.62270069999999999999999827158
716
84968.293501679999999999999998211324
717
85086.96430265999999999999999815106
718
85205.63510363999999999999999809080
719
85324.305904619999999999999998030538
720
85442.97670559999999999999999962463
721
85561.64750657999999999999999956437
722
85680.318307559999999999999999504113
723
85798.98910853999999999999999944385
724
85917.65990951999999999999999938358
725
86036.330710499999999999999999323326
726
86155.00151147999999999999999926306439
727
86273.67231245999999999999999920280
728
86392.343113439999999999999999142540
729
86511.0139144199999999999999990822779
730
86629.68471539999999999999999902201
731
86748.355516379999999999999998961753
732
86867.0263173599999999999999989014914
733
86985.69711833999999999999999884122
734
87104.367919319999999999999998780967
735
87223.0387202999999999999999987207049
736
87341.70952127999999999999999866044
737
87460.380322259999999999999998600180
738
87579.0511232399999999999999985399184
739
87697.72192421999999999999999847965
740
87816.392725199999999999999998419394
741
87935.063526179999999999999998359132
742
88053.73432715999999999999999829886
743
88172.405128139999999999999998238607
744
88291.075929119999999999999998178345
745
88409.74673009999999999999999811808
746
88528.417531079999999999999998057821
747
88647.088332059999999999999997997559
748
88765.75913303999999999999999959165
749
88884.429934019999999999999999531395
750
89003.100734999999999999999999471133
751
89121.77153597999999999999999941087
752
89240.442336959999999999999999350609
753
89359.113137939999999999999999290347
754
89477.78393891999999999999999923008
755
89596.454739899999999999999999169823
756
89715.125540879999999999999999109560
757
89833.79634185999999999999999904929
758
89952.467142839999999999999998989036
759
90071.137943819999999999999998928774
760
90189.80874479999999999999999886851
761
90308.479545779999999999999998808250
762
90427.150346759999999999999998747987
763
90545.82114773999999999999999868772
764
90664.491948719999999999999998627463
765
90783.162749699999999999999998567201
766
90901.83355067999999999999999850693
767
91020.50435165999999999999999844667
768
91139.175152639999999999999998386414
769
91257.84595361999999999999999832615
770
91376.51675459999999999999999826589
771
91495.187555579999999999999998205628
772
91613.85835655999999999999999814536
773
91732.52915753999999999999999808510
774
91851.199958519999999999999998024841
775
91969.87075949999999999999999961894
776
92088.54156047999999999999999955867
777
92207.212361459999999999999999498416
778
92325.88316243999999999999999943815
779
92444.55396341999999999999999937789
780
92563.224764399999999999999999317630
781
92681.89556537999999999999999925736
782
92800.56636635999999999999999919710
783
92919.237167339999999999999999136843
784
93037.90796831999999999999999907658
785
93156.57876929999999999999999901631
786
93275.249570279999999999999998956057
787
93393.92037125999999999999999889579
788
93512.59117223999999999999999883553
789
93631.261973219999999999999998775270
790
93749.93277419999999999999999871500
791
93868.60357517999999999999999865474
792
93987.274376159999999999999998594484
793
94105.94517713999999999999999853422
794
94224.61597811999999999999999847396
795
94343.286779099999999999999998413697
796
94461.95758007999999999999999835343
797
94580.62838105999999999999999829317
798
94699.299182039999999999999998232911
799
94817.96998301999999999999999817264
800
94936.64078399999999999999999811238
801
95055.311584979999999999999998052124
802
95173.98238595999999999999999799186
803
95292.65318693999999999999999958596
804
95411.323987919999999999999999525699
805
95529.99478889999999999999999946543
806
95648.66558987999999999999999940517
807
95767.336390859999999999999999344913
808
95886.00719183999999999999999928465102
809
96004.67799281999999999999999922438
810
96123.348793799999999999999999164126
811
96242.0195947799999999999999991038645
812
96360.69039575999999999999999904360
813
96479.361196739999999999999998983340
814
96598.0319977199999999999999989230780
815
96716.70279869999999999999999886281
816
96835.373599679999999999999998802553
817
96954.0444006599999999999999987422915
818
97072.71520163999999999999999868202
819
97191.386002619999999999999998621767
820
97310.0568035999999999999999985615051
821
97428.72760457999999999999999850124
822
97547.398405559999999999999998440980
823
97666.069206539999999999999998380718
824
97784.74000751999999999999999832045
825
97903.410808499999999999999998260194
826
98022.081609479999999999999998199932
827
98140.75241045999999999999999813967
828
98259.423211439999999999999998079407
829
98378.094012419999999999999998019145
830
98496.76481339999999999999999795888
831
98615.435614379999999999999999552982
832
98734.106415359999999999999999492720
833
98852.77721633999999999999999943245
834
98971.448017319999999999999999372196
835
99090.118818299999999999999999311933
836
99208.78961927999999999999999925167
837
99327.460420259999999999999999191409
838
99446.131221239999999999999999131147
839
99564.80202221999999999999999907088
840
99683.472823199999999999999999010623
841
99802.143624179999999999999998950361
842
99920.81442515999999999999999889009
843
100039.485226139999999999999998829836
844
100158.156027119999999999999998769574
845
100276.82682809999999999999999870931
846
100395.497629079999999999999998649050
847
100514.168430059999999999999998588788
848
100632.83923103999999999999999852852
849
100751.51003201999999999999999846826
850
100870.180832999999999999999998408001
851
100988.85163397999999999999999834773
852
101107.52243495999999999999999828747
853
101226.193235939999999999999998227215
854
101344.86403691999999999999999816695
855
101463.53483789999999999999999810669
856
101582.205638879999999999999998046428
857
101700.87643985999999999999999798616
858
101819.54724083999999999999999958026
859
101938.218041819999999999999999520003
860
102056.88884279999999999999999945974
861
102175.55964377999999999999999939947
862
102294.230444759999999999999999339216
863
102412.90124573999999999999999927895
864
102531.57204671999999999999999921869
865
102650.242847699999999999999999158430
866
102768.91364867999999999999999909816
867
102887.58444965999999999999999903790
868
103006.255250639999999999999998977643
869
103124.92605161999999999999999891738
870
103243.59685259999999999999999885711
871
103362.267653579999999999999998796857
872
103480.93845455999999999999999873659
873
103599.60925553999999999999999867633
874
103718.280056519999999999999998616070
875
103836.95085749999999999999999855580
876
103955.62165847999999999999999849554
877
104074.292459459999999999999998435284
878
104192.96326043999999999999999837502
879
104311.63406141999999999999999831476
880
104430.304862399999999999999998254498
881
104548.97566337999999999999999819423
882
104667.64646435999999999999999813397
883
104786.317265339999999999999998073711
884
104904.98806631999999999999999801344
885
105023.65886729999999999999999795318
886
105142.329668279999999999999999547286
887
105261.000469259999999999999999487024141
888
105379.67127023999999999999999942676
889
105498.342071219999999999999999366499
890
105617.0128721999999999999999993062376
891
105735.68367317999999999999999924597
892
105854.354474159999999999999999185713
893
105973.0252751399999999999999991254511
894
106091.69607611999999999999999906518
895
106210.366877099999999999999999004926
896
106329.0376780799999999999999989446647
897
106447.70847905999999999999999888440
898
106566.379280039999999999999998824140
899
106685.0500810199999999999999987638782
900
106803.72088199999999999999999870361
901
106922.391682979999999999999998643353
902
107041.0624839599999999999999985830917
903
107159.73328493999999999999999852282
904
107278.404085919999999999999998462567
905
107397.074886899999999999999998402305
906
107515.74568787999999999999999834204
907
107634.416488859999999999999998281780
908
107753.087289839999999999999998221518
909
107871.75809081999999999999999816125
910
107990.428891799999999999999998100994
911
108109.099692779999999999999998040732
912
108227.77049375999999999999999798047
913
108346.441294739999999999999997920208
914
108465.112095719999999999999999514307
915
108583.78289669999999999999999945404
916
108702.453697679999999999999999393782
917
108821.124498659999999999999999333520
918
108939.79529963999999999999999927325
919
109058.466100619999999999999999212996
920
109177.136901599999999999999999152734
921
109295.80770257999999999999999909247
922
109414.478503559999999999999999032209
923
109533.149304539999999999999998971947
924
109651.82010551999999999999999891168
925
109770.490906499999999999999998851423
926
109889.161707479999999999999998791161
927
110007.83250845999999999999999873089
928
110126.503309
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:23:45 2004

Input: x := 118.67080098 * 2047;

for i := 0 to 2500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:23:43 on modular  [Seed = 163513463]
   -------------------------------------

0
0
1
242919.129606059999999999999997411729
2
485838.259212119999999999999994823459
3
728757.388818179999999999999988926467
4
971676.51842423999999999999998964691
5
1214595.64803029999999999999997713248
6
1457514.77763635999999999999997785293
7
1700433.90724241999999999999997857338
8
1943353.0368484799999999999999792938391
9
2186272.166454539999999999999953544511
10
2429191.296060599999999999999954264964
11
2672110.425666659999999999999954985416
12
2915029.55527271999999999999995570586
13
3157948.68487877999999999999995642632
14
3400867.81448483999999999999995714677
15
3643786.94409089999999999999995786722
16
3886706.073696959999999999999958587678
17
4129625.203303019999999999999906368571
18
4372544.332909079999999999999907089023
19
4615463.462515139999999999999907809476
20
4858382.59212119999999999999990852992
21
5101301.72172725999999999999990925038
22
5344220.85133331999999999999990997083
23
5587139.98093937999999999999991069128
24
5830059.110545439999999999999911411737
25
6072978.240151499999999999999912132190
26
6315897.369757559999999999999912852642
27
6558816.499363619999999999999913573094
28
6801735.62896967999999999999991429354
29
7044654.75857573999999999999991501399
30
7287573.88818179999999999999991573445
31
7530493.0177878599999999999999164549042
32
7773412.147393919999999999999917175356
33
8016331.276999979999999999999812016690
34
8259250.406606039999999999999812737142
35
8502169.53621209999999999999981345759
36
8745088.66581815999999999999981417804
37
8988007.79542421999999999999981489849
38
9230926.92503027999999999999981561895
39
9473846.0546363399999999999998163394045
40
9716765.184242399999999999999817059856
41
9959684.313848459999999999999817780309
42
10202603.443454519999999999999818500761
43
10445522.57306057999999999999981922121
44
10688441.70266663999999999999981994166
45
10931360.83227269999999999999982066211
46
11174279.96187875999999999999982138257
47
11417199.091484819999999999999822103023
48
11660118.221090879999999999999822823475
49
11903037.350696939999999999999823543928
50
12145956.480302999999999999999824264380
51
12388875.60990905999999999999982498483
52
12631794.73951511999999999999982570528
53
12874713.86912117999999999999982642573
54
13117632.99872723999999999999982714618
55
13360552.128333299999999999999827866642
56
13603471.257939359999999999999828587094
57
13846390.387545419999999999999829307546
58
14089309.51715147999999999999983002799
59
14332228.64675753999999999999983074845
60
14575147.77636359999999999999983146890
61
14818066.90596965999999999999983218935
62
15060986.0355757199999999999998329098084
63
15303905.165181779999999999999833630260
64
15546824.294787839999999999999834350713
65
15789743.424393899999999999999623312928
66
16032662.55399995999999999999962403338
67
16275581.68360601999999999999962475383
68
16518500.81321207999999999999962547428
69
16761419.94281813999999999999962619473
70
17004339.072424199999999999999626915190
71
17247258.202030259999999999999415877405
72
17490177.331636319999999999999628356095
73
17733096.461242379999999999999417318310
74
17976015.59084843999999999999962979699
75
18218934.72045449999999999999941875921
76
18461853.85006055999999999999963123790
77
18704772.97966661999999999999942020012
78
18947692.109272679999999999999632678809
79
19190611.238878739999999999999421641024
80
19433530.368484799999999999999634119713
81
19676449.498090859999999999999423081929
82
19919368.62769691999999999999963556061
83
20162287.75730297999999999999942452283
84
20405206.88690903999999999999963700152
85
20648126.0165150999999999999994259637387
86
20891045.146121159999999999999638442427
87
21133964.275727219999999999999427404643
88
21376883.405333279999999999999639883332
89
21619802.53493933999999999999942884554
90
21862721.66454539999999999999964132423
91
22105640.79415145999999999999943028645
92
22348559.92375751999999999999964276514
93
22591479.0533635799999999999994317273575
94
22834398.182969639999999999999644206046
95
23077317.312575699999999999999433168262
96
23320236.442181759999999999999645646951
97
23563155.57178781999999999999943460916
98
23806074.70139387999999999999964708785
99
24048993.83099993999999999999943605007
100
24291912.96060599999999999999964852876
101
24534832.090212059999999999999437490976
102
24777751.219818119999999999999649969665
103
25020670.349424179999999999999438931880
104
25263589.479030239999999999999651410570
105
25506508.60863629999999999999944037278
106
25749427.73824235999999999999965285147
107
25992346.86784841999999999999944181369
108
26235265.99745447999999999999965429237
109
26478185.127060539999999999999443254595
110
26721104.256666599999999999999655733284
111
26964023.386272659999999999999444695499
112
27206942.51587871999999999999965717418
113
27449861.64548477999999999999944613640
114
27692780.77509083999999999999965861509
115
27935699.90469689999999999999944757730
116
28178619.0343029599999999999996600559982
117
28421538.163909019999999999999449018213
118
28664457.293515079999999999999661496902
119
28907376.423121139999999999999450459118
120
29150295.55272719999999999999966293780
121
29393214.68233325999999999999945190002
122
29636133.81193931999999999999966437871
123
29879052.94154537999999999999945334092
124
30121972.071151439999999999999665819616
125
30364891.200757499999999999999454781832
126
30607810.330363559999999999999667260521
127
30850729.459969619999999999999456222737
128
31093648.58957567999999999999966870142
129
31336567.71918173999999999999945766364
130
31579486.84878779999999999999924662585
131
31822405.97839385999999999999945910454
132
32065325.107999919999999999999248066762
133
32308244.237605979999999999999460545451
134
32551163.367212039999999999999249507666
135
32794082.496818099999999999999461986355
136
33037001.62642415999999999999925094857
137
33279920.75603021999999999999946342726
138
33522839.88563627999999999999925238947
139
33765759.0152423399999999999994
140
34008678.144848399999999999999253830380
141
34251597.274454459999999999999042792596
142
34494516.404060519999999999998831754811
143
34737435.53366657999999999999946774997
144
34980354.66327263999999999999925671219
145
35223273.79287869999999999999904567440
146
35466192.92248475999999999999883463662
147
35709112.0520908199999999999994706317840
148
35952031.181696879999999999999259593999
149
36194950.311302939999999999999048556215
150
36437869.440908999999999999998837518430
151
36680788.57051505999999999999947351359
152
36923707.70012111999999999999926247580
153
37166626.82972717999999999999905143802
154
37409545.95933323999999999999884040024
155
37652465.088939299999999999999476395402
156
37895384.218545359999999999999265357618
157
38138303.348151419999999999999054319833
158
38381222.477757479999999999998843282049
159
38624141.60736353999999999999947927721
160
38867060.73696959999999999999926823942
161
39109979.86657565999999999999905720164
162
39352898.99618171999999999999884616385
163
39595818.125787779999999999999482159021
164
39838737.255393839999999999999271121237
165
40081656.384999899999999999999060083452
166
40324575.51460595999999999999884904566
167
40567494.64421201999999999999948504083
168
40810413.77381807999999999999927400304
169
41053332.90342413999999999999906296526
170
41296252.0330301999999999999988519274775
171
41539171.162636259999999999999487922640
172
41782090.292242319999999999999276884855
173
42025009.421848379999999999999065847071
174
42267928.55145443999999999999885480928
175
42510847.68106049999999999999949080444
176
42753766.81066655999999999999927976666
177
42996685.94027261999999999999906872888
178
43239605.069878679999999999998857691096
179
43482524.199484739999999999999493686259
180
43725443.329090799999999999999282648474
181
43968362.458696859999999999999071610690
182
44211281.58830291999999999999886057290
183
44454200.71790897999999999999949656806
184
44697119.84751503999999999999928553028
185
44940038.97712109999999999999907449249
186
45182958.106727159999999999998863454715
187
45425877.236333219999999999999499449877
188
45668796.365939279999999999999288412093
189
45911715.495545339999999999999077374308
190
46154634.62515139999999999999886633652
191
46397553.75475745999999999999950233168
192
46640472.88436351999999999999929129390
193
46883392.0139695799999999999990
194
47126311.143575639999999999998869218333
195
47369230.273181699999999999998658180549
196
47612149.402787759999999999999294175712
197
47855068.53239381999999999999908313792
198
48097987.66199987999999999999887210014
199
48340906.79160593999999999999866106235
200
48583825.92121199999999999999929705752
201
48826745.0508180599999999999990860197369
202
49069664.180424119999999999998874981952
203
49312583.310030179999999999998663944168
204
49555502.439636239999999999999299939330
205
49798421.56924229999999999999908890154
206
50041340.69884835999999999999887786376
207
50284259.82845441999999999999866682597
208
50527178.95806047999999999999930282114
209
50770098.087666539999999999999091783355
210
51013017.217272599999999999998880745571
211
51255936.346878659999999999998669707786
212
51498855.476484719999999999999305702949
213
51741774.60609077999999999999909466516
214
51984693.73569683999999999999888362738
215
52227612.86530289999999999999867258959
216
52470531.99490895999999999999930858475
217
52713451.124515019999999999999097546974
218
52956370.254121079999999999998886509190
219
53199289.383727139999999999998675471405
220
53442208.51333319999999999999931146656
221
53685127.64293925999999999999910042878
222
53928046.77254531999999999999888939099
223
54170965.90215137999999999999867835321
224
54413885.0317574399999999999993143483777
225
54656804.161363499999999999999103310593
226
54899723.290969559999999999998892272808
227
55142642.420575619999999999998681235024
228
55385561.55018167999999999999931723018
229
55628480.67978773999999999999910619240
230
55871399.80939379999999999999889515461
231
56114318.93899985999999999999
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Thu Jul 15 05:26:58 2004

Input: x := 118.6708 * 2047;

for i := 0 to 2500 do
print(i);
print(i * x);
end for;


Output: Magma V2.10-22    Thu Jul 15 2004 05:26:55 on modular  [Seed = 346167722]
   -------------------------------------

0
0
1
242919.127599999999999999999996643631
2
485838.255199999999999999999993287263
3
728757.382799999999999999999983313450
4
971676.51039999999999999999998657452
5
1214595.63799999999999999999996336582
6
1457514.76559999999999999999996662690
7
1700433.89319999999999999999996988797
8
1943353.0207999999999999999999731490555
9
2186272.148399999999999999999949940352
10
2429191.275999999999999999999926731650
11
2672110.403599999999999999999956462506
12
2915029.53119999999999999999993325380
13
3157948.65879999999999999999991004510
14
3400867.78639999999999999999993977595
15
3643786.91399999999999999999991656725
16
3886706.0415999999999999999999462981111
17
4129625.169199999999999999999923089408
18
4372544.296799999999999999999899880705
19
4615463.424399999999999999999876672002
20
4858382.55199999999999999999985346330
21
5101301.67959999999999999999983025459
22
5344220.80719999999999999999991292501
23
5587139.93479999999999999999988971631
24
5830059.0623999999999999999998665076075
25
6072978.189999999999999999999843298904
26
6315897.317599999999999999999820090202
27
6558816.445199999999999999999902760617
28
6801735.57279999999999999999987955191
29
7044654.70039999999999999999985634321
30
7287573.82799999999999999999983313450
31
7530492.95559999999999999999980992580
32
7773412.083199999999999999999892596222
33
8016331.210799999999999999999869387519
34
8259250.338399999999999999999846178816
35
8502169.465999999999999999999717090995
36
8745088.59359999999999999999979976141
37
8988007.72119999999999999999967067359
38
9230926.84879999999999999999975334400
39
9473845.97639999999999999999983601442
40
9716765.103999999999999999999706926600
41
9959684.231599999999999999999789597015
42
10202603.359199999999999999999660509194
43
10445522.486799999999999999999743179610
44
10688441.61439999999999999999982585002
45
10931360.74199999999999999999969676220
46
11174279.86959999999999999999977943262
47
11417198.99719999999999999999965034479
48
11660118.124799999999999999999733015215
49
11903037.252399999999999999999815685630
50
12145956.379999999999999999999686597809
51
12388875.50759999999999999999976926822
52
12631794.63519999999999999999964018040
53
12874713.76279999999999999999972285081
54
13117632.89039999999999999999980552123
55
13360552.0179999999999999999996764334141
56
13603471.145599999999999999999759103829
57
13846390.273199999999999999999630016008
58
14089309.400799999999999999999712686424
59
14332228.52839999999999999999979535683
60
14575147.65599999999999999999966626901
61
14818066.78359999999999999999974893943
62
15060985.91119999999999999999961985161
63
15303905.0387999999999999999997025220289
64
15546824.166399999999999999999785192444
65
15789743.293999999999999999999656104623
66
16032662.421599999999999999999738775039
67
16275581.54919999999999999999960968721
68
16518500.67679999999999999999969235763
69
16761419.80439999999999999999956326981
70
17004338.93199999999999999999943418199
71
17247258.0595999999999999999995168524068
72
17490177.187199999999999999999599522822
73
17733096.314799999999999999999682193238
74
17976015.442399999999999999999341347180
75
18218934.56999999999999999999942401759
76
18461853.69759999999999999999950668801
77
18704772.82519999999999999999958935842
78
18947691.95279999999999999999967202884
79
19190611.080399999999999999999331182784
80
19433530.207999999999999999999413853200
81
19676449.335599999999999999999496523616
82
19919368.463199999999999999999579194031
83
20162287.59079999999999999999966186444
84
20405206.71839999999999999999932101838
85
20648125.84599999999999999999940368880
86
20891044.97359999999999999999948635922
87
21133964.101199999999999999999569029636
88
21376883.228799999999999999999651700052
89
21619802.356399999999999999999310853994
90
21862721.483999999999999999999393524409
91
22105640.61159999999999999999947619482
92
22348559.73919999999999999999955886524
93
22591478.86679999999999999999964153565
94
22834397.99439999999999999999930068959
95
23077317.121999999999999999999383360014
96
23320236.249599999999999999999466030430
97
23563155.377199999999999999999548700845
98
23806074.50479999999999999999963137126
99
24048993.63239999999999999999929052520
100
24291912.75999999999999999999937319561
101
24534831.88759999999999999999945586603
102
24777751.0151999999999999999995385364503
103
25020670.142799999999999999999621206865
104
25263589.270399999999999999999280360808
105
25506508.397999999999999999999363031223
106
25749427.52559999999999999999944570163
107
25992346.65319999999999999999952837205
108
26235265.78079999999999999999961104247
109
26478184.90839999999999999999927019641
110
26721104.0359999999999999999993528668282
111
26964023.163599999999999999999435537243
112
27206942.291199999999999999999518207659
113
27449861.418799999999999999999600878075
114
27692780.54639999999999999999926003201
115
27935699.67399999999999999999934270243
116
28178618.80159999999999999999942537284
117
28421537.92919999999999999999950804326
118
28664457.0567999999999999999995907136798
119
28907376.184399999999999999999249867621
120
29150295.311999999999999999999332538037
121
29393214.439599999999999999999415208453
122
29636133.56719999999999999999949787886
123
29879052.69479999999999999999958054928
124
30121971.82239999999999999999923970322
125
30364890.94999999999999999999932237364
126
30607810.077599999999999999999405044057
127
30850729.205199999999999999999487714473
128
31093648.332799999999999999999570384889
129
31336567.460399999999999999999229538831
130
31579486.58799999999999999999931220924
131
31822405.71559999999999999999939487966
132
32065324.84319999999999999999947755007
133
32308243.97079999999999999999913670402
134
32551163.098399999999999999999219374435
135
32794082.225999999999999999999302044851
136
33037001.353599999999999999999384715267
137
33279920.481199999999999999999467385682
138
33522839.60879999999999999999912653962
139
33765758.73639999999999999999878569356
140
34008677.86399999999999999999886836398
141
34251596.99159999999999999999895103439
142
34494516.119199999999999999999033704813
143
34737435.246799999999999999999116375229
144
34980354.374399999999999999999199045645
145
35223273.50199999999999999999928171606
146
35466192.62959999999999999999936438647
147
35709111.75719999999999999999944705689
148
35952030.88479999999999999999868269436
149
36194950.0123999999999999999987
150
36437869.139999999999999999998848035191
151
36680788.267599999999999999998930705607
152
36923707.395199999999999999999013376023
153
37166626.52279999999999999999909604643
154
37409545.65039999999999999999917871685
155
37652464.77799999999999999999926138726
156
37895383.90559999999999999999934405768
157
38138303.0331999999999999999994267281012
158
38381222.160799999999999999998662365569
159
38624141.288399999999999999998745035985
160
38867060.415999999999999999998827706401
161
39109979.54359999999999999999891037681
162
39352898.67119999999999999999899304723
163
39595817.79879999999999999999907571764
164
39838736.92639999999999999999915838806
165
40081656.0539999999999999999992410584792
166
40324575.181599999999999999999323728894
167
40567494.309199999999999999999406399310
168
40810413.436799999999999999998642036778
169
41053332.56439999999999999999872470719
170
41296251.69199999999999999999880737761
171
41539170.81959999999999999999889004802
172
41782089.94719999999999999999897271844
173
42025009.074799999999999999999055388857
174
42267928.202399999999999999999138059272
175
42510847.329999999999999999999220729688
176
42753766.457599999999999999999303400104
177
42996685.58519999999999999999938607051
178
43239604.71279999999999999999862170798
179
43482523.84039999999999999999870437840
180
43725442.96799999999999999999878704881
181
43968362.095599999999999999998869719235
182
44211281.223199999999999999998952389650
183
44454200.350799999999999999999035060066
184
44697119.478399999999999999999117730482
185
44940038.60599999999999999999920040089
186
45182957.73359999999999999999928307131
187
45425876.86119999999999999999936574172
188
45668795.98879999999999999999860137919
189
45911715.116399999999999999998684049613
190
46154634.243999999999999999998766720028
191
46397553.371599999999999999998849390444
192
46640472.499199999999999999998932060860
193
46883391.62679999999999999999901473127
194
47126310.75439999999999999999909740169
195
47369229.88199999999999999999918007210
196
47612149.0095999999999999999992
197
47855068.137199999999999999998498379991
198
48097987.264799999999999999998581050406
199
48340906.392399999999999999998663720822
200
48583825.51999999999999999999874639123
201
48826744.64759999999999999999882906165
202
49069663.77519999999999999999891173206
203
49312582.90279999999999999999899440248
204
49555502.0303999999999999999990770729006
205
49798421.157999999999999999999159743316
206
50041340.285599999999999999999242413731
207
50284259.413199999999999999998478051200
208
50527178.54079999999999999999856072161
209
50770097.66839999999999999999864339203
210
51013016.79599999999999999999872606244
211
51255935.92359999999999999999880873286
212
51498855.0511999999999999999988914032786
213
51741774.178799999999999999998974073694
214
51984693.306399999999999999999056744109
215
52227612.433999999999999999999139414525
216
52470531.56159999999999999999922208494
217
52713450.68919999999999999999845772240
218
52956369.81679999999999999999854039282
219
53199288.94439999999999999999862306324
220
53442208.071999999999999999998705733656
221
53685127.199599999999999999998788404072
222
53928046.327199999999999999998871074487
223
54170965.454799999999999999998953744903
224
54413884.58239999999999999999903641531
225
54656803.70999999999999999999911908573
226
54899722.83759999999999999999920175615
227
55142641.96519999999999999999843739361
228
55385561.092799999999999999998520064034
229
55628480.220399999999999999998602734450
230
55871399.347999999999999999998685404865
231
56114318.475599999999999999
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host pD95354CF.dip.t-dialin.net. (217.83.84.207)
Time: Thu Jul 15 06:03:59 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^2>;
G<x>:=sub<F|a*b>;
Order(G);
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 06:03:50 on modular  [Seed = 3748251960]
   -------------------------------------

3
6

Total time: 2.899 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95354CF.dip.t-dialin.net. (217.83.84.207)
Time: Thu Jul 15 06:04:24 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,a^3>;
G<x>:=sub<F|a*b>;
Order(G);
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 06:04:21 on modular  [Seed = 2786111586]
   -------------------------------------

6
24

Total time: 2.889 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD95354CF.dip.t-dialin.net. (217.83.84.207)
Time: Thu Jul 15 06:05:22 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,a*c=c*a,b*c*b=c*b*c,a^2>;
G<x>:=sub<F|a*b*c>;
Order(G);
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 06:05:19 on modular  [Seed = 2920855568]
   -------------------------------------

4
24

Total time: 2.749 seconds, Total memory usage: 17.67MB


************** MAGMA *****************
Host pD95354CF.dip.t-dialin.net. (217.83.84.207)
Time: Thu Jul 15 06:05:40 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,a*c=c*a,b*c*b=c*b*c,a^3>;
G<x>:=sub<F|a*b*c>;
Order(G);
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 06:05:37 on modular  [Seed = 3053494310]
   -------------------------------------

12
648

Total time: 2.759 seconds, Total memory usage: 17.67MB


************** MAGMA *****************
Host KILIMANDSCHARO.UNI-MUENSTER.DE. (128.176.180.83)
Time: Thu Jul 15 08:26:24 2004

Input: F<a,d>:=Group<a,d|a*d*a*d^-1*a*d=d*a*d^-1*a*d*a,a*d^2=d^2*a,a^4>;
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 08:26:16 on modular  [Seed = 2485297944]
   -------------------------------------

Infinity

Total time: 6.369 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host KILIMANDSCHARO.UNI-MUENSTER.DE. (128.176.180.83)
Time: Thu Jul 15 08:27:23 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^2>;
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 08:27:21 on modular  [Seed = 2636883408]
   -------------------------------------

4

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host KILIMANDSCHARO.UNI-MUENSTER.DE. (128.176.180.83)
Time: Thu Jul 15 08:28:35 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^3>;
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 08:28:31 on modular  [Seed = 1691507822]
   -------------------------------------

0

Total time: 4.189 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host KILIMANDSCHARO.UNI-MUENSTER.DE. (128.176.180.83)
Time: Thu Jul 15 08:29:10 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^4>;
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 08:29:07 on modular  [Seed = 1826247834]
   -------------------------------------

8

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host KILIMANDSCHARO.UNI-MUENSTER.DE. (128.176.180.83)
Time: Thu Jul 15 08:29:28 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^5>;
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 08:29:25 on modular  [Seed = 1958890676]
   -------------------------------------

10

Total time: 2.739 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host KILIMANDSCHARO.UNI-MUENSTER.DE. (128.176.180.83)
Time: Thu Jul 15 08:29:50 2004

Input: F<a,b>:=Group<a,b|a*b*a=b*a*b,(a*b)^6>;
Order(F);

Output: Magma V2.10-22    Thu Jul 15 2004 08:29:45 on modular  [Seed = 2143897507]
   -------------------------------------

0

Total time: 4.549 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host fiber-83.aub.edu.lb. (69.60.65.83)
Time: Thu Jul 15 10:44:44 2004

Input: help

Output: Magma V2.10-22    Thu Jul 15 2004 10:44:41 on modular  [Seed = 4232717507]
   -------------------------------------


>> help;
   ^
User error: Identifier 'help' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Thu Jul 15 13:38:51 2004

Input: factorization(1983);

Output: Magma V2.10-22    Thu Jul 15 2004 13:38:49 on modular  [Seed = 798600812]
   -------------------------------------


>> factorization(1983);;
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-78-25-217.dsl.emhril.ameritech.net. (68.78.25.217)
Time: Thu Jul 15 13:39:00 2004

Input: Factorization(1983);

Output: Magma V2.10-22    Thu Jul 15 2004 13:38:57 on modular  [Seed = 663856764]
   -------------------------------------

[ <3, 1>, <661, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:42:21 2004

Input: fk


Output: Magma V2.10-22    Fri Jul 16 2004 13:42:18 on modular  [Seed = 2042702368]
   -------------------------------------


>> fk
   ^
User error: Identifier 'fk' has not been declared or assigned

Total time: 2.490 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:52:16 2004

Input: S4 := Sym(4)


Output: Magma V2.10-22    Fri Jul 16 2004 13:52:14 on modular  [Seed = 1324751779]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:53:10 2004

Input: S4 := Sym(4)
Z3 := CyclicGroup(3)


Output: Magma V2.10-22    Fri Jul 16 2004 13:53:08 on modular  [Seed = 1541606780]
   -------------------------------------


>> Z3 := CyclicGroup(3)
   ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:53:21 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3)


Output: Magma V2.10-22    Fri Jul 16 2004 13:53:19 on modular  [Seed = 2736518543]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:53:31 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3)


Output: Magma V2.10-22    Fri Jul 16 2004 13:53:28 on modular  [Seed = 2870214032]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:54:00 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
G1 := S4/Z3


Output: Magma V2.10-22    Fri Jul 16 2004 13:53:58 on modular  [Seed = 3003901350]
   -------------------------------------


>> G1 := S4/Z3
           ^
Runtime error in '/': Could not find a covering group

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:54:15 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
G1 := S4Z3


Output: Magma V2.10-22    Fri Jul 16 2004 13:54:13 on modular  [Seed = 3137596893]
   -------------------------------------


>> G1 := S4Z3
         ^
User error: Identifier 'S4Z3' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:56:50 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
G1 := quo < S4 | Z3> ;


Output: Magma V2.10-22    Fri Jul 16 2004 13:56:47 on modular  [Seed = 2201736575]
   -------------------------------------


>> G1 := quo < S4 | Z3> ;
             ^
Runtime error in quo< ... >: Can not build a generator from the arguments given

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:57:06 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
G1 , n := quo < S4 | Z3> ;


Output: Magma V2.10-22    Fri Jul 16 2004 13:57:04 on modular  [Seed = 2335432024]
   -------------------------------------


>> G1 , n := quo < S4 | Z3> ;
                 ^
Runtime error in quo< ... >: Can not build a generator from the arguments given

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:57:25 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
S4;
G1 , n := quo < S4 | Z3> ;


Output: Magma V2.10-22    Fri Jul 16 2004 13:57:22 on modular  [Seed = 2469119154]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3

>> G1 , n := quo < S4 | Z3> ;
                 ^
Runtime error in quo< ... >: Can not build a generator from the arguments given

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 13:57:44 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
S4;
Z3;
G1 , n := quo < S4 | Z3> ;


Output: Magma V2.10-22    Fri Jul 16 2004 13:57:42 on modular  [Seed = 2602814638]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

>> G1 , n := quo < S4 | Z3> ;
                 ^
Runtime error in quo< ... >: Can not build a generator from the arguments given

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:00:22 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
S4;
Z3;
G1:= quo<S4 | Z3> ;


Output: Magma V2.10-22    Fri Jul 16 2004 14:00:19 on modular  [Seed = 4132348262]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

>> G1:= quo<S4 | Z3> ;
           ^
Runtime error in quo< ... >: Can not build a generator from the arguments given

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:07:21 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
S4;
Z3;
quo<S4 | Z3> ;


Output: Magma V2.10-22    Fri Jul 16 2004 14:07:19 on modular  [Seed = 4249199753]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

>> quo<S4 | Z3> ;
      ^
Runtime error in quo< ... >: Can not build a generator from the arguments given

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:07:41 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
S4;
Z3;
S4/Z3;


Output: Magma V2.10-22    Fri Jul 16 2004 14:07:38 on modular  [Seed = 3313343628]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

>> S4/Z3;
     ^
Runtime error in '/': Could not find a covering group

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:33:13 2004

Input: S4 := Sym(4);
Z3 := CyclicGroup(3);
S4;
Z3;


S4<x,y>, S4 := Group< x, y | x^2, y^4, (x*y)^2 >;
S4;

Output: Magma V2.10-22    Fri Jul 16 2004 14:33:11 on modular  [Seed = 864775280]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)
Mapping from: GrpFP to GrpFP
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:33:51 2004

Input: Z3 := CyclicGroup(3);
Z3;
S4<x,y>, S4 := Group< x, y | x^2, y^4, (x*y)^2 >;
S4;

Output: Magma V2.10-22    Fri Jul 16 2004 14:33:48 on modular  [Seed = 998466707]
   -------------------------------------

Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)
Mapping from: GrpFP to GrpFP
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:35:49 2004

Input: Z3 := CyclicGroup(3);
Z3;
S4<x,y>, S4 := Group< x, y | x^3, y^4, (x*y)^2 >;
S4;
Z3 := sub< S4 | t*s^2, u^4 >;
Z3 := CyclicGroup(3);
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:35:46 on modular  [Seed = 62612261]
   -------------------------------------

Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)
Mapping from: GrpFP to GrpFP
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP

>> Z3 := sub< S4 | t*s^2, u^4 >;
                   ^
User error: Identifier 't' has not been declared or assigned
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:36:18 2004

Input: Z3 := CyclicGroup(3);
Z3;
S4<x,y>, S4 := Group< x, y | x^3, y^4, (x*y)^2 >;
S4;
Z3 := sub< S4 | x >;
Z3 := CyclicGroup(3);
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:36:15 on modular  [Seed = 196307727]
   -------------------------------------

Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)
Mapping from: GrpFP to GrpFP
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP

>> Z3 := sub< S4 | x >;
            ^
Runtime error: No constructor provided for this type of object
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:37:57 2004

Input: Z3 := CyclicGroup(3);
Z3;
Q<x,y>, S4 := Group< x, y | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
Z3 := CyclicGroup(3);
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:37:54 on modular  [Seed = 330003381]
   -------------------------------------

Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)
Permutation group Z3 acting on a set of cardinality 3
Order = 3
    (1, 2, 3)

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:38:43 2004

Input: Q<x,y>, S4 := Group< x, y | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
S4;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:38:41 on modular  [Seed = 1725826803]
   -------------------------------------

Mapping from: GrpFP to GrpFP: Q
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP: Q
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = x^3

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:39:11 2004

Input: Q<x,y>, S4 := Group< x, y | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
S4;
Z3;
S4/Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:39:09 on modular  [Seed = 1859522183]
   -------------------------------------

Mapping from: GrpFP to GrpFP: Q
Composition of Mapping from: GrpFP to GrpFP and
Mapping from: GrpFP to GrpFP: Q
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = x^3

>> S4/Z3;;
     ^
Runtime error in '/': Bad argument types
Argument types given: Map, GrpFP

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:39:36 2004

Input: Q<x,y>, S4 := sub< x, y | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
S4;
Z3;
S4/Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:39:34 on modular  [Seed = 1993217716]
   -------------------------------------


>> Q<x,y>, S4 := sub< x, y | x^3, y^4, (x*y)^2 >;
                             ^
User error: bad syntax

>> Z3 := sub< Q | x^3 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> S4;
   ^
User error: Identifier 'S4' has not been declared or assigned

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

>> S4/Z3;;
   ^
User error: Identifier 'S4' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:39:50 2004

Input: Q<x,y>, S4 := sub< Q | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
S4;
Z3;
S4/Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:39:48 on modular  [Seed = 2143756207]
   -------------------------------------


>> Q<x,y>, S4 := sub< Q | x^3, y^4, (x*y)^2 >;
                      ^
User error: Identifier 'Q' has not been declared or assigned

>> Z3 := sub< Q | x^3 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> S4;
   ^
User error: Identifier 'S4' has not been declared or assigned

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

>> S4/Z3;;
   ^
User error: Identifier 'S4' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:40:26 2004

Input: F2 = <x,y>;
S4 := sub< Q | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
S4;
Z3;
S4/Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:40:23 on modular  [Seed = 1391080289]
   -------------------------------------


>> F2 = <x,y>;
         ^
User error: Identifier 'x' has not been declared or assigned

>> S4 := sub< Q | x^3, y^4, (x*y)^2 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> Z3 := sub< Q | x^3 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> S4;
   ^
User error: Identifier 'S4' has not been declared or assigned

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

>> S4/Z3;;
   ^
User error: Identifier 'S4' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:44:18 2004

Input: F2 = <x,y>;
S4 := sub< Q | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
S4;
Z3;
S4/Z3;

SX := Sym(4); G := sub< SX | (1,2,3) >; 


Output: Magma V2.10-22    Fri Jul 16 2004 14:44:15 on modular  [Seed = 2685976955]
   -------------------------------------


>> F2 = <x,y>;
         ^
User error: Identifier 'x' has not been declared or assigned

>> S4 := sub< Q | x^3, y^4, (x*y)^2 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> Z3 := sub< Q | x^3 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> S4;
   ^
User error: Identifier 'S4' has not been declared or assigned

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

>> S4/Z3;
   ^
User error: Identifier 'S4' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:44:38 2004

Input: F2 = <x,y>;
S4 := sub< Q | x^3, y^4, (x*y)^2 >;
Z3 := sub< Q | x^3 >;
SX := Sym(4); G := sub< SX | (1,2,3) >; 
G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:44:36 on modular  [Seed = 2819672728]
   -------------------------------------


>> F2 = <x,y>;
         ^
User error: Identifier 'x' has not been declared or assigned

>> S4 := sub< Q | x^3, y^4, (x*y)^2 >;
              ^
User error: Identifier 'Q' has not been declared or assigned

>> Z3 := sub< Q | x^3 >;
              ^
User error: Identifier 'Q' has not been declared or assigned
Permutation group G acting on a set of cardinality 4
    (1, 2, 3)

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:45:00 2004

Input: SX := Sym(4); G := sub< SX | (1,2,3) >; 
G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:44:58 on modular  [Seed = 2953368254]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2, 3)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:45:20 2004

Input: SX := Sym(4); G := sub< SX | (1,2,3) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:45:17 on modular  [Seed = 3087063713]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2, 3)

>> SX/G;;
     ^
Runtime error in '/': Subgroup is not a normal subgroup

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:45:52 2004

Input: SX := Sym(4); G := sub< SX | (1,2,3,4) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:45:50 on modular  [Seed = 2151211770]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2, 3, 4)

>> SX/G;;
     ^
Runtime error in '/': Subgroup is not a normal subgroup

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:46:33 2004

Input: SX := Sym(4); G := sub< SX | (1,2), (3,4) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:46:30 on modular  [Seed = 2284907050]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2)
    (3, 4)

>> SX/G;;
     ^
Runtime error in '/': Subgroup is not a normal subgroup

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:46:48 2004

Input: SX := Sym(4); G := sub< SX | (1,2), (3,4), (1,2,3) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:46:45 on modular  [Seed = 2418602529]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2)
    (3, 4)
    (1, 2, 3)
Permutation group acting on a set of cardinality 1
    Id($)
    Id($)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:47:44 2004

Input: SX := Sym(4); G := sub< SX | (1,2), (1,2,3) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:47:41 on modular  [Seed = 2552298097]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2)
    (1, 2, 3)

>> SX/G;;
     ^
Runtime error in '/': Subgroup is not a normal subgroup

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:47:55 2004

Input: SX := Sym(4); G := sub< SX | (1), (1,2,3) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:47:52 on modular  [Seed = 3763896860]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    Id(G)
    (1, 2, 3)

>> SX/G;;
     ^
Runtime error in '/': Subgroup is not a normal subgroup

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:48:24 2004

Input: SX := Sym(4); G := sub< SX | (1,2), (1,2,3) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:48:22 on modular  [Seed = 3914435387]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2)
    (1, 2, 3)

>> SX/G;;
     ^
Runtime error in '/': Subgroup is not a normal subgroup

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:48:37 2004

Input: SX := Sym(4); G := sub< SX | (1,2), (3,4), (1,2,3) >; 
G;
SX/G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:48:34 on modular  [Seed = 4048130775]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2)
    (3, 4)
    (1, 2, 3)
Permutation group acting on a set of cardinality 1
    Id($)
    Id($)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:49:16 2004

Input: SX := Sym(4); G := sub< SX | (1,2)>; 
G;


Output: Magma V2.10-22    Fri Jul 16 2004 14:49:14 on modular  [Seed = 4198668788]
   -------------------------------------

Permutation group G acting on a set of cardinality 4
    (1, 2)

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:51:53 2004

Input: G := Sym({ 0..3 });
G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:51:51 on modular  [Seed = 3480726572]
   -------------------------------------

Symmetric group G acting on a set of cardinality 4
Order = 24 = 2^3 * 3

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:53:12 2004

Input: G := Sym({ 0..3 });
G;

Output: Magma V2.10-22    Fri Jul 16 2004 14:53:10 on modular  [Seed = 3530208992]
   -------------------------------------

Symmetric group G acting on a set of cardinality 4
Order = 24 = 2^3 * 3

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:54:53 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(0,1,2);

Output: Magma V2.10-22    Fri Jul 16 2004 14:54:50 on modular  [Seed = 614219898]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:55:04 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(0,1,2);
g;

Output: Magma V2.10-22    Fri Jul 16 2004 14:55:01 on modular  [Seed = 747915404]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(0, 1, 2)

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:57:39 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(0,1,2);
g;
Z3 := ncl<S4 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:57:36 on modular  [Seed = 881611057]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(0, 1, 2)
Permutation group Z3 acting on a set of cardinality 4
Order = 12 = 2^2 * 3
    (0, 1, 2)
    (1, 2, 3)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:58:09 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(0,1);
g;
Z3 := ncl<S4 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:58:06 on modular  [Seed = 1048992548]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(0, 1)
Permutation group Z3 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
    (0, 1)
    (1, 2)
    (2, 3)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:58:28 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(0,1,2,3);
g;
Z3 := ncl<S4 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:58:26 on modular  [Seed = 113140593]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(0, 1, 2, 3)
Permutation group Z3 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
    (0, 1, 2, 3)
    (1, 2)
    (2, 3)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 14:59:40 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(0,1,3);
g;
Z3 := ncl<S4 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 14:59:37 on modular  [Seed = 162622645]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(0, 1, 3)
Permutation group Z3 acting on a set of cardinality 4
Order = 12 = 2^2 * 3
    (0, 1, 3)
    (1, 2, 3)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:00:28 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(1,2,3);
g;
Z3 := ncl<S4 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 15:00:26 on modular  [Seed = 1658455949]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(1, 2, 3)
Permutation group Z3 acting on a set of cardinality 4
Order = 12 = 2^2 * 3
    (1, 2, 3)
    (0, 2, 3)

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:00:36 2004

Input: S4 := Sym({ 0..3 });
S4;
g := S4!(1,2,3);
g;
Z3 := ncl<S4 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 15:00:34 on modular  [Seed = 1792151453]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
(1, 2, 3)
Permutation group Z3 acting on a set of cardinality 4
Order = 12 = 2^2 * 3
    (1, 2, 3)
    (0, 2, 3)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:10:27 2004

Input: S8 := Sym({ 0..7 });
S8;
g := S8!(1,2,3);
g;
Z3 := ncl<S8 | g>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 15:10:24 on modular  [Seed = 1140534086]
   -------------------------------------

Symmetric group S8 acting on a set of cardinality 8
Order = 40320 = 2^7 * 3^2 * 5 * 7
(1, 2, 3)
Permutation group Z3 acting on a set of cardinality 8
Order = 20160 = 2^6 * 3^2 * 5 * 7
    (1, 2, 3)
    (2, 3, 4)
    (0, 4, 3)
    (3, 4, 5)
    (4, 5, 6)
    (5, 6, 7)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:14:17 2004

Input: S8 := Sym({ 0..7 });
S8;
g1 := S8!(1,2,3);
g2 := S8!(5,6,7);
S4 := sub < S8 | g1 , g2 >;
Z3 := ncl<S8 | g1 , g2>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 15:14:14 on modular  [Seed = 1424768375]
   -------------------------------------

Symmetric group S8 acting on a set of cardinality 8
Order = 40320 = 2^7 * 3^2 * 5 * 7
Permutation group Z3 acting on a set of cardinality 8
Order = 20160 = 2^6 * 3^2 * 5 * 7
    (1, 2, 3)
    (5, 6, 7)
    (2, 3, 4)
    (0, 4, 3)
    (0, 6, 7)
    (3, 4, 6)
    (4, 6, 7)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:14:42 2004

Input: S8 := Sym({ 0..7 });
S8;
g1 := S8!(1,2,3);
g2 := S8!(5,6,7);
S4 := sub < S8 | g1 , g2 >;
S4;
Z3 := ncl<S8 | g1 , g2>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 15:14:39 on modular  [Seed = 1558459750]
   -------------------------------------

Symmetric group S8 acting on a set of cardinality 8
Order = 40320 = 2^7 * 3^2 * 5 * 7
Permutation group S4 acting on a set of cardinality 8
    (1, 2, 3)
    (5, 6, 7)
Permutation group Z3 acting on a set of cardinality 8
Order = 20160 = 2^6 * 3^2 * 5 * 7
    (1, 2, 3)
    (5, 6, 7)
    (2, 3, 4)
    (0, 4, 3)
    (0, 6, 7)
    (3, 4, 6)
    (4, 6, 7)

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:15:13 2004

Input: S8 := Sym({ 0..7 });
S8;
g1 := S8!(1,2,3);
g2 := S8!(5,6,7);
S4 := sub < S8 | g1 >;
S4;
Z3 := ncl<S8 | g1 , g2>;
Z3;

Output: Magma V2.10-22    Fri Jul 16 2004 15:15:10 on modular  [Seed = 2753351103]
   -------------------------------------

Symmetric group S8 acting on a set of cardinality 8
Order = 40320 = 2^7 * 3^2 * 5 * 7
Permutation group S4 acting on a set of cardinality 8
    (1, 2, 3)
Permutation group Z3 acting on a set of cardinality 8
Order = 20160 = 2^6 * 3^2 * 5 * 7
    (1, 2, 3)
    (5, 6, 7)
    (2, 3, 4)
    (0, 4, 3)
    (0, 6, 7)
    (3, 4, 6)
    (4, 6, 7)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:17:47 2004

Input: S4 := Sym({ 0..3 });
S4;
NormalSubgroups(S4);
g2 := S8!(5,6,7);
S4 := sub < S8 | g1 >;
S4;
Z3 := ncl<S8 | g1 , g2>;
Z3;
order

Output: Magma V2.10-22    Fri Jul 16 2004 15:17:44 on modular  [Seed = 2920728403]
   -------------------------------------

Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
Conjugacy classes of subgroups
------------------------------

[1]     Order 1            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 1
[2]     Order 4            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 4 = 2^2
            (0, 3)(1, 2)
            (0, 2)(1, 3)
[3]     Order 12           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 12 = 2^2 * 3
            (1, 2, 3)
            (0, 3)(1, 2)
            (0, 2)(1, 3)
[4]     Order 24           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 24 = 2^3 * 3
            (2, 3)
            (1, 2, 3)
            (0, 3)(1, 2)
            (0, 2)(1, 3)

>> g2 := S8!(5,6,7);
         ^
User error: Identifier 'S8' has not been declared or assigned

>> S4 := sub < S8 | g1 >;
               ^
User error: Identifier 'S8' has not been declared or assigned
Symmetric group S4 acting on a set of cardinality 4
Order = 24 = 2^3 * 3
    (0, 1, 2, 3)
    (0, 1)

>> Z3 := ncl<S8 | g1 , g2>;
             ^
User error: Identifier 'S8' has not been declared or assigned

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

>> order;
   ^
User error: Identifier 'order' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:36:58 2004

Input: G3<a,b> := PolycyclicGroup< a,b | a^2, (a*b)^3>;
G3<a,b>;


Output: Magma V2.10-22    Fri Jul 16 2004 15:36:55 on modular  [Seed = 2335434233]
   -------------------------------------


>> G3<a,b> := PolycyclicGroup< a,b | a^2, (a*b)^3>;
                             ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : ($.1 
* $.2)^3 = Id($)

>> G3<a,b>;
     ^
User error: Bad print expression

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:37:41 2004

Input: G3<a,b> := PolycyclicGroup< a,b | a^2, (a*b)^3>;
G3;


Output: Magma V2.10-22    Fri Jul 16 2004 15:37:39 on modular  [Seed = 2469133621]
   -------------------------------------


>> G3<a,b> := PolycyclicGroup< a,b | a^2, (a*b)^3>;
                             ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : ($.1 
* $.2)^3 = Id($)

>> G3;
   ^
User error: Identifier 'G3' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:38:47 2004

Input: G3<a,b> := PolycyclicGroup< a,b | a^2, (a*b)^3>;
G3;
G1<a,b> := PolycyclicGroup< a,b | a^2, b^5, b^a=b^4 >;
G1;

Output: Magma V2.10-22    Fri Jul 16 2004 15:38:45 on modular  [Seed = 3831269892]
   -------------------------------------


>> G3<a,b> := PolycyclicGroup< a,b | a^2, (a*b)^3>;
                             ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : ($.1 
* $.2)^3 = Id($)

>> G3;
   ^
User error: Identifier 'G3' has not been declared or assigned
GrpPC : G1 of order 10 = 2 * 5
PC-Relations:
    a^2 = Id(G1), 
    b^5 = Id(G1), 
    b^a = b^4

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:42:27 2004

Input: G1<a,b> := PolycyclicGroup< a,b | a^2, b^4, (a*b)^3 >;
G1;

Output: Magma V2.10-22    Fri Jul 16 2004 15:42:25 on modular  [Seed = 4164982652]
   -------------------------------------


>> G1<a,b> := PolycyclicGroup< a,b | a^2, b^4, (a*b)^3 >;
                             ^
Runtime error in PolycyclicGroup< ... >: Invalid LHS for the pc relation : ($.1 
* $.2)^3 = Id($)

>> G1;;
   ^
User error: Identifier 'G1' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:43:16 2004

Input: G3<a,b> := PolycyclicGroup< a,b | a^2, b^3>;
G3;
G1<a,b> := PolycyclicGroup< a,b | a^2, b^5, b^a=b^4 >;
G1;

Output: Magma V2.10-22    Fri Jul 16 2004 15:43:13 on modular  [Seed = 3279662132]
   -------------------------------------

GrpPC : G3 of order 6 = 2 * 3
PC-Relations:
    a^2 = Id(G3), 
    b^3 = Id(G3)
GrpPC : G1 of order 10 = 2 * 5
PC-Relations:
    a^2 = Id(G1), 
    b^5 = Id(G1), 
    b^a = b^4

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:43:42 2004

Input: G3<a,b> := PolycyclicGroup< a,b | a^2, b^5>;
G3;
G1<a,b> := PolycyclicGroup< a,b | a^2, b^5, b^a=b^4 >;
G1;

Output: Magma V2.10-22    Fri Jul 16 2004 15:43:39 on modular  [Seed = 3413353477]
   -------------------------------------

GrpPC : G3 of order 10 = 2 * 5
PC-Relations:
    a^2 = Id(G3), 
    b^5 = Id(G3)
GrpPC : G1 of order 10 = 2 * 5
PC-Relations:
    a^2 = Id(G1), 
    b^5 = Id(G1), 
    b^a = b^4

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:48:29 2004

Input: Q<s,t,u>, h := Group< s, t, u | t^2, u^17, s^2 = t^s = t, u^s = u^16, u^t = u >;
Q;

Output: Magma V2.10-22    Fri Jul 16 2004 15:48:27 on modular  [Seed = 3697585650]
   -------------------------------------

Finitely presented group Q on 3 generators
Relations
    t^2 = Id(Q)
    u^17 = Id(Q)
    s^2 = t
    t^s = t
    u^s = u^16
    u^t = u

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:49:28 2004

Input: Q<s,t>, h := Group< s, t, | s^2, t^4, (s*t)^3 >;
Q;

Output: Magma V2.10-22    Fri Jul 16 2004 15:49:25 on modular  [Seed = 664753732]
   -------------------------------------


>> Q<s,t>, h := Group< s, t, | s^2, t^4, (s*t)^3 >;
                             ^
User error: bad syntax

>> Q;;
   ^
User error: Identifier 'Q' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:49:43 2004

Input: Q<s,t>, h := Group< s, t, | s^2, t^4, (s*t)^3=1 >;
Q;

Output: Magma V2.10-22    Fri Jul 16 2004 15:49:41 on modular  [Seed = 747920735]
   -------------------------------------


>> Q<s,t>, h := Group< s, t, | s^2, t^4, (s*t)^3=1 >;
                             ^
User error: bad syntax

>> Q;;
   ^
User error: Identifier 'Q' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:50:07 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;

Output: Magma V2.10-22    Fri Jul 16 2004 15:50:05 on modular  [Seed = 1065832052]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:50:49 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
order(Q);

Output: Magma V2.10-22    Fri Jul 16 2004 15:50:47 on modular  [Seed = 129988278]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)

>> order(Q);;
   ^
User error: Identifier 'order' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:51:05 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);

Output: Magma V2.10-22    Fri Jul 16 2004 15:51:02 on modular  [Seed = 263683727]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:51:42 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
NormalSubgorups(Q);


Output: Magma V2.10-22    Fri Jul 16 2004 15:51:40 on modular  [Seed = 514224116]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> NormalSubgorups(Q);
   ^
User error: Identifier 'NormalSubgorups' has not been declared or assigned

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:52:01 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
NormalSubgroups(Q);


Output: Magma V2.10-22    Fri Jul 16 2004 15:51:58 on modular  [Seed = 1742673567]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> NormalSubgroups(Q);
                  ^
Runtime error in 'NormalSubgroups': Bad argument types
Argument types given: GrpFP

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:53:37 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
NormalSubgroups(Q);

Output: Magma V2.10-22    Fri Jul 16 2004 15:53:35 on modular  [Seed = 1758468721]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> NormalSubgroups(Q);;
                  ^
Runtime error in 'NormalSubgroups': Bad argument types
Argument types given: GrpFP

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:55:27 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
NormalSubgroups(h);


Output: Magma V2.10-22    Fri Jul 16 2004 15:55:24 on modular  [Seed = 1892156154]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> NormalSubgroups(h);
                  ^
Runtime error in 'NormalSubgroups': Bad argument types
Argument types given: Map

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:55:48 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
NormalSubgroups(Q<s,t>);


Output: Magma V2.10-22    Fri Jul 16 2004 15:55:45 on modular  [Seed = 2025851551]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> NormalSubgroups(Q<s,t>);
                    ^
User error: bad syntax

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:56:00 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
NormalSubgroups(Q);


Output: Magma V2.10-22    Fri Jul 16 2004 15:55:57 on modular  [Seed = 1090007723]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> NormalSubgroups(Q);
                  ^
Runtime error in 'NormalSubgroups': Bad argument types
Argument types given: GrpFP

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:58:17 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
ncl
sub<Q | s*t>;



Output: Magma V2.10-22    Fri Jul 16 2004 15:58:15 on modular  [Seed = 1424762661]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> sub<Q | s*t>;
   ^
User error: bad syntax

Total time: 2.649 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:58:40 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
ncl
Z3 := sub<Q | s*t>;
Z3;


Output: Magma V2.10-22    Fri Jul 16 2004 15:58:38 on modular  [Seed = 1558458132]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> Z3 := sub<Q | s*t>;
   ^
User error: bad syntax

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

Total time: 2.629 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 15:58:58 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
ncl
Z3 := sub< Q | s*t >;
Z3;


Output: Magma V2.10-22    Fri Jul 16 2004 15:58:55 on modular  [Seed = 2753353725]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24

>> Z3 := sub< Q | s*t >;
   ^
User error: bad syntax

>> Z3;
   ^
User error: Identifier 'Z3' has not been declared or assigned

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:00:53 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
> Q<s,t,u>, h := Group< s, t, u |
>     t^2, u^17, s^2 = t^s = t, u^s = u^16, u^t = u >;
> S := sub< Q | t*s^2, u^4 >;
> S;
Finitely presented group S on 2 generators
Generators as words
    S.1 = $.2 * $.1^2
    S.2 = $.3^4



Output: Magma V2.10-22    Fri Jul 16 2004 16:00:50 on modular  [Seed = 3103902317]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
Finitely presented group S on 2 generators
Generators as words in group Q
    S.1 = t * s^2
    S.2 = u^4

>> Finitely presented group S on 2 generators
            ^
User error: bad syntax

>> Generators as words
              ^
User error: bad syntax

>>     S.2 = $.3^4
       ^
User error: bad syntax

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:01:18 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;



Output: Magma V2.10-22    Fri Jul 16 2004 16:01:15 on modular  [Seed = 2402810786]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t

Total time: 2.639 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:01:34 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);


Output: Magma V2.10-22    Fri Jul 16 2004 16:01:31 on modular  [Seed = 2536498090]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3

Total time: 2.769 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:02:12 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;

Output: Magma V2.10-22    Fri Jul 16 2004 16:02:09 on modular  [Seed = 2670193656]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)

Total time: 2.879 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:26:23 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
IsAbelian(G);

Output: Magma V2.10-22    Fri Jul 16 2004 16:26:20 on modular  [Seed = 3614420509]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)

>> IsAbelian(G);;
            ^
Runtime error in 'IsAbelian': Bad argument types
Argument types given: GrpFP

Total time: 2.839 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:27:44 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
IsAbelian(Q);

Output: Magma V2.10-22    Fri Jul 16 2004 16:27:41 on modular  [Seed = 3748111812]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)

>> IsAbelian(Q);;
            ^
Runtime error in 'IsAbelian': Bad argument types
Argument types given: GrpFP

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:28:01 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
IsAbelian(Z3);

Output: Magma V2.10-22    Fri Jul 16 2004 16:27:58 on modular  [Seed = 647912527]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)

>> IsAbelian(Z3);;
            ^
Runtime error in 'IsAbelian': Bad argument types
Argument types given: GrpFP

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:28:30 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
T := sym(4);
T;
IsAbelian(Z3);

Output: Magma V2.10-22    Fri Jul 16 2004 16:28:27 on modular  [Seed = 764761953]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)

>> T := sym(4);
        ^
User error: Identifier 'sym' has not been declared or assigned

>> T;
   ^
User error: Identifier 'T' has not been declared or assigned

>> IsAbelian(Z3);;
            ^
Runtime error in 'IsAbelian': Bad argument types
Argument types given: GrpFP

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:28:42 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
T := Sym(4);
T;
IsAbelian(Z3);

Output: Magma V2.10-22    Fri Jul 16 2004 16:28:39 on modular  [Seed = 898453354]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)
Symmetric group T acting on a set of cardinality 4
Order = 24 = 2^3 * 3

>> IsAbelian(Z3);;
            ^
Runtime error in 'IsAbelian': Bad argument types
Argument types given: GrpFP

Total time: 2.789 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Fri Jul 16 16:28:53 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
T := Sym(4);
T;
IsAbelian(T);

Output: Magma V2.10-22    Fri Jul 16 2004 16:28:50 on modular  [Seed = 1032144792]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)
Symmetric group T acting on a set of cardinality 4
Order = 24 = 2^3 * 3
false

Total time: 2.819 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host p508C3DB9.dip.t-dialin.net. (80.140.61.185)
Time: Sat Jul 17 13:37:46 2004

Input: x=1

Output: Magma V2.10-22    Sat Jul 17 2004 13:37:41 on modular  [Seed = 1491172330]
   -------------------------------------


>> x=1;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.629 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host rn-recltn107.uwaterloo.ca. (129.97.228.171)
Time: Sat Jul 17 13:40:25 2004

Input: constr_field := function(q)
local F;
local P2;
F<w> := GF(q);
P2<x,y,z> := ProjectiveSpace(F,2);
return F, P2;

end function;


constr_curve := function(P2, f)
local X;
local g;

X := Curve(P2,f);
g := Genus(X);
return X,g;

end function;




K<w>,P2<x,y,z> := constr_field(19);
f := -y^2*z^3 + (x-z)*(x-2*z)*(x-3*z)*(x-4*z)*(x-5*z);

X,g := constr_curve(P2,f);
DG := DivisorGroup(X);
//place1 gives all places of degree 1
place1 := Places(X,1);
F<a,b> := FunctionField(X);

//D are the places where we evaluate the elements of G
D := Exclude(place1,place1[1]);
Exclude(~D,place1[2]);Exclude(~D,place1[3]);Exclude(~D,place1[19]);Exclude(~D,place1[20]);Exclude(~D,place1[14]);
//D3 is corresponding divisor of the places D[i]
//D3 := DG! &+D;
D3 := DG!D[1] + DG!D[2] + DG!D[3] + DG!D[4] + DG!D[5] + DG!D[6] + DG!D[7] + DG!D[8] + DG!D[9] + DG!D[10] + DG!D[11] + DG!D[12] + DG!D[13] + DG!D[14];

//W is canonical divisor
W := - D3 + (#D + (2*g-2)) * DG!place1[1];

//differential corresponding to W
isornot, k := IsCanonical(W);

//residues of k at the D[i]'s
for i:= 1 to #D do
Residue(k,D[i]);
end for;







Output: Magma V2.10-22    Sat Jul 17 2004 13:40:21 on modular  [Seed = 279524546]
   -------------------------------------

3
16
11
8
1
18
10
9
14
5
5
14
12
7

Total time: 3.479 seconds, Total memory usage: 1.96MB


************** MAGMA *****************
Host rn-recltn107.uwaterloo.ca. (129.97.228.171)
Time: Sat Jul 17 13:44:08 2004

Input: constr_field := function(q)
local F;
local P2;
F<w> := GF(q);
P2<x,y,z> := ProjectiveSpace(F,2);
return F, P2;

end function;


constr_curve := function(P2, f)
local X;
local g;

X := Curve(P2,f);
g := Genus(X);
return X,g;

end function;




K<w>,P2<x,y,z> := constr_field(9);
f := -y^2*z^3 + x^5 - 2*x^3*z^2 + x^2*z^3 + z^5;

X,g := constr_curve(P2,f);
DG := DivisorGroup(X);
//place1 gives all places of degree 1
place1 := Places(X,1);
F<a,b> := FunctionField(X);

//D are the places where we evaluate the elements of G
D := Exclude(place1,place1[1]);
Exclude(~D,place1[4]);Exclude(~D,place1[5]);Exclude(~D,place1[8]);
//D3 is corresponding divisor of the places D[i]
//D3 := DG! &+D;
D3 := DG!D[1] + DG!D[2] + DG!D[3] + DG!D[4] + DG!D[5] + DG!D[6] + DG!D[7] +
DG!D[8];

//W is canonical divisor
W := - D3 + (#D + (2*g-2)) * DG!place1[1];

//differential corresponding to W
isornot, k := IsCanonical(W);

//residues of k at the D[i]'s
for i:= 1 to #D do
Residue(k,D[i]);
end for;







Output: Magma V2.10-22    Sat Jul 17 2004 13:44:05 on modular  [Seed = 4165066186]
   -------------------------------------

2
1
w^2
w^6
w^6
w^2
1
2

Total time: 3.479 seconds, Total memory usage: 8.47MB


************** MAGMA *****************
Host bzq-218-125-6.red.bezeqint.net. (81.218.125.6)
Time: Sat Jul 17 16:36:37 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sat Jul 17 2004 16:36:34 on modular  [Seed = 3480617584]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.669 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host c-67-180-30-179.client.comcast.net. (67.180.30.179)
Time: Sat Jul 17 22:42:03 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sat Jul 17 2004 22:42:01 on modular  [Seed = 1324870989]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD953518F.dip.t-dialin.net. (217.83.81.143)
Time: Sun Jul 18 10:46:22 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a*b=b*a*b*a*b*a,a^4>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 10:45:49 on modular  [Seed = 2552386948]
   -------------------------------------

0

Total time: 10.179 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD953518F.dip.t-dialin.net. (217.83.81.143)
Time: Sun Jul 18 10:46:56 2004

Input: F<a,b>:=Group<a,b|a*b*a*b*a*b=b*a*b*a*b*a,a^4,a^2*b^2=b^2*a^2>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 10:46:45 on modular  [Seed = 2686086646]
   -------------------------------------

0

Total time: 9.650 seconds, Total memory usage: 18.35MB


************** MAGMA *****************
Host pD953518F.dip.t-dialin.net. (217.83.81.143)
Time: Sun Jul 18 10:47:48 2004

Input: F<a,b>:=Group<a,b|(a*b)^3=(b*a)^3,a^4,a^2*b^2=b^2*a^2>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 10:47:35 on modular  [Seed = 2819777836]
   -------------------------------------

0

Total time: 10.559 seconds, Total memory usage: 18.25MB


************** MAGMA *****************
Host pD953518F.dip.t-dialin.net. (217.83.81.143)
Time: Sun Jul 18 10:48:27 2004

Input: F<a,b>:=Group<a,b|(a*b)^3=(b*a)^3,a^4,b^4,a^2*b^2=b^2*a^2>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 10:48:12 on modular  [Seed = 2953477407]
   -------------------------------------

0

Total time: 12.890 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD953518F.dip.t-dialin.net. (217.83.81.143)
Time: Sun Jul 18 10:50:28 2004

Input: F<x,y>:=Group<x,y|(x*y)^3=(y*x)^3,x^4,y^4,x^2*y^2=y^2*x^2>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 10:50:12 on modular  [Seed = 3187962008]
   -------------------------------------

0

Total time: 13.169 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host pD9FF076F.dip.t-dialin.net. (217.255.7.111)
Time: Sun Jul 18 12:47:08 2004

Input: F<x,y>:=Group<x,y|(x*y)^3=(y*x)^3,x^4,y^4,x^2*y^2=y^2*x^2,x^2*y*x^2*y=y*x^2*y*x^2>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 12:47:05 on modular  [Seed = 1592047570]
   -------------------------------------

1536

Total time: 2.659 seconds, Total memory usage: 17.68MB


************** MAGMA *****************
Host pD9FF076F.dip.t-dialin.net. (217.255.7.111)
Time: Sun Jul 18 12:47:43 2004

Input: F<x,y>:=Group<x,y|(x*y)^3=(y*x)^3,x^4,y^4,x^2*y^2=y^2*x^2,x^2*y*x^2*y=y*x^2*y*x^2,x*y^2*x*y^2=y^2*x*y^2*x>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 12:47:40 on modular  [Seed = 1641777352]
   -------------------------------------

768

Total time: 2.639 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9FF076F.dip.t-dialin.net. (217.255.7.111)
Time: Sun Jul 18 12:49:11 2004

Input: F<x,y>:=Group<x,y|(x*y)^3=(y*x)^3,x^4,y^4,x^2*y^2=y^2*x^2,x^2*y*x^2*y=y*x^2*y*x^2,x*y^2*x*y^2=y^2*x*y^2*x,x*y*x^2*y*x=y*x*y^2*x*y>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 12:49:09 on modular  [Seed = 1808892267]
   -------------------------------------

384

Total time: 2.639 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9FF076F.dip.t-dialin.net. (217.255.7.111)
Time: Sun Jul 18 12:49:43 2004

Input: F<x,y>:=Group<x,y|(x*y)^3=(y*x)^3,x^4,y^4,x^2*y^2=y^2*x^2,x^2*y*x^2*y=y*x^2*y*x^2,x*y^2*x*y^2=y^2*x*y^2*x,x*y*x^2*y*x=y*x*y^2*x*y>;
Order(F);
G:=Simplify(F);
G

Output: Magma V2.10-22    Sun Jul 18 2004 12:49:40 on modular  [Seed = 1942591826]
   -------------------------------------

384
Finitely presented group G on 2 generators
Generators as words in group F
    G.1 = x
    G.2 = y
Relations
    G.1^4 = Id(G)
    G.2^4 = Id(G)
    G.1^-2 * G.2^2 * G.1^-2 * G.2^-2 = Id(G)
    G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^-1 * G.2^-1 * G.1^-1 * G.2^-1 * 
    G.1^-1 * G.2^-1 = Id(G)
    G.1^-2 * G.2^-1 * G.1^2 * G.2 * G.1^2 * G.2^-1 * G.1^2 * G.2 = Id(G)
    (G.1^-1 * G.2^-2)^4 = Id(G)
    G.1 * G.2 * G.1^-2 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 = 
    Id(G)

Total time: 2.649 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9E5178A.dip.t-dialin.net. (217.229.23.138)
Time: Sun Jul 18 13:02:00 2004

Input: F<x,y>:=Group<x,y|x^4,y^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x*y*x^2*y*x=y*x*y^2*x*y>;
Order(F);


Output: Magma V2.10-22    Sun Jul 18 2004 13:01:57 on modular  [Seed = 2619765148]
   -------------------------------------

768

Total time: 2.699 seconds, Total memory usage: 17.68MB


************** MAGMA *****************
Host pD9E5178A.dip.t-dialin.net. (217.229.23.138)
Time: Sun Jul 18 13:05:46 2004

Input: F<x,y>:=Group<x,y|x^4,y^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2,x*y^2*x*y^2=x^2*y*x^2*y>;
Order(F);


Output: Magma V2.10-22    Sun Jul 18 2004 13:05:43 on modular  [Seed = 2786872132]
   -------------------------------------

96

Total time: 2.649 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:40:51 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^2>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 14:40:48 on modular  [Seed = 3747961833]
   -------------------------------------

120

Total time: 2.639 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:41:03 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^3>;
Order(F);

Output: Magma V2.10-22    Sun Jul 18 2004 14:40:59 on modular  [Seed = 3881657306]
   -------------------------------------

155520

Total time: 3.309 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:42:28 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^3>;
Order(F);
G<x>:=sub<F|a*b*c*d>;
Order(G);

Output: Magma V2.10-22    Sun Jul 18 2004 14:42:25 on modular  [Seed = 4015352696]
   -------------------------------------

155520
30

Total time: 3.489 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:43:54 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^2>;
Order(F);
G<x>:=sub<F|a*b*c*d>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a*d*c*b*a>;
Order(H);

Output: Magma V2.10-22    Sun Jul 18 2004 14:43:51 on modular  [Seed = 4149048086]
   -------------------------------------

120
5
2

Total time: 2.939 seconds, Total memory usage: 17.69MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:44:14 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^3>;
Order(F);
G<x>:=sub<F|a*b*c*d>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a*d*c*b*a>;
Order(H);

Output: Magma V2.10-22    Sun Jul 18 2004 14:44:10 on modular  [Seed = 4232476672]
   -------------------------------------

155520
30
12

Total time: 3.669 seconds, Total memory usage: 17.97MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:45:48 2004

Input: F<a,b,c,d,e>:=Group<a,b,c,d,e|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,d*e*d=e*d*e,a*c=c*a,a*d=d*a,a*e=e*a,b*d=d*b,b*e=e*b,c*e=e*c,a^2>;
Order(F);
G<x>:=sub<F|a*b*c*d*e>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a*d*c*b*a*e*d*c*b*a>;
Order(H);

Output: Magma V2.10-22    Sun Jul 18 2004 14:45:45 on modular  [Seed = 96436315]
   -------------------------------------

720
6
2

Total time: 2.959 seconds, Total memory usage: 17.70MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:46:46 2004

Input: F<a,b,c,d,e>:=Group<a,b,c,d,e|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,d*e*d=e*d*e,a*c=c*a,a*d=d*a,a*e=e*a,b*d=d*b,b*e=e*b,c*e=e*c,a^3>;
Order(F);
G<x>:=sub<F|a*b*c*d*e>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a*d*c*b*a*e*d*c*b*a>;
Order(H);

Output: Magma V2.10-22    Sun Jul 18 2004 14:46:30 on modular  [Seed = 230131852]
   -------------------------------------

0
0
0

Total time: 16.250 seconds, Total memory usage: 26.32MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:54:47 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^3>;
Order(F);
G<x>:=sub<F|a*b*c*d>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a*d*c*b*a>;
Order(H);

Output: Magma V2.10-22    Sun Jul 18 2004 14:54:43 on modular  [Seed = 530946155]
   -------------------------------------

155520
30
12

Total time: 3.669 seconds, Total memory usage: 17.97MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:55:27 2004

Input: F<a,b,c,d>:=Group<a,b,c,d|a*b*a=b*a*b,b*c*b=c*b*c,c*d*c=d*c*d,a*c=c*a,a*d=d*a,b*d=d*b,a^3>;
Order(F);
G<x>:=sub<F|a*b*c*d>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a*d*c*b*a>;
Order(H);
I<z>:=sub<F|a^2*b^2*c^2*d^2>;
Order(I);

Output: Magma V2.10-22    Sun Jul 18 2004 14:55:23 on modular  [Seed = 664641723]
   -------------------------------------

155520
30
12
30

Total time: 3.779 seconds, Total memory usage: 18.07MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 14:56:32 2004

Input: F<a,b,c>:=Group<a,b,c|a*b*a=b*a*b,b*c*b=c*b*c,a*c=c*a,a^3>;
Order(F);
G<x>:=sub<F|a*b*c>;
Order(G);
H<y>:=sub<F|a*b*a*c*b*a>;
Order(H);
I<z>:=sub<F|a^2*b^2*c^2>;
Order(I);

Output: Magma V2.10-22    Sun Jul 18 2004 14:56:29 on modular  [Seed = 730967281]
   -------------------------------------

648
12
6
12

Total time: 3.099 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host pD9E51DD4.dip.t-dialin.net. (217.229.29.212)
Time: Sun Jul 18 15:02:55 2004

Input: F<a,b>:=Group<a,b|a^12,b^12,a^6*b^6=b^6*a^6,(a^3*b^3)^3=(b^3*a^3)^3,a^6*b^3*a^6*b^3=b^3*a^6*b^3*a^6,a^3*b^3*a^6*b^3*a^3=b^3*a^3*b^6*a^3*b^3>;
Order(F);


Output: Magma V2.10-22    Sun Jul 18 2004 15:02:43 on modular  [Seed = 1324664602]
   -------------------------------------

0

Total time: 12.469 seconds, Total memory usage: 17.79MB


************** MAGMA *****************
Host lns-vlq-20-82-255-42-161.adsl.proxad.net. (82.255.42.161)
Time: Sun Jul 18 16:04:24 2004

Input: 



/*
 *  An implementation of algorithm 12.1 in the paper
 *  "Factoring Integers with the Number Field Sieve" by J.P. Buhler,
 *  H.W. Lenstra, and Carl Pomerance.  This is the variant of the
 *  Number Field Sieve that uses a homogenous polynomial.
 *
 *  This code is not at all optimized - it is demonstration of the
 *  Magma computer algebra package, and to for people who want to
 *  learn the Number Field Sieve algorithm or how to code it.  It is
 *  recommended to try this on numbers of no bigger than 30-digits.
 *  There are various problems that can happen for larger numbers,
 *  such as running out of memory due to not taking advantage of
 *  the sparseness of the matrix!
 *
 *  Three methods for selecting the polynomial are included here.
 *  None of them are optimized or complete.  However, the polynomials
 *  should work most of the time.  This implementation of NFS takes  n
 *  along with the polynomial  f, m1, m2,  and  d  for input.
 *
 *  "print" statements that can be ommitted are left justified.
 *
 *  by Contini - March 23, 2000.
 *  updated: November 12, 2003.
 */



/*
 *  This method of selecting the polynomial takes  m2 = 1  but allows
 *  c_d != 1 .
 */
function SelectPolynomial1(n);
    /* select a degree according to the asymptotic formula */
    d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) );
print "degree ", d;

    P<X,Y> := PolynomialRing( IntegerRing(), 2 );

    m2 := 1;
    m1 := Iroot( n, d+1 ) ;

    coeffs := [];
    for i := d to 0 by -1 do
        temp := m1^i;
        coeff := n div temp;
        Append (~coeffs, coeff);
        n -:= coeff*temp;
    end for;
 
    m1div2 := m1 div 2;
    /* adjust the coefficients to be between  -m1div2  and  m1div2  */
    for i := d+1 to 2 by -1 do
	if coeffs[i] gt m1div2 then
	    coeffs[i] -:= m1;
	    coeffs[i-1] +:= 1;
	end if;
    end for;

    f := P!0;
    for i in [0..d] do
	f +:= coeffs[i+1]*X^(d-i)*Y^i;
    end for;

print f, m1, m2;

    return f, m1, m2, d;
end function;


/*
 *  This method of selecting the polynomial takes  c_d = 1  but allows
 *  m2 != 1 .  See (12.3) in the paper of Buhler, Lenstra, and Pomerance.
 */
function SelectPolynomial2(n);
    /* select a degree according to the asymptotic formula */
    d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) );
print "degree ", d;

    P<X,Y> := PolynomialRing( IntegerRing(), 2 );

    /* A not very optimized algorithm for choosing  m1  and  m2  */
    m1 := Iroot( n, d+1 );
    closeness_ratio := 0.90;
    min_m2 := Round( m1 * closeness_ratio );
    max_m2 := Round( m1 * 1/closeness_ratio );

    while true do
	m1 +:= 1;
	tmp := n - m1^d;
	m2 := 0;
	for j in Divisors( tmp ) do
	    if j ge min_m2 and j le max_m2 then
		if Gcd( m1, j ) ne 1 then
		    continue;
		end if;
		if Abs( m1 - j ) lt Abs( m1 - m2 ) then
		    m2 := j;
		end if;
	    end if;
	end for;
	if m2 ne 0 then
	    break;
	end if;
    end while;

    f := P!0;
    quot := (n-m1^d) div m2;
    rem := quot;
    if false then
	m1div2 := m1 div 2;
	for i in [0..d-2] do
	    tmp := m2^(d-1-i);
	    c_i := (rem * Modinv( tmp, m1 ) ) mod m1;
	    if c_i gt m1div2 then
		c_i -:= m1;
	    end if;
	    rem := (rem - c_i*tmp) div m1;
	    f +:= c_i*X^i*Y^(d-i);
	end for;
	f +:= rem*X^(d-1)*Y;
    else
	for i in [0..d-2] do
	    tmp := m1^(d-1-i);
	    c_i := (rem * Modinv( tmp, m2 ) ) mod m2;
	    rem := (rem - c_i*tmp) div m2;
	    f +:= c_i*X^(d-1-i)*Y^(i+1);
	end for;
	f +:= rem*Y^d;
    end if;
    f := f + X^d;

print f, m1, m2;

    return f, m1, m2, d;
end function;



/*
 *  This method of selecting the polynomial allows  c_d != 1  and
 *  m2 != 1 .  See (12.4) in the paper of Buhler, Lenstra, and Pomerance.
 */
function SelectPolynomial3(n);
    /* select a degree according to the asymptotic formula */
    d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) );
print "degree ", d;

    P<X,Y> := PolynomialRing( IntegerRing(), 2 );
    m1 := Iroot( n, d+1 );
    m2 := m1 + 1;

    L := RMatrixSpace( IntegerRing(), d+2, d+3 )!0;
    L[1][1] := n^2;
    L[1][2] := 1;
    for i in [0..d] do
	L[i+2][1] := n*m1^i * m2^(d-i);
	L[i+2][i+3] := 1;
    end for;
    RL := LLL(L);

    j := 0;
    for i := 1 to d+2 do
	if RL[i][1] eq 0 and RL[i][2] ne 0 then
	    j := i;
	    break;
	end if;
    end for;
    if j eq 0 then
	print "ERROR- LLL failed";
	return 0;
    end if;

    f := 0;
    for i in [0..d] do
	f +:= RL[1][i+3]*X^i*Y^(d-i);
    end for;
 
    /*  need to put in checks to make sure we get a good polynomial */

print f, m1, m2;

    return f, m1, m2, d;

end function;


/*
 *  Find the values of  a*m1 - b*m2  that are smooth
 */
procedure RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots,
  m1_times_m2_inv, sieve_len, b );
    /*  
     *  RATIONAL SIEVE
     */
    sieve_array := [0 : i in [1..sieve_len]];

    for i in [1..#FB] do
	p := FB[i];
	logp := log_primes[i];
	/*
	 *  Compute  loc  - the first location in the sieve array
	 *  where  p  divides the corresponding residue
	 */
	loc := m1_times_m2_inv[i];
	if loc eq -1 then
	    /*  m2  is divisible by p */
	    if b mod p ne 0 then
		/*  p  does not divide any of the values in the sieve array */
		continue;
	    end if;
	    /*  if we get here,  p  divides every location in the sieve
		array */
	    for loc in [1..sieve_len] do
		sieve_array[loc] +:= logp;
	    end for;
	    continue;
	end if;

	loc +:= prev_roots[i];
	if loc ge p then
	    loc -:= p;
	end if;
	prev_roots[i] := loc;

	/*  sieve begins at location 1, so skip location 0 */
	if loc eq 0 then
	    loc := p;
	end if;

	/*  MAIN SIEVE LOOP  */
	while loc le sieve_len do
	    sieve_array[loc] +:= logp;
	    loc +:= p;
	end while;

    end for;

end procedure;


/*
 *  Determine values of  a  such that  f(a, b)  is divisible by the
 *  primes in the factor base.  Sieve on these values to find smooth
 *  elements.
 */
procedure AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes,
  R_p_set, sieve_len, b );
    /*  
     *  NUMBER FIELD SIEVE
     */
    nf_sieve_array := [0 : i in [1..sieve_len]];
    for i in [1..#R_p_set] do
	R_p := R_p_set[i];
	p := R_p[1];
	r := R_p[2];
	logp := R_p[3];

	if r eq -1 then
	    /*  -1 represents the infinity element */
	    if b mod p ne 0 then
		/*  p  does not divide anywhere in the sieve array */
		continue;
	    end if;
	    /*  if we get here,  p  divides every location in the sieve
		array */
	    for loc in [1..sieve_len] do
		nf_sieve_array[loc] +:= logp;
	    end for;
	    continue;
	end if;

	loc := nf_prev_roots[i] + r;
	if loc ge p then
	    loc -:= p;
	end if;
	nf_prev_roots[i] := loc;
	if loc eq 0 then
	    loc := p;
	end if;

	/*  MAIN SIEVE LOOP  */
	while loc le sieve_len do
	    nf_sieve_array[loc] +:= logp;
	    loc +:= p;
	end while;

    end for;
end procedure;


procedure ScanSieveArray( J, f, m2, m1, b, y, d, sieve_array, nf_sieve_array,
  error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots,
  R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset, cols, c_d );

    bm1 := b*m1;
    threshold := Round( Log( Abs( m2 - bm1 ) ) ) - error_term;
    zero := [0: i in [1..d]];
    nf_threshold := Round( Log( Abs( Evaluate(f, [1, b]) ) ) ) - error_term;
    for a in [1..sieve_len] do
	if sieve_array[a] ge threshold then
	    /*  rational side appears to be smooth */
	    if nf_sieve_array[a] ge nf_threshold then
		/*  number field side appears to be smooth */
		if Gcd(b, a) ne 1 then
		    /*  relation is redundant */
		    continue;
		end if;

		/*  see if rational side really is smooth */
		relation := [];
		rational_side := a*m2 - bm1;
		for i in [1..#FB] do
		    p := FB[i];
		    pr := prev_roots[i];
		    if a mod p eq pr or (pr eq -1 and b mod p eq 0) then
			e := 0;
			quot, rem := Quotrem( rational_side, p );
			repeat
			    rational_side := quot;
			    e +:= 1;
			    quot, rem := Quotrem( rational_side, p );
			until rem ne 0;
			Append( ~relation, [i, e] );
		    end if;
		end for;
		if Abs(rational_side) ne 1 then
		    /*  rational side is not smooth :-( */
		    continue;
		end if;

		/*  try algebraic side */
		f_ab := IntegerRing()!Evaluate(f, [a, b]);

		for i in [1..#R_p_set] do
		    R_p := R_p_set[i];
		    p := R_p[1];
		    pr := nf_prev_roots[i];
		    if a mod p eq pr or (pr eq -1 and b mod p eq 0) then
			e := 0;
			quot, rem := Quotrem( f_ab, p );
			repeat
			    f_ab := quot;
			    e +:= 1;
			    quot, rem := Quotrem( f_ab, p );
			until rem ne 0;
			Append( ~relation, [i+#FB, e] );
		    end if;
		end for;
		if Abs(f_ab) ne 1 then
		    /*  algebraic side is not smooth :-( */
		    continue;
		end if;

		/*  The relation is a keeper! */
print "a := ", a, "; b:= ", b,";";
		num_rels +:= 1;

		/*  store relation in matrix */
		for j in [1..#relation] do
		    M[num_rels, relation[j, 1]] := relation[j, 2];
		end for;

		/*  Compute the character columns corresponding to
		    alg_elt  */
		for i in [1..#char_cols] do
		    p := char_cols[i][1];
		    r := char_cols[i][2];
		    ls := LegendreSymbol( (c_d * (a - b * r) ) mod p, p );
		    if ls eq -1 then
			M[num_rels, i + char_offset] := 1;
		    end if;
		end for;

		/*  store the algebraic element */
		x := zero;
		x[1] := c_d * a; x[2] := -b;
		alg_elt := J!x;
		Append( ~smooth_alg_elts, alg_elt );

		/*  store the sign */
		if rational_side eq -1 then
		    M[num_rels, cols-1] := 1;
		end if;
		/*  this column is to assure that an even  number of
		    elements are used in the final relation */
		M[num_rels, cols] := 1;

		if num_rels eq enough_rels then
		    break;
		end if;

		/*  update the thresholds to minimize false reports */
		f_ab := IntegerRing()!Evaluate(f, [a, b]);
		nf_threshold := Round( Log( Abs( f_ab ) ) );
		nf_threshold -:= error_term;
		threshold := Round( Log( Abs( a*m2 - bm1 ) ) ) - error_term;
	    end if;
	end if;
    end for;
end procedure;



/*
 *  This version requires you to send in the polynomial  f
 *  along with  m1, m2,  and  d .
 */
function NFS( n, f, m1, m2, d )

    f_X := Derivative( f, 1 );

    /*  choose  y  - the bound for smoothness  */
    dlogd := d*Log(d);
    temp := 1.0/d * Log( n );
    e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) );
    y := Round( Exp( 0.5*e ) );
print "smoothness bound is ", y;

    /*  prepare data for rational sieve */
    FB := [p : p in [2..y] | IsPrime( p ) ];
    log_primes := [Round(Log(p)) : p in FB];
    prev_roots := [0: p in FB];
    m1_times_m2_inv := [];
    i := 0;
    for p in FB do
	i +:= 1;
	if m2 mod p eq 0 then
	    /*  flag no solution */
	    Append( ~m1_times_m2_inv, -1 );
	    prev_roots[i] := -1;
	else
	    Append( ~m1_times_m2_inv, (Modinv(m2, p) * m1) mod p );
	end if;
    end for;
print "primes in FB: ",#FB;

    /*  prepare data for the algebraic sieve */
    Q<X> := PolynomialRing( Integers() );
    f1 := Q!Evaluate( f, [X,1] );
    c_d := Coefficient( f1, d );
    f_c_d := Q!Evaluate( f, [X, c_d] );
    J<omega> := NumberField( f_c_d div c_d );

    cols := #FB;
    R_p_set := [];
    nf_prev_roots := [];
    for p in FB do
	K := GF(p);
	roots_mod_p := Roots( f1, K );
	for i in [1..#roots_mod_p] do
	    r := IntegerRing()!roots_mod_p[i][1];
	    /*  also include the rounded logarithm of  p  in the storage */
	    Append( ~R_p_set, [p, r, Round(Log(p))] );
	    Append( ~nf_prev_roots, 0 );
	    cols +:= 1;
	end for;
	if c_d mod p eq 0 then
	    /*  add the infinity element, which will be represented by -1 */
	    Append( ~R_p_set, [p, -1, Round(Log(p))] );
	    Append( ~nf_prev_roots, -1 );
	    cols +:= 1;
	end if;
    end for;
    smooth_alg_elts := [];

    /*  create the character columns */
    char_offset := cols;
    num_char_cols := 3 * Ilog2( n );
    char_cols := [];
    p := NextPrime( y );
    i := 0;
    repeat
	while c_d mod p eq 0 do
	    p := NextPrime( p );
	end while;
	K := GF(p);
	roots_mod_p := Roots( f1, K );
	for j in [1..#roots_mod_p] do
	    r := IntegerRing()!roots_mod_p[j][1];
	    Append( ~char_cols, [p, r] );
	    i +:= 1;
	    if i eq num_char_cols then
		break;
	    end if;
	end for;
	p := NextPrime( p );
    until i eq num_char_cols;
    cols +:= num_char_cols;

    /*  Add one column for the sign of  a*m2 - b*m1  and one column
    which will always be 1 to make sure that the number of relations
    in any dependency is even */
    cols +:= 2;

    enough_rels := cols+50;
print "will quit after", enough_rels," relations";

    /*  allow for an error in the sieve threshold */
    error_term := 3;

    /*  set up matrix */
    M := RMatrixSpace (IntegerRing(), enough_rels, cols)!0;

    num_rels := 0;
    b := 1;
    sieve_len := y;

    while true do
	RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots,
	  m1_times_m2_inv, sieve_len, b );

	AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes,
	  R_p_set, sieve_len, b );

	ScanSieveArray( J, f, m2, m1, b, y, d, sieve_array, nf_sieve_array,
	  error_term, ~num_rels, sieve_len, ~M, FB, prev_roots,
	  nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts,
	  char_cols, char_offset, cols, c_d );

        b +:= 1;

print "b = ",b,",         Number of relations: ", num_rels;

	if num_rels ge enough_rels then
	    break;
	end if;
    end while;


print "matrix size: ",num_rels," by ", cols;
print "finding null space";

    gf2 := GF(2);
    Mprime := RMatrixSpace( gf2, num_rels, cols )!M;
    time null_space := NullSpace( Mprime );

    /*  "free" Mprime */
    Mprime := 0;

    for j in  [1..Dimension(null_space)] do
print "trying null space vector #",j;

	/*  get the first element of the solution vector */
	soln := ChangeUniverse (Eltseq (null_space.j), IntegerRing());

	/*  compute the exponents of a relation that involves an
	    algebraic square and an integer square
	 */

	exps := RSpace(IntegerRing(), cols)!0;
	for i in [1..num_rels] do
	    if soln[i] eq 1 then
		exps +:= M[i];
	    end if;
	end for;

	S_size := 0;
	list := [];
	for i in [1..num_rels] do
	    if soln[i] eq 1 then
		Append( ~list, smooth_alg_elts[i] );
		S_size +:= 1;
	    end if;
	end for;
	Append( ~list, (Evaluate( f_X, [omega, c_d] )/c_d)^2 );

	/*  Compute the number field element of the relation.
	    In a real implementation, we wouldn't actually multiply this
	    element out.
	 */
	prod := &*list;

	/*  Compute the square root of the algebraic element */
	beta := Root(prod, 2);

	/* map  beta  to an integer modulo n */
	m2inv := Modinv( m2, n );
	seq := Eltseq(beta);
	elt := 0;
	for k in [0..d-1] do
	    num := Numerator( seq[k+1] ) mod n;
	    den := Denominator( seq[k+1] ) mod n;
	    elt +:= ( ( num * Modinv( den, n ) mod n) *
	      Modexp( (c_d * m1 * m2inv) mod n, k, n ) ) mod n;
	end for;
	v := (elt * Modexp( m2, d-1, n) ) mod n;

	/*  compute the integer element of the relation.
	 */
	w := 1;
	for i in [1..#FB] do
	    e := exps[i];
	    if e gt 0 then
		w := (w * ( FB[i]^(e div 2) ) ) mod n;
	    end if;
	end for;

	h := Modexp( c_d, d-2+(S_size div 2), n ) * Evaluate( f_X, [m1, m2] )
	  mod n;
	l := Modexp( m2, S_size div 2, n );

	tmp := (h*w-l*v) mod n;
	gcd := Gcd(tmp, n);
print "Gcd of ",tmp," and ",n," is ", gcd;
	if gcd ne 1 and gcd ne n then
	    print "FACTOR: ", gcd;
	    return gcd;
	end if;
    end for;

    print "no factor found :-( ";
    return 0;

end function;



















Output: WARNING: MAGMA command contains unsafe command 'memory', so it will not be executed.

************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Sun Jul 18 16:19:14 2004

Input: C:=ComplexField();
R<v,t>:=PolynomialRing(C,2);
v^2;


Output: Magma V2.10-22    Sun Jul 18 2004 16:19:11 on modular  [Seed = 2803711120]
   -------------------------------------

v^2

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (143.248.25.216)
Time: Sun Jul 18 16:56:25 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sun Jul 18 2004 16:56:22 on modular  [Seed = 714115541]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-66-127-52-127.dsl.snfc21.pacbell.net. (66.127.52.127)
Time: Sun Jul 18 17:49:42 2004

Input: E:=EllipticCurve([1,1,0,-2582,48720]);
AnalyticRank(E : Precision:=9);

Output: Magma V2.10-22    Sun Jul 18 2004 17:49:39 on modular  [Seed = 4149036937]
   -------------------------------------


>> AnalyticRank(E : Precision:=9);;
   ^
User error: Identifier 'AnalyticRank' has not been declared or assigned

Total time: 2.809 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-66-127-52-127.dsl.snfc21.pacbell.net. (66.127.52.127)
Time: Sun Jul 18 18:26:46 2004

Input: uvEll:=function(uv,s,t)
u:=uv[1]; v:=uv[2];
a:=(s^2+t^2)^3;
b:=2*(s^2+t^2)*(-t^6-8*s*t^5+3*s^2*t^4-8*s^3*t^3-s^4*t^2+3*s^6);
c:=4*(-t^6+8*s*t^5+3*s^2*t^4+8*s^3*t^3-s^4*t^2+3*s^6)*(t^4+s^4);
d:=8*(t^4+s^4)^3;
l:=2*t*u*v; m:=l*a;  A2:=l*b; A4:=l*c*m; A6:=l*d*m^2;
E:=EllipticCurve([0,A2,0,A4,A6]);
return(E);
end function;

s:=2; t:=3;
a:=(s^2+t^2)^3;
b:=2*(s^2+t^2)*(-t^6-8*s*t^5+3*s^2*t^4-8*s^3*t^3-s^4*t^2+3*s^6);
c:=4*(-t^6+8*s*t^5+3*s^2*t^4+8*s^3*t^3-s^4*t^2+3*s^6)*(t^4+s^4);
d:=8*(t^4+s^4)^3;
us:=[u : u in Divisors(2*t*(s^4+t^4)) | IsSquarefree(u)];
vs:=[v : v in Divisors(2*t*(s^2+t^2)) | IsSquarefree(v)];
uvs:=[ [u,v] : u in us , v in vs | Gcd(u,v) eq 1 ];
ells:=[uvEll(uv,s,t) : uv in uvs];

MordellWeilGroup(MinimalModel(ells[1]):Bound:=1, HeightBound:=8);

Output: Magma V2.10-22    Sun Jul 18 2004 18:26:43 on modular  [Seed = 3362943478]
   -------------------------------------


>> MordellWeilGroup(MinimalModel(ells[1]):Bound:=1, HeightBound:=8);;
                   ^
Runtime error in 'MordellWeilGroup': Bound must be at least 2

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-66-127-52-127.dsl.snfc21.pacbell.net. (66.127.52.127)
Time: Sun Jul 18 18:27:24 2004

Input: uvEll:=function(uv,s,t)
u:=uv[1]; v:=uv[2];
a:=(s^2+t^2)^3;
b:=2*(s^2+t^2)*(-t^6-8*s*t^5+3*s^2*t^4-8*s^3*t^3-s^4*t^2+3*s^6);
c:=4*(-t^6+8*s*t^5+3*s^2*t^4+8*s^3*t^3-s^4*t^2+3*s^6)*(t^4+s^4);
d:=8*(t^4+s^4)^3;
l:=2*t*u*v; m:=l*a;  A2:=l*b; A4:=l*c*m; A6:=l*d*m^2;
E:=EllipticCurve([0,A2,0,A4,A6]);
return(E);
end function;

s:=2; t:=3;
a:=(s^2+t^2)^3;
b:=2*(s^2+t^2)*(-t^6-8*s*t^5+3*s^2*t^4-8*s^3*t^3-s^4*t^2+3*s^6);
c:=4*(-t^6+8*s*t^5+3*s^2*t^4+8*s^3*t^3-s^4*t^2+3*s^6)*(t^4+s^4);
d:=8*(t^4+s^4)^3;
us:=[u : u in Divisors(2*t*(s^4+t^4)) | IsSquarefree(u)];
vs:=[v : v in Divisors(2*t*(s^2+t^2)) | IsSquarefree(v)];
uvs:=[ [u,v] : u in us , v in vs | Gcd(u,v) eq 1 ];
ells:=[uvEll(uv,s,t) : uv in uvs];

MordellWeilGroup(MinimalModel(ells[1]):Bound:=2, HeightBound:=8);

Output: Magma V2.10-22    Sun Jul 18 2004 18:27:01 on modular  [Seed = 3881656015]
   -------------------------------------



************** MAGMA *****************
Host adsl-66-127-52-127.dsl.snfc21.pacbell.net. (66.127.52.127)
Time: Sun Jul 18 18:29:55 2004

Input: uvEll:=function(uv,s,t)
u:=uv[1]; v:=uv[2];
a:=(s^2+t^2)^3;
b:=2*(s^2+t^2)*(-t^6-8*s*t^5+3*s^2*t^4-8*s^3*t^3-s^4*t^2+3*s^6);
c:=4*(-t^6+8*s*t^5+3*s^2*t^4+8*s^3*t^3-s^4*t^2+3*s^6)*(t^4+s^4);
d:=8*(t^4+s^4)^3;
l:=2*t*u*v; m:=l*a;  A2:=l*b; A4:=l*c*m; A6:=l*d*m^2;
E:=EllipticCurve([0,A2,0,A4,A6]);
return(E);
end function;

s:=2; t:=3;
a:=(s^2+t^2)^3;
b:=2*(s^2+t^2)*(-t^6-8*s*t^5+3*s^2*t^4-8*s^3*t^3-s^4*t^2+3*s^6);
c:=4*(-t^6+8*s*t^5+3*s^2*t^4+8*s^3*t^3-s^4*t^2+3*s^6)*(t^4+s^4);
d:=8*(t^4+s^4)^3;
us:=[u : u in Divisors(2*t*(s^4+t^4)) | IsSquarefree(u)];
vs:=[v : v in Divisors(2*t*(s^2+t^2)) | IsSquarefree(v)];
uvs:=[ [u,v] : u in us , v in vs | Gcd(u,v) eq 1 ];
ells:=[uvEll(uv,s,t) : uv in uvs];

MordellWeilGroup(MinimalModel(ells[2]):Bound:=2, HeightBound:=4);

Output: Magma V2.10-22    Sun Jul 18 2004 18:29:32 on modular  [Seed = 1491263883]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:15:49 2004

Input: x := 2^23-1;
for i:= 3000000 to 4000000 do

if i*i eq 1 mod x
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:15:47 on modular  [Seed = 1959755502]
   -------------------------------------


>> print(i);
   ^
User error: bad syntax

>> end if;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 2.759 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:16:02 2004

Input: x := 2^23-1;
for i:= 3000000 to 4000000 do

if i*i eq 1 mod x then
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:15:58 on modular  [Seed = 1106922454]
   -------------------------------------


Total time: 3.829 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:17:07 2004

Input: x := (2^23)-1;

for i:= 3000000 to 4000000 do
b:= i*i;
if b eq 1 mod x then
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:17:03 on modular  [Seed = 1441684995]
   -------------------------------------


Total time: 4.009 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:17:40 2004

Input: x := (2^29)-1;

for i:= 3000000 to 4000000 do
b:= i*i;
if b eq 1 mod x then
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:17:36 on modular  [Seed = 547040041]
   -------------------------------------


Total time: 4.029 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:17:52 2004

Input: x := (2^23)-1;

for i:= 3000000 to 4000000 do
b:= i*i;
if b eq 1 mod x then
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:17:48 on modular  [Seed = 1065628730]
   -------------------------------------


Total time: 4.019 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:18:01 2004

Input: x := (2^23)-1;

for i:= 3000000 to 4000000 do
b:= i*i;
if b = 1 mod x then
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:17:59 on modular  [Seed = 931937321]
   -------------------------------------


>> if b = 1 mod x then
   ^
Runtime error in if: Logical expected

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (147.76.180.135)
Time: Mon Jul 19 00:18:30 2004

Input: x := (2^23)-1;

for i:= 3000000 to 4000000 do
b:= i*i;
if b mod x eq 1 then
print(i);
end if;

end for;

Output: Magma V2.10-22    Mon Jul 19 2004 00:18:25 on modular  [Seed = 279649256]
   -------------------------------------

3034178

Total time: 4.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 07:44:49 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G;
CharacterTable(G);

Output: Magma V2.10-22    Mon Jul 19 2004 07:44:46 on modular  [Seed = 2937347043]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3
Finitely presented group G on 2 generators
Relations
    G.1^2 = Id(G)
    G.2^4 = Id(G)
    (G.1 * G.2)^3 = Id(G)
    G.1 * G.2 = Id(G)

>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.839 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 07:51:12 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G := sym(4);
CharacterTable(G);

Output: Magma V2.10-22    Mon Jul 19 2004 07:51:09 on modular  [Seed = 964873457]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3

>> G := sym(4);
        ^
User error: Identifier 'sym' has not been declared or assigned

>> CharacterTable(G);;
                 ^
Runtime error in 'CharacterTable': No characters for this group type

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 07:56:08 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G := Sym(4);
CharacterTable(G);

Output: Magma V2.10-22    Mon Jul 19 2004 07:56:05 on modular  [Seed = 1458413796]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3


Character Table of Group G
--------------------------


-------------------
Class |   1 2 3 4 5
Size  |   1 3 6 8 6
Order |   1 2 2 3 4
-------------------
p  =  2   1 1 1 4 2
p  =  3   1 2 3 1 5
-------------------
X.1   +   1 1 1 1 1
X.2   +   1 1-1 1-1
X.3   +   2 2 0-1 0
X.4   +   3-1 1 0-1
X.5   +   3-1-1 0 1




Total time: 3.049 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host 200-204-144-106.dsl.telesp.net.br. (200.204.144.106)
Time: Mon Jul 19 09:36:18 2004

Input: 2*12

Output: Magma V2.10-22    Mon Jul 19 2004 09:36:15 on modular  [Seed = 2268858842]
   -------------------------------------

24

Total time: 2.819 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD953527B.dip.t-dialin.net. (217.83.82.123)
Time: Mon Jul 19 10:03:01 2004

Input: F<a,b>:=Group<a,b|a^6,b^6,(a*b)^6=(b*a)^6,a^3*b^3=b^3*a^3,(a^2*b^2)^3=(b^2*a^2)^3>;
Order(F);

Output: Magma V2.10-22    Mon Jul 19 2004 10:02:52 on modular  [Seed = 3797513849]
   -------------------------------------

0

Total time: 7.299 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host pD953527B.dip.t-dialin.net. (217.83.82.123)
Time: Mon Jul 19 10:03:34 2004

Input: F<a,b>:=Group<a,b|a^6,b^6,(a*b)^6=(b*a)^6,a^3*b^3=b^3*a^3,(a^2*b^2)^3=(b^2*a^2)^3>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.10-22    Mon Jul 19 2004 10:03:27 on modular  [Seed = 196124604]
   -------------------------------------

0

Total time: 7.709 seconds, Total memory usage: 17.78MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 11:33:26 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^4, (s*t)^3 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G := Sym(4);
CharacterTable(G);
NormalSubgroups(G);


Output: Magma V2.10-22    Mon Jul 19 2004 11:33:23 on modular  [Seed = 764839115]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^4 = Id(Q)
    (s * t)^3 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
3


Character Table of Group G
--------------------------


-------------------
Class |   1 2 3 4 5
Size  |   1 3 6 8 6
Order |   1 2 2 3 4
-------------------
p  =  2   1 1 1 4 2
p  =  3   1 2 3 1 5
-------------------
X.1   +   1 1 1 1 1
X.2   +   1 1-1 1-1
X.3   +   2 2 0-1 0
X.4   +   3-1 1 0-1
X.5   +   3-1-1 0 1



Conjugacy classes of subgroups
------------------------------

[1]     Order 1            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 1
[2]     Order 4            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 4 = 2^2
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[3]     Order 12           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 12 = 2^2 * 3
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[4]     Order 24           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 24 = 2^3 * 3
            (3, 4)
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 11:35:35 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^3, (s*t)^4 >;
Q;
Order(Q);
Z3 := sub< Q | s*t >;
Z3;
Order(Z3);
G := Q/Z3;
G := Sym(4);
CharacterTable(G);
NormalSubgroups(G);


Output: Magma V2.10-22    Mon Jul 19 2004 11:35:32 on modular  [Seed = 2143606046]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^3 = Id(Q)
    (s * t)^4 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = s * t
4


Character Table of Group G
--------------------------


-------------------
Class |   1 2 3 4 5
Size  |   1 3 6 8 6
Order |   1 2 2 3 4
-------------------
p  =  2   1 1 1 4 2
p  =  3   1 2 3 1 5
-------------------
X.1   +   1 1 1 1 1
X.2   +   1 1-1 1-1
X.3   +   2 2 0-1 0
X.4   +   3-1 1 0-1
X.5   +   3-1-1 0 1



Conjugacy classes of subgroups
------------------------------

[1]     Order 1            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 1
[2]     Order 4            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 4 = 2^2
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[3]     Order 12           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 12 = 2^2 * 3
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[4]     Order 24           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 24 = 2^3 * 3
            (3, 4)
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)

Total time: 2.819 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 11:36:13 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^3, (s*t)^4 >;
Q;
Order(Q);
Z3 := sub< Q | t >;
Z3;
Order(Z3);
G := Q/Z3;
G := Sym(4);
CharacterTable(G);
NormalSubgroups(G);


Output: Magma V2.10-22    Mon Jul 19 2004 11:36:10 on modular  [Seed = 1608840464]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^3 = Id(Q)
    (s * t)^4 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = t
3


Character Table of Group G
--------------------------


-------------------
Class |   1 2 3 4 5
Size  |   1 3 6 8 6
Order |   1 2 2 3 4
-------------------
p  =  2   1 1 1 4 2
p  =  3   1 2 3 1 5
-------------------
X.1   +   1 1 1 1 1
X.2   +   1 1-1 1-1
X.3   +   2 2 0-1 0
X.4   +   3-1 1 0-1
X.5   +   3-1-1 0 1



Conjugacy classes of subgroups
------------------------------

[1]     Order 1            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 1
[2]     Order 4            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 4 = 2^2
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[3]     Order 12           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 12 = 2^2 * 3
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[4]     Order 24           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 24 = 2^3 * 3
            (3, 4)
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)

Total time: 2.809 seconds, Total memory usage: 17.77MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 11:36:41 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^3, (s*t)^4 >;
Q;
Order(Q);
Z3 := sub< Q | t >;
Z3;
Order(Z3);
G := Q/Z3;
Order(G);
G := Sym(4);
CharacterTable(G);
NormalSubgroups(G);


Output: Magma V2.10-22    Mon Jul 19 2004 11:36:38 on modular  [Seed = 3071024404]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^3 = Id(Q)
    (s * t)^4 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = t
3
2


Character Table of Group G
--------------------------


-------------------
Class |   1 2 3 4 5
Size  |   1 3 6 8 6
Order |   1 2 2 3 4
-------------------
p  =  2   1 1 1 4 2
p  =  3   1 2 3 1 5
-------------------
X.1   +   1 1 1 1 1
X.2   +   1 1-1 1-1
X.3   +   2 2 0-1 0
X.4   +   3-1 1 0-1
X.5   +   3-1-1 0 1



Conjugacy classes of subgroups
------------------------------

[1]     Order 1            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 1
[2]     Order 4            Length 1
        Permutation group acting on a set of cardinality 4
        Order = 4 = 2^2
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[3]     Order 12           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 12 = 2^2 * 3
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)
[4]     Order 24           Length 1
        Permutation group acting on a set of cardinality 4
        Order = 24 = 2^3 * 3
            (3, 4)
            (2, 3, 4)
            (1, 4)(2, 3)
            (1, 3)(2, 4)

Total time: 2.929 seconds, Total memory usage: 23.02MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 11:37:53 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^3, (s*t)^4 >;
Q;
Order(Q);
Z3 := sub< Q | t >;
Z3;
Order(Z3);
G := Q/Z3;
Order(G);



Output: Magma V2.10-22    Mon Jul 19 2004 11:37:50 on modular  [Seed = 3897770499]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^3 = Id(Q)
    (s * t)^4 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = t
3
2

Total time: 3.009 seconds, Total memory usage: 23.02MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 11:37:58 2004

Input: C:=ComplexField();
P<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
GenerList:=[*(z-t)*delt,(z-1)*(delz+delt)*];
GenerList;
I:=ideal<P,L>;
I;
GB:=GroebnerBasis(I);
GB;


Output: Magma V2.10-22    Mon Jul 19 2004 11:37:56 on modular  [Seed = 4249245452]
   -------------------------------------

[*
z*delt - t*delt,
z*delz + z*delt - delz - delt
*]

>> I:=ideal<P,L>;
               ^
User error: bad syntax

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> GB;
   ^
User error: Identifier 'GB' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host mpiat4223.ag4.mpi-sb.mpg.de. (139.19.40.93)
Time: Mon Jul 19 11:47:01 2004

Input: Q<s,t>, h := Group< s, t | s^2, t^3, (s*t)^4 >;
Q;
Order(Q);
Z3 := sub< Q | t >;
Z3;
Order(Z3);
G := Q/Z3;
Order(G);



Output: Magma V2.10-22    Mon Jul 19 2004 11:46:58 on modular  [Seed = 96381392]
   -------------------------------------

Finitely presented group Q on 2 generators
Relations
    s^2 = Id(Q)
    t^3 = Id(Q)
    (s * t)^4 = Id(Q)
24
Finitely presented group Z3 on 1 generator
Generators as words in group Q
    Z3.1 = t
3
2

Total time: 2.899 seconds, Total memory usage: 23.02MB


************** MAGMA *****************
Host ip-66-80-251-179.nyc.megapath.net. (66.80.251.179)
Time: Mon Jul 19 12:01:51 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Mon Jul 19 2004 12:01:49 on modular  [Seed = 1324744202]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 12:03:40 2004

Input: C:=ComplexField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
GenerList;
I:=ideal<R|GenerList>;
I;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,P:=PrimaryDecomposition(I);
print "Primary Decomposition", P;


Output: Magma V2.10-22    Mon Jul 19 2004 12:03:37 on modular  [Seed = 3814216467]
   -------------------------------------

{
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
}

>> I:=ideal<R|GenerList>;
           ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> print "Groebner basis is:", GB;
                               ^
User error: Identifier 'GB' has not been declared or assigned

>> Q,P:=PrimaryDecomposition(I);
                             ^
User error: Identifier 'I' has not been declared or assigned

>> print "Primary Decomposition", P;
                                  ^
User error: Identifier 'P' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 12:04:30 2004

Input: C:=ComplexField();
P<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
GenerList;
I:=ideal<P|GenerList>;
I;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,S:=PrimaryDecomposition(I);
print "Primary Decomposition", S;

Output: Magma V2.10-22    Mon Jul 19 2004 12:04:27 on modular  [Seed = 3513409779]
   -------------------------------------

{
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
}

>> I:=ideal<P|GenerList>;
           ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> print "Groebner basis is:", GB;
                               ^
User error: Identifier 'GB' has not been declared or assigned

>> Q,S:=PrimaryDecomposition(I);
                             ^
User error: Identifier 'I' has not been declared or assigned

>> print "Primary Decomposition", S;;
                                  ^
User error: Identifier 'S' has not been declared or assigned

Total time: 2.639 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 12:06:07 2004

Input: C:=ComplexField();
P<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
C;
P;
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
GenerList;
I:=ideal<P|GenerList>;
I;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,S:=PrimaryDecomposition(I);
print "Primary Decomposition", S;

Output: Magma V2.10-22    Mon Jul 19 2004 12:06:05 on modular  [Seed = 1658442533]
   -------------------------------------

Complex Field
Polynomial ring of rank 4 over Complex Field
Graded Reverse Lexicographical Order
Variables: z, t, delz, delt
{
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
}

>> I:=ideal<P|GenerList>;
           ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> print "Groebner basis is:", GB;
                               ^
User error: Identifier 'GB' has not been declared or assigned

>> Q,S:=PrimaryDecomposition(I);
                             ^
User error: Identifier 'I' has not been declared or assigned

>> print "Primary Decomposition", S;;
                                  ^
User error: Identifier 'S' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 12:06:48 2004

Input: C:=ComplexField();
P<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
IsField(C);
BaseRing(P);
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
GenerList;
I:=ideal<P|GenerList>;
I;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,S:=PrimaryDecomposition(I);
print "Primary Decomposition", S;

Output: Magma V2.10-22    Mon Jul 19 2004 12:06:45 on modular  [Seed = 1491331559]
   -------------------------------------

true
Complex Field
{
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
}

>> I:=ideal<P|GenerList>;
           ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> print "Groebner basis is:", GB;
                               ^
User error: Identifier 'GB' has not been declared or assigned

>> Q,S:=PrimaryDecomposition(I);
                             ^
User error: Identifier 'I' has not been declared or assigned

>> print "Primary Decomposition", S;;
                                  ^
User error: Identifier 'S' has not been declared or assigned

Total time: 2.599 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 12:07:24 2004

Input: C:=ComplexField();
P<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
IsField(C);
BaseRing(P);
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
GenerList;
I := ideal< P | GenerList >;
I;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,S:=PrimaryDecomposition(I);
print "Primary Decomposition", S;

Output: Magma V2.10-22    Mon Jul 19 2004 12:07:22 on modular  [Seed = 2151362832]
   -------------------------------------

true
Complex Field
{
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
}

>> I := ideal< P | GenerList >;
             ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> print "Groebner basis is:", GB;
                               ^
User error: Identifier 'GB' has not been declared or assigned

>> Q,S:=PrimaryDecomposition(I);
                             ^
User error: Identifier 'I' has not been declared or assigned

>> print "Primary Decomposition", S;;
                                  ^
User error: Identifier 'S' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 12:07:49 2004

Input: C:=RationalField();
P<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
IsField(C);
BaseRing(P);
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
GenerList;
I := ideal< P | GenerList >;
I;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,S:=PrimaryDecomposition(I);
print "Primary Decomposition", S;

Output: Magma V2.10-22    Mon Jul 19 2004 12:07:46 on modular  [Seed = 3764080920]
   -------------------------------------

true
Rational Field
{
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
}
Ideal of Polynomial ring of rank 4 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t, delz, delt
Basis:
[
    z*delt - t*delt,
    z*delz + z*delt - delz - delt
]
Groebner basis is: [
    t*delz*delt + t*delt^2 - delz*delt - delt^2,
    z*delz + t*delt - delz - delt,
    z*delt - t*delt
]
Primary Decomposition [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - t,
        delz + delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delz,
        delt
    ]
]

Total time: 2.539 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:46:58 2004

Input: x = eulerphi(6)

Output: Magma V2.10-22    Mon Jul 19 2004 14:46:55 on modular  [Seed = 1976115727]
   -------------------------------------


>> x = eulerphi(6);
       ^
User error: Identifier 'eulerphi' has not been declared or assigned

Total time: 2.899 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:49:45 2004

Input: totient(6)

Output: Magma V2.10-22    Mon Jul 19 2004 14:49:43 on modular  [Seed = 397099190]
   -------------------------------------


>> totient(6);
   ^
User error: Identifier 'totient' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:52:16 2004

Input: K := GF(2);
P<D> := PolynomialRing(K);
P;

Output: Magma V2.10-22    Mon Jul 19 2004 14:52:14 on modular  [Seed = 430260512]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:53:25 2004

Input: K := GF(2);
P<D> := PolomialRing(K);
P;


Output: Magma V2.10-22    Mon Jul 19 2004 14:53:22 on modular  [Seed = 2502544720]
   -------------------------------------


>> P<D> := PolomialRing(K);
           ^
User error: Identifier 'PolomialRing' has not been declared or assigned

>> P;
   ^
User error: Identifier 'P' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:53:39 2004

Input: K := GF(2);
P<D> := PolynomialRing(K);
P;


Output: Magma V2.10-22    Mon Jul 19 2004 14:53:37 on modular  [Seed = 2059805347]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:55:05 2004

Input: K := GF(2);
P<D> := PolynomialRing(K);
P;
C := 1 + D + D^4;
S := [ K | 1, 0, 0, 1];
S;


Output: Magma V2.10-22    Mon Jul 19 2004 14:55:02 on modular  [Seed = 2886792642]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 1, 0, 0, 1 ]

Total time: 3.009 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:55:58 2004

Input: K := GF(2);
P<D> := PolynomialRing(K);
P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0];
S;
LFSRSequence(C, S, 15);


Output: Magma V2.10-22    Mon Jul 19 2004 14:55:55 on modular  [Seed = 1508179979]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
[ 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1 ]

Total time: 2.839 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:56:13 2004

Input: K := GF(2);
P<D> := PolynomialRing(K);
P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0];
S;
LFSRSequence(C, S, 31);


Output: Magma V2.10-22    Mon Jul 19 2004 14:56:10 on modular  [Seed = 965042202]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
[ 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 
1, 1, 0, 1, 0 ]

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 14:57:53 2004

Input: K := GF(2);
P<D> := PolynomialRing(K);
P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0];
S;
LFSRSequence(C, S, 31);
C ^ 2;

Output: Magma V2.10-22    Mon Jul 19 2004 14:57:50 on modular  [Seed = 1792422830]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
[ 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 
1, 1, 0, 1, 0 ]
D^8 + D^2 + 1

Total time: 2.939 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 15:01:44 2004

Input: K := GF(2);
P<D> := PolynomialRing(K); P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0]; S;
C(D) := PrimitivePolynomial(K, 18);
C;

Output: Magma V2.10-22    Mon Jul 19 2004 15:01:42 on modular  [Seed = 3530459183]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]

>> C(D) := PrimitivePolynomial(K, 18);
        ^
User error: Illegal left hand side of an assignment statement
D^4 + D + 1

Total time: 2.599 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 15:02:07 2004

Input: K := GF(2);
P<D> := PolynomialRing(K); P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0]; S;
C<D> := PrimitivePolynomial(K, 18);
C;

Output: Magma V2.10-22    Mon Jul 19 2004 15:02:04 on modular  [Seed = 2168314694]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
D^18 + D^12 + D^10 + D + 1

Total time: 2.859 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 15:02:15 2004

Input: K := GF(2);
P<D> := PolynomialRing(K); P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0]; S;
C<D> := PrimitivePolynomial(K, 18);
C;

Output: Magma V2.10-22    Mon Jul 19 2004 15:02:12 on modular  [Seed = 1775580081]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
D^18 + D^12 + D^10 + D + 1

Total time: 2.599 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 15:05:31 2004

Input: K := GF(2);
P<D> := PolynomialRing(K); P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0]; S;
C<D> := PrimitivePolynomial(K, 18);
C;
D := C^37; D;
IsPrimitive(D);


Output: Magma V2.10-22    Mon Jul 19 2004 15:05:28 on modular  [Seed = 229725721]
   -------------------------------------

Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
D^18 + D^12 + D^10 + D + 1
D^666 + D^660 + D^658 + D^649 + D^648 + D^642 + D^636 + D^628 + D^626 + D^625 + 
    D^624 + D^617 + D^616 + D^598 + D^594 + D^592 + D^590 + D^588 + D^586 + 
    D^581 + D^580 + D^577 + D^576 + D^474 + D^468 + D^466 + D^457 + D^456 + 
    D^450 + D^444 + D^436 + D^434 + D^433 + D^432 + D^425 + D^424 + D^410 + 
    D^406 + D^404 + D^400 + D^398 + D^396 + D^394 + D^393 + D^392 + D^389 + 
    D^388 + D^386 + D^385 + D^384 + D^380 + D^372 + D^370 + D^369 + D^368 + 
    D^361 + D^360 + D^342 + D^338 + D^336 + D^334 + D^332 + D^330 + D^325 + 
    D^324 + D^321 + D^320 + D^122 + D^116 + D^114 + D^105 + D^104 + D^98 + D^92 
    + D^90 + D^81 + D^80 + D^66 + D^60 + D^54 + D^52 + D^49 + D^46 + D^44 + D^42
    + D^41 + D^40 + D^37 + D^36 + D^33 + D^32 + D^22 + D^18 + D^16 + D^14 + D^12
    + D^10 + D^5 + D^4 + D + 1
false

Total time: 2.609 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 15:07:25 2004

Input: Totient(6);
K := GF(2);
P<D> := PolynomialRing(K); P;
C := 1 + D + D^4;
S := [ K | 0, 1, 1, 0]; S;
C<D> := PrimitivePolynomial(K, 18);
C;
D := C^37; D;
IsPrimitive(D);


Output: Magma V2.10-22    Mon Jul 19 2004 15:07:22 on modular  [Seed = 1475022035]
   -------------------------------------


>> Totient(6);
   ^
User error: Identifier 'Totient' has not been declared or assigned
Univariate Polynomial Ring in D over GF(2)
[ 0, 1, 1, 0 ]
D^18 + D^12 + D^10 + D + 1
D^666 + D^660 + D^658 + D^649 + D^648 + D^642 + D^636 + D^628 + D^626 + D^625 + 
    D^624 + D^617 + D^616 + D^598 + D^594 + D^592 + D^590 + D^588 + D^586 + 
    D^581 + D^580 + D^577 + D^576 + D^474 + D^468 + D^466 + D^457 + D^456 + 
    D^450 + D^444 + D^436 + D^434 + D^433 + D^432 + D^425 + D^424 + D^410 + 
    D^406 + D^404 + D^400 + D^398 + D^396 + D^394 + D^393 + D^392 + D^389 + 
    D^388 + D^386 + D^385 + D^384 + D^380 + D^372 + D^370 + D^369 + D^368 + 
    D^361 + D^360 + D^342 + D^338 + D^336 + D^334 + D^332 + D^330 + D^325 + 
    D^324 + D^321 + D^320 + D^122 + D^116 + D^114 + D^105 + D^104 + D^98 + D^92 
    + D^90 + D^81 + D^80 + D^66 + D^60 + D^54 + D^52 + D^49 + D^46 + D^44 + D^42
    + D^41 + D^40 + D^37 + D^36 + D^33 + D^32 + D^22 + D^18 + D^16 + D^14 + D^12
    + D^10 + D^5 + D^4 + D + 1
false

Total time: 2.789 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 15:25:13 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"grevlex");
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
I:=ideal<R|GenerList>;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,P:=PrimaryDecomposition(I);
print "Primary Decomposition", P;

print "Infinity:";

GenerList2:={(1-v)^2*(1-v*t2)^2*(delv-delt2),((1-v*t2)*delt2)^2,(1-v)^2*(v*delv+delt2),
(1-t2*v)*(v^2*(1-v)*delv-(2-t2*v-v)*delt2)};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
Q2,P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;


Output: Magma V2.10-22    Mon Jul 19 2004 15:24:51 on modular  [Seed = 1207641906]
   -------------------------------------

Groebner basis is: [
    t*delz*delt + t*delt^2 - delz*delt - delt^2,
    z*delz + t*delt - delz - delt,
    z*delt - t*delt
]
Primary Decomposition [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - t,
        delz + delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Graded Reverse Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delz,
        delt
    ]
]
Infinity:


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:33:49 2004

Input: K<w> := GF(2^10);

C<D> := PrimitivePolynomial(K, 9);

Output: Magma V2.10-22    Mon Jul 19 2004 16:33:47 on modular  [Seed = 1458185838]
   -------------------------------------


Total time: 2.719 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:34:04 2004

Input: K<w> := GF(2^10);

C<D> := PrimitivePolynomial(K, 9); C;


Output: Magma V2.10-22    Mon Jul 19 2004 16:34:01 on modular  [Seed = 2126646868]
   -------------------------------------

D^9 + w^12*D^8 + w^955*D^7 + w^85*D^6 + w^94*D^5 + w^651*D^4 + w^326*D^3 + 
    w^568*D^2 + w^544*D + w^287

Total time: 2.799 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:34:29 2004

Input: K := GF(2^10);

C<D> := PrimitivePolynomial(K, 9); C;


Output: Magma V2.10-22    Mon Jul 19 2004 16:34:26 on modular  [Seed = 3037316596]
   -------------------------------------

D^9 + K.1^12*D^8 + K.1^955*D^7 + K.1^85*D^6 + K.1^94*D^5 + K.1^651*D^4 + 
    K.1^326*D^3 + K.1^568*D^2 + K.1^544*D + K.1^287

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:37:35 2004

Input: K := GF(2^10);
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
B := C^37; B;
IsPrimitive(B);


Output: Magma V2.10-22    Mon Jul 19 2004 16:37:32 on modular  [Seed = 3597313998]
   -------------------------------------

D^9 + K.1^12*D^8 + K.1^955*D^7 + K.1^85*D^6 + K.1^94*D^5 + K.1^651*D^4 + 
    K.1^326*D^3 + K.1^568*D^2 + K.1^544*D + K.1^287
true
D^333 + K.1^12*D^332 + K.1^955*D^331 + K.1^85*D^330 + K.1^62*D^329 + 
    K.1^898*D^328 + K.1^265*D^327 + K.1^152*D^326 + K.1^321*D^325 + 
    K.1^508*D^324 + K.1^599*D^323 + K.1^129*D^322 + K.1^354*D^321 + K.1^90*D^320
    + K.1^552*D^319 + K.1^636*D^318 + K.1^535*D^317 + K.1^238*D^316 + 
    K.1^657*D^315 + K.1^55*D^314 + K.1^313*D^313 + K.1^19*D^312 + K.1^59*D^311 +
    K.1^155*D^310 + K.1^108*D^309 + K.1^752*D^308 + K.1^443*D^307 + 
    K.1^965*D^306 + K.1^874*D^305 + K.1^99*D^304 + K.1^606*D^303 + K.1^385*D^302
    + K.1^64*D^301 + K.1^494*D^300 + K.1^970*D^299 + K.1^220*D^298 + 
    K.1^534*D^297 + K.1^161*D^296 + K.1^507*D^295 + K.1^563*D^294 + K.1^99*D^293
    + K.1^948*D^292 + K.1^284*D^291 + K.1^433*D^290 + K.1^341*D^289 + 
    K.1^674*D^288 + K.1^936*D^287 + K.1^1020*D^286 + K.1^919*D^285 + 
    K.1^622*D^284 + K.1^18*D^283 + K.1^439*D^282 + K.1^697*D^281 + K.1^403*D^280
    + K.1^443*D^279 + K.1^539*D^278 + K.1^492*D^277 + K.1^113*D^276 + 
    K.1^827*D^275 + K.1^326*D^274 + K.1^235*D^273 + K.1^483*D^272 + 
    K.1^990*D^271 + K.1^769*D^270 + K.1^731*D^269 + K.1^747*D^268 + 
    K.1^469*D^267 + K.1^13*D^266 + K.1^788*D^265 + K.1^856*D^264 + K.1^782*D^263
    + K.1^274*D^262 + K.1^871*D^261 + K.1^1009*D^260 + K.1^923*D^259 + 
    K.1^133*D^258 + K.1^332*D^257 + K.1^11*D^256 + K.1^422*D^255 + K.1^506*D^254
    + K.1^405*D^253 + K.1^108*D^252 + K.1^527*D^251 + K.1^948*D^250 + 
    K.1^183*D^249 + K.1^912*D^248 + K.1^952*D^247 + K.1^25*D^246 + 
    K.1^1001*D^245 + K.1^622*D^244 + K.1^313*D^243 + K.1^835*D^242 + 
    K.1^744*D^241 + K.1^992*D^240 + K.1^476*D^239 + K.1^255*D^238 + 
    K.1^315*D^237 + K.1^1005*D^236 + K.1^791*D^235 + K.1^786*D^234 + 
    K.1^503*D^233 + K.1^737*D^232 + K.1^64*D^231 + K.1^700*D^230 + K.1^204*D^229
    + K.1^401*D^228 + K.1^46*D^227 + K.1^952*D^226 + K.1^1018*D^225 + 
    K.1^568*D^224 + K.1^203*D^223 + K.1^287*D^222 + K.1^186*D^221 + 
    K.1^912*D^220 + K.1^308*D^219 + K.1^729*D^218 + K.1^987*D^217 + 
    K.1^693*D^216 + K.1^733*D^215 + K.1^829*D^214 + K.1^782*D^213 + 
    K.1^403*D^212 + K.1^94*D^211 + K.1^616*D^210 + K.1^525*D^209 + K.1^773*D^208
    + K.1^257*D^207 + K.1^36*D^206 + K.1^16*D^205 + K.1^506*D^204 + 
    K.1^931*D^203 + K.1^820*D^202 + K.1^187*D^201 + K.1^289*D^200 + 
    K.1^116*D^199 + K.1^576*D^198 + K.1^749*D^197 + K.1^229*D^196 + K.1^75*D^195
    + K.1^802*D^194 + K.1^756*D^193 + K.1^669*D^192 + K.1^491*D^191 + 
    K.1^575*D^190 + K.1^474*D^189 + K.1^177*D^188 + K.1^596*D^187 + 
    K.1^1017*D^186 + K.1^252*D^185 + K.1^981*D^184 + K.1^1021*D^183 + 
    K.1^94*D^182 + K.1^47*D^181 + K.1^691*D^180 + K.1^382*D^179 + K.1^904*D^178 
    + K.1^813*D^177 + K.1^38*D^176 + K.1^545*D^175 + K.1^324*D^174 + 
    K.1^602*D^173 + K.1^814*D^172 + K.1^828*D^171 + K.1^200*D^170 + K.1^32*D^169
    + K.1^174*D^168 + K.1^798*D^167 + K.1^69*D^166 + K.1^45*D^165 + K.1^85*D^164
    + K.1^716*D^163 + K.1^532*D^162 + K.1^847*D^161 + K.1^1002*D^160 + 
    K.1^924*D^159 + K.1^1008*D^158 + K.1^907*D^157 + K.1^610*D^156 + K.1^6*D^155
    + K.1^427*D^154 + K.1^685*D^153 + K.1^391*D^152 + K.1^431*D^151 + 
    K.1^527*D^150 + K.1^480*D^149 + K.1^101*D^148 + K.1^815*D^147 + 
    K.1^314*D^146 + K.1^223*D^145 + K.1^471*D^144 + K.1^978*D^143 + 
    K.1^757*D^142 + K.1^306*D^141 + K.1^366*D^140 + K.1^967*D^139 + 
    K.1^855*D^138 + K.1^626*D^137 + K.1^554*D^136 + K.1^721*D^135 + 
    K.1^815*D^134 + K.1^185*D^133 + K.1^771*D^132 + K.1^198*D^131 + 
    K.1^607*D^130 + K.1^92*D^129 + K.1^613*D^128 + K.1^754*D^127 + K.1^838*D^126
    + K.1^737*D^125 + K.1^440*D^124 + K.1^859*D^123 + K.1^257*D^122 + 
    K.1^515*D^121 + K.1^221*D^120 + K.1^261*D^119 + K.1^357*D^118 + 
    K.1^310*D^117 + K.1^954*D^116 + K.1^645*D^115 + K.1^144*D^114 + K.1^53*D^113
    + K.1^301*D^112 + K.1^808*D^111 + K.1^587*D^110 + K.1^491*D^109 + 
    K.1^836*D^108 + K.1^498*D^107 + K.1^609*D^106 + K.1^571*D^105 + 
    K.1^269*D^104 + K.1^740*D^103 + K.1^574*D^102 + K.1^139*D^101 + 
    K.1^599*D^100 + K.1^516*D^99 + K.1^307*D^98 + K.1^981*D^97 + K.1^536*D^96 + 
    K.1^314*D^95 + K.1^398*D^94 + K.1^297*D^93 + D^92 + K.1^419*D^91 + 
    K.1^840*D^90 + K.1^75*D^89 + K.1^804*D^88 + K.1^844*D^87 + K.1^940*D^86 + 
    K.1^893*D^85 + K.1^514*D^84 + K.1^205*D^83 + K.1^727*D^82 + K.1^636*D^81 + 
    K.1^884*D^80 + K.1^368*D^79 + K.1^147*D^78 + K.1^678*D^77 + K.1^61*D^76 + 
    K.1^143*D^75 + K.1^301*D^74 + K.1^632*D^73 + K.1^148*D^72 + K.1^329*D^71 + 
    K.1^381*D^70 + K.1^114*D^69 + K.1^1002*D^68 + K.1^761*D^67 + K.1^371*D^66 + 
    K.1^724*D^65 + K.1^646*D^64 + K.1^569*D^63 + K.1^653*D^62 + K.1^552*D^61 + 
    K.1^255*D^60 + K.1^674*D^59 + K.1^72*D^58 + K.1^330*D^57 + K.1^36*D^56 + 
    K.1^76*D^55 + K.1^172*D^54 + K.1^125*D^53 + K.1^769*D^52 + K.1^460*D^51 + 
    K.1^982*D^50 + K.1^891*D^49 + K.1^116*D^48 + K.1^623*D^47 + K.1^402*D^46 + 
    K.1^882*D^45 + K.1^267*D^44 + K.1^260*D^43 + K.1^269*D^42 + K.1^797*D^41 + 
    K.1^79*D^40 + K.1^285*D^39 + K.1^507*D^38 + K.1^717*D^37 + K.1^83*D^36 + 
    K.1^274*D^35 + K.1^494*D^34 + K.1^413*D^33 + K.1^255*D^32 + K.1^529*D^31 + 
    K.1^613*D^30 + K.1^512*D^29 + K.1^215*D^28 + K.1^634*D^27 + K.1^32*D^26 + 
    K.1^290*D^25 + K.1^1019*D^24 + K.1^36*D^23 + K.1^132*D^22 + K.1^85*D^21 + 
    K.1^729*D^20 + K.1^420*D^19 + K.1^942*D^18 + K.1^851*D^17 + K.1^76*D^16 + 
    K.1^583*D^15 + K.1^362*D^14 + K.1^58*D^13 + K.1^230*D^12 + K.1^466*D^11 + 
    K.1^306*D^10 + K.1^57*D^9 + K.1^1018*D^8 + K.1^76*D^7 + K.1^976*D^6 + 
    K.1^42*D^5 + K.1^30*D^4 + K.1^428*D^3 + K.1^670*D^2 + K.1^646*D + K.1^389
false

Total time: 2.859 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:38:06 2004

Input: K<w> := GF(2^10);
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
B := C^3; B;
IsPrimitive(B);


Output: Magma V2.10-22    Mon Jul 19 2004 16:38:04 on modular  [Seed = 3664161762]
   -------------------------------------

D^9 + w^12*D^8 + w^955*D^7 + w^85*D^6 + w^94*D^5 + w^651*D^4 + w^326*D^3 + 
    w^568*D^2 + w^544*D + w^287
true
D^27 + w^12*D^26 + w^983*D^25 + w^476*D^24 + w^70*D^23 + w^946*D^22 + w^919*D^21
    + w^229*D^20 + w^92*D^19 + w^634*D^18 + w^459*D^17 + w^1004*D^16 + 
    w^599*D^15 + w^41*D^14 + w^339*D^13 + w^59*D^12 + w^279*D^11 + w^272*D^10 + 
    w^537*D^9 + w^617*D^8 + w^974*D^7 + w^272*D^6 + w^765*D^5 + w^952*D^4 + 
    w^785*D^3 + w^589*D^2 + w^95*D + w^861
false

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 16:39:31 2004

Input: E:=EllipticCurve([-16,16]);
RankBounds(E);

Output: Magma V2.10-22    Mon Jul 19 2004 16:39:27 on modular  [Seed = 1658721271]
   -------------------------------------

1 1

Total time: 2.859 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:40:06 2004

Input: K<w> := GF(2^18);  K;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);


Output: Magma V2.10-22    Mon Jul 19 2004 16:40:02 on modular  [Seed = 3346773616]
   -------------------------------------

Finite field of size 2^18
D^9 + w^141349*D^8 + w^43479*D^7 + w^10881*D^6 + w^174426*D^5 + w^27278*D^4 + 
    w^217886*D^3 + w^256899*D^2 + w^131407*D + w^246784
true

Total time: 3.069 seconds, Total memory usage: 4.91MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 16:40:36 2004

Input: E:=EllipticCurve([-16,16]);
RankBounds(E);
Q,pts:=IntegralPoints(E);Q;


Output: Magma V2.10-22    Mon Jul 19 2004 16:40:33 on modular  [Seed = 3948386879]
   -------------------------------------

1 1

IntegralPoints(
    E: Elliptic Curve defined by y^2 = x^3 - 16*x + 16 over Rationa...
)
SIntegralPoints(
    E: Elliptic Curve defined by y^2 = x^3 - 16*x + 16 over Rationa...,
    S: []
)
IntPoints(
    E: E
)
IntPointsUpperBound(
    E: E,
    MWG2: [ (0 : 4 : 1) ],
    lambda: 0.05111140823996884047231148429091263096779584884643
)
ReduceBound(
    E: E,
    MWG: [ (0 : 4 : 1) ],
    lambda: 0.05111140823996884047231148429091263096779584884643,
    N: 13
)
In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 988, 
column 20:
>>         N:= Ceiling(x);
                      ^
Runtime error in 'Ceiling': Argument 1 should be real

>> Q,pts:=IntegralPoints(E);Q;
                            ^
User error: Identifier 'Q' has not been declared or assigned

Total time: 3.239 seconds, Total memory usage: 2.16MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:41:10 2004

Input: K<w> := GF(2^18);  K;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1
IsPrimitive(C);


Output: Magma V2.10-22    Mon Jul 19 2004 16:41:07 on modular  [Seed = 1307655352]
   -------------------------------------

Finite field of size 2^18
D^9 + w^141349*D^8 + w^43479*D^7 + w^10881*D^6 + w^174426*D^5 + w^27278*D^4 + 
    w^217886*D^3 + w^256899*D^2 + w^131407*D + w^246784
true

>> IsPrimitive(C);
   ^
User error: bad syntax

Total time: 2.689 seconds, Total memory usage: 4.91MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:41:33 2004

Input: K<w> := GF(2^18);  K;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1;
IsPrimitive(C);


Output: Magma V2.10-22    Mon Jul 19 2004 16:41:30 on modular  [Seed = 2636246129]
   -------------------------------------

Finite field of size 2^18
D^9 + w^141349*D^8 + w^43479*D^7 + w^10881*D^6 + w^174426*D^5 + w^27278*D^4 + 
    w^217886*D^3 + w^256899*D^2 + w^131407*D + w^246784
true
false

Total time: 2.679 seconds, Total memory usage: 4.91MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:42:48 2004

Input: K<w> := GF(2);  K;
P<D> := PolynomialRing(K); P;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1;
IsPrimitive(C);


Output: Magma V2.10-22    Mon Jul 19 2004 16:42:45 on modular  [Seed = 46035024]
   -------------------------------------

Finite field of size 2
Univariate Polynomial Ring in D over GF(2)
D^9 + D^4 + 1
true
true

Total time: 2.879 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:43:38 2004

Input: K<w> := GF(2);  K;
P<D> := PolynomialRing(K); P;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1;
IsPrimitive(C);
b := c^37;
IsPrimitive(b);


Output: Magma V2.10-22    Mon Jul 19 2004 16:43:35 on modular  [Seed = 2126646302]
   -------------------------------------

Finite field of size 2
Univariate Polynomial Ring in D over GF(2)
D^9 + D^4 + 1
true
true

>> b := c^37;
        ^
User error: Identifier 'c' has not been declared or assigned

>> IsPrimitive(b);
               ^
User error: Identifier 'b' has not been declared or assigned

Total time: 2.879 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:43:55 2004

Input: K<w> := GF(2);  K;
P<D> := PolynomialRing(K); P;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1;
IsPrimitive(C);
B := C^37;
IsPrimitive(B);


Output: Magma V2.10-22    Mon Jul 19 2004 16:43:52 on modular  [Seed = 2252010521]
   -------------------------------------

Finite field of size 2
Univariate Polynomial Ring in D over GF(2)
D^9 + D^4 + 1
true
true
false

Total time: 2.569 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:44:36 2004

Input: K<w> := GF(2);  K;
P<D> := PolynomialRing(K); P;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1;
IsPrimitive(C);
B := C^3;
IsPrimitive(B);


Output: Magma V2.10-22    Mon Jul 19 2004 16:44:33 on modular  [Seed = 4098393682]
   -------------------------------------

Finite field of size 2
Univariate Polynomial Ring in D over GF(2)
D^9 + D^4 + 1
true
true
false

Total time: 2.869 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:44:47 2004

Input: K<w> := GF(2);  K;
P<D> := PolynomialRing(K); P;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
C := D^18 + D^7 + 1;
IsPrimitive(C);
B := C^3; B;
IsPrimitive(B);


Output: Magma V2.10-22    Mon Jul 19 2004 16:44:44 on modular  [Seed = 413428412]
   -------------------------------------

Finite field of size 2
Univariate Polynomial Ring in D over GF(2)
D^9 + D^4 + 1
true
true
D^54 + D^43 + D^36 + D^32 + D^21 + D^18 + D^14 + D^7 + 1
false

Total time: 2.779 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host vader.integrinautics.com. (209.172.74.2)
Time: Mon Jul 19 16:45:28 2004

Input: K<w> := GF(2);  K;
C<D> := PrimitivePolynomial(K, 9); C;
IsPrimitive(C);
P<D> := PolynomialRing(K, C); P;
C := D^18 + D^7 + 1;
IsPrimitive(C);
B := C^3; B;
IsPrimitive(B);


Output: Magma V2.10-22    Mon Jul 19 2004 16:45:25 on modular  [Seed = 1123954879]
   -------------------------------------

Finite field of size 2
D^9 + D^4 + 1
true

>> P<D> := PolynomialRing(K, C); P;
                         ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: FldFin, RngUPolElt

>> P<D> := PolynomialRing(K, C); P;
                                 ^
User error: Identifier 'P' has not been declared or assigned
true
D^54 + D^43 + D^36 + D^32 + D^21 + D^18 + D^14 + D^7 + 1
false

Total time: 2.579 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 17:15:50 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
I:=ideal<R|GenerList>;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,P:=PrimaryDecomposition(I);
print "Primary Decomposition", P;

print "Infinity:";

GenerList2:={(1-v)^2*(1-v*t2)^2*(delv-delt2),((1-v*t2)*delt2)^2,(1-v)^2*(v*delv+delt2),
(1-t2*v)*(v^2*(1-v)*delv-(2-t2*v-v)*delt2),
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
Q2,P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 17:15:27 on modular  [Seed = 2385704772]
   -------------------------------------

Groebner basis is: [
    z*delz + t*delt - delz - delt,
    z*delt - t*delt,
    t*delz*delt + t*delt^2 - delz*delt - delt^2
]
Primary Decomposition [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - t,
        delz + delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delz,
        delt
    ]
]
Infinity:
Groebner Basis [
    v^2*t2*delt2 - 10/27*v*t2^4*delv + 2/3*v*t2^3*delv + 11/27*v*t2^2*delv - 
        5/3*v*t2*delv - v*t2*delt2 + 26/27*v*delv - v*delt2 + 10/27*t2^5*delt2 +
        10/27*t2^4*delv - 28/27*t2^4*delt2 - 2/3*t2^3*delv + 7/27*t2^3*delt2 - 
        11/27*t2^2*delv + 56/27*t2^2*delt2 + 5/3*t2*delv - 71/27*t2*delt2 - 
        26/27*delv + 53/27*delt2,
    v^2*delv - 14/27*v*t2^4*delv + 2/3*v*t2^3*delv + 28/27*v*t2^2*delv - 
        5/3*v*t2*delv - v*t2*delt2 - 41/27*v*delv + v*delt2 + 14/27*t2^5*delt2 +
        14/27*t2^4*delv - 32/27*t2^4*delt2 - 2/3*t2^3*delv - 10/27*t2^3*delt2 - 
        28/27*t2^2*delv + 73/27*t2^2*delt2 + 5/3*t2*delv - 31/27*t2*delt2 + 
        14/27*delv - 14/27*delt2,
    v^2*delt2^2 - 2*v*t2*delv*delt2 - 4*v*t2*delt2^2 + 2*v*delv*delt2 + 
        2*v*delt2^2 + 4*t2^5*delt2^2 - 7*t2^4*delt2^2 - 6*t2^3*delt2^2 + 
        17*t2^2*delt2^2 + 2*t2*delv*delt2 - 4*t2*delt2^2 - 2*delv*delt2 - 
        3*delt2^2,
    v*t2^5*delv - v*t2^4*delv - 2*v*t2^3*delv + 2*v*t2^2*delv + v*t2*delv - 
        v*delv - t2^6*delt2 - t2^5*delv + 2*t2^5*delt2 + t2^4*delv + t2^4*delt2 
        + 2*t2^3*delv - 4*t2^3*delt2 - 2*t2^2*delv + t2^2*delt2 - t2*delv + 
        2*t2*delt2 + delv - delt2,
    v*t2^2*delv*delt2 - 3*v*t2*delv*delt2 - 3*v*t2*delt2^2 + 2*v*delv*delt2 + 
        3*v*delt2^2 + 3*t2^5*delt2^2 - 6*t2^4*delt2^2 - 4*t2^3*delt2^2 - 
        t2^2*delv*delt2 + 16*t2^2*delt2^2 + 3*t2*delv*delt2 - 8*t2*delt2^2 - 
        2*delv*delt2 - delt2^2,
    v*t2^2*delt2^2 + v*t2*delv*delt2 + v*t2*delt2^2 - v*delv*delt2 - 2*v*delt2^2
        - 2*t2^5*delt2^2 + 4*t2^4*delt2^2 + 2*t2^3*delt2^2 - 9*t2^2*delt2^2 - 
        t2*delv*delt2 + 3*t2*delt2^2 + delv*delt2 + 2*delt2^2,
    v*t2*delv^2 - v*t2*delv*delt2 - v*delv^2 + v*delv*delt2 - t2^2*delv*delt2 + 
        t2^2*delt2^2 - t2*delv^2 + 3*t2*delv*delt2 - 2*t2*delt2^2 + delv^2 - 
        2*delv*delt2 + delt2^2,
    v*t2*delv*delt2^2 - v*delv*delt2^2 + 5/8*t2^4*delt2^3 + 
        5/8*t2^3*delv*delt2^2 - 9/8*t2^3*delt2^3 - 9/8*t2^2*delv*delt2^2 - 
        5/8*t2^2*delt2^3 - 5/8*t2*delv*delt2^2 + 17/8*t2*delt2^3 + 
        9/8*delv*delt2^2 - delt2^3,
    v*t2*delt2^3 - v*delt2^3 + t2^4*delv*delt2^2 - 3/8*t2^4*delt2^3 - 
        19/8*t2^3*delv*delt2^2 + 15/8*t2^3*delt2^3 + 7/8*t2^2*delv*delt2^2 - 
        21/8*t2^2*delt2^3 + 11/8*t2*delv*delt2^2 + 1/8*t2*delt2^3 - 
        7/8*delv*delt2^2 + delt2^3,
    t2^6*delt2^2 - 2*t2^5*delt2^2 - t2^4*delt2^2 + 4*t2^3*delt2^2 - t2^2*delt2^2
        - 2*t2*delt2^2 + delt2^2,
    t2^5*delv*delt2^2 - 2*t2^4*delv*delt2^2 + t2^4*delt2^3 - 2*t2^3*delt2^3 + 
        2*t2^2*delv*delt2^2 - t2*delv*delt2^2 + 2*t2*delt2^3 - delt2^3,
    t2^5*delt2^3 + t2^4*delv*delt2^2 - 2*t2^4*delt2^3 - 2*t2^3*delv*delt2^2 + 
        2*t2^2*delt2^3 + 2*t2*delv*delt2^2 - t2*delt2^3 - delv*delt2^2,
    t2^4*delv^2*delt2^2 - t2^4*delt2^4 - 2*t2^3*delv^2*delt2^2 + 2*t2^3*delt2^4 
        + 2*t2*delv^2*delt2^2 - 2*t2*delt2^4 - delv^2*delt2^2 + delt2^4,
    t2^3*delv^3*delt2^2 - t2^3*delt2^5 - 2*t2^2*delv^3*delt2^2 + 
        2*t2^2*delv^2*delt2^3 - t2^2*delv*delt2^4 + t2^2*delt2^5 + 
        t2*delv^3*delt2^2 - 4*t2*delv^2*delt2^3 + 2*t2*delv*delt2^4 + t2*delt2^5
        + 2*delv^2*delt2^3 - delv*delt2^4 - delt2^5,
    t2^3*delv*delt2^3 - t2^3*delt2^4 + t2^2*delv^2*delt2^2 - 3*t2^2*delv*delt2^3
        + 2*t2^2*delt2^4 - 2*t2*delv^2*delt2^2 + 3*t2*delv*delt2^3 - t2*delt2^4 
        + delv^2*delt2^2 - delv*delt2^3,
    t2^2*delv^4*delt2^2 - 2*t2^2*delv^2*delt2^4 + t2^2*delt2^6 - 
        2*t2*delv^4*delt2^2 + 4*t2*delv^2*delt2^4 - 2*t2*delt2^6 + 
        delv^4*delt2^2 - 2*delv^2*delt2^4 + delt2^6
]


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 17:16:56 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
I:=ideal<R|GenerList>;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,P:=PrimaryDecomposition(I);
print "Primary Decomposition", P;

print "Infinity:";

GenerList2:={(1-v)^2*(1-v*t2)^2*(delv-delt2),((1-v*t2)*delt2)^2,(1-v)^2*(v*delv+delt2),
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
Q2,P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 17:16:33 on modular  [Seed = 1691885171]
   -------------------------------------

Groebner basis is: [
    z*delz + t*delt - delz - delt,
    z*delt - t*delt,
    t*delz*delt + t*delt^2 - delz*delt - delt^2
]
Primary Decomposition [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - t,
        delz + delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delz,
        delt
    ]
]
Infinity:
Groebner Basis [
    v^4*t2^2*delt2 - v^3*t2^2*delt2 - 2*v^3*t2*delt2 - v^2*t2^2*delt2 + 
        2*v^2*t2*delt2 - v^2*delv + v^2*delt2 + v*t2^2*delt2 + 2*v*t2*delt2 + 
        2*v*delv - 2*v*delt2 - 2*t2*delt2 - delv + delt2,
    v^3*delv - 2*v^2*delv + v^2*delt2 + v*delv - 2*v*delt2 + delt2,
    v^2*delv^2 + 2*v*t2^3*delt2^2 - 2*v*t2^2*delt2^2 - 2*v*delv^2 - 
        3*t2^2*delt2^2 + 4*t2*delt2^2 + delv^2 - delt2^2,
    v^2*delv*delt2 - v*t2^2*delt2^2 - 2*v*delv*delt2 + v*delt2^2 + 2*t2*delt2^2 
        + delv*delt2 - 2*delt2^2,
    v^2*delt2^2 - 2*v*t2^4*delt2^2 + 2*v*t2^3*delt2^2 + 4*v*t2^2*delt2^2 - 
        4*v*t2*delt2^2 - 2*v*delt2^2 - 1/2*t2^6*delt2^2 + t2^5*delt2^2 + 
        3/2*t2^4*delt2^2 - 2*t2^3*delt2^2 - 5/2*t2^2*delt2^2 + t2*delt2^2 + 
        5/2*delt2^2,
    v*t2^5*delt2^2 - v*t2^4*delt2^2 - 2*v*t2^3*delt2^2 + 2*v*t2^2*delt2^2 + 
        v*t2*delt2^2 - v*delt2^2 + 3/4*t2^6*delt2^2 - 5/2*t2^5*delt2^2 + 
        1/4*t2^4*delt2^2 + 5*t2^3*delt2^2 - 11/4*t2^2*delt2^2 - 5/2*t2*delt2^2 +
        7/4*delt2^2,
    v*t2^2*delv*delt2^2 - 8/3*v*t2*delv*delt2^2 - 2/3*v*t2*delt2^3 + 
        5/3*v*delv*delt2^2 + 2/3*v*delt2^3 + 2/3*t2^5*delv*delt2^2 + 
        4/3*t2^5*delt2^3 - 2/3*t2^4*delv*delt2^2 - 8/3*t2^4*delt2^3 - 
        2*t2^3*delv*delt2^2 - 4/3*t2^3*delt2^3 + 2*t2^2*delv*delt2^2 + 
        19/3*t2^2*delt2^3 + 2*t2*delv*delt2^2 - 4*t2*delt2^3 - 2*delv*delt2^2 + 
        1/3*delt2^3,
    v*t2^2*delt2^3 + 2/3*v*t2*delv*delt2^2 - 4/3*v*t2*delt2^3 - 
        2/3*v*delv*delt2^2 + 1/3*v*delt2^3 + 2/3*t2^5*delv*delt2^2 + 
        2*t2^5*delt2^3 + 1/3*t2^4*delv*delt2^2 - 8/3*t2^4*delt2^3 - 
        8/3*t2^3*delv*delt2^2 - 10/3*t2^3*delt2^3 - 1/3*t2^2*delv*delt2^2 + 
        16/3*t2^2*delt2^3 + 10/3*t2*delv*delt2^2 - 2/3*t2*delt2^3 - 
        4/3*delv*delt2^2 - 2/3*delt2^3,
    v*t2*delv^2*delt2^2 + 2*v*t2*delv*delt2^3 + v*t2*delt2^4 - v*delv^2*delt2^2 
        - 2*v*delv*delt2^3 - v*delt2^4 + 3/2*t2^4*delv^2*delt2^2 + 
        5*t2^4*delv*delt2^3 - 4*t2^4*delt2^4 + t2^3*delv^2*delt2^2 - 
        16*t2^3*delv*delt2^3 + 13*t2^3*delt2^4 - 23/2*t2^2*delv^2*delt2^2 + 
        19*t2^2*delv*delt2^3 - 29/2*t2^2*delt2^4 + 13*t2*delv^2*delt2^2 - 
        12*t2*delv*delt2^3 + 5*t2*delt2^4 - 4*delv^2*delt2^2 + 4*delv*delt2^3 + 
        1/2*delt2^4,
    t2^7*delt2^2 - 3*t2^6*delt2^2 + t2^5*delt2^2 + 5*t2^4*delt2^2 - 
        5*t2^3*delt2^2 - t2^2*delt2^2 + 3*t2*delt2^2 - delt2^2,
    t2^6*delv*delt2^2 - 10/3*t2^5*delv*delt2^2 - 4/3*t2^5*delt2^3 + 
        1/3*t2^4*delv*delt2^2 + 4/3*t2^4*delt2^3 + 20/3*t2^3*delv*delt2^2 + 
        8/3*t2^3*delt2^3 - 11/3*t2^2*delv*delt2^2 - 8/3*t2^2*delt2^3 - 
        10/3*t2*delv*delt2^2 - 4/3*t2*delt2^3 + 7/3*delv*delt2^2 + 4/3*delt2^3,
    t2^6*delt2^3 + 4/3*t2^5*delv*delt2^2 - 2/3*t2^5*delt2^3 - 
        4/3*t2^4*delv*delt2^2 - 7/3*t2^4*delt2^3 - 8/3*t2^3*delv*delt2^2 + 
        4/3*t2^3*delt2^3 + 8/3*t2^2*delv*delt2^2 + 5/3*t2^2*delt2^3 + 
        4/3*t2*delv*delt2^2 - 2/3*t2*delt2^3 - 4/3*delv*delt2^2 - 1/3*delt2^3,
    t2^5*delv^2*delt2^2 - 4*t2^4*delv^2*delt2^2 - 4*t2^4*delv*delt2^3 + 
        7*t2^4*delt2^4 - t2^3*delv^2*delt2^2 + 18*t2^3*delv*delt2^3 - 
        19*t2^3*delt2^4 + 17*t2^2*delv^2*delt2^2 - 30*t2^2*delv*delt2^3 + 
        15*t2^2*delt2^4 - 20*t2*delv^2*delt2^2 + 22*t2*delv*delt2^3 - t2*delt2^4
        + 7*delv^2*delt2^2 - 6*delv*delt2^3 - 2*delt2^4,
    t2^5*delv*delt2^3 + 3/2*t2^4*delv^2*delt2^2 - 5/2*t2^4*delt2^4 - 
        t2^3*delv^2*delt2^2 - 8*t2^3*delv*delt2^3 + 7*t2^3*delt2^4 - 
        6*t2^2*delv^2*delt2^2 + 14*t2^2*delv*delt2^3 - 6*t2^2*delt2^4 + 
        9*t2*delv^2*delt2^2 - 9*t2*delv*delt2^3 + t2*delt2^4 - 
        7/2*delv^2*delt2^2 + 2*delv*delt2^3 + 1/2*delt2^4,
    t2^5*delt2^4 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 + t2^3*delv^2*delt2^2 - 
        6*t2^3*delv*delt2^3 + 3*t2^3*delt2^4 - 3*t2^2*delv^2*delt2^2 + 
        6*t2^2*delv*delt2^3 - t2^2*delt2^4 + 3*t2*delv^2*delt2^2 - 
        2*t2*delv*delt2^3 - delv^2*delt2^2,
    t2^4*delv^3*delt2^2 + 17*t2^4*delv*delt2^4 - 18*t2^4*delt2^5 - 
        6*t2^3*delv^3*delt2^2 + 22*t2^3*delv^2*delt2^3 - 66*t2^3*delv*delt2^4 + 
        50*t2^3*delt2^5 + 12*t2^2*delv^3*delt2^2 - 66*t2^2*delv^2*delt2^3 + 
        96*t2^2*delv*delt2^4 - 42*t2^2*delt2^5 - 10*t2*delv^3*delt2^2 + 
        66*t2*delv^2*delt2^3 - 62*t2*delv*delt2^4 + 6*t2*delt2^5 + 
        3*delv^3*delt2^2 - 22*delv^2*delt2^3 + 15*delv*delt2^4 + 4*delt2^5,
    t2^4*delv^2*delt2^3 - 6*t2^4*delv*delt2^4 + 5*t2^4*delt2^5 + 
        2*t2^3*delv^3*delt2^2 - 10*t2^3*delv^2*delt2^3 + 22*t2^3*delv*delt2^4 - 
        14*t2^3*delt2^5 - 6*t2^2*delv^3*delt2^2 + 24*t2^2*delv^2*delt2^3 - 
        30*t2^2*delv*delt2^4 + 12*t2^2*delt2^5 + 6*t2*delv^3*delt2^2 - 
        22*t2*delv^2*delt2^3 + 18*t2*delv*delt2^4 - 2*t2*delt2^5 - 
        2*delv^3*delt2^2 + 7*delv^2*delt2^3 - 4*delv*delt2^4 - delt2^5,
    t2^4*delv*delt2^5 - t2^4*delt2^6 - 1/24*t2^3*delv^4*delt2^2 - 
        1/6*t2^3*delv^3*delt2^3 + 5/4*t2^3*delv^2*delt2^4 - 
        23/6*t2^3*delv*delt2^5 + 67/24*t2^3*delt2^6 + 1/8*t2^2*delv^4*delt2^2 + 
        1/2*t2^2*delv^3*delt2^3 - 15/4*t2^2*delv^2*delt2^4 + 
        11/2*t2^2*delv*delt2^5 - 19/8*t2^2*delt2^6 - 1/8*t2*delv^4*delt2^2 - 
        1/2*t2*delv^3*delt2^3 + 15/4*t2*delv^2*delt2^4 - 7/2*t2*delv*delt2^5 + 
        3/8*t2*delt2^6 + 1/24*delv^4*delt2^2 + 1/6*delv^3*delt2^3 - 
        5/4*delv^2*delt2^4 + 5/6*delv*delt2^5 + 5/24*delt2^6,
    t2^3*delv^5*delt2^2 - t2^3*delv^4*delt2^3 - 2*t2^3*delv^3*delt2^4 + 
        2*t2^3*delv^2*delt2^5 + t2^3*delv*delt2^6 - t2^3*delt2^7 - 
        3*t2^2*delv^5*delt2^2 + 3*t2^2*delv^4*delt2^3 + 6*t2^2*delv^3*delt2^4 - 
        6*t2^2*delv^2*delt2^5 - 3*t2^2*delv*delt2^6 + 3*t2^2*delt2^7 + 
        3*t2*delv^5*delt2^2 - 3*t2*delv^4*delt2^3 - 6*t2*delv^3*delt2^4 + 
        6*t2*delv^2*delt2^5 + 3*t2*delv*delt2^6 - 3*t2*delt2^7 - delv^5*delt2^2 
        + delv^4*delt2^3 + 2*delv^3*delt2^4 - 2*delv^2*delt2^5 - delv*delt2^6 + 
        delt2^7
]


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 17:52:19 2004

Input: E:=EllipticCurve([0,12,0,0,144]);
RankBounds(E);

Output: Magma V2.10-22    Mon Jul 19 2004 17:52:16 on modular  [Seed = 1140802021]
   -------------------------------------

1 1

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 17:52:54 2004

Input: E:=EllipticCurve([0,12,0,0,144]);
RankBounds(E);
Q,pts:=IntegralPoints(E);Q;


Output: Magma V2.10-22    Mon Jul 19 2004 17:52:51 on modular  [Seed = 3881559394]
   -------------------------------------

1 1

IntegralPoints(
    E: Elliptic Curve defined by y^2 = x^3 + 12*x^2 + 144 over Rati...
)
SIntegralPoints(
    E: Elliptic Curve defined by y^2 = x^3 + 12*x^2 + 144 over Rati...,
    S: []
)
IntPoints(
    E: E
)
IntPointsUpperBound(
    E: E,
    MWG2: [ (576 : 12960 : 1) ],
    lambda: 0.02954568524734930631825413627211673883721232414245
)
ReduceBound(
    E: E,
    MWG: [ (576 : 12960 : 1) ],
    lambda: 0.02954568524734930631825413627211673883721232414245,
    N: 14
)
In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 988, 
column 20:
>>         N:= Ceiling(x);
                      ^
Runtime error in 'Ceiling': Argument 1 should be real

>> Q,pts:=IntegralPoints(E);Q;
                            ^
User error: Identifier 'Q' has not been declared or assigned

Total time: 3.359 seconds, Total memory usage: 2.16MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 18:26:16 2004

Input: P<x>:=PolynomialRing(Integers());
K:=NumberField(x^3-16*x+16);
FundamentalUnits(K);


Output: Magma V2.10-22    Mon Jul 19 2004 18:26:13 on modular  [Seed = 146014923]
   -------------------------------------


>> FundamentalUnits(K);
                   ^
Runtime error in 'FundamentalUnits': Bad argument types
Argument types given: FldNum

Total time: 2.799 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 18:35:19 2004

Input: P<x>:=PolynomialRing(Integers());
K:=NumberField(x^3-16*x+16);
O:=MaximalOrder(K);
SetOrderUnitsFundamental(O);


Output: Magma V2.10-22    Mon Jul 19 2004 18:35:16 on modular  [Seed = 4232114195]
   -------------------------------------


>> SetOrderUnitsFundamental(O);
   ^
User error: Identifier 'SetOrderUnitsFundamental' has not been declared or 
assigned

Total time: 2.559 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 18:35:51 2004

Input: P<x>:=PolynomialRing(Integers());
K:=NumberField(x^3-16*x+16);
O:=MaximalOrder(K);
FundamentalUnits(O);

Output: Magma V2.10-22    Mon Jul 19 2004 18:35:48 on modular  [Seed = 2970467647]
   -------------------------------------


>> FundamentalUnits(O);;
                   ^
Runtime error in 'FundamentalUnits': Bad argument types
Argument types given: RngOrd

Total time: 2.679 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 18:36:16 2004

Input: P<x>:=PolynomialRing(Integers());
K:=NumberField(x^3-16*x+16);
O:=MaximalOrder(K);UnitRank(O);


Output: Magma V2.10-22    Mon Jul 19 2004 18:36:13 on modular  [Seed = 1758749950]
   -------------------------------------

2

Total time: 2.549 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 18:36:59 2004

Input: P<x>:=PolynomialRing(Integers());
K:=NumberField(x^3-16*x+16);
O:=MaximalOrder(K);UnitRank(O);Norm(3*x^2-16);


Output: Magma V2.10-22    Mon Jul 19 2004 18:36:56 on modular  [Seed = 2109829182]
   -------------------------------------

2

>> O:=MaximalOrder(K);UnitRank(O);Norm(3*x^2-16);
                                      ^
Runtime error in 'Norm': Bad argument types
Argument types given: RngUPolElt

Total time: 2.579 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:36:59 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
I:=ideal<R|GenerList>;
GB:=GroebnerBasis(I);
print "Groebner basis is:", GB;
Q,P:=PrimaryDecomposition(I);
print "Primary Decomposition", P;

print "Infinity:";

GenerList2:={(1-v)^2*(1-v*t2)^2*(delv-delt2),((1-v*t2)*delt2)^2,(1-v)^2*(v*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
Q2,P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:36:36 on modular  [Seed = 2059826885]
   -------------------------------------

Groebner basis is: [
    z*delz + t*delt - delz - delt,
    z*delt - t*delt,
    t*delz*delt + t*delt^2 - delz*delt - delt^2
]
Primary Decomposition [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - t,
        delz + delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        z - 1,
        delt
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: z, t, delz, delt
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delz,
        delt
    ]
]
Infinity:
Groebner Basis [
    v^4*t2^2*delt2 - v^3*t2^2*delt2 - 2*v^3*t2*delt2 - v^2*t2^2*delt2 + 
        2*v^2*t2*delt2 - v^2*delv + v^2*delt2 + v*t2^2*delt2 + 2*v*t2*delt2 + 
        2*v*delv - 2*v*delt2 - 2*t2*delt2 - delv + delt2,
    v^3*delv - 2*v^2*delv + v^2*delt2 + v*delv - 2*v*delt2 + delt2,
    v^2*delv^2 + 2*v*t2^3*delt2^2 - 2*v*t2^2*delt2^2 - 2*v*delv^2 - 
        3*t2^2*delt2^2 + 4*t2*delt2^2 + delv^2 - delt2^2,
    v^2*delv*delt2 - v*t2^2*delt2^2 - 2*v*delv*delt2 + v*delt2^2 + 2*t2*delt2^2 
        + delv*delt2 - 2*delt2^2,
    v^2*delt2^2 - 2*v*t2^4*delt2^2 + 2*v*t2^3*delt2^2 + 4*v*t2^2*delt2^2 - 
        4*v*t2*delt2^2 - 2*v*delt2^2 - 1/2*t2^6*delt2^2 + t2^5*delt2^2 + 
        3/2*t2^4*delt2^2 - 2*t2^3*delt2^2 - 5/2*t2^2*delt2^2 + t2*delt2^2 + 
        5/2*delt2^2,
    v*t2^5*delt2^2 - v*t2^4*delt2^2 - 2*v*t2^3*delt2^2 + 2*v*t2^2*delt2^2 + 
        v*t2*delt2^2 - v*delt2^2 + 3/4*t2^6*delt2^2 - 5/2*t2^5*delt2^2 + 
        1/4*t2^4*delt2^2 + 5*t2^3*delt2^2 - 11/4*t2^2*delt2^2 - 5/2*t2*delt2^2 +
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 13/6*t2^5*delt2^3 + 
        5/4*t2^4*delv*delt2^2 - 47/12*t2^4*delt2^3 - 2*t2^3*delv*delt2^2 - 
        7/3*t2^3*delt2^3 - 3/2*t2^2*delv*delt2^2 + 47/6*t2^2*delt2^3 + 
        4*t2*delv*delt2^2 - 23/6*t2*delt2^3 - 7/4*delv*delt2^2 + 1/12*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 - 
        5/4*t2^5*delt2^3 - 3/8*t2^4*delv*delt2^2 + 23/8*t2^4*delt2^3 + 
        t2^3*delv*delt2^2 + 1/2*t2^3*delt2^3 - 1/4*t2^2*delv*delt2^2 - 
        23/4*t2^2*delt2^3 - 2*t2*delv*delt2^2 + 15/4*t2*delt2^3 + 
        13/8*delv*delt2^2 - 1/8*delt2^3,
    t2^7*delt2^2 - 3*t2^6*delt2^2 + t2^5*delt2^2 + 5*t2^4*delt2^2 - 
        5*t2^3*delt2^2 - t2^2*delt2^2 + 3*t2*delt2^2 - delt2^2,
    t2^6*delt2^3 - 2*t2^5*delt2^3 - t2^4*delt2^3 + 4*t2^3*delt2^3 - t2^2*delt2^3
        - 2*t2*delt2^3 + delt2^3,
    t2^5*delv*delt2^2 + t2^5*delt2^3 - t2^4*delv*delt2^2 - t2^4*delt2^3 - 
        2*t2^3*delv*delt2^2 - 2*t2^3*delt2^3 + 2*t2^2*delv*delt2^2 + 
        2*t2^2*delt2^3 + t2*delv*delt2^2 + t2*delt2^3 - delv*delt2^2 - delt2^3,
    t2^5*delt2^4 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 + t2^3*delv^2*delt2^2 - 
        6*t2^3*delv*delt2^3 + 3*t2^3*delt2^4 - 3*t2^2*delv^2*delt2^2 + 
        6*t2^2*delv*delt2^3 - t2^2*delt2^4 + 3*t2*delv^2*delt2^2 - 
        2*t2*delv*delt2^3 - delv^2*delt2^2,
    t2^4*delv^2*delt2^2 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 - 
        8*t2^3*delv*delt2^3 + 8*t2^3*delt2^4 - 6*t2^2*delv^2*delt2^2 + 
        12*t2^2*delv*delt2^3 - 6*t2^2*delt2^4 + 8*t2*delv^2*delt2^2 - 
        8*t2*delv*delt2^3 - 3*delv^2*delt2^2 + 2*delv*delt2^3 + delt2^4,
    t2^4*delv*delt2^4 - t2^4*delt2^5 - 1/4*t2^3*delv^3*delt2^2 + 
        5/4*t2^3*delv^2*delt2^3 - 15/4*t2^3*delv*delt2^4 + 11/4*t2^3*delt2^5 + 
        3/4*t2^2*delv^3*delt2^2 - 15/4*t2^2*delv^2*delt2^3 + 
        21/4*t2^2*delv*delt2^4 - 9/4*t2^2*delt2^5 - 3/4*t2*delv^3*delt2^2 + 
        15/4*t2*delv^2*delt2^3 - 13/4*t2*delv*delt2^4 + 1/4*t2*delt2^5 + 
        1/4*delv^3*delt2^2 - 5/4*delv^2*delt2^3 + 3/4*delv*delt2^4 + 
        1/4*delt2^5,
    t2^3*delv^4*delt2^2 - 2*t2^3*delv^3*delt2^3 + 2*t2^3*delv*delt2^5 - 
        t2^3*delt2^6 - 3*t2^2*delv^4*delt2^2 + 6*t2^2*delv^3*delt2^3 - 
        6*t2^2*delv*delt2^5 + 3*t2^2*delt2^6 + 3*t2*delv^4*delt2^2 - 
        6*t2*delv^3*delt2^3 + 6*t2*delv*delt2^5 - 3*t2*delt2^6 - delv^4*delt2^2 
        + 2*delv^3*delt2^3 - 2*delv*delt2^5 + delt2^6
]


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 18:37:32 2004

Input: P<x>:=PolynomialRing(Integers());
K:=NumberField(x^3-16*x+16);
O:=MaximalOrder(K);UnitRank(O);Norm(3*a^2-16);


Output: Magma V2.10-22    Mon Jul 19 2004 18:37:29 on modular  [Seed = 4015252109]
   -------------------------------------

2

>> O:=MaximalOrder(K);UnitRank(O);Norm(3*a^2-16);
                                         ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.569 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:38:37 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={(1-v)^2*(1-v*t2)^2*(delv-delt2),((1-v*t2)*delt2)^2,(1-v)^2*(v*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:38:33 on modular  [Seed = 2092986713]
   -------------------------------------

Infinity:
Groebner Basis [
    v^4*t2^2*delt2 - v^3*t2^2*delt2 - 2*v^3*t2*delt2 - v^2*t2^2*delt2 + 
        2*v^2*t2*delt2 - v^2*delv + v^2*delt2 + v*t2^2*delt2 + 2*v*t2*delt2 + 
        2*v*delv - 2*v*delt2 - 2*t2*delt2 - delv + delt2,
    v^3*delv - 2*v^2*delv + v^2*delt2 + v*delv - 2*v*delt2 + delt2,
    v^2*delv^2 + 2*v*t2^3*delt2^2 - 2*v*t2^2*delt2^2 - 2*v*delv^2 - 
        3*t2^2*delt2^2 + 4*t2*delt2^2 + delv^2 - delt2^2,
    v^2*delv*delt2 - v*t2^2*delt2^2 - 2*v*delv*delt2 + v*delt2^2 + 2*t2*delt2^2 
        + delv*delt2 - 2*delt2^2,
    v^2*delt2^2 - 2*v*t2^4*delt2^2 + 2*v*t2^3*delt2^2 + 4*v*t2^2*delt2^2 - 
        4*v*t2*delt2^2 - 2*v*delt2^2 - 1/2*t2^6*delt2^2 + t2^5*delt2^2 + 
        3/2*t2^4*delt2^2 - 2*t2^3*delt2^2 - 5/2*t2^2*delt2^2 + t2*delt2^2 + 
        5/2*delt2^2,
    v*t2^5*delt2^2 - v*t2^4*delt2^2 - 2*v*t2^3*delt2^2 + 2*v*t2^2*delt2^2 + 
        v*t2*delt2^2 - v*delt2^2 + 3/4*t2^6*delt2^2 - 5/2*t2^5*delt2^2 + 
        1/4*t2^4*delt2^2 + 5*t2^3*delt2^2 - 11/4*t2^2*delt2^2 - 5/2*t2*delt2^2 +
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 13/6*t2^5*delt2^3 + 
        5/4*t2^4*delv*delt2^2 - 47/12*t2^4*delt2^3 - 2*t2^3*delv*delt2^2 - 
        7/3*t2^3*delt2^3 - 3/2*t2^2*delv*delt2^2 + 47/6*t2^2*delt2^3 + 
        4*t2*delv*delt2^2 - 23/6*t2*delt2^3 - 7/4*delv*delt2^2 + 1/12*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 - 
        5/4*t2^5*delt2^3 - 3/8*t2^4*delv*delt2^2 + 23/8*t2^4*delt2^3 + 
        t2^3*delv*delt2^2 + 1/2*t2^3*delt2^3 - 1/4*t2^2*delv*delt2^2 - 
        23/4*t2^2*delt2^3 - 2*t2*delv*delt2^2 + 15/4*t2*delt2^3 + 
        13/8*delv*delt2^2 - 1/8*delt2^3,
    t2^7*delt2^2 - 3*t2^6*delt2^2 + t2^5*delt2^2 + 5*t2^4*delt2^2 - 
        5*t2^3*delt2^2 - t2^2*delt2^2 + 3*t2*delt2^2 - delt2^2,
    t2^6*delt2^3 - 2*t2^5*delt2^3 - t2^4*delt2^3 + 4*t2^3*delt2^3 - t2^2*delt2^3
        - 2*t2*delt2^3 + delt2^3,
    t2^5*delv*delt2^2 + t2^5*delt2^3 - t2^4*delv*delt2^2 - t2^4*delt2^3 - 
        2*t2^3*delv*delt2^2 - 2*t2^3*delt2^3 + 2*t2^2*delv*delt2^2 + 
        2*t2^2*delt2^3 + t2*delv*delt2^2 + t2*delt2^3 - delv*delt2^2 - delt2^3,
    t2^5*delt2^4 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 + t2^3*delv^2*delt2^2 - 
        6*t2^3*delv*delt2^3 + 3*t2^3*delt2^4 - 3*t2^2*delv^2*delt2^2 + 
        6*t2^2*delv*delt2^3 - t2^2*delt2^4 + 3*t2*delv^2*delt2^2 - 
        2*t2*delv*delt2^3 - delv^2*delt2^2,
    t2^4*delv^2*delt2^2 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 - 
        8*t2^3*delv*delt2^3 + 8*t2^3*delt2^4 - 6*t2^2*delv^2*delt2^2 + 
        12*t2^2*delv*delt2^3 - 6*t2^2*delt2^4 + 8*t2*delv^2*delt2^2 - 
        8*t2*delv*delt2^3 - 3*delv^2*delt2^2 + 2*delv*delt2^3 + delt2^4,
    t2^4*delv*delt2^4 - t2^4*delt2^5 - 1/4*t2^3*delv^3*delt2^2 + 
        5/4*t2^3*delv^2*delt2^3 - 15/4*t2^3*delv*delt2^4 + 11/4*t2^3*delt2^5 + 
        3/4*t2^2*delv^3*delt2^2 - 15/4*t2^2*delv^2*delt2^3 + 
        21/4*t2^2*delv*delt2^4 - 9/4*t2^2*delt2^5 - 3/4*t2*delv^3*delt2^2 + 
        15/4*t2*delv^2*delt2^3 - 13/4*t2*delv*delt2^4 + 1/4*t2*delt2^5 + 
        1/4*delv^3*delt2^2 - 5/4*delv^2*delt2^3 + 3/4*delv*delt2^4 + 
        1/4*delt2^5,
    t2^3*delv^4*delt2^2 - 2*t2^3*delv^3*delt2^3 + 2*t2^3*delv*delt2^5 - 
        t2^3*delt2^6 - 3*t2^2*delv^4*delt2^2 + 6*t2^2*delv^3*delt2^3 - 
        6*t2^2*delv*delt2^5 + 3*t2^2*delt2^6 + 3*t2*delv^4*delt2^2 - 
        6*t2*delv^3*delt2^3 + 6*t2*delv*delt2^5 - 3*t2*delt2^6 - delv^4*delt2^2 
        + 2*delv^3*delt2^3 - 2*delv*delt2^5 + delt2^6
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 1, Radical, Prime
    Groebner basis:
    [
        v + 1,
        t2 + 1,
        delv - delt2
    ]
]

Total time: 3.579 seconds, Total memory usage: 2.10MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:42:12 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={((1-v*t2)*delt2)^2,(1-v)^2*(v*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:42:08 on modular  [Seed = 196543749]
   -------------------------------------

Infinity:
Groebner Basis [
    v^3*delv - 2*v^2*delv + v^2*delt2 + v*delv - 2*v*delt2 + delt2,
    v^2*delt2^2 - 2*v*t2^4*delt2^2 + 2*v*t2^3*delt2^2 + 4*v*t2^2*delt2^2 - 
        4*v*t2*delt2^2 - 2*v*delt2^2 - 1/2*t2^6*delt2^2 + t2^5*delt2^2 + 
        3/2*t2^4*delt2^2 - 2*t2^3*delt2^2 - 5/2*t2^2*delt2^2 + t2*delt2^2 + 
        5/2*delt2^2,
    v*t2^5*delt2^2 - v*t2^4*delt2^2 - 2*v*t2^3*delt2^2 + 2*v*t2^2*delt2^2 + 
        v*t2*delt2^2 - v*delt2^2 + 3/4*t2^6*delt2^2 - 5/2*t2^5*delt2^2 + 
        1/4*t2^4*delt2^2 + 5*t2^3*delt2^2 - 11/4*t2^2*delt2^2 - 5/2*t2*delt2^2 +
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 13/6*t2^5*delt2^3 + 
        5/4*t2^4*delv*delt2^2 - 47/12*t2^4*delt2^3 - 2*t2^3*delv*delt2^2 - 
        7/3*t2^3*delt2^3 - 3/2*t2^2*delv*delt2^2 + 47/6*t2^2*delt2^3 + 
        4*t2*delv*delt2^2 - 23/6*t2*delt2^3 - 7/4*delv*delt2^2 + 1/12*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 - 
        5/4*t2^5*delt2^3 - 3/8*t2^4*delv*delt2^2 + 23/8*t2^4*delt2^3 + 
        t2^3*delv*delt2^2 + 1/2*t2^3*delt2^3 - 1/4*t2^2*delv*delt2^2 - 
        23/4*t2^2*delt2^3 - 2*t2*delv*delt2^2 + 15/4*t2*delt2^3 + 
        13/8*delv*delt2^2 - 1/8*delt2^3,
    t2^7*delt2^2 - 3*t2^6*delt2^2 + t2^5*delt2^2 + 5*t2^4*delt2^2 - 
        5*t2^3*delt2^2 - t2^2*delt2^2 + 3*t2*delt2^2 - delt2^2,
    t2^6*delt2^3 - 2*t2^5*delt2^3 - t2^4*delt2^3 + 4*t2^3*delt2^3 - t2^2*delt2^3
        - 2*t2*delt2^3 + delt2^3,
    t2^5*delv*delt2^2 + t2^5*delt2^3 - t2^4*delv*delt2^2 - t2^4*delt2^3 - 
        2*t2^3*delv*delt2^2 - 2*t2^3*delt2^3 + 2*t2^2*delv*delt2^2 + 
        2*t2^2*delt2^3 + t2*delv*delt2^2 + t2*delt2^3 - delv*delt2^2 - delt2^3,
    t2^5*delt2^4 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 + t2^3*delv^2*delt2^2 - 
        6*t2^3*delv*delt2^3 + 3*t2^3*delt2^4 - 3*t2^2*delv^2*delt2^2 + 
        6*t2^2*delv*delt2^3 - t2^2*delt2^4 + 3*t2*delv^2*delt2^2 - 
        2*t2*delv*delt2^3 - delv^2*delt2^2,
    t2^4*delv^2*delt2^2 + 2*t2^4*delv*delt2^3 - 3*t2^4*delt2^4 - 
        8*t2^3*delv*delt2^3 + 8*t2^3*delt2^4 - 6*t2^2*delv^2*delt2^2 + 
        12*t2^2*delv*delt2^3 - 6*t2^2*delt2^4 + 8*t2*delv^2*delt2^2 - 
        8*t2*delv*delt2^3 - 3*delv^2*delt2^2 + 2*delv*delt2^3 + delt2^4,
    t2^4*delv*delt2^4 - t2^4*delt2^5 - 1/4*t2^3*delv^3*delt2^2 + 
        5/4*t2^3*delv^2*delt2^3 - 15/4*t2^3*delv*delt2^4 + 11/4*t2^3*delt2^5 + 
        3/4*t2^2*delv^3*delt2^2 - 15/4*t2^2*delv^2*delt2^3 + 
        21/4*t2^2*delv*delt2^4 - 9/4*t2^2*delt2^5 - 3/4*t2*delv^3*delt2^2 + 
        15/4*t2*delv^2*delt2^3 - 13/4*t2*delv*delt2^4 + 1/4*t2*delt2^5 + 
        1/4*delv^3*delt2^2 - 5/4*delv^2*delt2^3 + 3/4*delv*delt2^4 + 
        1/4*delt2^5,
    t2^3*delv^4*delt2^2 - 2*t2^3*delv^3*delt2^3 + 2*t2^3*delv*delt2^5 - 
        t2^3*delt2^6 - 3*t2^2*delv^4*delt2^2 + 6*t2^2*delv^3*delt2^3 - 
        6*t2^2*delv*delt2^5 + 3*t2^2*delt2^6 + 3*t2*delv^4*delt2^2 - 
        6*t2*delv^3*delt2^3 + 6*t2*delv*delt2^5 - 3*t2*delt2^6 - delv^4*delt2^2 
        + 2*delv^3*delt2^3 - 2*delv*delt2^5 + delt2^6
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 1, Radical, Prime
    Groebner basis:
    [
        v + 1,
        t2 + 1,
        delv - delt2
    ]
]

Total time: 3.620 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:47:40 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={(1-v)^2*(1-t2*v)^2*(delv-delt2),
((1-v*t2)*delt2)^2,
(1-v)^2*(v^2*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:47:37 on modular  [Seed = 1525044610]
   -------------------------------------

Infinity:
Groebner Basis [
    v^4*t2^2*delt2 - 2*v^3*t2^2*delt2 + 2*v^3*t2*delv - 2*v^3*t2*delt2 + 
        2*v^2*t2^2*delt2 - 4*v^2*t2*delv + 4*v^2*t2*delt2 - v^2*delv + v^2*delt2
        - 2*v*t2^2*delt2 + 2*v*t2*delv - 2*v*t2*delt2 + 2*v*delv - 2*v*delt2 + 
        t2^2*delt2 - delv + delt2,
    v^4*delv - 2*v^3*delv + v^2*delv + v^2*delt2 - 2*v*delt2 + delt2,
    v^2*delv^2 + 10*v*t2^2*delt2^2 - 18*v*t2*delt2^2 - 2*v*delv^2 + 8*v*delt2^2 
        - 9/2*t2^4*delt2^2 + 24*t2^3*delt2^2 - 54*t2^2*delt2^2 + 52*t2*delt2^2 +
        delv^2 - 35/2*delt2^2,
    v^2*delv*delt2 - 4*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 2*v*delv*delt2 - 
        2*v*delt2^2 + 3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 
        16*t2*delt2^2 + delv*delt2 + 9/2*delt2^2,
    v^2*delt2^2 - 2*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 6*v*delt2^2 + 
        3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 20*t2*delt2^2 + 
        19/2*delt2^2,
    v*t2^3*delt2^2 - 3*v*t2^2*delt2^2 + 3*v*t2*delt2^2 - v*delt2^2 + 
        3/4*t2^4*delt2^2 - 4*t2^3*delt2^2 + 15/2*t2^2*delt2^2 - 6*t2*delt2^2 + 
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 2/3*t2^3*delt2^3 - 
        3*t2^2*delt2^3 + 4*t2*delt2^3 - 5/3*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 + 
        1/2*t2^2*delv*delt2^2 + 1/2*t2^2*delt2^3 - 2*t2*delv*delt2^2 - 
        2*t2*delt2^3 + 3/2*delv*delt2^2 + 3/2*delt2^3,
    t2^5*delt2^2 - 5*t2^4*delt2^2 + 10*t2^3*delt2^2 - 10*t2^2*delt2^2 + 
        5*t2*delt2^2 - delt2^2,
    t2^4*delt2^3 - 4*t2^3*delt2^3 + 6*t2^2*delt2^3 - 4*t2*delt2^3 + delt2^3,
    t2^3*delv*delt2^2 + t2^3*delt2^3 - 3*t2^2*delv*delt2^2 - 3*t2^2*delt2^3 + 
        3*t2*delv*delt2^2 + 3*t2*delt2^3 - delv*delt2^2 - delt2^3
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ]
]

Total time: 2.839 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:48:39 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={(1-v)^2*(1-t2*v)^2*(delv-delt2),
((1-v*t2)*delt2)^2,
(1-v)^2*(v^2*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:48:16 on modular  [Seed = 865025234]
   -------------------------------------

Infinity:
Groebner Basis [
    v^4*t2^2*delt2 - 2*v^3*t2^2*delt2 + 2*v^3*t2*delv - 2*v^3*t2*delt2 + 
        2*v^2*t2^2*delt2 - 4*v^2*t2*delv + 4*v^2*t2*delt2 - v^2*delv + v^2*delt2
        - 2*v*t2^2*delt2 + 2*v*t2*delv - 2*v*t2*delt2 + 2*v*delv - 2*v*delt2 + 
        t2^2*delt2 - delv + delt2,
    v^4*delv - 2*v^3*delv + v^2*delv + v^2*delt2 - 2*v*delt2 + delt2,
    v^2*delv^2 + 10*v*t2^2*delt2^2 - 18*v*t2*delt2^2 - 2*v*delv^2 + 8*v*delt2^2 
        - 9/2*t2^4*delt2^2 + 24*t2^3*delt2^2 - 54*t2^2*delt2^2 + 52*t2*delt2^2 +
        delv^2 - 35/2*delt2^2,
    v^2*delv*delt2 - 4*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 2*v*delv*delt2 - 
        2*v*delt2^2 + 3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 
        16*t2*delt2^2 + delv*delt2 + 9/2*delt2^2,
    v^2*delt2^2 - 2*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 6*v*delt2^2 + 
        3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 20*t2*delt2^2 + 
        19/2*delt2^2,
    v*t2^3*delt2^2 - 3*v*t2^2*delt2^2 + 3*v*t2*delt2^2 - v*delt2^2 + 
        3/4*t2^4*delt2^2 - 4*t2^3*delt2^2 + 15/2*t2^2*delt2^2 - 6*t2*delt2^2 + 
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 2/3*t2^3*delt2^3 - 
        3*t2^2*delt2^3 + 4*t2*delt2^3 - 5/3*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 + 
        1/2*t2^2*delv*delt2^2 + 1/2*t2^2*delt2^3 - 2*t2*delv*delt2^2 - 
        2*t2*delt2^3 + 3/2*delv*delt2^2 + 3/2*delt2^3,
    t2^5*delt2^2 - 5*t2^4*delt2^2 + 10*t2^3*delt2^2 - 10*t2^2*delt2^2 + 
        5*t2*delt2^2 - delt2^2,
    t2^4*delt2^3 - 4*t2^3*delt2^3 + 6*t2^2*delt2^3 - 4*t2*delt2^3 + delt2^3,
    t2^3*delv*delt2^2 + t2^3*delt2^3 - 3*t2^2*delv*delt2^2 - 3*t2^2*delt2^3 + 
        3*t2*delv*delt2^2 + 3*t2*delt2^3 - delv*delt2^2 - delt2^3
]


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:49:16 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={(1-v)^2*(1-t2*v)^2*(delv-delt2),
((1-v*t2)*delt2)^2,
(1-v)^2*(v^2*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:49:13 on modular  [Seed = 3121001730]
   -------------------------------------

Infinity:
Groebner Basis [
    v^4*t2^2*delt2 - 2*v^3*t2^2*delt2 + 2*v^3*t2*delv - 2*v^3*t2*delt2 + 
        2*v^2*t2^2*delt2 - 4*v^2*t2*delv + 4*v^2*t2*delt2 - v^2*delv + v^2*delt2
        - 2*v*t2^2*delt2 + 2*v*t2*delv - 2*v*t2*delt2 + 2*v*delv - 2*v*delt2 + 
        t2^2*delt2 - delv + delt2,
    v^4*delv - 2*v^3*delv + v^2*delv + v^2*delt2 - 2*v*delt2 + delt2,
    v^2*delv^2 + 10*v*t2^2*delt2^2 - 18*v*t2*delt2^2 - 2*v*delv^2 + 8*v*delt2^2 
        - 9/2*t2^4*delt2^2 + 24*t2^3*delt2^2 - 54*t2^2*delt2^2 + 52*t2*delt2^2 +
        delv^2 - 35/2*delt2^2,
    v^2*delv*delt2 - 4*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 2*v*delv*delt2 - 
        2*v*delt2^2 + 3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 
        16*t2*delt2^2 + delv*delt2 + 9/2*delt2^2,
    v^2*delt2^2 - 2*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 6*v*delt2^2 + 
        3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 20*t2*delt2^2 + 
        19/2*delt2^2,
    v*t2^3*delt2^2 - 3*v*t2^2*delt2^2 + 3*v*t2*delt2^2 - v*delt2^2 + 
        3/4*t2^4*delt2^2 - 4*t2^3*delt2^2 + 15/2*t2^2*delt2^2 - 6*t2*delt2^2 + 
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 2/3*t2^3*delt2^3 - 
        3*t2^2*delt2^3 + 4*t2*delt2^3 - 5/3*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 + 
        1/2*t2^2*delv*delt2^2 + 1/2*t2^2*delt2^3 - 2*t2*delv*delt2^2 - 
        2*t2*delt2^3 + 3/2*delv*delt2^2 + 3/2*delt2^3,
    t2^5*delt2^2 - 5*t2^4*delt2^2 + 10*t2^3*delt2^2 - 10*t2^2*delt2^2 + 
        5*t2*delt2^2 - delt2^2,
    t2^4*delt2^3 - 4*t2^3*delt2^3 + 6*t2^2*delt2^3 - 4*t2*delt2^3 + delt2^3,
    t2^3*delv*delt2^2 + t2^3*delt2^3 - 3*t2^2*delv*delt2^2 - 3*t2^2*delt2^3 + 
        3*t2*delv*delt2^2 + 3*t2*delt2^3 - delv*delt2^2 - delt2^3
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ]
]

Total time: 2.869 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:52:29 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
I:=ideal<S|{1-v*t2,v^2*delv-delt2}>;
IsPrime(I);

Output: Magma V2.10-22    Mon Jul 19 2004 18:52:27 on modular  [Seed = 3597321774]
   -------------------------------------

true

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 18:53:57 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={((1-v*t2)*delt2)^2,
(1-v)^2*(v^2*delv+delt2),
((1-v)*(delt2-v^2*delv))^3,
((1-v)^2*(v*delv-t2*delt2))^2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 18:53:54 on modular  [Seed = 1307663387]
   -------------------------------------

Infinity:
Groebner Basis [
    v^4*delv - 2*v^3*delv + v^2*delv + v^2*delt2 - 2*v*delt2 + delt2,
    v^2*delv*delt2 - 4*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 2*v*delv*delt2 - 
        2*v*delt2^2 + 3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 
        16*t2*delt2^2 + delv*delt2 + 9/2*delt2^2,
    v^2*delt2^2 - 2*v*t2^2*delt2^2 + 6*v*t2*delt2^2 - 6*v*delt2^2 + 
        3/2*t2^4*delt2^2 - 8*t2^3*delt2^2 + 18*t2^2*delt2^2 - 20*t2*delt2^2 + 
        19/2*delt2^2,
    v*t2^3*delt2^2 - 3*v*t2^2*delt2^2 + 3*v*t2*delt2^2 - v*delt2^2 + 
        3/4*t2^4*delt2^2 - 4*t2^3*delt2^2 + 15/2*t2^2*delt2^2 - 6*t2*delt2^2 + 
        7/4*delt2^2,
    v*t2^2*delt2^3 - 2*v*t2*delt2^3 + v*delt2^3 + 2/3*t2^3*delt2^3 - 
        3*t2^2*delt2^3 + 4*t2*delt2^3 - 5/3*delt2^3,
    v*t2*delv*delt2^2 + v*t2*delt2^3 - v*delv*delt2^2 - v*delt2^3 + 
        1/2*t2^2*delv*delt2^2 + 1/2*t2^2*delt2^3 - 2*t2*delv*delt2^2 - 
        2*t2*delt2^3 + 3/2*delv*delt2^2 + 3/2*delt2^3,
    t2^5*delt2^2 - 5*t2^4*delt2^2 + 10*t2^3*delt2^2 - 10*t2^2*delt2^2 + 
        5*t2*delt2^2 - delt2^2,
    t2^4*delt2^3 - 4*t2^3*delt2^3 + 6*t2^2*delt2^3 - 4*t2*delt2^3 + delt2^3,
    t2^3*delv*delt2^2 + t2^3*delt2^3 - 3*t2^2*delv*delt2^2 - 3*t2^2*delt2^3 + 
        3*t2*delv*delt2^2 + 3*t2*delt2^3 - delv*delt2^2 - delt2^3
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ]
]

Total time: 3.069 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 19:53:30 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={((1-v*t2)*delt2)^3,
((1-v)*(delt2-delv))^3,
((1-v)*(v*delv-t2*delt2))^3};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 19:53:07 on modular  [Seed = 3814718832]
   -------------------------------------

Infinity:
Groebner Basis [
    v^6*delv^2*delt2 - v^6*delv*delt2^2 + 1/3*v^6*delt2^3 - v^5*t2*delv^2*delt2 
        - 3*v^5*delv^2*delt2 + 3*v^5*delv*delt2^2 - v^5*delt2^3 + 
        v^4*t2^2*delv*delt2^2 + 3*v^4*t2*delv^2*delt2 + 3*v^4*delv^2*delt2 - 
        3*v^4*delv*delt2^2 + v^4*delt2^3 - 3*v^3*t2^2*delv*delt2^2 - 
        3*v^3*t2*delv^2*delt2 - v^3*delv^2*delt2 + v^3*delv*delt2^2 - 
        1/3*v^3*delt2^3 + v^2*t2^3*delt2^3 + 3*v^2*t2^2*delv*delt2^2 - 
        v^2*t2^2*delt2^3 + v^2*t2*delv^2*delt2 - v*t2^3*delt2^3 - 
        v*t2^2*delv*delt2^2 + v*t2*delt2^3 + 1/3*t2^3*delt2^3 - 1/3*delt2^3,
    v^5*t2*delv^2*delt2^2 - 1/6*v^5*t2*delt2^4 - v^4*t2^2*delv^2*delt2^2 - 
        1/2*v^4*t2^2*delt2^4 - 3*v^4*t2*delv^2*delt2^2 + 1/2*v^4*t2*delt2^4 + 
        3*v^3*t2^2*delv^2*delt2^2 + 3/2*v^3*t2^2*delt2^4 + 
        3*v^3*t2*delv^2*delt2^2 - 1/2*v^3*t2*delt2^4 - 
        102/11*v^2*t2^8*delv*delt2^3 - 81/11*v^2*t2^8*delt2^4 + 
        314/11*v^2*t2^7*delv*delt2^3 + 431/33*v^2*t2^7*delt2^4 + 
        105/11*v^2*t2^6*delv*delt2^3 - 69/11*v^2*t2^6*delt2^4 - 
        1041/11*v^2*t2^5*delv*delt2^3 + 174/11*v^2*t2^5*delt2^4 + 
        62*v^2*t2^4*delv*delt2^3 - 40/3*v^2*t2^4*delt2^4 + 
        513/11*v^2*t2^3*delv*delt2^3 - 273/11*v^2*t2^3*delt2^4 - 
        3*v^2*t2^2*delv^2*delt2^2 - 732/11*v^2*t2^2*delv*delt2^3 + 
        366/11*v^2*t2^2*delt2^4 - v^2*t2*delv^2*delt2^2 + 
        390/11*v^2*t2*delv*delt2^3 - 1159/66*v^2*t2*delt2^4 - 
        129/11*v^2*delv*delt2^3 + 129/22*v^2*delt2^4 - 
        2429/352*v*t2^12*delv*delt2^3 + 2429/704*v*t2^12*delt2^4 + 
        3525/176*v*t2^11*delv*delt2^3 - 3525/352*v*t2^11*delt2^4 + 
        1409/88*v*t2^10*delv*delt2^3 - 1409/176*v*t2^10*delt2^4 - 
        16569/176*v*t2^9*delv*delt2^3 + 18201/352*v*t2^9*delt2^4 + 
        6399/352*v*t2^8*delv*delt2^3 - 16447/704*v*t2^8*delt2^4 + 
        16969/88*v*t2^7*delv*delt2^3 - 1043/16*v*t2^7*delt2^4 - 
        1522/11*v*t2^6*delv*delt2^3 + 69/2*v*t2^6*delt2^4 - 
        18825/88*v*t2^5*delv*delt2^3 + 14161/176*v*t2^5*delt2^4 + 
        111025/352*v*t2^4*delv*delt2^3 - 61265/704*v*t2^4*delt2^4 + 
        3129/176*v*t2^3*delv*delt2^3 - 9369/352*v*t2^3*delt2^4 + 
        v*t2^2*delv^2*delt2^2 - 20337/88*v*t2^2*delv*delt2^3 + 
        17305/176*v*t2^2*delt2^4 + 17851/176*v*t2*delv*delt2^3 - 
        16315/352*v*t2*delt2^4 + 973/352*v*delv*delt2^3 - 973/704*v*delt2^4 + 
        2429/704*t2^13*delt2^4 - 3525/352*t2^12*delt2^4 - 1409/176*t2^11*delt2^4
        + 16569/352*t2^10*delt2^4 - 6399/704*t2^9*delt2^4 - 
        16969/176*t2^8*delt2^4 + 761/11*t2^7*delt2^4 + 12489/176*t2^6*delt2^4 - 
        53297/704*t2^5*delt2^4 + 24*t2^4*delv*delt2^3 - 8761/352*t2^4*delt2^4 - 
        55*t2^3*delv*delt2^3 + 8457/176*t2^3*delt2^4 + 3*t2^2*delv*delt2^3 + 
        101/352*t2^2*delt2^4 + 63*t2*delv*delt2^3 - 23149/704*t2*delt2^4 - 
        35*delv*delt2^3 + 18*delt2^4,
    v^3*t2^3*delt2^3 - 3*v^2*t2^2*delt2^3 + 3*v*t2*delt2^3 - delt2^3,
    v^3*delv^3 - 3*v^3*delv^2*delt2 + 3*v^3*delv*delt2^2 - v^3*delt2^3 - 
        3*v^2*delv^3 + 9*v^2*delv^2*delt2 - 9*v^2*delv*delt2^2 + 3*v^2*delt2^3 +
        3*v*delv^3 - 9*v*delv^2*delt2 + 9*v*delv*delt2^2 - 3*v*delt2^3 - delv^3 
        + 3*delv^2*delt2 - 3*delv*delt2^2 + delt2^3,
    v^3*delv*delt2^3 - 1/2*v^3*delt2^4 - 2*v^2*t2^8*delv*delt2^3 - 
        5/2*v^2*t2^8*delt2^4 + 7*v^2*t2^7*delv*delt2^3 + 11/2*v^2*t2^7*delt2^4 -
        3*v^2*t2^6*delt2^4 - 21*v^2*t2^5*delv*delt2^3 + 2*v^2*t2^5*delt2^4 + 
        19*v^2*t2^4*delv*delt2^3 - 3*v^2*t2^4*delt2^4 + 4*v^2*t2^3*delv*delt2^3 
        - 2*v^2*t2^3*delt2^4 - 10*v^2*t2^2*delv*delt2^3 + 5*v^2*t2^2*delt2^4 + 
        7*v^2*t2*delv*delt2^3 - 4*v^2*t2*delt2^4 - 7*v^2*delv*delt2^3 + 
        7/2*v^2*delt2^4 - 25/8*v*t2^12*delv*delt2^3 + 25/16*v*t2^12*delt2^4 + 
        115/12*v*t2^11*delv*delt2^3 - 115/24*v*t2^11*delt2^4 + 
        35/6*v*t2^10*delv*delt2^3 - 35/12*v*t2^10*delt2^4 - 
        535/12*v*t2^9*delv*delt2^3 + 559/24*v*t2^9*delt2^4 + 
        409/24*v*t2^8*delv*delt2^3 - 577/48*v*t2^8*delt2^4 + 
        505/6*v*t2^7*delv*delt2^3 - 379/12*v*t2^7*delt2^4 - 
        230/3*v*t2^6*delv*delt2^3 + 131/6*v*t2^6*delt2^4 - 
        449/6*v*t2^5*delv*delt2^3 + 443/12*v*t2^5*delt2^4 + 
        3199/24*v*t2^4*delv*delt2^3 - 2071/48*v*t2^4*delt2^4 - 
        149/12*v*t2^3*delv*delt2^3 - 199/24*v*t2^3*delt2^4 - 
        469/6*v*t2^2*delv*delt2^3 + 427/12*v*t2^2*delt2^4 + 
        457/12*v*t2*delv*delt2^3 - 373/24*v*t2*delt2^4 + 115/24*v*delv*delt2^3 -
        115/48*v*delt2^4 + 25/16*t2^13*delt2^4 - 115/24*t2^12*delt2^4 - 
        35/12*t2^11*delt2^4 + 535/24*t2^10*delt2^4 - 409/48*t2^9*delt2^4 - 
        505/12*t2^8*delt2^4 + 115/3*t2^7*delt2^4 + 323/12*t2^6*delt2^4 - 
        1903/48*t2^5*delt2^4 + 7*t2^4*delv*delt2^3 - 151/24*t2^4*delt2^4 - 
        18*t2^3*delv*delt2^3 + 271/12*t2^3*delt2^4 + 6*t2^2*delv*delt2^3 - 
        61/24*t2^2*delt2^4 + 17*t2*delv*delt2^3 - 523/48*t2*delt2^4 - 
        13*delv*delt2^3 + 13/2*delt2^4,
    v^3*delt2^5 - 54/11*v^2*t2^4*delv*delt2^4 + 87/11*v^2*t2^4*delt2^5 - 
        30/11*v^2*t2^3*delv^2*delt2^3 + 201/11*v^2*t2^3*delv*delt2^4 - 
        270/11*v^2*t2^3*delt2^5 + 117/11*v^2*t2^2*delv^2*delt2^3 - 
        333/11*v^2*t2^2*delv*delt2^4 + 282/11*v^2*t2^2*delt2^5 - 
        144/11*v^2*t2*delv^2*delt2^3 + 279/11*v^2*t2*delv*delt2^4 - 
        69/11*v^2*t2*delt2^5 + 57/11*v^2*delv^2*delt2^3 - 93/11*v^2*delv*delt2^4
        - 63/11*v^2*delt2^5 + 190/11*v*t2^9*delt2^5 + 
        1131/44*v*t2^8*delv*delt2^4 - 3759/44*v*t2^8*delt2^5 + 
        2337/44*v*t2^7*delv^2*delt2^3 - 2625/11*v*t2^7*delv*delt2^4 + 
        9255/44*v*t2^7*delt2^5 - 4065/22*v*t2^6*delv^2*delt2^3 + 
        12219/22*v*t2^6*delv*delt2^4 - 2581/11*v*t2^6*delt2^5 + 
        7959/44*v*t2^5*delv^2*delt2^3 - 2940/11*v*t2^5*delv*delt2^4 - 
        3771/44*v*t2^5*delt2^5 + 783/11*v*t2^4*delv^2*delt2^3 - 
        6240/11*v*t2^4*delv*delt2^4 + 5010/11*v*t2^4*delt2^5 - 
        10941/44*v*t2^3*delv^2*delt2^3 + 8175/11*v*t2^3*delv*delt2^4 - 
        13987/44*v*t2^3*delt2^5 + 3549/22*v*t2^2*delv^2*delt2^3 - 
        4023/22*v*t2^2*delv*delt2^4 - 498/11*v*t2^2*delt2^5 - 
        1275/44*v*t2*delv^2*delt2^3 - 126*v*t2*delv*delt2^4 + 
        4767/44*v*t2*delt2^5 - 45/11*v*delv^2*delt2^3 + 231/4*v*delv*delt2^4 - 
        857/44*v*delt2^5 - 29519/660*t2^13*delt2^5 + 
        1115611/21120*t2^12*delv^2*delt2^3 - 361111/2112*t2^12*delv*delt2^4 + 
        1886441/7040*t2^12*delt2^5 - 2282867/10560*t2^11*delv^2*delt2^3 + 
        4435331/5280*t2^11*delv*delt2^4 - 6137347/10560*t2^11*delt2^5 + 
        1839857/5280*t2^10*delv^2*delt2^3 - 3406393/2640*t2^10*delv*delt2^4 + 
        1463521/5280*t2^10*delt2^5 - 841021/2112*t2^9*delv^2*delt2^3 - 
        92203/1056*t2^9*delv*delt2^4 + 2015699/2112*t2^9*delt2^5 + 
        267755/4224*t2^8*delv^2*delt2^3 + 5745085/2112*t2^8*delv*delt2^4 - 
        7476725/4224*t2^8*delt2^5 + 1685597/1056*t2^7*delv^2*delt2^3 - 
        2069029/528*t2^7*delv*delt2^4 + 1071581/1056*t2^7*delt2^5 - 
        187751/66*t2^6*delv^2*delt2^3 + 123941/66*t2^6*delv*delt2^4 + 
        15322/33*t2^6*delt2^5 + 262211/1056*t2^5*delv^2*delt2^3 + 
        1377037/528*t2^5*delv*delt2^4 - 144223/96*t2^5*delt2^5 + 
        13743077/4224*t2^4*delv^2*delt2^3 - 10458157/2112*t2^4*delv*delt2^4 + 
        6450373/4224*t2^4*delt2^5 - 4946963/2112*t2^3*delv^2*delt2^3 + 
        2297203/1056*t2^3*delv*delt2^4 - 4736911/10560*t2^3*delt2^5 - 
        2856769/5280*t2^2*delv^2*delt2^3 + 64615/48*t2^2*delv*delt2^4 - 
        3025217/5280*t2^2*delt2^5 + 11450947/10560*t2*delv^2*delt2^3 - 
        8183291/5280*t2*delv*delt2^4 + 1995249/3520*t2*delt2^5 - 
        2144761/7040*delv^2*delt2^3 + 1412129/3520*delv*delt2^4 - 
        3245899/21120*delt2^5,
    v^2*t2^9*delv*delt2^3 - 37/11*v^2*t2^8*delv*delt2^3 + 2/11*v^2*t2^8*delt2^4 
        + 8/11*v^2*t2^7*delv*delt2^3 + 7/11*v^2*t2^7*delt2^4 + 
        96/11*v^2*t2^6*delv*delt2^3 - 37/11*v^2*t2^6*delt2^4 - 
        101/11*v^2*t2^5*delv*delt2^3 + 34/11*v^2*t2^5*delt2^4 - 
        3*v^2*t2^4*delv*delt2^3 + 2*v^2*t2^4*delt2^4 + 
        90/11*v^2*t2^3*delv*delt2^3 - 45/11*v^2*t2^3*delt2^4 - 
        30/11*v^2*t2^2*delv*delt2^3 + 15/11*v^2*t2^2*delt2^4 - 
        8/11*v^2*t2*delv*delt2^3 + 4/11*v^2*t2*delt2^4 + 4/11*v^2*delv*delt2^3 -
        2/11*v^2*delt2^4 + 283/1056*v*t2^12*delv*delt2^3 - 
        283/2112*v*t2^12*delt2^4 - 129/176*v*t2^11*delv*delt2^3 + 
        129/352*v*t2^11*delt2^4 - 271/264*v*t2^10*delv*delt2^3 + 
        7/528*v*t2^10*delt2^4 + 821/176*v*t2^9*delv*delt2^3 - 
        229/352*v*t2^9*delt2^4 - 675/352*v*t2^8*delv*delt2^3 - 
        637/704*v*t2^8*delt2^4 - 1655/264*v*t2^7*delv*delt2^3 + 
        157/48*v*t2^7*delt2^4 + 248/33*v*t2^6*delv*delt2^3 - 13/6*v*t2^6*delt2^4
        - 339/88*v*t2^5*delv*delt2^3 + 75/176*v*t2^5*delt2^4 + 
        1273/1056*v*t2^4*delv*delt2^3 - 409/2112*v*t2^4*delt2^4 + 
        619/176*v*t2^3*delv*delt2^3 - 667/352*v*t2^3*delt2^4 - 
        507/88*v*t2^2*delv*delt2^3 + 571/176*v*t2^2*delt2^4 + 
        1411/528*v*t2*delv*delt2^3 - 1603/1056*v*t2*delt2^4 - 
        299/1056*v*delv*delt2^3 + 299/2112*v*delt2^4 - 283/2112*t2^13*delt2^4 + 
        129/352*t2^12*delt2^4 + 271/528*t2^11*delt2^4 - 821/352*t2^10*delt2^4 + 
        675/704*t2^9*delt2^4 + 1655/528*t2^8*delt2^4 - 149/66*t2^7*delt2^4 - 
        453/176*t2^6*delt2^4 - t2^5*delv*delt2^3 + 6119/2112*t2^5*delt2^4 + 
        3*t2^4*delv*delt2^3 - 91/352*t2^4*delt2^4 - 2*t2^3*delv*delt2^3 - 
        109/176*t2^3*delt2^4 - 2*t2^2*delv*delt2^3 + 1229/1056*t2^2*delt2^4 + 
        3*t2*delv*delt2^3 - 2869/2112*t2*delt2^4 - delv*delt2^3 + 1/2*delt2^4,
    v^2*t2^9*delt2^4 - 8/11*v^2*t2^8*delv*delt2^3 - 29/11*v^2*t2^8*delt2^4 + 
        16/11*v^2*t2^7*delv*delt2^3 + 14/11*v^2*t2^7*delt2^4 + 
        16/11*v^2*t2^6*delv*delt2^3 + 14/11*v^2*t2^6*delt2^4 - 
        70/11*v^2*t2^5*delv*delt2^3 + 2/11*v^2*t2^5*delt2^4 + 
        6*v^2*t2^4*
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 19:54:15 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={((1-v*t2)*delt2)^3,
((1-v)*(delt2-delv))^3,
((1-v)*(v*delv-t2*delt2))^3};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
//print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 19:53:52 on modular  [Seed = 2402521327]
   -------------------------------------

Infinity:


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 19:54:40 2004

Input: C:=RationalField();
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");

print "Infinity:";

GenerList2:={((1-v*t2)*delt2),
((1-v)*(delt2-delv)),
((1-v)*(v*delv-t2*delt2))};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
//print "Groebner Basis", GB2;
P2:=RadicalDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Mon Jul 19 2004 19:54:37 on modular  [Seed = 279711580]
   -------------------------------------

Infinity:
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 1, Radical, Prime
    Groebner basis:
    [
        v + 1,
        t2 + 1,
        delv - delt2
    ]
]

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:11:11 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
I:=ideal<S|{t*v^3-t*v^2-v^2+2*v,v^3-v^4}>;
EliminationIdeal(I,t);
EliminationIdeal(I,v);

Output: Magma V2.10-22    Mon Jul 19 2004 20:11:09 on modular  [Seed = 2819918796]
   -------------------------------------


>> EliminationIdeal(I,t);
                   ^
Runtime error in 'EliminationIdeal': Bad argument types
Argument types given: RngMPol, RngMPolElt

>> EliminationIdeal(I,v);;
                   ^
Runtime error in 'EliminationIdeal': Bad argument types
Argument types given: RngMPol, RngMPolElt

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:11:59 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
I:=ideal<S|{t*v^3-t*v^2-v^2+2*v,v^3-v^4}>;
EliminationIdeal(I,{t});
EliminationIdeal(I,v);

Output: Magma V2.10-22    Mon Jul 19 2004 20:11:56 on modular  [Seed = 1190815088]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
]

>> EliminationIdeal(I,v);;
                   ^
Runtime error in 'EliminationIdeal': Bad argument types
Argument types given: RngMPol, RngMPolElt

Total time: 3.169 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:12:15 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
I:=ideal<S|{t*v^3-t*v^2-v^2+2*v,v^3-v^4}>;
EliminationIdeal(I,{t});
EliminationIdeal(I,{v});

Output: Magma V2.10-22    Mon Jul 19 2004 20:12:12 on modular  [Seed = 380253488]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
    v
]

Total time: 2.789 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:13:48 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
I:=ideal<S|{t*v^3-t*v^2-v^2+2*v,v^3-v^4}>;
J:=EliminationIdeal(I,{t});
K:=EliminationIdeal(I,{v});

Output: Magma V2.10-22    Mon Jul 19 2004 20:13:45 on modular  [Seed = 1525053848]
   -------------------------------------


Total time: 2.749 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:14:04 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
I:=ideal<S|{t*v^3-t*v^2-v^2+2*v,v^3-v^4}>;
J:=EliminationIdeal(I,{t});
K:=EliminationIdeal(I,{v});
J;
K;


Output: Magma V2.10-22    Mon Jul 19 2004 20:14:01 on modular  [Seed = 898176647]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
    v
]

Total time: 2.609 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:16:24 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
I:=ideal<S|{t*v^3-t*v^2-v^2+2*v,v^3-v^4}>;
J:=ideal<S|{1-v}>;
K:=I meet J;
K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:16:21 on modular  [Seed = 3513644536]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
    v^2 - v
]

Total time: 2.859 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:19:02 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
K:=RelationIdeal(L1 cat L2);

Output: Magma V2.10-22    Mon Jul 19 2004 20:19:00 on modular  [Seed = 2418848793]
   -------------------------------------


>> K:=RelationIdeal(L1 cat L2);;
                       ^
Runtime error in 'cat': Bad argument types
Argument types given: SetEnum[RngMPolElt], SetEnum[RngMPolElt]

Total time: 2.530 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:19:14 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
K:=RelationIdeal(L1 & L2);

Output: Magma V2.10-22    Mon Jul 19 2004 20:19:12 on modular  [Seed = 1959285002]
   -------------------------------------


>> K:=RelationIdeal(L1 & L2);;
                       ^
User error: Bad reduction operator

Total time: 2.810 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:19:31 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L1&L2;
//K:=RelationIdeal(L1 & L2);

Output: Magma V2.10-22    Mon Jul 19 2004 20:19:28 on modular  [Seed = 1207657001]
   -------------------------------------


>> L1&L2;
     ^
User error: Bad reduction operator

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:20:35 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L1 cat L2;
//K:=RelationIdeal(L1 & L2);

Output: Magma V2.10-22    Mon Jul 19 2004 20:20:32 on modular  [Seed = 3070988953]
   -------------------------------------


>> L1 cat L2;
      ^
Runtime error in 'cat': Bad argument types
Argument types given: SetEnum[RngMPolElt], SetEnum[RngMPolElt]

Total time: 2.709 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:20:50 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L1 union L2;
//K:=RelationIdeal(L1 & L2);

Output: Magma V2.10-22    Mon Jul 19 2004 20:20:48 on modular  [Seed = 2536223369]
   -------------------------------------


>> L1 union L2;
      ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:21:44 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L1 join L2;
//K:=RelationIdeal(L1 & L2);

Output: Magma V2.10-22    Mon Jul 19 2004 20:21:41 on modular  [Seed = 831329499]
   -------------------------------------

{
    -v + 1,
    -v^4 + v^3,
    v^3*t - v^2*t - v^2 + 2*v
}

Total time: 2.719 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:22:00 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L1 join L2;
K:=RelationIdeal($1);
K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:21:57 on modular  [Seed = 46016472]
   -------------------------------------

{
    -v + 1,
    -v^4 + v^3,
    v^3*t - v^2*t - v^2 + 2*v
}

>> K:=RelationIdeal($1);
                   ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: SetEnum[RngMPolElt]

>> K;;
   ^
User error: Identifier 'K' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:22:36 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
List!(L1 join L2);
//K:=RelationIdeal($1);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:22:33 on modular  [Seed = 2819919134]
   -------------------------------------


>> List!(L1 join L2);
       ^
Runtime error in '!': Illegal coercion

Total time: 2.859 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:23:15 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L:=L1 join L2;
K:=RelationIdeal(L);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:23:12 on modular  [Seed = 613941716]
   -------------------------------------


>> K:=RelationIdeal(L);
                   ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: SetEnum[RngMPolElt]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:24:52 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L:=[!x in (L1 join L2) !];
L;
//K:=RelationIdeal(L);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:24:50 on modular  [Seed = 3881550261]
   -------------------------------------


>> L:=[!x in (L1 join L2) !];
       ^
User error: bad syntax

>> L;
   ^
User error: Identifier 'L' has not been declared or assigned

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:25:06 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L:=[! x in (L1 join L2) !];
L;
//K:=RelationIdeal(L);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:25:03 on modular  [Seed = 146026070]
   -------------------------------------


>> L:=[! x in (L1 join L2) !];
       ^
User error: bad syntax

>> L;
   ^
User error: Identifier 'L' has not been declared or assigned

Total time: 2.609 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:25:19 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L:=[! x in (L1 join L2)| !];
L;
//K:=RelationIdeal(L);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:25:16 on modular  [Seed = 814487133]
   -------------------------------------


>> L:=[! x in (L1 join L2)| !];
       ^
User error: bad syntax

>> L;
   ^
User error: Identifier 'L' has not been declared or assigned

Total time: 2.969 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:26:33 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:={t*v^3-t*v^2-v^2+2*v,v^3-v^4};
I:=ideal<S|L1>;
L2:={1-v};
J:=ideal<S|L2>;
L:=[ (L1 join L2) ];
L;
//K:=RelationIdeal(L);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:26:30 on modular  [Seed = 46015670]
   -------------------------------------

[
    {
        -v + 1,
        -v^4 + v^3,
        v^3*t - v^2*t - v^2 + 2*v
    }
]

Total time: 2.699 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Mon Jul 19 20:27:34 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S|L1>;
L2:=[1-v];
J:=ideal<S|L2>;
L:=[ (L1 join L2) ];
L;
//K:=RelationIdeal(L);
//K;

Output: Magma V2.10-22    Mon Jul 19 2004 20:27:31 on modular  [Seed = 3446795068]
   -------------------------------------


>> L:=[ (L1 join L2) ];
            ^
Runtime error in 'join': Bad argument types
Argument types given: SeqEnum[RngMPolElt], SeqEnum[RngMPolElt]

>> L;
   ^
User error: Identifier 'L' has not been declared or assigned

Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 20:34:35 2004

Input: R<x>:=PolynomialRing(Integers());
f:=x^3+3*x^2-3*x-3;
T:=Thue(f);
Solutions(T,1);


Output: Magma V2.10-22    Mon Jul 19 2004 20:34:32 on modular  [Seed = 3313102174]
   -------------------------------------

[
    [ -2, 3 ],
    [ 1, 0 ]
]

Total time: 2.869 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Mon Jul 19 20:50:19 2004

Input: R<x>:=PolynomialRing(Integers());
f:=x^5+5*x^4-10*x^3-30*x^2-5*x+5;
T:=Thue(f);
Solutions(T,1);

Output: Magma V2.10-22    Mon Jul 19 2004 20:50:14 on modular  [Seed = 4082098110]
   -------------------------------------

[
    [ 1, 0 ]
]

Total time: 4.390 seconds, Total memory usage: 2.30MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:18:35 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
RelationIdeal({t*v^3-t*v^2-v^2+2*v,v^3-v^4});


Output: Magma V2.10-22    Tue Jul 20 2004 00:18:33 on modular  [Seed = 1274517002]
   -------------------------------------


>> RelationIdeal({t*v^3-t*v^2-v^2+2*v,v^3-v^4});
                ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: SetEnum[RngMPolElt]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:18:51 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
RelationIdeal(t*v^3-t*v^2-v^2+2*v,v^3-v^4);

Output: Magma V2.10-22    Tue Jul 20 2004 00:18:48 on modular  [Seed = 1140825651]
   -------------------------------------


>> RelationIdeal(t*v^3-t*v^2-v^2+2*v,v^3-v^4);;
                ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: RngMPolElt, RngMPolElt

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:19:05 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
RelationIdeal([t*v^3-t*v^2-v^2+2*v,v^3-v^4]);

Output: Magma V2.10-22    Tue Jul 20 2004 00:19:02 on modular  [Seed = 2076681749]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: $.1, $.2
Basis:
[
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:21:04 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L2:=[1-v];
J:=ideal<S | L2>;
L:=L1 cat L2;
L;
K:=RelationIdeal(L);
K;

Output: Magma V2.10-22    Tue Jul 20 2004 00:21:02 on modular  [Seed = 1742453393]
   -------------------------------------

[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3,
    -v + 1
]
Ideal of Polynomial ring of rank 3 over Rational Field
Graded Reverse Lexicographical Order
Variables: $.1, $.2, $.3
Basis:
[
    $.3^4 - 3*$.3^3 + 3*$.3^2 + $.2 - $.3
]

Total time: 2.589 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:22:51 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L2:=[1-t*v];
J:=ideal<S | L2>;
L:=L1 cat L2;
L;
K:=RelationIdeal(L);
K;

Output: Magma V2.10-22    Tue Jul 20 2004 00:22:48 on modular  [Seed = 279760464]
   -------------------------------------

[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3,
    -v*t + 1
]
Ideal of Polynomial ring of rank 3 over Rational Field
Graded Reverse Lexicographical Order
Variables: $.1, $.2, $.3
Basis:
[
    $.2^2*$.3^4 + 2*$.1^2*$.2*$.3^2 - $.1*$.2*$.3^3 + $.1^4 - 5*$.1*$.2*$.3^2 + 
        $.2*$.3^3 - $.1^3 - 4*$.1*$.2*$.3 + 3*$.2*$.3^2 + 3*$.2*$.3 + $.2
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:23:17 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L2:=[1-t*v];
J:=ideal<S | L2>;
L:=L1 cat L2;
L;
K<a,b,c>:=RelationIdeal(L);
K;

Output: Magma V2.10-22    Tue Jul 20 2004 00:23:14 on modular  [Seed = 179754080]
   -------------------------------------

[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3,
    -v*t + 1
]
Ideal of Polynomial ring of rank 3 over Rational Field
Graded Reverse Lexicographical Order
Variables: a, b, c
Basis:
[
    b^2*c^4 + 2*a^2*b*c^2 - a*b*c^3 + a^4 - 5*a*b*c^2 + b*c^3 - a^3 - 4*a*b*c + 
        3*b*c^2 + 3*b*c + b
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:26:55 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L2:=[1-v];
J:=ideal<S | L2>;
L:=L1 cat L2;
L;
K<a,b,c>:=RelationIdeal(L);
K;

Output: Magma V2.10-22    Tue Jul 20 2004 00:26:52 on modular  [Seed = 79223632]
   -------------------------------------

[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3,
    -v + 1
]
Ideal of Polynomial ring of rank 3 over Rational Field
Graded Reverse Lexicographical Order
Variables: a, b, c
Basis:
[
    c^4 - 3*c^3 + 3*c^2 + b - c
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:27:34 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L2:=[v*(1-v)];
J:=ideal<S | L2>;
L:=L1 cat L2;
L;
K<a,b,c>:=RelationIdeal(L);
K;

Output: Magma V2.10-22    Tue Jul 20 2004 00:27:31 on modular  [Seed = 1015079767]
   -------------------------------------

[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3,
    -v^2 + v
]
Ideal of Polynomial ring of rank 3 over Rational Field
Graded Reverse Lexicographical Order
Variables: a, b, c
Basis:
[
    c^4 + 2*b*c^2 + b^2 - b*c
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:49:33 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
Coordinates(I,v*(1-v));


Output: Magma V2.10-22    Tue Jul 20 2004 00:49:30 on modular  [Seed = 12379136]
   -------------------------------------

[
    -v + 1
]

Total time: 2.639 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:50:22 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
Coordinates(I,v*(1-v));
Basis(I);

Output: Magma V2.10-22    Tue Jul 20 2004 00:50:20 on modular  [Seed = 3513595143]
   -------------------------------------

[
    -v + 1
]
[
    v
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:50:41 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
I;
Coordinates(I,v*(1-v));
Basis(I);

Output: Magma V2.10-22    Tue Jul 20 2004 00:50:39 on modular  [Seed = 4232058937]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3
]
[
    -v + 1
]
[
    v
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:51:01 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
I;
Basis(I);
Coordinates(I,v*(1-v));


Output: Magma V2.10-22    Tue Jul 20 2004 00:50:58 on modular  [Seed = 2603057011]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3
]
[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3
]
[
    -v + 1
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:51:17 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
I;
Basis(I);
Coordinates(I,v*(1-v));
Basis(I);

Output: Magma V2.10-22    Tue Jul 20 2004 00:51:14 on modular  [Seed = 2385668630]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Basis:
[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3
]
[
    v^3*t - v^2*t - v^2 + 2*v,
    -v^4 + v^3
]
[
    -v + 1
]
[
    v
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:51:49 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L:=GroebnerBasis(I);
L;
I;
Basis(I);
Coordinates(I,v*(1-v));
Basis(I);

Output: Magma V2.10-22    Tue Jul 20 2004 00:51:46 on modular  [Seed = 2953597960]
   -------------------------------------

[
    v
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Groebner basis:
[
    v
]
[
    v
]
[
    -v + 1
]
[
    v
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:53:18 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[t*v^3-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
SetVerbose("Groebner",4);
L:=GroebnerBasis(I);
L;
I;
Basis(I);
Coordinates(I,v*(1-v));
Basis(I);

Output: Magma V2.10-22    Tue Jul 20 2004 00:53:15 on modular  [Seed = 1307682861]
   -------------------------------------

(Recurse with homogenization)
********************
BUCHBERGER ALGORITHM
********************

Coefficient ring: Rational Field
Rank: 3
Order: Graded Reverse Lexicographical
Initial length: 2
Using monomial division list
Initial Reduce: false
Remove Redundant: true
New Reduce: true
Final Reduce: true
Homogenization: true
Initial basis:
[
    v^3*t - v^2*t*H - v^2*H^2 + 2*v*H^3,
    -v^4 + v^3*H
]
Remove Redundant Polynomials
Length: 2
Reduce 0
Reduce 1

Insert 0:
    v^3*t - v^2*t*H - v^2*H^2 + 2*v*H^3

    Total degree: 4


Insert 1:
    v^4 - v^3*H

    Total degree: 4

Reduce pairs

0 [0, 1] (0 done): Degree: 5, lcm = v^4*t
New 2:
    v^3*H^2 + [1 term] (max coefficient: 2)
Reduce 0/2: Old length 4Reduce 0
    Before: v^3*t + [3 terms] (max coefficient: 2)
    After:  v^3*t + [3 terms] (max coefficient: 2)
; New length 4
Reduce 1/2: Old length 2Reduce 1
    Before: v^4 + [1 term] (max coefficient: 1)
    After:  v^4 + [1 term] (max coefficient: 1)
; New length 2

Insert 2:
    v^3*H^2 - 2*v^2*H^3

    Total degree: 5

1 [0, 2] (1 done): Degree: 6, lcm = v^3*t*H^2
New 3:
    v^2*t*H^3 + [2 terms] (max coefficient: 2)
Reduce 0/3: Old length 4Reduce 0
    Before: v^3*t + [3 terms] (max coefficient: 2)
    After:  v^3*t + [3 terms] (max coefficient: 2)
; New length 4
Reduce 1/3: Old length 2Reduce 1
    Before: v^4 + [1 term] (max coefficient: 1)
    After:  v^4 + [1 term] (max coefficient: 1)
; New length 2
Reduce 2/3: Old length 2Reduce 2
    Before: v^3*H^2 + [1 term] (max coefficient: 2)
    After:  v^3*H^2 + [1 term] (max coefficient: 2)
; New length 2

Insert 3:
    v^2*t*H^3 - v^2*H^4 + 2*v*H^5

    Total degree: 6

1 [1, 2] (2 done): Degree: 6, lcm = v^4*H^2
New 4:
    v^2*H^4 (max coefficient: 1)
Reduce 0/4: Old length 4Reduce 0
    Before: v^3*t + [3 terms] (max coefficient: 2)
    After:  v^3*t + [3 terms] (max coefficient: 2)
; New length 4
Reduce 1/4: Old length 2Reduce 1
    Before: v^4 + [1 term] (max coefficient: 1)
    After:  v^4 + [1 term] (max coefficient: 1)
; New length 2
Reduce 2/4: Old length 2Reduce 2
    Before: v^3*H^2 + [1 term] (max coefficient: 2)
    After:  v^3*H^2 + [1 term] (max coefficient: 2)
; New length 2
Reduce 3/4: Old length 3Reduce 3
    Before: v^2*t*H^3 + [2 terms] (max coefficient: 2)
    After:  v^2*t*H^3 + [1 term] (max coefficient: 2)
; New length 2

Insert 4:
    v^2*H^4

    Total degree: 6

2 [3, 4] (3 done): Degree: 7, lcm = v^2*t*H^4
New 5:
    v*H^6 (max coefficient: 1)
Reduce 0/5: Old length 4Reduce 0
    Before: v^3*t + [3 terms] (max coefficient: 2)
    After:  v^3*t + [3 terms] (max coefficient: 2)
; New length 4
Reduce 1/5: Old length 2Reduce 1
    Before: v^4 + [1 term] (max coefficient: 1)
    After:  v^4 + [1 term] (max coefficient: 1)
; New length 2
Reduce 2/5: Old length 2Reduce 2
    Before: v^3*H^2 + [1 term] (max coefficient: 2)
    After:  v^3*H^2 + [1 term] (max coefficient: 2)
; New length 2
Reduce 3/5: Old length 2Reduce 3
    Before: v^2*t*H^3 + [1 term] (max coefficient: 2)
    After:  v^2*t*H^3 + [1 term] (max coefficient: 2)
; New length 2
Reduce 4/5: Old length 1Reduce 4
    Before: v^2*H^4 (max coefficient: 1)
    After:  v^2*H^4 (max coefficient: 1)
; New length 1

Insert 5:
    v*H^6

    Total degree: 7

1 [2, 4] (4 done): Degree: 7, lcm = v^3*H^4
0 [2, 3] (5 done): Degree: 7, lcm = v^3*t*H^3
Reduce final polynomials
Reduce 0
Reduce 1
Reduce 2
Reduce 3
Reduce 4
Reduce 5
Number of pairs reduced: 6
Reduction time: 0.000
Total Buchberger time: 0.000
Reduce Groebner Basis
Length: 6
Reduce Basis
Length: 6
Reduce 5
[
    v
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Groebner basis:
[
    v
]
[
    v
]
[
    -v + 1
]
[
    v
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:57:47 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L:=GroebnerBasis(I);
L;
I;
Basis(I);
Coordinates(I,v*(1-v));
Basis(I);

Output: Magma V2.10-22    Tue Jul 20 2004 00:57:44 on modular  [Seed = 112910357]
   -------------------------------------

[
    v^2 - v,
    v*t - v
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: v, t
Groebner basis:
[
    v^2 - v,
    v*t - v
]
[
    v^2 - v,
    v*t - v
]
[
    -1,
    0
]
[
    v^2 - v,
    v*t - v
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 00:59:26 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L:=GroebnerBasis(I);
L;
RelationIdeal(L1);

Output: Magma V2.10-22    Tue Jul 20 2004 00:59:24 on modular  [Seed = 613991123]
   -------------------------------------

[
    v^2 - v,
    v*t - v
]
Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: $.1, $.2
Basis:
[
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 01:00:13 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L:=GroebnerBasis(I);
L;
R<a,b,c>:=RelationIdeal(L1 cat L);

Output: Magma V2.10-22    Tue Jul 20 2004 01:00:11 on modular  [Seed = 4115207029]
   -------------------------------------

[
    v^2 - v,
    v*t - v
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 01:00:21 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L:=GroebnerBasis(I);
L;
R<a,b,c>:=RelationIdeal(L1 cat L);
R;

Output: Magma V2.10-22    Tue Jul 20 2004 01:00:18 on modular  [Seed = 3981511508]
   -------------------------------------

[
    v^2 - v,
    v*t - v
]
Ideal of Polynomial ring of rank 4 over Rational Field
Graded Reverse Lexicographical Order
Variables: a, b, c, $.4
Basis:
[
    b*$.4^4 + a^4 + a^3*$.4 - 8*a*b*$.4^2 - 6*b*$.4^3 + 8*a^2*b + 20*a*b*$.4 + 
        12*b*$.4^2 - 8*a*b + 16*b^2 - 8*b*$.4,
    c^4 + 2*b*c^2 + b^2 + b*c,
    a^2*c - 4*c^3 + b*$.4^2 - 4*a*b - 8*b*c - 4*b*$.4,
    a*c^2 + 2*c^3 + a*b + 2*b*c + b*$.4,
    c^2*$.4 - a*c - 2*c^2 + b*$.4,
    c*$.4^2 - a^2 - 4*a*c - 4*c^2 - a*$.4 - 2*c*$.4
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Tue Jul 20 01:00:31 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t>:=PolynomialRing(C,2,"lex");
L1:=[-t*v^2-v^2+2*v,v^3-v^4];
I:=ideal<S | L1>;
L:=GroebnerBasis(I);
L;
R<a,b,c,d>:=RelationIdeal(L1 cat L);
R;

Output: Magma V2.10-22    Tue Jul 20 2004 01:00:28 on modular  [Seed = 3847816018]
   -------------------------------------

[
    v^2 - v,
    v*t - v
]
Ideal of Polynomial ring of rank 4 over Rational Field
Graded Reverse Lexicographical Order
Variables: a, b, c, d
Basis:
[
    b*d^4 + a^4 + a^3*d - 8*a*b*d^2 - 6*b*d^3 + 8*a^2*b + 20*a*b*d + 12*b*d^2 - 
        8*a*b + 16*b^2 - 8*b*d,
    c^4 + 2*b*c^2 + b^2 + b*c,
    a^2*c - 4*c^3 + b*d^2 - 4*a*b - 8*b*c - 4*b*d,
    a*c^2 + 2*c^3 + a*b + 2*b*c + b*d,
    c^2*d - a*c - 2*c^2 + b*d,
    c*d^2 - a^2 - 4*a*c - 4*c^2 - a*d - 2*c*d
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508AC42F.dip0.t-ipconnect.de. (80.138.196.47)
Time: Tue Jul 20 03:27:23 2004

Input: RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;


Output: Magma V2.10-22    Tue Jul 20 2004 03:27:19 on modular  [Seed = 4248925389]
   -------------------------------------


Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:06:21 2004

Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
(a*1.0)/306081861814779930870284746489150827533191403596899901891268043568693301497428877548465065538600270841277018017409312617

Output: Magma V2.10-22    Tue Jul 20 2004 04:06:18 on modular  [Seed = 3730984149]
   -------------------------------------


>> (a*1.0)/3060818618147799308702847464891508275331914035968999018912680435686
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 3.010 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:07:29 2004

Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
((a*1.0)/306081861814779930870284746489150827533191403596899901891268043568693301497428877548465065538600270841277018017409312617*1.0) *271*8950393

Output: Magma V2.10-22    Tue Jul 20 2004 04:07:26 on modular  [Seed = 1943003583]
   -------------------------------------


>> ((a*1.0)/306081861814779930870284746489150827533191403596899901891268043568
     ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.899 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:56:12 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b:=3439122042862695852475109511114054241945970826931459571812000489535879792105942444364776017287643492598618179970891153
print(a mod b)

Output: Magma V2.10-22    Tue Jul 20 2004 04:56:09 on modular  [Seed = 1993009246]
   -------------------------------------


>> b:=343912204286269585247510951111405424194597082693145957181200048953587979
   ^
User error: bad syntax

>> print(a mod b);
         ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.659 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:56:37 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b:=3439122042862695852475109511114054241945970826931459571812000489535879792105942444364776017287643492598618179970891153
x := a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 04:56:34 on modular  [Seed = 2736733664]
   -------------------------------------


>> b:=343912204286269585247510951111405424194597082693145957181200048953587979
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.859 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:57:01 2004

Input: a := 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431

b :=3439122042862695852475109511114054241945970826931459571812000489535879792105942444364776017287643492598618179970891153

x := a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 04:56:58 on modular  [Seed = 3229376155]
   -------------------------------------


>> b :=34391220428626958524751095111140542419459708269314595718120004895358797
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:59:08 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b:=3439122042862695852475109511114054241945970826931459571812000489535879792105942444364776017287643492598618179970891153
x := a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 04:59:05 on modular  [Seed = 1775630258]
   -------------------------------------


>> b:=343912204286269585247510951111405424194597082693145957181200048953587979
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.879 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:59:38 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b:=0
x:= a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 04:59:35 on modular  [Seed = 2987273287]
   -------------------------------------


>> b:=0
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.899 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 04:59:52 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431

x:= a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 04:59:49 on modular  [Seed = 3630450655]
   -------------------------------------


>> x:= a mod b
   ^
User error: bad syntax

>> print(x);
         ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.550 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 05:00:11 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b=2
x:= a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 05:00:09 on modular  [Seed = 530808837]
   -------------------------------------


>> b=2
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 05:00:26 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b:=2
x:= a mod b
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 05:00:23 on modular  [Seed = 915056914]
   -------------------------------------


>> b:=2
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.849 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 05:00:41 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
c:=2
x:= a mod c
print(x)

Output: Magma V2.10-22    Tue Jul 20 2004 05:00:38 on modular  [Seed = 1324536187]
   -------------------------------------


>> c:=2
   ^
User error: bad syntax

>> print(x);
   ^
User error: bad syntax

Total time: 2.679 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 05:01:12 2004

Input: a:=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b:=3439122042862695852475109511114054241945970826931459571812000489535879792105942444364776017287643492598618179970891153


Output: Magma V2.10-22    Tue Jul 20 2004 05:01:09 on modular  [Seed = 2335642845]
   -------------------------------------


>> b:=343912204286269585247510951111405424194597082693145957181200048953587979
   ^
User error: bad syntax

Total time: 2.819 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Tue Jul 20 05:02:08 2004

Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431
b=3439122042862695852475109511114054241945970826931459571812000489535879792105942444364776017287643492598618179970891153
c=Mod(a,b)
c

Output: Magma V2.10-22    Tue Jul 20 2004 05:02:05 on modular  [Seed = 4182074999]
   -------------------------------------


>> b=3439122042862695852475109511114054241945970826931459571812000489535879792
   ^
User error: bad syntax

>> c;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Tue Jul 20 07:36:06 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,2);
M:=space![0,1-a,a,2-2a,-(1-a),a,0,1-a,a];
Eigenvalues(M);


Output: Magma V2.10-22    Tue Jul 20 2004 07:36:01 on modular  [Seed = 2786846020]
   -------------------------------------


>> M:=space![0,1-a,a,2-2a,-(1-a),a,0,1-a,a];
                        ^
User error: bad syntax

>> Eigenvalues(M);
               ^
User error: Identifier 'M' has not been declared or assigned

Total time: 2.879 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Tue Jul 20 07:36:25 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,2);
M:=space![0,1-a,a,2-2*a,-(1-a),a,0,1-a,a];
Eigenvalues(M);


Output: Magma V2.10-22    Tue Jul 20 2004 07:36:22 on modular  [Seed = 1525094824]
   -------------------------------------


>> M:=space![0,1-a,a,2-2*a,-(1-a),a,0,1-a,a];
           ^
Runtime error in '!': Sequence argument length (9) should be 4 to be coerced 
into a matrix

>> Eigenvalues(M);
               ^
User error: Identifier 'M' has not been declared or assigned

Total time: 2.859 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Tue Jul 20 07:36:42 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,2);
M:=space![0,1-a,a,2-2*a,-(1-a),a,0,1-a,a];
Eigenvalues(M);


Output: Magma V2.10-22    Tue Jul 20 2004 07:36:39 on modular  [Seed = 79251335]
   -------------------------------------


>> M:=space![0,1-a,a,2-2*a,-(1-a),a,0,1-a,a];
           ^
Runtime error in '!': Sequence argument length (9) should be 4 to be coerced 
into a matrix

>> Eigenvalues(M);
               ^
User error: Identifier 'M' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Tue Jul 20 07:36:55 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![0,1-a,a,2-2*a,-(1-a),a,0,1-a,a];
Eigenvalues(M);


Output: Magma V2.10-22    Tue Jul 20 2004 07:36:52 on modular  [Seed = 747728828]
   -------------------------------------

{
    <0, 1>,
    <1, 1>,
    <2*a - 2, 1>
}

Total time: 2.800 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host DN800c8407.Stanford.EDU. (128.12.132.7)
Time: Tue Jul 20 07:37:25 2004

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![0,1-a,a,2-2*a,-(1-a),a,0,1-a,a];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,0);
Eigenspace(M,2*a-2);


Output: Magma V2.10-22    Tue Jul 20 2004 07:37:22 on modular  [Seed = 3881477201]
   -------------------------------------

{
    <0, 1>,
    <1, 1>,
    <2*a - 2, 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
(1   -1/2/(a - 1)   (-a^2 + 3/2*a)/(a^2 - 2*a + 1))
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
( 1  0 -1)
Vector space of degree 3, dimension 1 over Univariate rational function field 
over Rational Field
Echelonized basis:
( 1 -1  0)

Total time: 2.849 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 220-136-171-93.dynamic.hinet.net. (220.136.171.93)
Time: Tue Jul 20 08:37:47 2004

Input: factor(10^64+1)

Output: Magma V2.10-22    Tue Jul 20 2004 08:37:44 on modular  [Seed = 981952636]
   -------------------------------------


>> factor(10^64+1);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 2.859 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host locutus.wh27.tu-dresden.de. (141.30.210.155)
Time: Tue Jul 20 13:15:03 2004

Input: jkjlkj

Output: Magma V2.10-22    Tue Jul 20 2004 13:14:59 on modular  [Seed = 2235078280]
   -------------------------------------


>> jkjlkj;
   ^
User error: Identifier 'jkjlkj' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Tue Jul 20 13:44:23 2004

Input: E:=EllipticCurve([-48,-272]);
RankBounds(E);


Output: Magma V2.10-22    Tue Jul 20 2004 13:44:21 on modular  [Seed = 898116835]
   -------------------------------------

1 1

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host gokyo.math.ubc.ca. (137.82.36.148)
Time: Tue Jul 20 13:45:51 2004

Input: E:=EllipticCurve([-21*16,-89*16]);
RankBounds(E);

Output: Magma V2.10-22    Tue Jul 20 2004 13:45:48 on modular  [Seed = 2059886613]
   -------------------------------------

0 2

Total time: 2.689 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 15:22:17 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
GenerList2:={(1-v)(v^2*delv-delt2),
(1-t2*v)*delt2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;


Output: Magma V2.10-22    Tue Jul 20 2004 15:22:14 on modular  [Seed = 2368781610]
   -------------------------------------


>> GenerList2:={(1-v)(v^2*delv-delt2),
                     ^
Runtime error: Bad argument types
Argument types given: RngMPolElt, RngMPolElt

>> I2:=ideal<S|GenerList2>;
               ^
User error: Identifier 'GenerList2' has not been declared or assigned

>> GB2:=GroebnerBasis(I2);
                      ^
User error: Identifier 'I2' has not been declared or assigned

>> print "Groebner Basis", GB2;
                           ^
User error: Identifier 'GB2' has not been declared or assigned

>> P2:=PrimaryDecomposition(I2);
                            ^
User error: Identifier 'I2' has not been declared or assigned

>> print "Primary Decomposition:", P2;
                                   ^
User error: Identifier 'P2' has not been declared or assigned

Total time: 2.659 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 15:22:30 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
GenerList2:={(1-v)*(v^2*delv-delt2),
(1-t2*v)*delt2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Tue Jul 20 2004 15:22:27 on modular  [Seed = 2753139734]
   -------------------------------------

Groebner Basis [
    v^3*delv - v^2*delv - v*delt2 + delt2,
    v*t2*delt2 - delt2,
    v*delv*delt2 + t2^2*delt2^2 - t2*delt2^2 - delv*delt2,
    t2^3*delt2^2 - t2^2*delt2^2 - t2*delv*delt2 + delv*delt2
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Non-radical, Primary, Non-prime
    Groebner basis:
    [
        v^2,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v*t2 - 1,
        v*delv - t2*delt2,
        t2^2*delt2 - delv
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ]
]

Total time: 3.099 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 15:24:24 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"lex");
S<v,t2,delv,delt2>:=PolynomialRing(C,4,"lex");
GenerList2:={(1-v)*(v^2*delv-delt2),
(1-t2*v)*delt2};
I2:=ideal<S|GenerList2>;
GB2:=GroebnerBasis(I2);
print "Groebner Basis", GB2;
Q2,P2:=PrimaryDecomposition(I2);
print "Primary Decomposition:", P2;

Output: Magma V2.10-22    Tue Jul 20 2004 15:24:21 on modular  [Seed = 4082025172]
   -------------------------------------

Groebner Basis [
    v^3*delv - v^2*delv - v*delt2 + delt2,
    v*t2*delt2 - delt2,
    v*delv*delt2 + t2^2*delt2^2 - t2*delt2^2 - delv*delt2,
    t2^3*delt2^2 - t2^2*delt2^2 - t2*delv*delt2 + delv*delt2
]
Primary Decomposition: [
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v*t2 - 1,
        v*delv - t2*delt2,
        t2^2*delt2 - delv
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        t2 - 1
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        v - 1,
        delt2
    ],
    Ideal of Polynomial ring of rank 4 over Rational Field
    Lexicographical Order
    Variables: v, t2, delv, delt2
    Dimension 2, Radical, Prime
    Groebner basis:
    [
        delv,
        delt2
    ]
]

Total time: 2.719 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:27:34 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal(x,x*t);
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:27:32 on modular  [Seed = 2920502927]
   -------------------------------------


>> I:=RelationIdeal(x,x*t);
                   ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: RngMPolElt, RngMPolElt

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:27:57 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal({x,x*t});
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:27:54 on modular  [Seed = 1641847229]
   -------------------------------------


>> I:=RelationIdeal({x,x*t});
                   ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: SetEnum[RngMPolElt]

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.810 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:28:10 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal([x,x*t]);
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:28:07 on modular  [Seed = 263387086]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: $.1, $.2
Basis:
[
]

Total time: 2.649 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:28:33 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal(R|[x,x*t]);
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:28:30 on modular  [Seed = 3346677567]
   -------------------------------------


>> I:=RelationIdeal(R|[x,x*t]);
                     ^
User error: bad syntax

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:28:43 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal(R,[x,x*t]);
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:28:40 on modular  [Seed = 4148825881]
   -------------------------------------


>> I:=RelationIdeal(R,[x,x*t]);
                   ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: RngMPol, SeqEnum[RngMPolElt]

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.879 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:29:02 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal(R,{x,x*t});
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:28:59 on modular  [Seed = 3087351845]
   -------------------------------------


>> I:=RelationIdeal(R,{x,x*t});
                   ^
Runtime error in 'RelationIdeal': Bad argument types
Argument types given: RngMPol, SetEnum[RngMPolElt]

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.899 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:29:18 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
I:=RelationIdeal([x,x*t],R);
I;

Output: Magma V2.10-22    Tue Jul 20 2004 20:29:15 on modular  [Seed = 2093057264]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: x, t
Basis:
[
]

Total time: 2.889 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:32:06 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
M<a,b>:=Module(R,2);
M;

Output: Magma V2.10-22    Tue Jul 20 2004 20:32:03 on modular  [Seed = 3864731453]
   -------------------------------------


>> M<a,b>:=Module(R,2);
    ^
Runtime error in 'AssignNames': Bad argument types
Argument types given: ModMPol ~, SeqEnum[MonStgElt]
Full Module of degree 2
TOP Order
Coefficient ring:
    Polynomial ring of rank 2 over Rational Field
    Lexicographical Order
    Variables: x, t

Total time: 2.899 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Tue Jul 20 20:33:40 2004

Input: C:=RationalField();
R<x,t>:=PolynomialRing(C,2);
M:=Module(R,2);
M;

Output: Magma V2.10-22    Tue Jul 20 2004 20:33:38 on modular  [Seed = 4248831046]
   -------------------------------------

Full Module of degree 2
TOP Order
Coefficient ring:
    Polynomial ring of rank 2 over Rational Field
    Lexicographical Order
    Variables: x, t

Total time: 2.599 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Wed Jul 21 03:53:35 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jul 21 2004 03:53:32 on modular  [Seed = 3897985097]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:39:41 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
x1+x2+x7+x9+x11+x12+x19+x20+x21+x25+x1*x4+x1*x6+x1*x9+x1*x13+x1*x16+x1*x21+x1*x23+x2*x3+x2*x4+x2*x5+x2*x7+x2*x9+x2*x10+x2*x13+x2*x16+x2*x17+x2*x18+x2*x19+x2*x20+x2*x23+x3*x6+x3*x9+x3*x11+x3*x16+x3*x19+x3*x20+x3*x22+x3*x25+x4*x6+x4*x7+x4*x9+x4*x10+x4*x11+x4*x12+x4*x16+x4*x17+x4*x18+x4*x19+x4*x22+x4*x24+x5*x6+x5*x12+x5*x13+x5*x14+x5*x18+x5*x20+x5*x21+x5*x23+x5*x25+x6*x8+x6*x11+x6*x12+x6*x13+x6*x14+x6*x15+x6*x17+x6*x19+x6*x20+x6*x22+x6*x23+x7*x8+x7*x9+x7*x10+x7*x11+x7*x12+x7*x15+x7*x16+x7*x18+x7*x19+x7*x21+x7*x22+x7*x24+x8*x10+x8*x11+x8*x15+x8*x19+x8*x23+x8*x24+x8*x25+x9*x11+x9*x12+x9*x13+x9*x15+x9*x16+x9*x17+x9*x21+x9*x22+x9*x24+x9*x25+x10*x11+x10*x12+x10*x15+x10*x16+x10*x17+x10*x18+x10*x19+x10*x21+x10*x22+x10*x23+x10*x24+x11*x12+x11*x13+x11*x14+x11*x17+x11*x20+x11*x25+x12*x13+x12*x15+x12*x16+x12*x19+x12*x20+x12*x22+x12*x23+x12*x24+x12*x25+x13*x14+x13*x15+x13*x16+x13*x18+x13*x19+x13*x20+x13*x24+x13*x25+x14*x16+x14*x18+x14*x20+x14*x22+x14*x24+x14*x25+x15*x16+x15*x17+x15*x19+x15*x22+x15*x25+x16*x17+x16*x18+x16*x19+x16*x21+x17*x18+x17*x19+x17*x20+x17*x21+x17*x22+x17*x23+x18*x19+x18*x22+x18*x23+x19*x20+x19*x21+x19*x22+x19*x23+x19*x24+x20*x22+x20*x25+x21*x22+x21*x24+x21*x25+x22*x25+x23*x25,
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x1+x2+x6+x7+x8+x10+x11+x13+x15+x16+x17+x19+x22+x23+x25+x1*x3+x1*x4+x1*x5+x1*x9+x1*x11+x1*x13+x1*x15+x1*x16+x1*x17+x1*x21+x1*x25+x2*x3+x2*x4+x2*x5+x2*x8+x2*x12+x2*x13+x2*x14+x2*x16+x2*x18+x2*x24+x3*x7+x3*x9+x3*x10+x3*x12+x3*x13+x3*x14+x3*x15+x3*x16+x3*x18+x3*x19+x3*x20+x3*x21+x3*x22+x3*x23+x3*x24+x4*x8+x4*x10+x4*x17+x4*x18+x4*x19+x4*x20+x4*x21+x4*x22+x4*x23+x4*x24+x4*x25+x5*x11+x5*x12+x5*x16+x5*x17+x5*x18+x5*x19+x5*x23+x5*x24+x5*x25+x6*x7+x6*x9+x6*x10+x6*x13+x6*x14+x6*x15+x6*x17+x6*x18+x6*x19+x6*x20+x6*x24+x6*x25+x7*x13+x7*x14+x7*x15+x7*x21+x8*x10+x8*x12+x8*x13+x8*x14+x8*x15+x8*x24+x8*x25+x9*x10+x9*x11+x9*x14+x9*x15+x9*x16+x9*x17+x9*x19+x9*x21+x9*x22+x9*x23+x9*x25+x10*x12+x10*x14+x10*x16+x10*x17+x10*x19+x10*x22+x10*x23+x11*x12+x11*x14+x11*x17+x11*x18+x11*x20+x11*x21+x11*x22+x11*x24+x12*x14+x12*x17+x12*x18+x12*x21+x12*x23+x12*x24+x12*x25+x13*x14+x13*x15+x13*x16+x13*x17+x13*x18+x13*x19+x13*x20+x13*x23+x13*x25+x14*x21+x14*x25+x15*x16+x15*x17+x15*x18+x15*x23+x16*x19+x16*x21+x16*x23+x17*x19+x17*x20+x17*x21+x17*x23+x17*x25+x18*x21+x18*x22+x19*x20+x19*x21+x20*x24+x21*x22+x21*x23+x21*x24+x21*x25+x22*x23+x22*x24+x22*x25,
1+x2+x4+x5+x6+x9+x10+x11+x12+x13+x15+x17+x18+x19+x20+x21+x22+x24+x25+x1*x5+x1*x8+x1*x10+x1*x11+x1*x13+x1*x14+x1*x17+x1*x18+x1*x19+x1*x22+x2*x3+x2*x4+x2*x5+x2*x7+x2*x8+x2*x10+x2*x12+x2*x14+x2*x15+x2*x16+x2*x22+x2*x23+x2*x25+x3*x8+x3*x9+x3*x11+x3*x12+x3*x13+x3*x15+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x24+x3*x25+x4*x8+x4*x9+x4*x11+x4*x14+x4*x17+x4*x18+x4*x21+x4*x22+x4*x23+x4*x24+x4*x25+x5*x8+x5*x9+x5*x12+x5*x14+x5*x16+x5*x20+x5*x21+x5*x22+x5*x23+x5*x25+x6*x7+x6*x8+x6*x9+x6*x12+x6*x15+x6*x18+x6*x20+x7*x9+x7*x10+x7*x13+x7*x15+x7*x18+x7*x19+x7*x20+x7*x21+x7*x22+x7*x23+x7*x24+x8*x17+x8*x18+x8*x19+x8*x20+x8*x22+x8*x23+x9*x10+x9*x12+x9*x14+x9*x15+x9*x17+x9*x21+x9*x22+x9*x24+x10*x11+x10*x14+x10*x16+x10*x17+x10*x18+x10*x20+x10*x25+x11*x12+x11*x16+x11*x18+x11*x21+x11*x23+x11*x25+x12*x16+x12*x18+x12*x19+x12*x20+x12*x22+x12*x23+x12*x24+x12*x25+x13*x14+x13*x15+x13*x20+x13*x21+x13*x22+x13*x24+x14*x16+x14*x17+x14*x19+x14*x20+x14*x24+x15*x16+x15*x17+x15*x18+x15*x20+x15*x22+x15*x23+x15*x24+x15*x25+x16*x17+x16*x21+x16*x22+x16*x24+x17*x19+x17*x21+x17*x25+x18*x22+x18*x24+x19*x20+x20*x21+x20*x22+x20*x24+x21*x22+x21*x25+x23*x25,
1+x1+x3+x5+x13+x14+x16+x17+x18+x19+x20+x22+x23+x1*x2+x1*x7+x1*x8+x1*x9+x1*x11+x1*x13+x1*x15+x1*x16+x1*x19+x1*x20+x1*x21+x2*x7+x2*x11+x2*x13+x2*x14+x2*x15+x2*x16+x2*x21+x2*x23+x2*x24+x2*x25+x3*x4+x3*x5+x3*x8+x3*x10+x3*x11+x3*x13+x3*x14+x3*x15+x3*x17+x3*x18+x3*x19+x3*x21+x3*x22+x3*x23+x3*x24+x3*x25+x4*x6+x4*x7+x4*x8+x4*x9+x4*x11+x4*x13+x4*x14+x4*x16+x4*x17+x4*x20+x4*x21+x4*x25+x5*x7+x5*x9+x5*x12+x5*x13+x5*x14+x5*x15+x5*x19+x5*x20+x5*x22+x5*x23+x6*x7+x6*x8+x6*x9+x6*x10+x6*x13+x6*x15+x6*x17+x6*x21+x6*x25+x7*x9+x7*x11+x7*x13+x7*x15+x7*x17+x7*x21+x7*x23+x7*x25+x8*x11+x8*x14+x8*x18+x8*x19+x8*x22+x8*x24+x8*x25+x9*x10+x9*x13+x9*x17+x9*x20+x9*x21+x9*x22+x9*x23+x9*x24+x9*x25+x10*x11+x10*x14+x10*x16+x10*x17+x10*x21+x10*x24+x10*x25+x11*x12+x11*x16+x11*x19+x11*x21+x11*x23+x11*x25+x12*x13+x12*x16+x12*x17+x12*x19+x12*x20+x13*x14+x13*x15+x13*x16+x13*x17+x13*x19+x13*x20+x13*x21+x13*x22+x13*x24+x14*x16+x14*x19+x14*x20+x14*x22+x14*x24+x15*x17+x15*x23+x15*x24+x16*x22+x16*x24+x17*x18+x17*x21+x17*x22+x17*x23+x17*x24+x17*x25+x18*x19+x18*x20+x18*x22+x18*x23+x19*x21+x19*x25+x20*x23+x21*x22+x21*x23+x21*x24+x22*x23,
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SetVerbose("Groebner", 1);
time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:39:30 on modular  [Seed = 1992847860]
   -------------------------------------


>> 22*x25+x23*x24+x23*x25,x1+1    x2+1];
                                  ^
User error: bad syntax

>> time G := GroebnerBasis(B);
                           ^
User error: Identifier 'B' has not been declared or assigned

>> G;;
   ^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.629 seconds, Total memory usage: 3.69MB


************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:40:22 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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x1+x2+x3+x4+x5+x6+x8+x9+x10+x11+x12+x16+x19+x21+x22+x24+x1*x3+x1*x5+x1*x6+x1*x8+x1*x9+x1*x11+x1*x12+x1*x13+x1*x15+x1*x16+x1*x18+x1*x19+x1*x22+x1*x25+x2*x3+x2*x4+x2*x5+x2*x8+x2*x10+x2*x15+x2*x19+x2*x20+x2*x22+x2*x25+x3*x6+x3*x7+x3*x9+x3*x10+x3*x11+x3*x12+x3*x13+x3*x17+x3*x18+x3*x19+x3*x22+x3*x23+x3*x25+x4*x5+x4*x6+x4*x9+x4*x11+x4*x12+x4*x14+x4*x20+x4*x21+x4*x24+x5*x7+x5*x9+x5*x14+x5*x15+x5*x18+x5*x20+x5*x22+x5*x23+x5*x24+x5*x25+x6*x7+x6*x9+x6*x10+x6*x11+x6*x14+x6*x18+x6*x19+x6*x21+x6*x22+x6*x23+x7*x8+x7*x15+x7*x17+x7*x18+x7*x19+x7*x20+x7*x23+x7*x24+x8*x9+x8*x10+x8*x11+x8*x12+x8*x16+x8*x19+x8*x20+x8*x22+x8*x24+x9*x10+x9*x11+x9*x12+x9*x14+x9*x15+x9*x17+x9*x19+x9*x20+x9*x22+x9*x23+x10*x11+x10*x13+x10*x14+x10*x15+x10*x17+x10*x18+x10*x19+x10*x22+x10*x23+x10*x24+x11*x12+x11*x13+x11*x14+x11*x15+x11*x17+x11*x18+x11*x23+x11*x25+x12*x13+x12*x16+x12*x17+x12*x18+x12*x20+x12*x21+x13*x14+x13*x15+x13*x17+x13*x20+x13*x22+x13*x24+x13*x25+x14*x15+x14*x16+x14*x18+x14*x21+x14*x22+x14*x23+x14*x24+x15*x16+x15*x18+x15*x20+x15*x22+x15*x23+x15*x24+x15*x25+x16*x17+x16*x18+x16*x20+x16*x21+x16*x22+x16*x23+x16*x24+x16*x25+x17*x19+x17*x21+x17*x24+x17*x25+x18*x19+x18*x20+x18*x21+x18*x25+x19*x21+x19*x22+x19*x23+x19*x24+x19*x25+x20*x21+x20*x22+x20*x24+x20*x25+x21*x23+x21*x25+x22*x23+x22*x24+x23*x24+x23*x25+x24*x25,
x1+x3+x5+x6+x9+x11+x12+x15+x16+x17+x21+x22+x23+x25+x1*x2+x1*x4+x1*x8+x1*x10+x1*x12+x1*x13+x1*x16+x1*x17+x1*x19+x1*x20+x1*x22+x1*x24+x1*x25+x2*x4+x2*x6+x2*x7+x2*x10+x2*x14+x2*x19+x2*x20+x2*x21+x2*x22+x2*x23+x2*x24+x2*x25+x3*x11+x3*x12+x3*x13+x3*x17+x3*x18+x3*x19+x3*x23+x4*x6+x4*x8+x4*x10+x4*x11+x4*x12+x4*x13+x4*x15+x4*x22+x5*x6+x5*x7+x5*x9+x5*x10+x5*x11+x5*x12+x5*x13+x5*x14+x5*x15+x5*x17+x5*x18+x5*x23+x6*x7+x6*x8+x6*x10+x6*x11+x6*x12+x6*x15+x6*x16+x6*x17+x6*x21+x6*x24+x7*x9+x7*x11+x7*x12+x7*x17+x7*x18+x7*x19+x7*x22+x7*x23+x7*x24+x8*x10+x8*x13+x8*x15+x8*x16+x8*x19+x8*x20+x8*x24+x8*x25+x9*x10+x9*x11+x9*x13+x9*x14+x9*x15+x9*x16+x9*x17+x9*x18+x9*x24+x9*x25+x10*x12+x10*x13+x10*x17+x10*x19+x10*x22+x10*x24+x10*x25+x11*x13+x11*x14+x11*x20+x11*x23+x11*x24+x11*x25+x12*x14+x12*x15+x12*x17+x12*x18+x12*x19+x12*x20+x12*x24+x13*x17+x13*x21+x14*x15+x14*x19+x14*x22+x14*x24+x14*x25+x15*x17+x15*x18+x15*x20+x15*x23+x16*x19+x16*x21+x16*x22+x16*x25+x17*x18+x17*x20+x17*x21+x17*x23+x17*x25+x18*x21+x18*x22+x18*x25+x19*x20+x19*x22+x20*x21+x20*x23+x20*x24+x20*x25+x21*x22+x21*x23+x21*x24+x21*x25+x22*x23+x22*x24+x23*x25,
x1+x2+x5+x6+x8+x9+x10+x16+x19+x21+x22+x23+x24+x25+x1*x2+x1*x4+x1*x5+x1*x6+x1*x7+x1*x8+x1*x11+x1*x15+x1*x16+x1*x17+x1*x19+x1*x20+x1*x23+x2*x3+x2*x8+x2*x10+x2*x13+x2*x15+x2*x17+x2*x21+x2*x22+x2*x23+x2*x25+x3*x4+x3*x11+x3*x12+x3*x13+x3*x14+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x25+x4*x7+x4*x11+x4*x13+x4*x18+x4*x20+x4*x22+x4*x24+x4*x25+x5*x7+x5*x9+x5*x12+x5*x14+x5*x17+x6*x7+x6*x8+x6*x9+x6*x10+x6*x11+x6*x13+x6*x15+x6*x20+x6*x21+x6*x22+x6*x24+x7*x10+x7*x12+x7*x15+x7*x16+x7*x18+x7*x20+x7*x22+x7*x23+x7*x25+x8*x11+x8*x12+x8*x13+x8*x16+x8*x17+x8*x19+x8*x21+x9*x10+x9*x15+x9*x16+x9*x20+x9*x23+x10*x12+x10*x13+x10*x16+x10*x19+x10*x20+x10*x22+x10*x23+x10*x24+x11*x14+x11*x20+x11*x21+x11*x22+x11*x23+x11*x24+x11*x25+x12*x18+x12*x22+x12*x23+x13*x15+x13*x17+x13*x18+x13*x20+x13*x21+x13*x23+x13*x24+x13*x25+x14*x15+x14*x21+x14*x23+x14*x25+x15*x16+x15*x17+x15*x19+x15*x20+x15*x21+x15*x22+x15*x23+x16*x17+x16*x19+x16*x22+x16*x23+x16*x24+x17*x21+x17*x22+x17*x23+x17*x24+x18*x21+x19*x20+x19*x22+x19*x24+x20*x22+x20*x23+x20*x24+x20*x25+x21*x24+x22*x23+x22*x24+x22*x25+x23*x24+x23*x25,x1+1    ,x2+1];

SetVerbose("Groebner", 1);
time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:39:59 on modular  [Seed = 2143385824]
   -------------------------------------

********************
BUCHBERGER ALGORITHM
********************

Coefficient ring: GF(2)
Rank: 25
Order: Graded Reverse Lexicographical
Initial length: 52
Using monomial division list
Initial Reduce: true
Remove Redundant: true
New Reduce: false
Final Reduce: true
Homogenization: false
Reduce Basis
Length: 52
New polynomial 0, degree: 1; pairs done: 0, remaining: 0
New polynomial 1, degree: 1; pairs done: 0, remaining: 0
New polynomial 2, degree: 2; pairs done: 0, remaining: 0
New polynomial 3, degree: 2; pairs done: 0, remaining: 0
New polynomial 4, degree: 2; pairs done: 0, remaining: 0
New polynomial 5, degree: 2; pairs done: 0, remaining: 0
New polynomial 6, degree: 2; pairs done: 0, remaining: 0
New polynomial 7, degree: 2; pairs done: 0, remaining: 0
New polynomial 8, degree: 2; pairs done: 0, remaining: 0
New polynomial 9, degree: 2; pairs done: 0, remaining: 0
New polynomial 10, degree: 2; pairs done: 0, remaining: 0
New polynomial 11, degree: 2; pairs done: 0, remaining: 0
New polynomial 12, degree: 2; pairs done: 0, remaining: 0
New polynomial 13, degree: 2; pairs done: 0, remaining: 0
New polynomial 14, degree: 2; pairs done: 0, remaining: 0
New polynomial 15, degree: 2; pairs done: 0, remaining: 0
New polynomial 16, degree: 2; pairs done: 0, remaining: 0
New polynomial 17, degree: 2; pairs done: 0, remaining: 0
New polynomial 18, degree: 2; pairs done: 0, remaining: 0
New polynomial 19, degree: 2; pairs done: 0, remaining: 0
New polynomial 20, degree: 2; pairs done: 0, remaining: 0
New polynomial 21, degree: 2; pairs done: 0, remaining: 0
New polynomial 22, degree: 2; pairs done: 0, remaining: 0
New polynomial 23, degree: 2; pairs done: 0, remaining: 0
New polynomial 24, degree: 2; pairs done: 0, remaining: 1
New polynomial 25, degree: 2; pairs done: 0, remaining: 4
New polynomial 26, degree: 2; pairs done: 0, remaining: 6
New polynomial 27, degree: 2; pairs done: 0, remaining: 9
New polynomial 28, degree: 2; pairs done: 0, remaining: 12
New polynomial 29, degree: 2; pairs done: 0, remaining: 15
New polynomial 30, degree: 2; pairs done: 0, remaining: 20
New polynomial 31, degree: 2; pairs done: 0, remaining: 25
New polynomial 32, degree: 2; pairs done: 0, remaining: 29
New polynomial 33, degree: 2; pairs done: 0, remaining: 35
New polynomial 34, degree: 2; pairs done: 0, remaining: 40
New polynomial 35, degree: 2; pairs done: 0, remaining: 46
New polynomial 36, degree: 2; pairs done: 0, remaining: 52
New polynomial 37, degree: 2; pairs done: 0, remaining: 58
New polynomial 38, degree: 2; pairs done: 0, remaining: 64
New polynomial 39, degree: 2; pairs done: 0, remaining: 71
New polynomial 40, degree: 2; pairs done: 0, remaining: 77
New polynomial 41, degree: 2; pairs done: 0, remaining: 84
New polynomial 42, degree: 2; pairs done: 0, remaining: 92
New polynomial 43, degree: 2; pairs done: 0, remaining: 99
New polynomial 44, degree: 2; pairs done: 0, remaining: 107
New polynomial 45, degree: 2; pairs done: 0, remaining: 114
New polynomial 46, degree: 2; pairs done: 0, remaining: 121
New polynomial 47, degree: 2; pairs done: 0, remaining: 128
New polynomial 48, degree: 2; pairs done: 0, remaining: 136
New polynomial 49, degree: 2; pairs done: 0, remaining: 144
Reduce pairs
New polynomial 50, degree: 3; pairs done: 1, remaining: 152
New polynomial 51, degree: 3; pairs done: 2, remaining: 160
New polynomial 52, degree: 3; pairs done: 3, remaining: 169
New polynomial 53, degree: 3; pairs done: 4, remaining: 177
New polynomial 54, degree: 3; pairs done: 5, remaining: 186
New polynomial 55, degree: 3; pairs done: 6, remaining: 195
New polynomial 56, degree: 3; pairs done: 7, remaining: 204
New polynomial 57, degree: 3; pairs done: 8, remaining: 213
New polynomial 58, degree: 3; pairs done: 9, remaining: 222
New polynomial 59, degree: 3; pairs done: 10, remaining: 231
New polynomial 60, degree: 3; pairs done: 11, remaining: 240
New polynomial 61, degree: 3; pairs done: 12, remaining: 250
New polynomial 62, degree: 3; pairs done: 13, remaining: 259
New polynomial 63, degree: 3; pairs done: 14, remaining: 268
New polynomial 64, degree: 3; pairs done: 15, remaining: 277
New polynomial 65, degree: 3; pairs done: 16, remaining: 287
New polynomial 66, degree: 3; pairs done: 17, remaining: 297
New polynomial 67, degree: 3; pairs done: 18, remaining: 307
New polynomial 68, degree: 3; pairs done: 19, remaining: 317
New polynomial 69, degree: 3; pairs done: 20, remaining: 327
New polynomial 70, degree: 3; pairs done: 21, remaining: 337
New polynomial 71, degree: 3; pairs done: 22, remaining: 347
New polynomial 72, degree: 3; pairs done: 23, remaining: 357
New polynomial 73, degree: 3; pairs done: 24, remaining: 367
New polynomial 74, degree: 3; pairs done: 25, remaining: 377
New polynomial 75, degree: 3; pairs done: 26, remaining: 387
New polynomial 76, degree: 3; pairs done: 27, remaining: 397
New polynomial 77, degree: 3; pairs done: 28, remaining: 407
New polynomial 78, degree: 3; pairs done: 29, remaining: 418
New polynomial 79, degree: 3; pairs done: 30, remaining: 428
New polynomial 80, degree: 3; pairs done: 31, remaining: 438
New polynomial 81, degree: 3; pairs done: 32, remaining: 448
New polynomial 82, degree: 3; pairs done: 33, remaining: 458
New polynomial 83, degree: 3; pairs done: 34, remaining: 468
New polynomial 84, degree: 3; pairs done: 35, remaining: 478
New polynomial 85, degree: 3; pairs done: 36, remaining: 489
New polynomial 86, degree: 3; pairs done: 37, remaining: 500
New polynomial 87, degree: 3; pairs done: 38, remaining: 511
New polynomial 88, degree: 3; pairs done: 39, remaining: 522
New polynomial 89, degree: 3; pairs done: 40, remaining: 533
New polynomial 90, degree: 3; pairs done: 41, remaining: 544
New polynomial 91, degree: 3; pairs done: 42, remaining: 555
New polynomial 92, degree: 3; pairs done: 43, remaining: 566
New polynomial 93, degree: 3; pairs done: 44, remaining: 577
New polynomial 94, degree: 3; pairs done: 45, remaining: 588
New polynomial 95, degree: 3; pairs done: 46, remaining: 599
New polynomial 96, degree: 3; pairs done: 47, remaining: 610
New polynomial 97, degree: 3; pairs done: 48, remaining: 621
New polynomial 98, degree: 3; pairs done: 49, remaining: 632
New polynomial 99, degree: 3; pairs done: 50, remaining: 643
New polynomial 100, degree: 3; pairs done: 51, remaining: 654
New polynomial 101, degree: 3; pairs done: 52, remaining: 665
New polynomial 102, degree: 3; pairs done: 53, remaining: 676
New polynomial 103, degree: 3; pairs done: 54, remaining: 687
New polynomial 104, degree: 3; pairs done: 55, remaining: 698
New polynomial 105, degree: 3; pairs done: 56, remaining: 709
New polynomial 106, degree: 3; pairs done: 57, remaining: 720
New polynomial 107, degree: 3; pairs done: 58, remaining: 731
New polynomial 108, degree: 3; pairs done: 59, remaining: 742
New polynomial 109, degree: 3; pairs done: 60, remaining: 753
New polynomial 110, degree: 3; pairs done: 61, remaining: 764
New polynomial 111, degree: 3; pairs done: 62, remaining: 776
New polynomial 112, degree: 3; pairs done: 63, remaining: 787
New polynomial 113, degree: 3; pairs done: 64, remaining: 798
New polynomial 114, degree: 3; pairs done: 65, remaining: 810
New polynomial 115, degree: 3; pairs done: 66, remaining: 821
New polynomial 116, degree: 3; pairs done: 67, remaining: 833
New polynomial 117, degree: 3; pairs done: 68, remaining: 845
New polynomial 118, degree: 3; pairs done: 69, remaining: 857
New polynomial 119, degree: 3; pairs done: 70, remaining: 869
New polynomial 120, degree: 3; pairs done: 71, remaining: 881
New polynomial 121, degree: 3; pairs done: 72, remaining: 893
New polynomial 122, degree: 3; pairs done: 73, remaining: 905
New polynomial 123, degree: 3; pairs done: 74, remaining: 917
New polynomial 124, degree: 3; pairs done: 75, remaining: 929
New polynomial 125, degree: 3; pairs done: 76, remaining: 941
New polynomial 126, degree: 3; pairs done: 77, remaining: 953
New polynomial 127, degree: 3; pairs done: 78, remaining: 965
New polynomial 128, degree: 3; pairs done: 79, remaining: 977
New polynomial 129, degree: 3; pairs done: 80, remaining: 989
New polynomial 130, degree: 3; pairs done: 81, remaining: 1001
New polynomial 131, degree: 3; pairs done: 82, remaining: 1013
New polynomial 132, degree: 3; pairs done: 83, remaining: 1025
New polynomial 133, degree: 3; pairs done: 84, remaining: 1037
New polynomial 134, degree: 3; pairs done: 85, remaining: 1049
New polynomial 135, degree: 3; pairs done: 86, remaining: 1061
New polynomial 136, degree: 3; pairs done: 87, remaining: 1073
New polynomial 137, degree: 3; pairs done: 88, remaining: 1085
New polynomial 138, degree: 3; pairs done: 89, remaining: 1097
New polynomial 139, degree: 3; pairs done: 90, remaining: 1109
New polynomial 140, degree: 3; pairs done: 91, remaining: 1121
New polynomial 141, degree: 3; pairs done: 92, remaining: 1133
New polynomial 142, degree: 3; pairs done: 93, remaining: 1145
New polynomial 143, degree: 3; pairs done: 94, remaining: 1157
New polynomial 144, degree: 3; pairs done: 95, remaining: 1169
New polynomial 145, degree: 3; pairs done: 96, remaining: 1181
New polynomial 146, degree: 3; pairs done: 97, remaining: 1193
New polynomial 147, degree: 3; pairs done: 98, remaining: 1205
New polynomial 148, degree: 3; pairs done: 99, remaining: 1217
Pairs done: 100, remaining: 1216, current degree: 3, elapsed time: 5.819
New polynomial 149, degree: 3; pairs done: 100, remaining: 1229
New polynomial 150, degree: 3; pairs done: 101, remaining: 1241
New polynomial 151, degree: 3; pairs done: 102, remaining: 1253
New polynomial 152, degree: 3; pairs done: 103, remaining: 1265
New polynomial 153, degree: 3; pairs done: 104, remaining: 1278
New polynomial 154, degree: 3; pairs done: 105, remaining: 1290
New polynomial 155, degree: 3; pairs done: 106, remaining: 1302
New polynomial 156, deg
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:41:06 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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SetVerbose("Groebner", 0);
time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:40:44 on modular  [Seed = 1524912662]
   -------------------------------------



************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:42:03 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
x1+x2+x7+x9+x11+x12+x19+x20+x21+x25+x1*x4+x1*x6+x1*x9+x1*x13+x1*x16+x1*x21+x1*x23+x2*x3+x2*x4+x2*x5+x2*x7+x2*x9+x2*x10+x2*x13+x2*x16+x2*x17+x2*x18+x2*x19+x2*x20+x2*x23+x3*x6+x3*x9+x3*x11+x3*x16+x3*x19+x3*x20+x3*x22+x3*x25+x4*x6+x4*x7+x4*x9+x4*x10+x4*x11+x4*x12+x4*x16+x4*x17+x4*x18+x4*x19+x4*x22+x4*x24+x5*x6+x5*x12+x5*x13+x5*x14+x5*x18+x5*x20+x5*x21+x5*x23+x5*x25+x6*x8+x6*x11+x6*x12+x6*x13+x6*x14+x6*x15+x6*x17+x6*x19+x6*x20+x6*x22+x6*x23+x7*x8+x7*x9+x7*x10+x7*x11+x7*x12+x7*x15+x7*x16+x7*x18+x7*x19+x7*x21+x7*x22+x7*x24+x8*x10+x8*x11+x8*x15+x8*x19+x8*x23+x8*x24+x8*x25+x9*x11+x9*x12+x9*x13+x9*x15+x9*x16+x9*x17+x9*x21+x9*x22+x9*x24+x9*x25+x10*x11+x10*x12+x10*x15+x10*x16+x10*x17+x10*x18+x10*x19+x10*x21+x10*x22+x10*x23+x10*x24+x11*x12+x11*x13+x11*x14+x11*x17+x11*x20+x11*x25+x12*x13+x12*x15+x12*x16+x12*x19+x12*x20+x12*x22+x12*x23+x12*x24+x12*x25+x13*x14+x13*x15+x13*x16+x13*x18+x13*x19+x13*x20+x13*x24+x13*x25+x14*x16+x14*x18+x14*x20+x14*x22+x14*x24+x14*x25+x15*x16+x15*x17+x15*x19+x15*x22+x15*x25+x16*x17+x16*x18+x16*x19+x16*x21+x17*x18+x17*x19+x17*x20+x17*x21+x17*x22+x17*x23+x18*x19+x18*x22+x18*x23+x19*x20+x19*x21+x19*x22+x19*x23+x19*x24+x20*x22+x20*x25+x21*x22+x21*x24+x21*x25+x22*x25+x23*x25,
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SetVerbose("Groebner", 0);
time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:41:40 on modular  [Seed = 580659750]
   -------------------------------------



************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:42:46 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
x1+x2+x7+x9+x11+x12+x19+x20+x21+x25+x1*x4+x1*x6+x1*x9+x1*x13+x1*x16+x1*x21+x1*x23+x2*x3+x2*x4+x2*x5+x2*x7+x2*x9+x2*x10+x2*x13+x2*x16+x2*x17+x2*x18+x2*x19+x2*x20+x2*x23+x3*x6+x3*x9+x3*x11+x3*x16+x3*x19+x3*x20+x3*x22+x3*x25+x4*x6+x4*x7+x4*x9+x4*x10+x4*x11+x4*x12+x4*x16+x4*x17+x4*x18+x4*x19+x4*x22+x4*x24+x5*x6+x5*x12+x5*x13+x5*x14+x5*x18+x5*x20+x5*x21+x5*x23+x5*x25+x6*x8+x6*x11+x6*x12+x6*x13+x6*x14+x6*x15+x6*x17+x6*x19+x6*x20+x6*x22+x6*x23+x7*x8+x7*x9+x7*x10+x7*x11+x7*x12+x7*x15+x7*x16+x7*x18+x7*x19+x7*x21+x7*x22+x7*x24+x8*x10+x8*x11+x8*x15+x8*x19+x8*x23+x8*x24+x8*x25+x9*x11+x9*x12+x9*x13+x9*x15+x9*x16+x9*x17+x9*x21+x9*x22+x9*x24+x9*x25+x10*x11+x10*x12+x10*x15+x10*x16+x10*x17+x10*x18+x10*x19+x10*x21+x10*x22+x10*x23+x10*x24+x11*x12+x11*x13+x11*x14+x11*x17+x11*x20+x11*x25+x12*x13+x12*x15+x12*x16+x12*x19+x12*x20+x12*x22+x12*x23+x12*x24+x12*x25+x13*x14+x13*x15+x13*x16+x13*x18+x13*x19+x13*x20+x13*x24+x13*x25+x14*x16+x14*x18+x14*x20+x14*x22+x14*x24+x14*x25+x15*x16+x15*x17+x15*x19+x15*x22+x15*x25+x16*x17+x16*x18+x16*x19+x16*x21+x17*x18+x17*x19+x17*x20+x17*x21+x17*x22+x17*x23+x18*x19+x18*x22+x18*x23+x19*x20+x19*x21+x19*x22+x19*x23+x19*x24+x20*x22+x20*x25+x21*x22+x21*x24+x21*x25+x22*x25+x23*x25,
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SetVerbose("Groebner", 0);
time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:42:24 on modular  [Seed = 747775196]
   -------------------------------------



************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:43:28 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");
B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:43:05 on modular  [Seed = 881474797]
   -------------------------------------



************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:43:53 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");
B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:43:46 on modular  [Seed = 1032009151]
   -------------------------------------

Time: 4.360
[
    x1 + 1,
    x2 + 1,
    x3,
    x4 + 1,
    x5 + 1,
    x6 + 1,
    x7,
    x8,
    x9 + 1,
    x10 + 1,
    x11,
    x12 + 1,
    x13 + 1,
    x14 + 1,
    x15,
    x16,
    x17,
    x18 + 1,
    x19,
    x20 + 1,
    x21 + 1,
    x22,
    x23,
    x24 + 1,
    x25 + 1
]

Total time: 7.109 seconds, Total memory usage: 6.58MB


************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:44:17 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");
B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:44:06 on modular  [Seed = 96144787]
   -------------------------------------

Time: 8.410
[
    x1 + 1,
    x2 + 1,
    x3,
    x4 + 1,
    x5 + 1,
    x6 + 1,
    x7,
    x8,
    x9 + 1,
    x10 + 1,
    x11,
    x12 + 1,
    x13 + 1,
    x14 + 1,
    x15,
    x16,
    x17,
    x18 + 1,
    x19,
    x20 + 1,
    x21 + 1,
    x22,
    x23,
    x24 + 1,
    x25 + 1
]

Total time: 11.189 seconds, Total memory usage: 6.79MB


************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:44:51 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");
B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:44:28 on modular  [Seed = 229835873]
   -------------------------------------



************** MAGMA *****************
Host machine107.rd.francetelecom.com. (193.49.124.107)
Time: Wed Jul 21 06:49:26 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");
B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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x1+x2+x3+x4+x5+x6+x8+x9+x10+x11+x12+x16+x19+x21+x22+x24+x1*x3+x1*x5+x1*x6+x1*x8+x1*x9+x1*x11+x1*x12+x1*x13+x1*x15+x1*x16+x1*x18+x1*x19+x1*x22+x1*x25+x2*x3+x2*x4+x2*x5+x2*x8+x2*x10+x2*x15+x2*x19+x2*x20+x2*x22+x2*x25+x3*x6+x3*x7+x3*x9+x3*x10+x3*x11+x3*x12+x3*x13+x3*x17+x3*x18+x3*x19+x3*x22+x3*x23+x3*x25+x4*x5+x4*x6+x4*x9+x4*x11+x4*x12+x4*x14+x4*x20+x4*x21+x4*x24+x5*x7+x5*x9+x5*x14+x5*x15+x5*x18+x5*x20+x5*x22+x5*x23+x5*x24+x5*x25+x6*x7+x6*x9+x6*x10+x6*x11+x6*x14+x6*x18+x6*x19+x6*x21+x6*x22+x6*x23+x7*x8+x7*x15+x7*x17+x7*x18+x7*x19+x7*x20+x7*x23+x7*x24+x8*x9+x8*x10+x8*x11+x8*x12+x8*x16+x8*x19+x8*x20+x8*x22+x8*x24+x9*x10+x9*x11+x9*x12+x9*x14+x9*x15+x9*x17+x9*x19+x9*x20+x9*x22+x9*x23+x10*x11+x10*x13+x10*x14+x10*x15+x10*x17+x10*x18+x10*x19+x10*x22+x10*x23+x10*x24+x11*x12+x11*x13+x11*x14+x11*x15+x11*x17+x11*x18+x11*x23+x11*x25+x12*x13+x12*x16+x12*x17+x12*x18+x12*x20+x12*x21+x13*x14+x13*x15+x13*x17+x13*x20+x13*x22+x13*x24+x13*x25+x14*x15+x14*x16+x14*x18+x14*x21+x14*x22+x14*x23+x14*x24+x15*x16+x15*x18+x15*x20+x15*x22+x15*x23+x15*x24+x15*x25+x16*x17+x16*x18+x16*x20+x16*x21+x16*x22+x16*x23+x16*x24+x16*x25+x17*x19+x17*x21+x17*x24+x17*x25+x18*x19+x18*x20+x18*x21+x18*x25+x19*x21+x19*x22+x19*x23+x19*x24+x19*x25+x20*x21+x20*x22+x20*x24+x20*x25+x21*x23+x21*x25+x22*x23+x22*x24+x23*x24+x23*x25+x24*x25,
x1+x3+x5+x6+x9+x11+x12+x15+x16+x17+x21+x22+x23+x25+x1*x2+x1*x4+x1*x8+x1*x10+x1*x12+x1*x13+x1*x16+x1*x17+x1*x19+x1*x20+x1*x22+x1*x24+x1*x25+x2*x4+x2*x6+x2*x7+x2*x10+x2*x14+x2*x19+x2*x20+x2*x21+x2*x22+x2*x23+x2*x24+x2*x25+x3*x11+x3*x12+x3*x13+x3*x17+x3*x18+x3*x19+x3*x23+x4*x6+x4*x8+x4*x10+x4*x11+x4*x12+x4*x13+x4*x15+x4*x22+x5*x6+x5*x7+x5*x9+x5*x10+x5*x11+x5*x12+x5*x13+x5*x14+x5*x15+x5*x17+x5*x18+x5*x23+x6*x7+x6*x8+x6*x10+x6*x11+x6*x12+x6*x15+x6*x16+x6*x17+x6*x21+x6*x24+x7*x9+x7*x11+x7*x12+x7*x17+x7*x18+x7*x19+x7*x22+x7*x23+x7*x24+x8*x10+x8*x13+x8*x15+x8*x16+x8*x19+x8*x20+x8*x24+x8*x25+x9*x10+x9*x11+x9*x13+x9*x14+x9*x15+x9*x16+x9*x17+x9*x18+x9*x24+x9*x25+x10*x12+x10*x13+x10*x17+x10*x19+x10*x22+x10*x24+x10*x25+x11*x13+x11*x14+x11*x20+x11*x23+x11*x24+x11*x25+x12*x14+x12*x15+x12*x17+x12*x18+x12*x19+x12*x20+x12*x24+x13*x17+x13*x21+x14*x15+x14*x19+x14*x22+x14*x24+x14*x25+x15*x17+x15*x18+x15*x20+x15*x23+x16*x19+x16*x21+x16*x22+x16*x25+x17*x18+x17*x20+x17*x21+x17*x23+x17*x25+x18*x21+x18*x22+x18*x25+x19*x20+x19*x22+x20*x21+x20*x23+x20*x24+x20*x25+x21*x22+x21*x23+x21*x24+x21*x25+x22*x23+x22*x24+x23*x25,
x1+x2+x5+x6+x8+x9+x10+x16+x19+x21+x22+x23+x24+x25+x1*x2+x1*x4+x1*x5+x1*x6+x1*x7+x1*x8+x1*x11+x1*x15+x1*x16+x1*x17+x1*x19+x1*x20+x1*x23+x2*x3+x2*x8+x2*x10+x2*x13+x2*x15+x2*x17+x2*x21+x2*x22+x2*x23+x2*x25+x3*x4+x3*x11+x3*x12+x3*x13+x3*x14+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x25+x4*x7+x4*x11+x4*x13+x4*x18+x4*x20+x4*x22+x4*x24+x4*x25+x5*x7+x5*x9+x5*x12+x5*x14+x5*x17+x6*x7+x6*x8+x6*x9+x6*x10+x6*x11+x6*x13+x6*x15+x6*x20+x6*x21+x6*x22+x6*x24+x7*x10+x7*x12+x7*x15+x7*x16+x7*x18+x7*x20+x7*x22+x7*x23+x7*x25+x8*x11+x8*x12+x8*x13+x8*x16+x8*x17+x8*x19+x8*x21+x9*x10+x9*x15+x9*x16+x9*x20+x9*x23+x10*x12+x10*x13+x10*x16+x10*x19+x10*x20+x10*x22+x10*x23+x10*x24+x11*x14+x11*x20+x11*x21+x11*x22+x11*x23+x11*x24+x11*x25+x12*x18+x12*x22+x12*x23+x13*x15+x13*x17+x13*x18+x13*x20+x13*x21+x13*x23+x13*x24+x13*x25+x14*x15+x14*x21+x14*x23+x14*x25+x15*x16+x15*x17+x15*x19+x15*x20+x15*x21+x15*x22+x15*x23+x16*x17+x16*x19+x16*x22+x16*x23+x16*x24+x17*x21+x17*x22+x17*x23+x17*x24+x18*x21+x19*x20+x19*x22+x19*x24+x20*x22+x20*x23+x20*x24+x20*x25+x21*x24+x22*x23+x22*x24+x22*x25+x23*x24+x23*x25,x1+1    ,x2+1,x3,x4+1,x5+1,x6+1,x7,x8,x9+1];
time G := GroebnerBasis(B);
G;

Output: Magma V2.10-22    Wed Jul 21 2004 06:49:03 on modular  [Seed = 413536871]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (195.124.237.68)
Time: Wed Jul 21 06:52:44 2004

Input: x^5 = x^2 * 8 + 12 * x^4

Output: Magma V2.10-22    Wed Jul 21 2004 06:52:41 on modular  [Seed = 3630617153]
   -------------------------------------


>> x^5 = x^2 * 8 + 12 * x^4;
         ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (195.124.237.68)
Time: Wed Jul 21 06:53:15 2004

Input: x = 6
x^5 = x^2 * 8 + 12 * x^4

Output: Magma V2.10-22    Wed Jul 21 2004 06:53:13 on modular  [Seed = 2719787483]
   -------------------------------------


>> x^5 = x^2 * 8 + 12 * x^4;
   ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.20.139.107)
Time: Wed Jul 21 10:26:11 2004

Input: 12+34

Output: Magma V2.10-22    Wed Jul 21 2004 10:26:08 on modular  [Seed = 2235283687]
   -------------------------------------

46

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.20.139.107)
Time: Wed Jul 21 10:26:28 2004

Input: !34

Output: Magma V2.10-22    Wed Jul 21 2004 10:26:25 on modular  [Seed = 2586093545]
   -------------------------------------


>> !34;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ppp33-6-gw03.athens.access.acn.gr. (213.5.33.6)
Time: Wed Jul 21 11:53:12 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jul 21 2004 11:53:09 on modular  [Seed = 3580560592]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host bays140-0102-dhcp215.bu.edu. (168.122.223.215)
Time: Wed Jul 21 14:15:47 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jul 21 2004 14:15:45 on modular  [Seed = 1809160671]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:40:14 2004

Input: C:=RationalField();
//R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
S<v,t,z,w>:=PolynomialRing(C,4,"grevlex");
//GenerList:={(z-t)*delt,(z-1)*(delz+delt)};
//I:=ideal<R|GenerList>;
//GB:=GroebnerBasis(I);
//print "Groebner basis is:", GB;
//Q,P:=PrimaryDecomposition(I);
//print "Primary Decomposition", P;

print "Infinity:";

GenerList2:={((1-t*v)*(1-v)*z)^3,((1-t*v)*w)^3,((1-v)*(z-t^2*w))^3,
((1-v)*(v*z-t*w))^3,((1-v)*(v^2*z-w))^3};
print "List:";
//GenerList2;
I2:=ideal<S|GenerList2>;
//print "Ideal:";
//I2;
GB2:=GroebnerBasis(I2);
//print "Groebner Basis", GB2;
P2:=EquidimensionalDecomposition(I2);
print "Primary Decomposition:", P2;
print "Primary Ideals: ",Q2;

Output: Magma V2.10-22    Wed Jul 21 2004 14:40:12 on modular  [Seed = 998622162]
   -------------------------------------

Infinity:
List:

>> P2:=EquidimensionalDecomposition(I2);
       ^
User error: Identifier 'EquidimensionalDecomposition' has not been declared or 
assigned

>> print "Primary Decomposition:", P2;
                                   ^
User error: Identifier 'P2' has not been declared or assigned

>> print "Primary Ideals: ",Q2;;
                            ^
User error: Identifier 'Q2' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:52:19 2004

Input: R<z>:=PolynomialRing(RationalField());
I:=ideal<R|z^3>;
P:=ideal<R|z>;
S,f:=Localization(R,P);
S;
f;


Output: Magma V2.10-22    Wed Jul 21 2004 14:52:16 on modular  [Seed = 397011987]
   -------------------------------------


Localization(
    R: Univariate Polynomial Ring in z over Rational Field,
    P: Ideal of Univariate Polynomial Ring in z over Rational Field...
)
In file "/usr/local/magma/package/Ring/Rng/loc.m", line 41, column 23:
>>     V := ValuationRing(F, G);
                         ^
Runtime error in 'ValuationRing': Polynomial incompatible with field

>> S;
   ^
User error: Identifier 'S' has not been declared or assigned

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:53:31 2004

Input: R<z>:=PolynomialRing(FiniteField(9));
I:=ideal<R|z^3>;
P:=ideal<R|z>;
S,f:=Localization(R,P);
S;
f;

Output: Magma V2.10-22    Wed Jul 21 2004 14:53:28 on modular  [Seed = 447013335]
   -------------------------------------


Localization(
    R: Univariate Polynomial Ring in z over GF(3^2),
    P: Ideal of Univariate Polynomial Ring in z over GF(3^2) genera...
)
In file "/usr/local/magma/package/Ring/Rng/loc.m", line 41, column 23:
>>     V := ValuationRing(F, G);
                         ^
Runtime error in 'ValuationRing': Polynomial incompatible with field

>> S;
   ^
User error: Identifier 'S' has not been declared or assigned

>> f;;
   ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:54:14 2004

Input: R<z>:=PolynomialRing(FiniteField(7));
I:=ideal<R|z^3>;
P:=ideal<R|z>;
S,f:=Localization(R,P);
S;
f;

Output: Magma V2.10-22    Wed Jul 21 2004 14:54:12 on modular  [Seed = 3981645404]
   -------------------------------------


Localization(
    R: Univariate Polynomial Ring in z over GF(7),
    P: Ideal of Univariate Polynomial Ring in z over GF(7) generate...
)
In file "/usr/local/magma/package/Ring/Rng/loc.m", line 41, column 23:
>>     V := ValuationRing(F, G);
                         ^
Runtime error in 'ValuationRing': Polynomial incompatible with field

>> S;
   ^
User error: Identifier 'S' has not been declared or assigned

>> f;;
   ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:55:31 2004

Input: R<z>:=PolynomialRing(FiniteField(7));
I:=ideal<R|z^3>;
P:=ideal<R|z>;
S,f:=loc<R|z>;
S;
f;

Output: Magma V2.10-22    Wed Jul 21 2004 14:55:28 on modular  [Seed = 4131916467]
   -------------------------------------


Localization(
    R: Univariate Polynomial Ring in z over GF(7),
    P: Ideal of Univariate Polynomial Ring in z over GF(7) generate...
)
In file "/usr/local/magma/package/Ring/Rng/loc.m", line 41, column 23:
>>     V := ValuationRing(F, G);
                         ^
Runtime error in 'ValuationRing': Polynomial incompatible with field

>> S;
   ^
User error: Identifier 'S' has not been declared or assigned

>> f;;
   ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:56:12 2004

Input: R<z>:=PolynomialRing(RationalField());
I:=ideal<R|z^3>;
P:=ideal<R|z>;
S,f:=loc<R|z>;
S;
f;

Output: Magma V2.10-22    Wed Jul 21 2004 14:56:10 on modular  [Seed = 4265607889]
   -------------------------------------


Localization(
    R: Univariate Polynomial Ring in z over Rational Field,
    P: Ideal of Univariate Polynomial Ring in z over Rational Field...
)
In file "/usr/local/magma/package/Ring/Rng/loc.m", line 41, column 23:
>>     V := ValuationRing(F, G);
                         ^
Runtime error in 'ValuationRing': Polynomial incompatible with field

>> S;
   ^
User error: Identifier 'S' has not been declared or assigned

>> f;;
   ^
User error: Identifier 'f' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 14:57:52 2004

Input: R<z>:=PolynomialRing(RationalField());
//I:=ideal<R|z^3>;
//P:=ideal<R|z>;
S:=loc<R|z>;
S;


Output: Magma V2.10-22    Wed Jul 21 2004 14:57:49 on modular  [Seed = 3246341386]
   -------------------------------------


Localization(
    R: Univariate Polynomial Ring in z over Rational Field,
    P: Ideal of Univariate Polynomial Ring in z over Rational Field...
)
In file "/usr/local/magma/package/Ring/Rng/loc.m", line 41, column 23:
>>     V := ValuationRing(F, G);
                         ^
Runtime error in 'ValuationRing': Polynomial incompatible with field

>> S;
   ^
User error: Identifier 'S' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:19:41 2004

Input: Q:=RationalField();
A<x,y>:=AffineAlgebra<Q,x,y|x^2-2,y^3-5>;


Output: Magma V2.10-22    Wed Jul 21 2004 15:19:39 on modular  [Seed = 3037410331]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:19:51 2004

Input: Q:=RationalField();
A<x,y>:=AffineAlgebra<Q,x,y|x^2-2,y^3-5>;
A;


Output: Magma V2.10-22    Wed Jul 21 2004 15:19:48 on modular  [Seed = 3171105804]
   -------------------------------------

Affine Algebra of rank 2 over Rational Field
Lexicographical Order
Variables: x, y
Quotient relations:
[
    x^2 - 2,
    y^3 - 5
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:20:24 2004

Input: Q:=RationalField();
A<x,y>:=AffineAlgebra<Q,x,y|x^2-2,y^3-5>;
MinimalPolynomial(x+y);


Output: Magma V2.10-22    Wed Jul 21 2004 15:20:22 on modular  [Seed = 2519209733]
   -------------------------------------

$.1^6 - 6*$.1^4 - 10*$.1^3 + 12*$.1^2 - 60*$.1 + 17

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:20:55 2004

Input: Q:=RationalField();
A<x,y>:=AffineAlgebra<Q,x,y|x^2-2,y^3-5>;
UP<z>:=Polynomialring(Q);
MinimalPolynomial(x+y);

Output: Magma V2.10-22    Wed Jul 21 2004 15:20:52 on modular  [Seed = 2652904687]
   -------------------------------------


>> UP<z>:=Polynomialring(Q);
          ^
User error: Identifier 'Polynomialring' has not been declared or assigned
$.1^6 - 6*$.1^4 - 10*$.1^3 + 12*$.1^2 - 60*$.1 + 17

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:21:07 2004

Input: Q:=RationalField();
A<x,y>:=AffineAlgebra<Q,x,y|x^2-2,y^3-5>;
UP<z>:=PolynomialRing(Q);
MinimalPolynomial(x+y);

Output: Magma V2.10-22    Wed Jul 21 2004 15:21:04 on modular  [Seed = 1708910371]
   -------------------------------------

z^6 - 6*z^4 - 10*z^3 + 12*z^2 - 60*z + 17

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:21:16 2004

Input: Q:=RationalField();
A<x,y>:=AffineAlgebra<Q,x,y|x^2-2,y^3-5>;
U<z>:=PolynomialRing(Q);
MinimalPolynomial(x+y);

Output: Magma V2.10-22    Wed Jul 21 2004 15:21:14 on modular  [Seed = 1842605857]
   -------------------------------------

z^6 - 6*z^4 - 10*z^3 + 12*z^2 - 60*z + 17

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:22:05 2004

Input: Q:=RationalField();
A<x>:=AffineAlgebra<Q,x|x^3>;
U<z>:=PolynomialRing(Q);
IsNilpotent(x);


Output: Magma V2.10-22    Wed Jul 21 2004 15:22:02 on modular  [Seed = 1976301385]
   -------------------------------------

true 3

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:22:33 2004

Input: Q:=RationalField();
A<x>:=AffineAlgebra<Q,x|x^3>;
U<z>:=PolynomialRing(Q);
Zero(A);

Output: Magma V2.10-22    Wed Jul 21 2004 15:22:31 on modular  [Seed = 2109996908]
   -------------------------------------

0

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:22:50 2004

Input: Q:=RationalField();
A<x>:=AffineAlgebra<Q,x|x^3>;
U<z>:=PolynomialRing(Q);
Zero(A);
PrimaryDecomposition(Zero(A));

Output: Magma V2.10-22    Wed Jul 21 2004 15:22:47 on modular  [Seed = 1123860643]
   -------------------------------------

0

>> PrimaryDecomposition(Zero(A));;
                       ^
Runtime error in 'PrimaryDecomposition': Bad argument types
Argument types given: RngMPolResElt

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:23:14 2004

Input: Q:=RationalField();
A<x>:=AffineAlgebra<Q,x|x^3>;
U<z>:=PolynomialRing(Q);
I:=ideal<A|Zero(A)>;
PrimaryDecomposition(I);

Output: Magma V2.10-22    Wed Jul 21 2004 15:23:11 on modular  [Seed = 1224133297]
   -------------------------------------

[
    Affine Algebra of rank 1 over Rational Field
    Lexicographical Order
    Variables: x
    Quotient relations:
    [
        x^3
    ]
    Generating basis:
    [
    ]
]
[
    Affine Algebra of rank 1 over Rational Field
    Lexicographical Order
    Variables: x
    Quotient relations:
    [
        x^3
    ]
    Generating basis:
    [
        x
    ]
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:23:55 2004

Input: Q:=RationalField();
A<x>:=AffineAlgebra<Q,x|x^3>;
U<z>:=PolynomialRing(Q);
I:=ideal<A|Zero(A)>;
Q,P:=PrimaryDecomposition(I);
print "Q:", Q;
print "P:", P;


Output: Magma V2.10-22    Wed Jul 21 2004 15:23:53 on modular  [Seed = 1357828863]
   -------------------------------------

Q: [
    Affine Algebra of rank 1 over Rational Field
    Lexicographical Order
    Variables: x
    Quotient relations:
    [
        x^3
    ]
    Generating basis:
    [
    ]
]
P: [
    Affine Algebra of rank 1 over Rational Field
    Lexicographical Order
    Variables: x
    Quotient relations:
    [
        x^3
    ]
    Generating basis:
    [
        x
    ]
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:25:06 2004

Input: Q:=RationalField();
A<x>:=AffineAlgebra<Q,x|x^3>;
U<z>:=PolynomialRing(Q);
I:=ideal<A|Zero(A)>;
Q,P:=PrimaryDecomposition(I);
print "Q:", Q;
print "P:", P;
?multiplicity


Output: Magma V2.10-22    Wed Jul 21 2004 15:25:04 on modular  [Seed = 1508366895]
   -------------------------------------

Q: [
    Affine Algebra of rank 1 over Rational Field
    Lexicographical Order
    Variables: x
    Quotient relations:
    [
        x^3
    ]
    Generating basis:
    [
    ]
]
P: [
    Affine Algebra of rank 1 over Rational Field
    Lexicographical Order
    Variables: x
    Quotient relations:
    [
        x^3
    ]
    Generating basis:
    [
        x
    ]
]
5 matches:
     1   I   /magma/aggregate/set/detail/operation/Boolean/Multiplicity
     2   I   /magma/combinatorial-geometrical-incidence/network/\
             network-vertex-edge-set/EdgeMultiplicity
     3   I   /magma/geometry/algebraic-curve/local-curve/sing-test/Multiplicity
     4   I   /magma/geometry/schemes/linsys/linsys-linalg/properties/\
             Multiplicity
     5   I   /magma/geometry/schemes/schemes-local/constructions/Multiplicity
To view an entry, type ? followed by the number next to it

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:25:41 2004

Input: ?schemes


Output: Magma V2.10-22    Wed Jul 21 2004 15:25:38 on modular  [Seed = 564109941]
   -------------------------------------

19 matches:
     1   S   /magma/geometry/schemes
     2   S   /magma/geometry/schemes/introduction/intro-schemes
     3   S   /magma/geometry/schemes/maps/maps-schemes
     4   S   /magma/geometry/schemes/schemes-ambient
     5   S   /magma/geometry/schemes/schemes-ambient/schemes-ambient-functions
     6   S   /magma/geometry/schemes/schemes-ambient/schemes-ambient-points
     7   S   /magma/geometry/schemes/schemes-ambient/schemes-scrolls
     8   S   /magma/geometry/schemes/schemes-ambient/schemes-standard
     9   S   /magma/geometry/schemes/schemes-base-change
    10   S   /magma/geometry/schemes/schemes-basic
    11   S   /magma/geometry/schemes/schemes-basic/schemes-basic-ambient
    12   S   /magma/geometry/schemes/schemes-closure
    13   S   /magma/geometry/schemes/schemes-clusters
    14   S   /magma/geometry/schemes/schemes-creation
    15   S   /magma/geometry/schemes/schemes-function-elements
    16   S   /magma/geometry/schemes/schemes-global
    17   S   /magma/geometry/schemes/schemes-local
    18   S   /magma/geometry/schemes/schemes-points
    19   S   /magma/geometry/schemes/schemes-types
To view an entry, type ? followed by the number next to it

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:30:17 2004

Input: ?schemes
?1

Output: Magma V2.10-22    Wed Jul 21 2004 15:30:14 on modular  [Seed = 881504276]
   -------------------------------------

19 matches:
     1   S   /magma/geometry/schemes
     2   S   /magma/geometry/schemes/introduction/intro-schemes
     3   S   /magma/geometry/schemes/maps/maps-schemes
     4   S   /magma/geometry/schemes/schemes-ambient
     5   S   /magma/geometry/schemes/schemes-ambient/schemes-ambient-functions
     6   S   /magma/geometry/schemes/schemes-ambient/schemes-ambient-points
     7   S   /magma/geometry/schemes/schemes-ambient/schemes-scrolls
     8   S   /magma/geometry/schemes/schemes-ambient/schemes-standard
     9   S   /magma/geometry/schemes/schemes-base-change
    10   S   /magma/geometry/schemes/schemes-basic
    11   S   /magma/geometry/schemes/schemes-basic/schemes-basic-ambient
    12   S   /magma/geometry/schemes/schemes-closure
    13   S   /magma/geometry/schemes/schemes-clusters
    14   S   /magma/geometry/schemes/schemes-creation
    15   S   /magma/geometry/schemes/schemes-function-elements
    16   S   /magma/geometry/schemes/schemes-global
    17   S   /magma/geometry/schemes/schemes-local
    18   S   /magma/geometry/schemes/schemes-points
    19   S   /magma/geometry/schemes/schemes-types
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/geometry/schemes
KIND: Section
===============================================================================
SCHEMES.

Subsections:

    [+1] introduction
    [+2] schemes-ambient
    [+3] schemes-creation
    [+4] schemes-types
    [+5] schemes-basic
    [+6] schemes-function-elements
    [+7] schemes-points
    [+8] schemes-clusters
    [+9] schemes-local
    [+10] schemes-global
    [+11] schemes-base-change
    [+12] schemes-closure
    [+13] anfs
    [+14] maps
    [+15] linsys
    [+16] scheme-advanced
&nbsp; <BR><FONT SIZE="+1"><I><A HREF = "ackn.htm#Scheme">Acknowledgements</A><\
/I></FONT><BR><BR><BR><BR><BR><BR><BR><BR><H2>DETAILS</H2>
===============================================================================

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 15:30:36 2004

Input: ?schemes
?1
?+1

Output: Magma V2.10-22    Wed Jul 21 2004 15:30:33 on modular  [Seed = 1015199747]
   -------------------------------------

19 matches:
     1   S   /magma/geometry/schemes
     2   S   /magma/geometry/schemes/introduction/intro-schemes
     3   S   /magma/geometry/schemes/maps/maps-schemes
     4   S   /magma/geometry/schemes/schemes-ambient
     5   S   /magma/geometry/schemes/schemes-ambient/schemes-ambient-functions
     6   S   /magma/geometry/schemes/schemes-ambient/schemes-ambient-points
     7   S   /magma/geometry/schemes/schemes-ambient/schemes-scrolls
     8   S   /magma/geometry/schemes/schemes-ambient/schemes-standard
     9   S   /magma/geometry/schemes/schemes-base-change
    10   S   /magma/geometry/schemes/schemes-basic
    11   S   /magma/geometry/schemes/schemes-basic/schemes-basic-ambient
    12   S   /magma/geometry/schemes/schemes-closure
    13   S   /magma/geometry/schemes/schemes-clusters
    14   S   /magma/geometry/schemes/schemes-creation
    15   S   /magma/geometry/schemes/schemes-function-elements
    16   S   /magma/geometry/schemes/schemes-global
    17   S   /magma/geometry/schemes/schemes-local
    18   S   /magma/geometry/schemes/schemes-points
    19   S   /magma/geometry/schemes/schemes-types
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/geometry/schemes
KIND: Section
===============================================================================
SCHEMES.

Subsections:

    [+1] introduction
    [+2] schemes-ambient
    [+3] schemes-creation
    [+4] schemes-types
    [+5] schemes-basic
    [+6] schemes-function-elements
    [+7] schemes-points
    [+8] schemes-clusters
    [+9] schemes-local
    [+10] schemes-global
    [+11] schemes-base-change
    [+12] schemes-closure
    [+13] anfs
    [+14] maps
    [+15] linsys
    [+16] scheme-advanced
&nbsp; <BR><FONT SIZE="+1"><I><A HREF = "ackn.htm#Scheme">Acknowledgements</A><\
/I></FONT><BR><BR><BR><BR><BR><BR><BR><BR><H2>DETAILS</H2>
===============================================================================
===============================================================================
PATH: /magma/geometry/schemes/introduction
KIND: Section
===============================================================================
Introduction and First Examples.

Schemes are rather general objects of algebraic geometry.  A standard
reference is Hartshorne's introductory text [Har77].  Included among all
schemes are many familiar geometric objects such as plane curves.  In Magma
V version, one can work with many of these familiar objects but not with
entirely general schemes.  Roughly speaking, a scheme in Magma is any
geometric object defined by the vanishing of polynomial equations in affine
or projective space.  In particular, there is no facility for defining a
scheme a priori in terms of a collection of affine patches.  Maps between
schemes can be defined by polynomials or quotients of polynomials.

The sections in this introduction contain examples covering the basic idioms
understood by Magma, especially those for creation of geometric objects, and
are intended to be the first place of reference for newcomers to this
module.

The design of the general scheme module is not particularly subtle or
difficult but the philosophy behind it does require a small amount of
understanding.  There are two things in particular.  Firstly, while
constructing geometric objects is easy, many of the constructors take an
ambient scheme as an argument as well as some polynomials.  Thus one's
initial step is often to create some large ambient space which is not of
primary interest but in which many schemes will lie.  In doing so, one
usually assigns names to the coordinate functions of this space, and it is
these names which are used when writing the polynomials which define some
scheme.  Secondly, points are not considered to be elements of schemes, but
rather elements of one of a series of point sets of schemes indexed by the
rings containing the coefficients.  (Mathematically speaking, these rings
are really algebras over the base ring of the scheme, but in Magma the
algebra structure is usually implicitly determined by coercion.)

The objects that can be created include
ambient spaces: affine space, projective space, rational scrolls or weighted
projective space over a ring
schemes as subschemes: the zero locus of polynomials defined on a particular
ambient space or on any other scheme
points of schemes: sequences of ring elements, possibly defined over some
extension of the base ring
maps: sequences of polynomials or rational functions defined on the domain
linear systems: linear spaces of polynomials defined on ambient spaces

Schemes may be defined quite generally over any ring k, although of course
many functions require k to lie in some restricted class.  In Magma V
version the following restrictions hold: Gr"obner basis calculations may
only be performed over a field or Euclidean domain; resultant calculations
may only be carried out over an integral domain; GCD calculations work over
any field and the integers and over polynomial rings over either of these;
the factorisation of polynomials is possible only over the integers,
rationals, finite fields, number fields and rational function fields. Linear
systems are based on the linear algebra module in Magma and so are
restricted to ambient spaces defined over fields.

The functions described in this chapter are general ones that apply to all
schemes.  In particular situations additional functions are provided.  For
example, see Chapter H87E46 for many specialised functions that apply in the
case of curves.  In the final subsection of this introduction we say a few
words about the various different types of schemes that Magma admits.

To some extent we try to emulate Hartshorne's text [Har77] although we
remain only a fraction of the way through the material of that book and, of
course, we have made innumerable compromises.

In the examples below, > at the start of a line is the Magma prompt.  It is
followed by input which may be typed into a Magma session.  The remaining
lines are output which has been edited slightly in some circumstances, but
should nonetheless match closely what appears on screen.

Subsections:

    [+1] intro-ambient
    [+2] intro-schemes
    [+3] intro-points
    [+4] intro-closure
    [+5] intro-map
    [+6] intro-linsys
    [+7] intro-types
===============================================================================

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host na-148-243-20-33.na.avantel.net.mx. (148.243.32.33)
Time: Wed Jul 21 15:36:28 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Wed Jul 21 2004 15:36:25 on modular  [Seed = 196447956]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:09:33 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
dimension(X);
AmbientSpace(X);


Output: Magma V2.10-22    Wed Jul 21 2004 16:09:30 on modular  [Seed = 2469207695]
   -------------------------------------

Scheme over Rational Field defined by
x^3

>> dimension(X);
   ^
User error: Identifier 'dimension' has not been declared or assigned
Affine Space of dimension 1
Variables : x

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:09:45 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X);

Output: Magma V2.10-22    Wed Jul 21 2004 16:09:43 on modular  [Seed = 2552632697]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
Affine Space of dimension 1
Variables : x

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:10:02 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;

Output: Magma V2.10-22    Wed Jul 21 2004 16:09:59 on modular  [Seed = 1625222544]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:17:27 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
Support(X);


Output: Magma V2.10-22    Wed Jul 21 2004 16:17:25 on modular  [Seed = 2043147851]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:17:55 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
Support(X);
Degree(X);


Output: Magma V2.10-22    Wed Jul 21 2004 16:17:52 on modular  [Seed = 1107283542]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }
3

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:19:24 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
Degree(X);
Multiplicity(X,p);


Output: Magma V2.10-22    Wed Jul 21 2004 16:19:22 on modular  [Seed = 1424677881]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
3

>> Multiplicity(X,p);
               ^
Runtime error in 'Multiplicity': Bad argument types
Argument types given: Sch, SetEnum[Pt]

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:19:57 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
Multiplicity(X,p);

Output: Magma V2.10-22    Wed Jul 21 2004 16:19:54 on modular  [Seed = 1541788886]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

>> Multiplicity(X,p);;
               ^
Runtime error in 'Multiplicity': Bad argument types
Argument types given: Sch, SetEnum[Pt]

Total time: 2.500 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:20:13 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:20:11 on modular  [Seed = 814661548]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

>> Multiplicity(X,p[1]);;
                   ^
Runtime error in '[]': Bad argument types

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:20:31 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p;
//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:20:29 on modular  [Seed = 948349010]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:20:45 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p[1];
//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:20:42 on modular  [Seed = 12488829]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

>> p[1];
    ^
Runtime error in '[]': Bad argument types

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:20:54 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p_1;
//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:20:52 on modular  [Seed = 146184267]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

>> p_1;
   ^
User error: Identifier 'p_1' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:23:09 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p[1];
//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:23:07 on modular  [Seed = 513838802]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

>> p[1];
    ^
Runtime error in '[]': Bad argument types

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:23:25 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p[0];
//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:23:23 on modular  [Seed = 3864557114]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true

>> p[0];
    ^
Runtime error in '[]': Bad argument types

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:24:00 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
Parent(p);
//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:23:58 on modular  [Seed = 3981671764]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
Set of subsets of Set of points of Cluster over Rational Field defined by
x^3 with coordinates in Rational Field

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:25:02 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p;

//Multiplicity(X,p[1]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:25:00 on modular  [Seed = 4081934984]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:25:19 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p;

//Multiplicity(X,(0));

Output: Magma V2.10-22    Wed Jul 21 2004 16:25:17 on modular  [Seed = 4215630513]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:25:27 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p;
Multiplicity(X,(0));

Output: Magma V2.10-22    Wed Jul 21 2004 16:25:24 on modular  [Seed = 3279770256]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }

>> Multiplicity(X,(0));;
               ^
Runtime error in 'Multiplicity': Bad argument types
Argument types given: Sch, RngIntElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:25:47 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
X;
Dimension(X);
AmbientSpace(X) eq A;
p:=Support(X);
p;
Multiplicity(X,X!(0));

Output: Magma V2.10-22    Wed Jul 21 2004 16:25:44 on modular  [Seed = 3413465828]
   -------------------------------------

Scheme over Rational Field defined by
x^3
0
true
{ (0) }

>> Multiplicity(X,X!(0));;
                   ^
Runtime error in '!': Illegal coercion
LHS: Sch
RHS: RngIntElt

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:26:10 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
p:=Support(X);
p;
Multiplicity(X,X![0]);

Output: Magma V2.10-22    Wed Jul 21 2004 16:26:07 on modular  [Seed = 3547153131]
   -------------------------------------

{ (0) }
3

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:26:23 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
p:=Support(X);
p;
Multiplicity(X,X!p);

Output: Magma V2.10-22    Wed Jul 21 2004 16:26:20 on modular  [Seed = 3680848592]
   -------------------------------------

{ (0) }

>> Multiplicity(X,X!p);;
                   ^
Runtime error in '!': Illegal coercion
LHS: Sch
RHS: {Pt}

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:26:33 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
p:=Support(X);
p;
Multiplicity(X,p);

Output: Magma V2.10-22    Wed Jul 21 2004 16:26:31 on modular  [Seed = 2736599731]
   -------------------------------------

{ (0) }

>> Multiplicity(X,p);;
               ^
Runtime error in 'Multiplicity': Bad argument types
Argument types given: Sch, SetEnum[Pt]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:27:34 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
p:=Support(X);
Random(p);
//Multiplicity(X,p);

Output: Magma V2.10-22    Wed Jul 21 2004 16:27:31 on modular  [Seed = 2870295167]
   -------------------------------------

(0)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:27:48 2004

Input: k:=RationalField();
A<x>:=AffineSpace(k,1);
X:=Scheme(A,x^3);
p:=Support(X);
s:=Random(p);
Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 16:27:46 on modular  [Seed = 3003982358]
   -------------------------------------

3

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:38:50 2004

Input: k:=RationalField();
A<x,y>:=AffineSpace(k,2);
X:=Scheme(A,x*y^2);
p:=Support(X);
p;
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 16:38:47 on modular  [Seed = 1742336856]
   -------------------------------------


>> p:=Support(X);
             ^
Runtime error in 'Support': Scheme is not zero dimensional

>> p;
   ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:40:12 2004

Input: k:=RationalField();
A<x,y>:=AffineSpace(k,2);
X:=Scheme(A,x*y^2);
Degree(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 16:40:10 on modular  [Seed = 1491520666]
   -------------------------------------

3

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:40:55 2004

Input: k:=RationalField();
A<x,y>:=AffineSpace(k,2);
X:=Scheme(A,x*y^2);
Degree(X);
PrimeComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 16:40:52 on modular  [Seed = 1357825260]
   -------------------------------------

3
[
    Scheme over Rational Field defined by
    x,
    Scheme over Rational Field defined by
    y
]

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 16:41:14 2004

Input: k:=RationalField();
A<x,y>:=AffineSpace(k,2);
X:=Scheme(A,x*y^2);
Degree(X);
PrimaryComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 16:41:12 on modular  [Seed = 680967336]
   -------------------------------------

3
[
    Scheme over Rational Field defined by
    x,
    Scheme over Rational Field defined by
    y^2
]

Total time: 2.529 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9526C50.dip.t-dialin.net. (217.82.108.80)
Time: Wed Jul 21 17:31:46 2004

Input: 1+2

Output: Magma V2.10-22    Wed Jul 21 2004 17:31:44 on modular  [Seed = 3137674003]
   -------------------------------------

3

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:18:29 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,{z-t)^3*delt,(z-1)^3(delz+delt)});
Degree(X);
PrimaryComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 18:18:27 on modular  [Seed = 1876018358]
   -------------------------------------


>> X:=Scheme(A,{z-t)^3*delt,(z-1)^3(delz+delt)});
                   ^
User error: bad syntax

>> Degree(X);
          ^
User error: Identifier 'X' has not been declared or assigned

>> PrimaryComponents(X);
                     ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:18:47 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,{(z-t)^3*delt,(z-1)^3(delz+delt)});
Degree(X);
PrimaryComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 18:18:44 on modular  [Seed = 1742326985]
   -------------------------------------


>> X:=Scheme(A,{(z-t)^3*delt,(z-1)^3(delz+delt)});
                                    ^
Runtime error: Bad argument types
Argument types given: RngMPolElt, RngIntElt

>> Degree(X);
          ^
User error: Identifier 'X' has not been declared or assigned

>> PrimaryComponents(X);
                     ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:19:04 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3(delz+delt)]);
Degree(X);
PrimaryComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 18:19:01 on modular  [Seed = 2143409344]
   -------------------------------------


>> X:=Scheme(A,[(z-t)^3*delt,(z-1)^3(delz+delt)]);
                                    ^
Runtime error: Bad argument types
Argument types given: RngMPolElt, RngIntElt

>> Degree(X);
          ^
User error: Identifier 'X' has not been declared or assigned

>> PrimaryComponents(X);
                     ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:19:27 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt)]);
Degree(X);
PrimaryComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 18:19:21 on modular  [Seed = 2009718004]
   -------------------------------------


>> Degree(X);
         ^
Runtime error in 'Degree': Argument must be a hypersurface, a cluster or 
projective
[
    Scheme over Rational Field defined by
    z^3 - 3*z^2*t + 3*z*t^2 - t^3,
    delz + delt,
    Scheme over Rational Field defined by
    z^3 - 3*z^2 + 3*z - 1,
    z^2*t - z^2 - z*t^2 + z + 1/3*t^3 - 1/3,
    z*t^3 - 3*z*t^2 + 3*z*t - z - 1/2*t^4 + t^3 - t + 1/2,
    t^5 - 5*t^4 + 10*t^3 - 10*t^2 + 5*t - 1,
    Scheme over Rational Field defined by
    z^3 - 3*z^2 + 3*z - 1,
    delt,
    Scheme over Rational Field defined by
    delz,
    delt
]

Total time: 5.719 seconds, Total memory usage: 2.03MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:19:44 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt)]);
PrimaryComponents(X);
//Multiplicity(X,s);

Output: Magma V2.10-22    Wed Jul 21 2004 18:19:39 on modular  [Seed = 1290987485]
   -------------------------------------

[
    Scheme over Rational Field defined by
    z^3 - 3*z^2*t + 3*z*t^2 - t^3,
    delz + delt,
    Scheme over Rational Field defined by
    z^3 - 3*z^2 + 3*z - 1,
    z^2*t - z^2 - z*t^2 + z + 1/3*t^3 - 1/3,
    z*t^3 - 3*z*t^2 + 3*z*t - z - 1/2*t^4 + t^3 - t + 1/2,
    t^5 - 5*t^4 + 10*t^3 - 10*t^2 + 5*t - 1,
    Scheme over Rational Field defined by
    z^3 - 3*z^2 + 3*z - 1,
    delt,
    Scheme over Rational Field defined by
    delz,
    delt
]

Total time: 5.729 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:20:41 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt)]);
P:=PrimaryComponents(X);
P[1];

Output: Magma V2.10-22    Wed Jul 21 2004 18:20:35 on modular  [Seed = 680952945]
   -------------------------------------

Scheme over Rational Field defined by
z^3 - 3*z^2*t + 3*z*t^2 - t^3,
delz + delt

Total time: 5.669 seconds, Total memory usage: 2.01MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:21:05 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt)]);
P:=PrimaryComponents(X);
Q:=P[1];
IsPrimary(Q);

Output: Magma V2.10-22    Wed Jul 21 2004 18:20:59 on modular  [Seed = 630950148]
   -------------------------------------


>> IsPrimary(Q);;
            ^
Runtime error in 'IsPrimary': Bad argument types
Argument types given: Sch

Total time: 5.799 seconds, Total memory usage: 2.03MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:23:20 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt)]);
Q:=PrimaryComponents(X);
P:=PrimeComponents(X);
P;


Output: Magma V2.10-22    Wed Jul 21 2004 18:23:14 on modular  [Seed = 864919435]
   -------------------------------------

[
    Scheme over Rational Field defined by
    z - t,
    delz + delt,
    Scheme over Rational Field defined by
    z - 1,
    t - 1,
    Scheme over Rational Field defined by
    z - 1,
    delt,
    Scheme over Rational Field defined by
    delz,
    delt
]

Total time: 5.769 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:26:40 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt),(z-1)^2*(z-t)*delt,(z-1)*z-t)^2*(delz+delt)]);
Q:=PrimaryComponents(X);
P:=PrimeComponents(X);
P;
Q;


Output: Magma V2.10-22    Wed Jul 21 2004 18:26:38 on modular  [Seed = 146187772]
   -------------------------------------


>> X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt),(z-1)^2*(z-t)*delt,(z-1)*z-t)
                                                                             ^
User error: bad syntax

>> Q:=PrimaryComponents(X);
                        ^
User error: Identifier 'X' has not been declared or assigned

>> P:=PrimeComponents(X);
                      ^
User error: Identifier 'X' has not been declared or assigned

>> P;
   ^
User error: Identifier 'P' has not been declared or assigned

>> Q;
   ^
User error: Identifier 'Q' has not been declared or assigned

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:27:17 2004

Input: k:=RationalField();
A<z,t,delz,delt>:=AffineSpace(k,4);
X:=Scheme(A,[(z-t)^3*delt,(z-1)^3*(delz+delt),(z-1)^2*(z-t)*delt,(z-1)*(z-t)^2*(delz+delt)]);
Q:=PrimaryComponents(X);
P:=PrimeComponents(X);
P;
Q;

Output: Magma V2.10-22    Wed Jul 21 2004 18:27:14 on modular  [Seed = 12496296]
   -------------------------------------

[
    Scheme over Rational Field defined by
    z - t,
    delz + delt,
    Scheme over Rational Field defined by
    z - 1,
    t - 1,
    Scheme over Rational Field defined by
    z - 1,
    delt,
    Scheme over Rational Field defined by
    delz,
    delt
]
[
    Scheme over Rational Field defined by
    z^3 - 3*z^2 + 3*z - 1,
    z^2*t - z^2 - 2*z*t + 2*z + t - 1,
    z*t^2 - 2*z*t + z - t^2 + 2*t - 1,
    t^3 - 3*t^2 + 3*t - 1,
    Scheme over Rational Field defined by
    z - t,
    delz + delt,
    Scheme over Rational Field defined by
    z - 1,
    delt,
    Scheme over Rational Field defined by
    delz,
    delt,
    Scheme over Rational Field defined by
    z^3 - 3*z^2 - 3/2*z*t^2 + 3*z*t + 3/2*z + 3/2*t^2 - 3*t + 1/2,
    z^2*t - z^2 - 3/2*z*t^2 + z*t + 1/2*z + 3/2*t^2 - 2*t + 1/2,
    t^3 - 3*t^2 + 3*t - 1,
    delz + delt,
    Scheme over Rational Field defined by
    z^3 - 3*z^2 + 3*z - 1,
    z^2*t - z^2 - 1/2*z*t^2 - z*t + 3/2*z + 1/2*t^2 - 1/2,
    t^3 - 3*t^2 + 3*t - 1,
    delt
]

Total time: 2.769 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host p508E57DE.dip0.t-ipconnect.de. (80.142.87.222)
Time: Wed Jul 21 18:37:20 2004

Input: ((a+b)^2)*(1-b)

Output: Magma V2.10-22    Wed Jul 21 2004 18:37:17 on modular  [Seed = 4148774784]
   -------------------------------------


>> ((a+b)^2)*(1-b);
     ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E57DE.dip0.t-ipconnect.de. (80.142.87.222)
Time: Wed Jul 21 18:37:36 2004

Input: 1000!

Output: Magma V2.10-22    Wed Jul 21 2004 18:37:34 on modular  [Seed = 3313202561]
   -------------------------------------


>> 1000!;
        ^
User error: bad syntax

Total time: 2.569 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E57DE.dip0.t-ipconnect.de. (80.142.87.222)
Time: Wed Jul 21 18:37:48 2004

Input: 1000!;

Output: Magma V2.10-22    Wed Jul 21 2004 18:37:45 on modular  [Seed = 2736591856]
   -------------------------------------


>> 1000!;;
        ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E57DE.dip0.t-ipconnect.de. (80.142.87.222)
Time: Wed Jul 21 18:38:09 2004

Input: factor(1000)


Output: Magma V2.10-22    Wed Jul 21 2004 18:38:06 on modular  [Seed = 3053979282]
   -------------------------------------


>> factor(1000)
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p508E57DE.dip0.t-ipconnect.de. (80.142.87.222)
Time: Wed Jul 21 18:38:19 2004

Input: factors(1000)


Output: Magma V2.10-22    Wed Jul 21 2004 18:38:17 on modular  [Seed = 2218407095]
   -------------------------------------


>> factors(1000)
   ^
User error: Identifier 'factors' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:41:19 2004

Input: R<z,t>:=PolynomialRing(RationalField());
Factorize(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);

Output: Magma V2.10-22    Wed Jul 21 2004 18:41:16 on modular  [Seed = 731224652]
   -------------------------------------


>> R<z,t>:=PolynomialRing(RationalField());
    ^
Runtime error in 'AssignNames': Argument 2 must have length 1

>> Factorize(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);;
             ^
User error: Identifier 'z' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:41:44 2004

Input: ?Factorize

Output: Magma V2.10-22    Wed Jul 21 2004 18:41:41 on modular  [Seed = 981764980]
   -------------------------------------

No references for word "Factorize"

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:41:54 2004

Input: ?Factorise

Output: Magma V2.10-22    Wed Jul 21 2004 18:41:51 on modular  [Seed = 848069494]
   -------------------------------------

No references for word "Factorise"

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:42:01 2004

Input: ?Factor

Output: Magma V2.10-22    Wed Jul 21 2004 18:41:59 on modular  [Seed = 29339741]
   -------------------------------------

12 matches:
     1   S   /magma/ring-field-algebra/integer/factor
     2   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     3   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     4   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactorModChar
     5   I   /magma/group/braid/braid-groups-elements/\
             braid-groups-elements-access/CanonicalFactorRepresentation
     6   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/socle/SocleFactor
     7   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             ClassGroupCyclicFactorGenerators
     8   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
     9   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
    10   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
    11   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
    12   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
To view an entry, type ? followed by the number next to it

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:42:23 2004

Input: R<z,t>:=PolynomialRing(RationalField());
Factor(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);

Output: Magma V2.10-22    Wed Jul 21 2004 18:42:21 on modular  [Seed = 430417983]
   -------------------------------------


>> R<z,t>:=PolynomialRing(RationalField());
    ^
Runtime error in 'AssignNames': Argument 2 must have length 1

>> Factor(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);;
          ^
User error: Identifier 'z' has not been declared or assigned

Total time: 2.539 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:43:16 2004

Input: R<z,t>:=PolynomialRing(RationalField());
Factor(R,z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);

Output: Magma V2.10-22    Wed Jul 21 2004 18:43:14 on modular  [Seed = 3881391630]
   -------------------------------------


>> R<z,t>:=PolynomialRing(RationalField());
    ^
Runtime error in 'AssignNames': Argument 2 must have length 1

>> Factor(R,z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);;
            ^
User error: Identifier 'z' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:43:35 2004

Input: R<z,t>:=PolynomialRing(RationalField());
Factor(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2,R);

Output: Magma V2.10-22    Wed Jul 21 2004 18:43:33 on modular  [Seed = 4131931912]
   -------------------------------------


>> R<z,t>:=PolynomialRing(RationalField());
    ^
Runtime error in 'AssignNames': Argument 2 must have length 1

>> Factor(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2,R);;
          ^
User error: Identifier 'z' has not been declared or assigned

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:43:54 2004

Input: R<z,t>:=PolynomialRing(RationalField(),2);
Factor(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);

Output: Magma V2.10-22    Wed Jul 21 2004 18:43:52 on modular  [Seed = 3313202182]
   -------------------------------------


>> Factor(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);;
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngMPolElt

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:44:06 2004

Input: R<z,t>:=PolynomialRing(RationalField(),2);
Factor(R,z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);

Output: Magma V2.10-22    Wed Jul 21 2004 18:44:04 on modular  [Seed = 3714280450]
   -------------------------------------


>> Factor(R,z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);;
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngMPol, RngMPolElt

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:44:29 2004

Input: ?Factor
?1

Output: Magma V2.10-22    Wed Jul 21 2004 18:44:27 on modular  [Seed = 3580585077]
   -------------------------------------

12 matches:
     1   S   /magma/ring-field-algebra/integer/factor
     2   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     3   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     4   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactorModChar
     5   I   /magma/group/braid/braid-groups-elements/\
             braid-groups-elements-access/CanonicalFactorRepresentation
     6   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/socle/SocleFactor
     7   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             ClassGroupCyclicFactorGenerators
     8   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
     9   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
    10   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
    11   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
    12   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/ring-field-algebra/integer/factor
KIND: Section
===============================================================================
Factorization.

This section contains a description of most of the machinery provided in
Magma for the factorization of integers.  An account of the Number Field
Sieve is deferred until later in the chapter.

In the first subsection the general-purpose Factorization function is
described.  It employs a combination of methods in an attempt to find the
complete prime factorization of a given integer.  Some control is possible
over each of the methods, but in general default choices for the parameters
would give good results for a wide range of arguments.

In the second subsection we decribe functions that enable access to each of
the factorization methods available in Magma.  The user has control over
parameters for these methods.

Factorization functions in Magma return a factorization sequence.  This is a
sequence of two-element tuples [ <p_1, k_1>, ..., <p_r, k_r>], with p_1<p_2<
... <p_r distinct prime numbers and k_i positive, which is used to represent
integers in factored form: n is the product over i of p_i^(k_i).  Although
such sequences are printed like ordinary sequences, they form a separate
category RngIntEltfact.  Operations on such factorization sequences are
described in the next online help node.

Subsections:

    [+1] factorization-general
    [+2] factorization-specific
    [+3] factorization-related
===============================================================================

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:46:37 2004

Input: ?FactorPolynomial

Output: Magma V2.10-22    Wed Jul 21 2004 18:46:34 on modular  [Seed = 1675481413]
   -------------------------------------

No references for word "FactorPolynomial"

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:48:44 2004

Input: ?Factoring


Output: Magma V2.10-22    Wed Jul 21 2004 18:48:41 on modular  [Seed = 1608642042]
   -------------------------------------

No references for word "Factoring"

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:49:01 2004

Input: ?Factors


Output: Magma V2.10-22    Wed Jul 21 2004 18:48:59 on modular  [Seed = 1474946528]
   -------------------------------------

17 matches:
     1   S   /magma/group/matrix/characteristic-subgroup-normal-structure/\
             composition-factors
     2   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/creation/cyclic/CyclotomicFactors
     3   I   /magma/group/group-overview/\
             characteristic-subgroup-normal-structure/abstract-structure/\
             CompositionFactors
     4   I   /magma/group/matrix/characteristic-subgroup-normal-structure/\
             composition-factors/ChiefFactors
     5   I   /magma/group/matrix/characteristic-subgroup-normal-structure/\
             composition-factors/CompositionFactors
     6   I   /magma/group/matrix/large-degree/tensor-product/TensorFactors
     7   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/composition-series/\
             ChiefFactors
     8   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/composition-series/\
             CompositionFactors
     9   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/socle/SocleFactors
    10   I   /magma/group/soluble/normal-series/subgroup-series/\
             CompositionFactors
    11   I   /magma/module-lattice/general/structure/composition-series/\
             CompositionFactors
    12   I   /magma/module-lattice/general/structure/\
             minimal-submodule-socle-series/SocleFactors
    13   I   /magma/module-lattice/mat/canonical/canonical-field/\
             InvariantFactors
    14   I   /magma/module-lattice/mat/canonical/canonical-field/\
             PrimaryInvariantFactors
    15   I   /magma/ring-field-algebra/matrix/canonical-form/field/\
             InvariantFactors
    16   I   /magma/ring-field-algebra/matrix/canonical-form/field/\
             PrimaryInvariantFactors
    17   E   /magma/ring-field-algebra/local/polynomials/fact/Example-Factors
To view an entry, type ? followed by the number next to it

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:49:29 2004

Input: ?Factors
?17


Output: Magma V2.10-22    Wed Jul 21 2004 18:49:26 on modular  [Seed = 680958643]
   -------------------------------------

17 matches:
     1   S   /magma/group/matrix/characteristic-subgroup-normal-structure/\
             composition-factors
     2   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/creation/cyclic/CyclotomicFactors
     3   I   /magma/group/group-overview/\
             characteristic-subgroup-normal-structure/abstract-structure/\
             CompositionFactors
     4   I   /magma/group/matrix/characteristic-subgroup-normal-structure/\
             composition-factors/ChiefFactors
     5   I   /magma/group/matrix/characteristic-subgroup-normal-structure/\
             composition-factors/CompositionFactors
     6   I   /magma/group/matrix/large-degree/tensor-product/TensorFactors
     7   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/composition-series/\
             ChiefFactors
     8   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/composition-series/\
             CompositionFactors
     9   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/socle/SocleFactors
    10   I   /magma/group/soluble/normal-series/subgroup-series/\
             CompositionFactors
    11   I   /magma/module-lattice/general/structure/composition-series/\
             CompositionFactors
    12   I   /magma/module-lattice/general/structure/\
             minimal-submodule-socle-series/SocleFactors
    13   I   /magma/module-lattice/mat/canonical/canonical-field/\
             InvariantFactors
    14   I   /magma/module-lattice/mat/canonical/canonical-field/\
             PrimaryInvariantFactors
    15   I   /magma/ring-field-algebra/matrix/canonical-form/field/\
             InvariantFactors
    16   I   /magma/ring-field-algebra/matrix/canonical-form/field/\
             PrimaryInvariantFactors
    17   E   /magma/ring-field-algebra/local/polynomials/fact/Example-Factors
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/ring-field-algebra/local/polynomials/fact/Example-Factors
KIND: Example
===============================================================================
In this example we demonstrate how factorizations of a rational polynomial
over some local rings can give information on the Galois group.

> Zx<x> := PolynomialRing(Integers());
> g := x^5 - x + 1;
> Factorization(Discriminant(g));
[ <19, 1>, <151, 1> ]
> g2 := Factorization( PolynomialRing(pAdicRing(2, 10)) ! g );
> g2;
[
    <$.1^2 + 367*$.1 - 93, 1>,
    <$.1^3 - 367*$.1^2 - 386*$.1 + 11, 1>
]
> g3 := Factorization( PolynomialRing(pAdicRing(3, 10)) ! g );
> g3;
[
    <$.1^5 - $.1 + 1, 1>
]
> g7 := Factorization( PolynomialRing(pAdicRing(7, 10)) ! g );
> g7;
[
    <$.1^2 + 138071312*$.1 + 2963768, 1>,
    <$.1^3 - 138071312*$.1^2 + 132202817*$.1 - 84067650, 1>
]

This shows that the Galois group of g contains elements of orders 2, 3, 5
and 6, and therefore is isomorphic to S_5.

To run this example, type:
    load "H61E21";
(If you are in the Browser at the ??> prompt, type <Ctrl>-D first.)
===============================================================================

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:49:50 2004

Input: R<z,t>:=PolynomialRing(RationalField(),2);
Factorization(z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2);

Output: Magma V2.10-22    Wed Jul 21 2004 18:49:47 on modular  [Seed = 864911443]
   -------------------------------------

[
    <z - 1, 1>,
    <z^2 - 2*z - 3/2*t^2 + 3*t - 1/2, 1>
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:52:38 2004

Input: R<z,t>:=PolynomialRing(RationalField(),2);
p1:=z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2;
p2:=z^2*t-z^2-3/2*z*t^2+z*t+1/2*z+3/2*t^2-2*t+1/2;
Factorization(p1);
Factorization(p2);
p3:=p1-p2;
p3;
Factorization(p3);


Output: Magma V2.10-22    Wed Jul 21 2004 18:52:35 on modular  [Seed = 3547160588]
   -------------------------------------

[
    <z - 1, 1>,
    <z^2 - 2*z - 3/2*t^2 + 3*t - 1/2, 1>
]
[
    <t - 1, 1>,
    <z - 1, 1>,
    <z - 3/2*t + 1/2, 1>
]
z^3 - z^2*t - 2*z^2 + 2*z*t + z - t
[
    <z - 1, 2>,
    <z - t, 1>
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Wed Jul 21 18:56:52 2004

Input: R<z,t>:=PolynomialRing(RationalField(),2);
p1:=z^3-3*z^2-3/2*z*t^2+3*z*t+3/2*z+3/2*t^2-3*t+1/2;
p2:=z^2*t-z^2-3/2*z*t^2+z*t+1/2*z+3/2*t^2-2*t+1/2;
Factorization(p1);
Factorization(p2);
p3:=p1-p2;
p3;
Factorization(p3);
p4:= z^2*t - z^2 - 1/2*z*t^2 - z*t + 3/2*z + 1/2*t^2 - 1/2;
Factorization(p4);


Output: Magma V2.10-22    Wed Jul 21 2004 18:56:49 on modular  [Seed = 2059718310]
   -------------------------------------

[
    <z - 1, 1>,
    <z^2 - 2*z - 3/2*t^2 + 3*t - 1/2, 1>
]
[
    <t - 1, 1>,
    <z - 1, 1>,
    <z - 3/2*t + 1/2, 1>
]
z^3 - z^2*t - 2*z^2 + 2*z*t + z - t
[
    <z - 1, 2>,
    <z - t, 1>
]
[
    <t - 1, 1>,
    <z - 1, 1>,
    <z - 1/2*t - 1/2, 1>
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host br2-news.orthogon.de. (193.96.240.80)
Time: Thu Jul 22 03:41:45 2004

Input: solve(x=y+1, y)

Output: Magma V2.10-22    Thu Jul 22 2004 03:41:41 on modular  [Seed = 3948201054]
   -------------------------------------


>> solve(x=y+1, y);
           ^
User error: Identifier 'y' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host nelle.mathematik.uni-ulm.de. (134.60.67.219)
Time: Thu Jul 22 10:28:28 2004

Input: M2:= MatrixRing(Integers(), 2);
Z1:=[ M2!1, M2!1];
Z2:=[ M2!1, M2![2,1,1,2] ];

ok, T:= IsIsometric(Z1, Z2);
ok;
[ T * Z1[i] * Transpose(T) eq Z2[i]: i in [1..#Z1]];

ok, T:= IsIsometric( LatticeWithGram(Z1[1]), [Z1[2]],
             LatticeWithGram(Z2[1]), [Z2[2]]);

ok;
[ T * Z1[i] * Transpose(T) eq Z2[i]: i in [1..#Z1]];


Output: Magma V2.10-22    Thu Jul 22 2004 10:28:23 on modular  [Seed = 2302019209]
   -------------------------------------

true
[ true, false ]
true
[ true, false ]

Total time: 2.820 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host knox.pace.edu. (198.105.45.18)
Time: Thu Jul 22 12:01:31 2004

Input: 45*87

Output: Magma V2.10-22    Thu Jul 22 2004 12:01:28 on modular  [Seed = 1742259127]
   -------------------------------------

3915

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host knox.pace.edu. (198.105.45.18)
Time: Thu Jul 22 12:01:39 2004

Input: 45*87

Output: Magma V2.10-22    Thu Jul 22 2004 12:01:36 on modular  [Seed = 2143345559]
   -------------------------------------

3915

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host knox.pace.edu. (198.105.45.18)
Time: Thu Jul 22 12:01:52 2004

Input: 45*87

Output: Magma V2.10-22    Thu Jul 22 2004 12:01:49 on modular  [Seed = 2151621733]
   -------------------------------------

3915

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host CPE-61-9-136-222.vic.bigpond.net.au. (61.9.136.222)
Time: Fri Jul 23 02:13:27 2004

Input: (9303566201133291683996856107555769425055550895006840647160549767261729682167365769152925654455501900038403139609404401697463216287510105466508432170801 - 39096187556642394531977525045534720382003169681)/(3960*2)

Output: Magma V2.10-22    Fri Jul 23 2004 02:13:25 on modular  [Seed = 3035978047]
   -------------------------------------

1174692702163294404545057589337849674880751375632176849388958303947188091182748\
203175874451320139128792722732755283807992794348328594011457844246086

Total time: 2.559 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:44:05 2004

Input: cyc<zeta>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P3<X,Y,Z,W>:=ProjectiveSpace(cu,3);
R3:=CoordinateRing(P3);
line:=Scheme(P3,[1/2*X + 1/2*Y - 1/2*zeta^3*Z + 1/2*zeta^3*W,-1/2*X +
1/2*Y - 1/2*zeta^3*Z-1/2*zeta^3*W]);
S:=Scheme(P3,Y^3+X^2*Y-u*W^3-u^3*X^2*W);
intersection:=line meet S;


Output: Magma V2.10-22    Fri Jul 23 2004 10:44:02 on modular  [Seed = 3364400605]
   -------------------------------------


Total time: 2.549 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:44:15 2004

Input: cyc<zeta>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P3<X,Y,Z,W>:=ProjectiveSpace(cu,3);
R3:=CoordinateRing(P3);
line:=Scheme(P3,[1/2*X + 1/2*Y - 1/2*zeta^3*Z + 1/2*zeta^3*W,-1/2*X +
1/2*Y - 1/2*zeta^3*Z-1/2*zeta^3*W]);
S:=Scheme(P3,Y^3+X^2*Y-u*W^3-u^3*X^2*W);
intersection:=line meet S;
Points(intersection);


Output: Magma V2.10-22    Fri Jul 23 2004 10:44:12 on modular  [Seed = 3499144651]
   -------------------------------------

{@ (-zeta^3 : zeta^2*u : -zeta^3*u : 1) @}

Total time: 2.699 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:49:57 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.10-22    Fri Jul 23 2004 10:49:55 on modular  [Seed = 1048468107]
   -------------------------------------

-4*z^2/(u^2 - z*u + z^2)

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:50:38 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.10-22    Fri Jul 23 2004 10:50:36 on modular  [Seed = 256863125]
   -------------------------------------

-4*z^2/(u^2 - z*u + z^2)

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:51:18 2004

Input: //KUWATA'S EXAMPLE.

//THE FIELDS
Q:=Rationals();
cyc<z>:=CyclotomicField(8);
i:=z^2;
cu<u>:=FunctionField(cyc);
//THE AUTOMORPHISMS
gam:=hom<cu->cu|-u>;
s:=hom<cyc->cu|z^3>;
sig:=hom<cu->cu|s,u>;
t:=hom<cyc->cu|-z>;
tau:=hom<cu->cu|t,u>;
//THE CURVE
E:=EllipticCurve([cu|0,0,0,-3*u^4,-u^10-u^2]);
s0:=E![0,1,0];
s1:=E![-u*((i-1)*u^2-u-(i+1)),i*u*(u+1)*(u+i)*(u^2+i),1];
s4:=E![sig(s1[j]):j in [1..3]];
s5:=E![(gam*sig)(s1[j]):j in [1..3]];

//SETTING UP THE SURFACE AND 48 LINES IN P3

P3<X,Y,Z,W>:=ProjectiveSpace(cyc,3);
R3:=CoordinateRing(P3);
eqn:=X^4+Y^4-Z^4-W^4;
surf:=Scheme(P3,eqn);

lines10:=[];
for k in [0..3] do
lines10[k+1]:=Scheme(P3,[X-i^k*Z,Y-W]);
end for;
lines11:=[];
for k in [0..3] do
lines11[k+1]:=Scheme(P3,[X-i^k*Z,Y-i*W]);
end for;
lines12:=[];
for k in [0..3] do
lines12[k+1]:=Scheme(P3,[X-i^k*Z,Y-i^2*W]);
end for;
lines13:=[];
for k in [0..3] do
lines13[k+1]:=Scheme(P3,[X-i^k*Z,Y-i^3*W]);
end for;
linesA:=lines10 cat lines11 cat lines12 cat lines13;

lines20:=[];
for k in [0..3] do
lines20[k+1]:=Scheme(P3,[X-i^k*W,Y-Z]);
end for;
lines21:=[];
for k in [0..3] do
lines21[k+1]:=Scheme(P3,[X-i^k*W,Y-i*Z]);
end for;
lines22:=[];
for k in [0..3] do
lines22[k+1]:=Scheme(P3,[X-i^k*W,Y-i^2*Z]);
end for;
lines23:=[];
for k in [0..3] do
lines23[k+1]:=Scheme(P3,[X-i^k*W,Y-i^3*Z]);
end for;
linesB:=lines20 cat lines21 cat lines22 cat lines23;

lines30:=[];
for k in [0..3] do
lines30[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z*W]);
end for;
lines31:=[];
for k in [0..3] do
lines31[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^3*W]);
end for;
lines32:=[];
for k in [0..3] do
lines32[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^5*W]);
end for;
lines33:=[];
for k in [0..3] do
lines33[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^7*W]);
end for;
linesC:=lines30 cat lines31 cat lines32 cat lines33;

lines:=linesA cat linesB cat linesC;


//CHANGE VARIABLES TO XX,YY,ZZ,WW

PP3<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
RR3:=CoordinateRing(PP3);
changevars:=hom<R3->RR3|(XX+YY)/2,(WW-ZZ)/2,(YY-XX)/2,(WW+ZZ)/2>;
newlines:=[Scheme(PP3,changevars(DefiningPolynomials(l))): l in lines];

//SET UP THE NEW ELLIPTIC SURFACE S

S:=Scheme(PP3,YY^3+XX^2*YY-u*WW^3-u^3*XX^2*WW);

maptoE:=function(l)
if Dimension(l meet S) ne 0 then
return [];
else intpts:=Points(l meet S);
ii:=[];
for i in intpts do
if i[2]-u^3*i[4] eq 0 then
ii[Index(intpts,i)]:=0;
else ii[Index(intpts,i)]:=1;
end if;
end for;
ilist:=[i: i in intpts|ii[Index(intpts,i)] eq 1];
return [E![(u*(i[4]-u^5*i[2]))/(i[2]-u^3*i[4]),
(u*(u^8-1)*i[1])/(i[2]-u^3*i[4]),1]: i in ilist];
end if;
end function;


Output: Magma V2.10-22    Fri Jul 23 2004 10:51:15 on modular  [Seed = 391607250]
   -------------------------------------


Total time: 2.669 seconds, Total memory usage: 1.93MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:52:51 2004

Input: ints1:=[l meet S: l in newlines1];
idls:=[Ideal(l): l in ints1];
grbs:=[GroebnerBasis(i): i in idls];
RR2<x2,y2,z2>:=PolynomialRing(cu,3);
dehom:=hom<RR3->RR2|x2,y2,z2,1>;
dhgrbs:=[[dehom(j): j in g]: g in grbs];
R<x>:=PolynomialRing(cu);
univ:=hom<RR2->R|0,0,x>;
dhpols:=[univ(g[3]): g in dhgrbs];
dhpols:=[d:d in dhpols|Degree(d) ne 0];
discs:=[Discriminant(d): d in dhpols];


Output: Magma V2.10-22    Fri Jul 23 2004 10:52:49 on modular  [Seed = 458980476]
   -------------------------------------


>> ints1:=[l meet S: l in newlines1];
                          ^
User error: Identifier 'newlines1' has not been declared or assigned

>> idls:=[Ideal(l): l in ints1];
                         ^
User error: Identifier 'ints1' has not been declared or assigned

>> grbs:=[GroebnerBasis(i): i in idls];
                                 ^
User error: Identifier 'idls' has not been declared or assigned

>> RR2<x2,y2,z2>:=PolynomialRing(cu,3);
                                 ^
User error: Identifier 'cu' has not been declared or assigned

>> dehom:=hom<RR3->RR2|x2,y2,z2,1>;
              ^
User error: Identifier 'RR3' has not been declared or assigned

>> dhgrbs:=[[dehom(j): j in g]: g in grbs];
                                     ^
User error: Identifier 'grbs' has not been declared or assigned

>> R<x>:=PolynomialRing(cu);
                        ^
User error: Identifier 'cu' has not been declared or assigned

>> univ:=hom<RR2->R|0,0,x>;
             ^
User error: Identifier 'RR2' has not been declared or assigned

>> dhpols:=[univ(g[3]): g in dhgrbs];
                             ^
User error: Identifier 'dhgrbs' has not been declared or assigned

>> dhpols:=[d:d in dhpols|Degree(d) ne 0];
                   ^
User error: Identifier 'dhpols' has not been declared or assigned

>> discs:=[Discriminant(d): d in dhpols];
                                 ^
User error: Identifier 'dhpols' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:54:05 2004

Input: 
//KUWATA'S EXAMPLE.

//THE FIELDS
Q:=Rationals();
cyc<z>:=CyclotomicField(8);
i:=z^2;
cu<u>:=FunctionField(cyc);
//THE AUTOMORPHISMS
gam:=hom<cu->cu|-u>;
s:=hom<cyc->cu|z^3>;
sig:=hom<cu->cu|s,u>;
t:=hom<cyc->cu|-z>;
tau:=hom<cu->cu|t,u>;
//THE CURVE
E:=EllipticCurve([cu|0,0,0,-3*u^4,-u^10-u^2]);
s0:=E![0,1,0];
s1:=E![-u*((i-1)*u^2-u-(i+1)),i*u*(u+1)*(u+i)*(u^2+i),1];
s4:=E![sig(s1[j]):j in [1..3]];
s5:=E![(gam*sig)(s1[j]):j in [1..3]];

//SETTING UP THE SURFACE AND 48 LINES IN P3

P3<X,Y,Z,W>:=ProjectiveSpace(cyc,3);
R3:=CoordinateRing(P3);
eqn:=X^4+Y^4-Z^4-W^4;
surf:=Scheme(P3,eqn);

lines10:=[];
for k in [0..3] do
lines10[k+1]:=Scheme(P3,[X-i^k*Z,Y-W]);
end for;
lines11:=[];
for k in [0..3] do
lines11[k+1]:=Scheme(P3,[X-i^k*Z,Y-i*W]);
end for;
lines12:=[];
for k in [0..3] do
lines12[k+1]:=Scheme(P3,[X-i^k*Z,Y-i^2*W]);
end for;
lines13:=[];
for k in [0..3] do
lines13[k+1]:=Scheme(P3,[X-i^k*Z,Y-i^3*W]);
end for;
linesA:=lines10 cat lines11 cat lines12 cat lines13;

lines20:=[];
for k in [0..3] do
lines20[k+1]:=Scheme(P3,[X-i^k*W,Y-Z]);
end for;
lines21:=[];
for k in [0..3] do
lines21[k+1]:=Scheme(P3,[X-i^k*W,Y-i*Z]);
end for;
lines22:=[];
for k in [0..3] do
lines22[k+1]:=Scheme(P3,[X-i^k*W,Y-i^2*Z]);
end for;
lines23:=[];
for k in [0..3] do
lines23[k+1]:=Scheme(P3,[X-i^k*W,Y-i^3*Z]);
end for;
linesB:=lines20 cat lines21 cat lines22 cat lines23;

lines30:=[];
for k in [0..3] do
lines30[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z*W]);
end for;
lines31:=[];
for k in [0..3] do
lines31[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^3*W]);
end for;
lines32:=[];
for k in [0..3] do
lines32[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^5*W]);
end for;
lines33:=[];
for k in [0..3] do
lines33[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^7*W]);
end for;
linesC:=lines30 cat lines31 cat lines32 cat lines33;

lines:=linesA cat linesB cat linesC;


//CHANGE VARIABLES TO XX,YY,ZZ,WW

PP3<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
RR3:=CoordinateRing(PP3);
changevars:=hom<R3->RR3|(XX+YY)/2,(WW-ZZ)/2,(YY-XX)/2,(WW+ZZ)/2>;
newlines:=[Scheme(PP3,changevars(DefiningPolynomials(l))): l in lines];

//SET UP THE NEW ELLIPTIC SURFACE S

S:=Scheme(PP3,YY^3+XX^2*YY-u*WW^3-u^3*XX^2*WW);

maptoE:=function(l)
if Dimension(l meet S) ne 0 then
return [];
else intpts:=Points(l meet S);
ii:=[];
for i in intpts do
if i[2]-u^3*i[4] eq 0 then
ii[Index(intpts,i)]:=0;
else ii[Index(intpts,i)]:=1;
end if;
end for;
ilist:=[i: i in intpts|ii[Index(intpts,i)] eq 1];
return [E![(u*(i[4]-u^5*i[2]))/(i[2]-u^3*i[4]),
(u*(u^8-1)*i[1])/(i[2]-u^3*i[4]),1]: i in ilist];
end if;
end function;

//THERE ARE SOME LINES WHICH STILL CAUSE PROBLEMS (40 AND 46) SO
//WE REMOVE THESE FROM THE LIST.

linesx:=[l:l in newlines|not Index(newlines,l) in [40,46]];

//NOW MAP EVERYTHING TO POINTS ON THE ELLIPTIC CURVE E AND REMOVE REPEATED POINTS.

Epoints:=&cat[maptoE(l): l in linesx];
Epoints:=SetToSequence(SequenceToSet(Epoints));

//I think s2 in Kuwata's example is incorrect - it cannot be coerced
//into E as it is written, however a close match is Epoints[38] - the
//only point with the same y-coordinate as Kuwata's. No x-coordinate 
//matched. s6 is therefore going to be tau(s2) = Epoints[28].
//Similarly, it looks like s3 is Epoints[34].

s2:=Epoints[38];
s6:=E![tau(s2[j]): j in [1..3]];
s3:=Epoints[34];

//Re-labelling to match Kuwata

p1:=s1;
p2:=s4;
p3:=s5;
p4:=s2;
p5:=s6;
p6:=s3;
Egens:=[p1,p2,p3,p4,p5,p6];
M:=myHeightPairingMatrix(Egens);

//Now looking at the 15 lines which only intersect S at one point in Q(z)(u).

ll:=[];
for l in [L: L in newlines|not Index(newlines,L) in [40,46]] do
if Dimension(l meet S) eq 0 then
if #Points(l meet S) eq 1 then
ll:=ll cat[Index(newlines,l)];
end if;
end if;
end for;
newlines1:=[newlines[l]: l in ll];

//CONSTRUCTION OF THE HOMOMORPHISM EMBEDDING cu INTO Qbar(U):

Qbar:=AlgebraicClosure();
QU<U>:=FunctionField(Qbar);
A1<t>:=AffineSpace(Qbar,1);
PA1:=Points(Scheme(A1,t^4+1));
phi1:=hom<cyc->QU|Qbar.1>;
phi:=hom<cu->QU|phi1,U>;
// Unfortunately the above is of limited use as "QU has no polynomial roots
// algorithm".

////////////////////////////////////////////////////////////////////////////////
// The following calculates the vertices of the lattice generated by s1,...,s6.
// In fact the points are twice these otherwise they do not exist on E. 
// The heights of the lattice vertices are given however - since Height(P/2) is 
// Height(P)/4

F:=GF(2);
FQ:=hom<F->Q|>;
A:=AffineSpace(F,6);
PAF:=Points(A);
A:=[[FQ(p[i]):i in [1..6]]: p in PAF];
minusone:=function(y);
m:=function(yy);
if yy eq 0 then return 1;
else return -1;
end if;
end function;
return [m(a): a in y];
end function;
A:=[minusone(a): a in A];
latticevertices:=[];
for a in A do
latticevertices[Index(A,a)]:=&+[a[i]*Egens[i]: i in [1..6]];
end for;
latticeverticesheight:=[Height(l)/4:l in latticevertices];

/////////////////////////////////////////////////////////////////////////
// One of the "problem" lines - newlines[40] gave rise to this point when
// tried by John Cannon (john@maths.usyd.edu.au):

Pl40:=E![z^2*u^4-u^2-z^2,z^3*u^6-z*u^4-z^3*u^2+z,1];


/////////////////////////////////////////////////////////////////////////
// OPERATIONS ON THE GROEBNER BASES OF THE INTERSECTIONS OF THE LINES
// WITH S CONSISTING OF A SINGLE POINT.

ints1:=[l meet S: l in newlines1];
idls:=[Ideal(l): l in ints1];
grbs:=[GroebnerBasis(i): i in idls];
RR2<x2,y2,z2>:=PolynomialRing(cu,3);
dehom:=hom<RR3->RR2|x2,y2,z2,1>;
dhgrbs:=[[dehom(j): j in g]: g in grbs];
R<x>:=PolynomialRing(cu);
univ:=hom<RR2->R|0,0,x>;
dhpols:=[univ(g[3]): g in dhgrbs];
dhpols:=[d:d in dhpols|Degree(d) ne 0];
discs:=[Discriminant(d): d in dhpols];



Output: Magma V2.10-22    Fri Jul 23 2004 10:53:43 on modular  [Seed = 1747455801]
   -------------------------------------



************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Jul 23 10:54:53 2004

Input: //KUWATA'S EXAMPLE.

//THE FIELDS
Q:=Rationals();
cyc<z>:=CyclotomicField(8);
i:=z^2;
cu<u>:=FunctionField(cyc);
//THE AUTOMORPHISMS
gam:=hom<cu->cu|-u>;
s:=hom<cyc->cu|z^3>;
sig:=hom<cu->cu|s,u>;
t:=hom<cyc->cu|-z>;
tau:=hom<cu->cu|t,u>;
//THE CURVE
E:=EllipticCurve([cu|0,0,0,-3*u^4,-u^10-u^2]);
s0:=E![0,1,0];
s1:=E![-u*((i-1)*u^2-u-(i+1)),i*u*(u+1)*(u+i)*(u^2+i),1];
s4:=E![sig(s1[j]):j in [1..3]];
s5:=E![(gam*sig)(s1[j]):j in [1..3]];

//SETTING UP THE SURFACE AND 48 LINES IN P3

P3<X,Y,Z,W>:=ProjectiveSpace(cyc,3);
R3:=CoordinateRing(P3);
eqn:=X^4+Y^4-Z^4-W^4;
surf:=Scheme(P3,eqn);

lines10:=[];
for k in [0..3] do
lines10[k+1]:=Scheme(P3,[X-i^k*Z,Y-W]);
end for;
lines11:=[];
for k in [0..3] do
lines11[k+1]:=Scheme(P3,[X-i^k*Z,Y-i*W]);
end for;
lines12:=[];
for k in [0..3] do
lines12[k+1]:=Scheme(P3,[X-i^k*Z,Y-i^2*W]);
end for;
lines13:=[];
for k in [0..3] do
lines13[k+1]:=Scheme(P3,[X-i^k*Z,Y-i^3*W]);
end for;
linesA:=lines10 cat lines11 cat lines12 cat lines13;

lines20:=[];
for k in [0..3] do
lines20[k+1]:=Scheme(P3,[X-i^k*W,Y-Z]);
end for;
lines21:=[];
for k in [0..3] do
lines21[k+1]:=Scheme(P3,[X-i^k*W,Y-i*Z]);
end for;
lines22:=[];
for k in [0..3] do
lines22[k+1]:=Scheme(P3,[X-i^k*W,Y-i^2*Z]);
end for;
lines23:=[];
for k in [0..3] do
lines23[k+1]:=Scheme(P3,[X-i^k*W,Y-i^3*Z]);
end for;
linesB:=lines20 cat lines21 cat lines22 cat lines23;

lines30:=[];
for k in [0..3] do
lines30[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z*W]);
end for;
lines31:=[];
for k in [0..3] do
lines31[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^3*W]);
end for;
lines32:=[];
for k in [0..3] do
lines32[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^5*W]);
end for;
lines33:=[];
for k in [0..3] do
lines33[k+1]:=Scheme(P3,[X-z^(2*k+1)*Y,Z-z^7*W]);
end for;
linesC:=lines30 cat lines31 cat lines32 cat lines33;

lines:=linesA cat linesB cat linesC;


//CHANGE VARIABLES TO XX,YY,ZZ,WW

PP3<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
RR3:=CoordinateRing(PP3);
changevars:=hom<R3->RR3|(XX+YY)/2,(WW-ZZ)/2,(YY-XX)/2,(WW+ZZ)/2>;
newlines:=[Scheme(PP3,changevars(DefiningPolynomials(l))): l in lines];

//SET UP THE NEW ELLIPTIC SURFACE S

S:=Scheme(PP3,YY^3+XX^2*YY-u*WW^3-u^3*XX^2*WW);

maptoE:=function(l)
if Dimension(l meet S) ne 0 then
return [];
else intpts:=Points(l meet S);
ii:=[];
for i in intpts do
if i[2]-u^3*i[4] eq 0 then
ii[Index(intpts,i)]:=0;
else ii[Index(intpts,i)]:=1;
end if;
end for;
ilist:=[i: i in intpts|ii[Index(intpts,i)] eq 1];
return [E![(u*(i[4]-u^5*i[2]))/(i[2]-u^3*i[4]),
(u*(u^8-1)*i[1])/(i[2]-u^3*i[4]),1]: i in ilist];
end if;
end function;

//THERE ARE SOME LINES WHICH STILL CAUSE PROBLEMS (40 AND 46) SO
//WE REMOVE THESE FROM THE LIST.

linesx:=[l:l in newlines|not Index(newlines,l) in [40,46]];

//NOW MAP EVERYTHING TO POINTS ON THE ELLIPTIC CURVE E AND REMOVE REPEATED POINTS.

Epoints:=&cat[maptoE(l): l in linesx];
Epoints:=SetToSequence(SequenceToSet(Epoints));

//I think s2 in Kuwata's example is incorrect - it cannot be coerced
//into E as it is written, however a close match is Epoints[38] - the
//only point with the same y-coordinate as Kuwata's. No x-coordinate 
//matched. s6 is therefore going to be tau(s2) = Epoints[28].
//Similarly, it looks like s3 is Epoints[34].

s2:=Epoints[38];
s6:=E![tau(s2[j]): j in [1..3]];
s3:=Epoints[34];

//Re-labelling to match Kuwata

p1:=s1;
p2:=s4;
p3:=s5;
p4:=s2;
p5:=s6;
p6:=s3;
Egens:=[p1,p2,p3,p4,p5,p6];
M:=myHeightPairingMatrix(Egens);

//Now looking at the 15 lines which only intersect S at one point in Q(z)(u).

ll:=[];
for l in [L: L in newlines|not Index(newlines,L) in [40,46]] do
if Dimension(l meet S) eq 0 then
if #Points(l meet S) eq 1 then
ll:=ll cat[Index(newlines,l)];
end if;
end if;
end for;
newlines1:=[newlines[l]: l in ll];

//CONSTRUCTION OF THE HOMOMORPHISM EMBEDDING cu INTO Qbar(U):

Qbar:=AlgebraicClosure();
QU<U>:=FunctionField(Qbar);
A1<t>:=AffineSpace(Qbar,1);
PA1:=Points(Scheme(A1,t^4+1));
phi1:=hom<cyc->QU|Qbar.1>;
phi:=hom<cu->QU|phi1,U>;
// Unfortunately the above is of limited use as "QU has no polynomial roots
// algorithm".

////////////////////////////////////////////////////////////////////////////////
// The following calculates the vertices of the lattice generated by s1,...,s6.
// In fact the points are twice these otherwise they do not exist on E. 
// The heights of the lattice vertices are given however - since Height(P/2) is 
// Height(P)/4

F:=GF(2);
FQ:=hom<F->Q|>;
A:=AffineSpace(F,6);
PAF:=Points(A);
A:=[[FQ(p[i]):i in [1..6]]: p in PAF];
minusone:=function(y);
m:=function(yy);
if yy eq 0 then return 1;
else return -1;
end if;
end function;
return [m(a): a in y];
end function;
A:=[minusone(a): a in A];
latticevertices:=[];
for a in A do
latticevertices[Index(A,a)]:=&+[a[i]*Egens[i]: i in [1..6]];
end for;
latticeverticesheight:=[Height(l)/4:l in latticevertices];

/////////////////////////////////////////////////////////////////////////
// One of the "problem" lines - newlines[40] gave rise to this point when
// tried by John Cannon (john@maths.usyd.edu.au):

Pl40:=E![z^2*u^4-u^2-z^2,z^3*u^6-z*u^4-z^3*u^2+z,1];


/////////////////////////////////////////////////////////////////////////
// OPERATIONS ON THE GROEBNER BASES OF THE INTERSECTIONS OF THE LINES
// WITH S CONSISTING OF A SINGLE POINT.

ints1:=[l meet S: l in newlines1];
idls:=[Ideal(l): l in ints1];
grbs:=[GroebnerBasis(i): i in idls];
RR2<x2,y2,z2>:=PolynomialRing(cu,3);
dehom:=hom<RR3->RR2|x2,y2,z2,1>;
dhgrbs:=[[dehom(j): j in g]: g in grbs];
R<x>:=PolynomialRing(cu);
univ:=hom<RR2->R|0,0,x>;
dhpols:=[univ(g[3]): g in dhgrbs];
dhpols:=[d:d in dhpols|Degree(d) ne 0];
discs:=[Discriminant(d): d in dhpols];

discs;

Output: Magma V2.10-22    Fri Jul 23 2004 10:54:31 on modular  [Seed = 2134841598]
   -------------------------------------



************** MAGMA *****************
Host adsl-68-75-160-58.dsl.emhril.ameritech.net. (68.75.160.58)
Time: Fri Jul 23 12:49:11 2004

Input: LegendreSymbol(16,9);

Output: Magma V2.10-22    Fri Jul 23 2004 12:49:08 on modular  [Seed = 1915908831]
   -------------------------------------


>> LegendreSymbol(16,9);;
                 ^
Runtime error in 'LegendreSymbol': Argument 2 (9) should be prime

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-160-58.dsl.emhril.ameritech.net. (68.75.160.58)
Time: Fri Jul 23 12:49:27 2004

Input: JacobiSymbol(16,9);

Output: Magma V2.10-22    Fri Jul 23 2004 12:49:25 on modular  [Seed = 1242188534]
   -------------------------------------

1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host Mix-Dijon-115-2-114.w80-9.abo.wanadoo.fr. (80.9.101.114)
Time: Fri Jul 23 13:40:58 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Fri Jul 23 2004 13:40:56 on modular  [Seed = 4139186807]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host Toronto-HSE-ppp3718401.sympatico.ca. (65.95.48.132)
Time: Sat Jul 24 00:04:49 2004

Input: 2+3

Output: Magma V2.10-22    Sat Jul 24 2004 00:04:47 on modular  [Seed = 3920197380]
   -------------------------------------

5

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.42.2.29)
Time: Sat Jul 24 00:51:15 2004

Input: 123e3 345r6 rr4567 frtter 456456 45645 5rddd

Output: Magma V2.10-22    Sat Jul 24 2004 00:51:12 on modular  [Seed = 4290728970]
   -------------------------------------


>> 123e3 345r6 rr4567 frtter 456456 45645 5rddd;
         ^
User error: bad syntax

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p5089F5AE.dip.t-dialin.net. (80.137.245.174)
Time: Sat Jul 24 03:26:11 2004

Input: 1+2

Output: Magma V2.10-22    Sat Jul 24 2004 03:26:08 on modular  [Seed = 408639025]
   -------------------------------------

3

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p5089F5AE.dip.t-dialin.net. (80.137.245.174)
Time: Sat Jul 24 03:26:49 2004

Input: 1+2/45678

Output: Magma V2.10-22    Sat Jul 24 2004 03:26:47 on modular  [Seed = 273899038]
   -------------------------------------

22840/22839

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p5089F5AE.dip.t-dialin.net. (80.137.245.174)
Time: Sat Jul 24 03:27:20 2004

Input: x=3+6

Output: Magma V2.10-22    Sat Jul 24 2004 03:27:17 on modular  [Seed = 139150948]
   -------------------------------------


>> x=3+6;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host p5089F5AE.dip.t-dialin.net. (80.137.245.174)
Time: Sat Jul 24 03:28:29 2004

Input: for x, y, z in { 1..15 } do
   CheckPythagoras(x, y, z, ~h);
   if h then
      print "Yes, Pythagorean triple!", x, y, z;
   end if;
end for;

Output: Magma V2.10-22    Sat Jul 24 2004 03:28:27 on modular  [Seed = 54545825]
   -------------------------------------


>>    CheckPythagoras(x, y, z, ~h);
      ^
User error: Identifier 'CheckPythagoras' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 07:17:03 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(3603109844542291969,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 07:16:58 on modular  [Seed = 1915844122]
   -------------------------------------

[ <2, 4>, <3, 1>, <11, 1>, <6824071673648741, 1> ]

Total time: 3.049 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:25:10 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);

Output: Magma V2.10-22    Sat Jul 24 2004 07:25:08 on modular  [Seed = 492706635]
   -------------------------------------


Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:25:38 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);

Output: Magma V2.10-22    Sat Jul 24 2004 07:25:35 on modular  [Seed = 627450696]
   -------------------------------------

true

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:26:18 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);
M:=Lattice(E,8);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:26:15 on modular  [Seed = 829568804]
   -------------------------------------

true

>> M:=Lattice(E,8);
              ^
User error: Identifier 'E' has not been declared or assigned

>> L eq M;;
        ^
User error: Identifier 'M' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:27:10 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);
M:=Lattice("E",8);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:27:07 on modular  [Seed = 1031683060]
   -------------------------------------

true

>> L eq M;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:34:19 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);
N:=Lattice("E",8);
M:=DirectSum(N,N);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:34:16 on modular  [Seed = 3869634204]
   -------------------------------------

true

>> L eq M;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:34:57 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);
N:=Lattice("E",8);
M:=DirectSum(N,N);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:34:54 on modular  [Seed = 4021086195]
   -------------------------------------

true

>> L eq M;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:35:29 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);
N:=Lattice("E",8);
M:=DirectSum(N,N);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:35:26 on modular  [Seed = 4155834315]
   -------------------------------------

true

>> L eq M;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:35:56 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);Type(L);
N:=Lattice("E",8);
M:=DirectSum(N,N);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:35:54 on modular  [Seed = 4290574119]
   -------------------------------------

true
Lat

>> L eq M;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:37:19 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);IsPositiveDefinite(EHUT1);L:=LatticeWithGram(EHUT1);Type(L);
M:=Dual(L);
L eq M;

Output: Magma V2.10-22    Sat Jul 24 2004 07:37:17 on modular  [Seed = 2379121954]
   -------------------------------------

true
Lat
true

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:38:18 2004

Input: M:=DirectSum(Lattice("E",8),Lattice("E",8));
M eq Dual(M);

Output: Magma V2.10-22    Sat Jul 24 2004 07:38:15 on modular  [Seed = 2699275205]
   -------------------------------------


>> M eq Dual(M);;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.589 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:39:48 2004

Input: N:=Lattice("Lambda",16);
N eq Dual(N);

Output: Magma V2.10-22    Sat Jul 24 2004 07:39:45 on modular  [Seed = 1360157333]
   -------------------------------------


>> N eq Dual(N);;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.559 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:40:32 2004

Input: N:=Lattice("Lambda",16);
M:=Dual(N);
N eq N;


Output: Magma V2.10-22    Sat Jul 24 2004 07:40:29 on modular  [Seed = 121900271]
   -------------------------------------

true

Total time: 2.519 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:41:03 2004

Input: N:=Lattice("Kappa",16);
M:=Dual(N);
N eq N;

Output: Magma V2.10-22    Sat Jul 24 2004 07:41:00 on modular  [Seed = 256640134]
   -------------------------------------


>> N:=Lattice("Kappa",16);
             ^
Runtime error in 'Lattice': Argument 2 should be in the range [1 .. 13]

>> M:=Dual(N);
           ^
User error: Identifier 'N' has not been declared or assigned

>> N eq N;;
   ^
User error: Identifier 'N' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:42:30 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L:=LatticeWithGram(EHUT1);
M:=Dual(L);
L eq M;
N:=Lattice("Lambda",16);
L eq N;

Output: Magma V2.10-22    Sat Jul 24 2004 07:42:28 on modular  [Seed = 543369793]
   -------------------------------------

true
true

>> L eq N;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.519 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:44:42 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L:=LatticeWithGram(EHUT1);
M:=Dual(L);
L eq M;
N:=Lattice("Lambda",16);
Dimension(L);Dimension(N);

Output: Magma V2.10-22    Sat Jul 24 2004 07:44:39 on modular  [Seed = 4038326802]
   -------------------------------------

true
true
16
16

Total time: 2.579 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pD9FAB463.dip.t-dialin.net. (217.250.180.99)
Time: Sat Jul 24 07:47:06 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L:=LatticeWithGram(EHUT1);
M:=Dual(L);
L eq M;
N:=Lattice("Lambda",16);
Dimension(L);Dimension(N);
L eq N;

Output: Magma V2.10-22    Sat Jul 24 2004 07:47:04 on modular  [Seed = 3103503813]
   -------------------------------------

true
true
16
16

>> L eq N;;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 2.509 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host 3(NXDOMAIN) (193.194.89.21)
Time: Sat Jul 24 08:12:31 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-22    Sat Jul 24 2004 08:12:29 on modular  [Seed = 1764391424]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.480 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (193.194.89.21)
Time: Sat Jul 24 08:13:06 2004

Input: NextPrime(201365487985120)

Output: Magma V2.10-22    Sat Jul 24 2004 08:13:03 on modular  [Seed = 1899127418]
   -------------------------------------

201365487985201

Total time: 2.469 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host 3(NXDOMAIN) (193.194.89.21)
Time: Sat Jul 24 08:13:44 2004

Input: NextPrime(201365487985120)

Output: Magma V2.10-22    Sat Jul 24 2004 08:13:41 on modular  [Seed = 37818672]
   -------------------------------------

201365487985201

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FABBA5.dip.t-dialin.net. (217.250.187.165)
Time: Sat Jul 24 09:25:18 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L1:=LatticeWithGram(EHUT1);
M1:=Dual(L1);
L1 eq M1;
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
IsPositiveDefinite(EHUT3);
L3:=LatticeWithGram(EHUT3);
M3:=Dual(L3);
L3 eq M3; 

Output: Magma V2.10-22    Sat Jul 24 2004 09:25:15 on modular  [Seed = 1376874543]
   -------------------------------------

true
true
true
true

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FABBA5.dip.t-dialin.net. (217.250.187.165)
Time: Sat Jul 24 09:25:39 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L1:=LatticeWithGram(EHUT1);
M1:=Dual(L1);
L1 eq M1;
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
IsPositiveDefinite(EHUT3);
L3:=LatticeWithGram(EHUT3);
M3:=Dual(L3);
L3 eq M3; 
IsIsometric(L1,L3);

Output: Magma V2.10-22    Sat Jul 24 2004 09:25:33 on modular  [Seed = 1511618641]
   -------------------------------------

true
true
true
true
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]

Total time: 5.739 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host pD9FABBA5.dip.t-dialin.net. (217.250.187.165)
Time: Sat Jul 24 09:26:44 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
IsIsometric(L1,L3);

Output: Magma V2.10-22    Sat Jul 24 2004 09:26:42 on modular  [Seed = 1797802431]
   -------------------------------------


>> IsIsometric(L1,L3);;
               ^
User error: Identifier 'L1' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9FABBA5.dip.t-dialin.net. (217.250.187.165)
Time: Sat Jul 24 09:27:25 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L1:=LatticeWithGram(EHUT1);
M1:=Dual(L1);
L1 eq M1;
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
IsPositiveDefinite(EHUT3);
L3:=LatticeWithGram(EHUT3);
M3:=Dual(L3);
L3 eq M3; 
IsIsometric(L1,L3);

Output: Magma V2.10-22    Sat Jul 24 2004 09:27:19 on modular  [Seed = 1932546434]
   -------------------------------------

true
true
true
true
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]

Total time: 5.729 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 09:52:55 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(3603109844542291969,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 09:52:52 on modular  [Seed = 745473233]
   -------------------------------------

[ <2, 4>, <3, 1>, <11, 1>, <6824071673648741, 1> ]

Total time: 2.949 seconds, Total memory usage: 3.82MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 09:55:46 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(67280421310721,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 09:55:43 on modular  [Seed = 947589934]
   -------------------------------------

[ <2, 2>, <3, 1>, <13, 1>, <625267, 1>, <689761, 1> ]

Total time: 2.729 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 09:56:41 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(3603109844542291969,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 09:56:38 on modular  [Seed = 812850159]
   -------------------------------------

[ <2, 4>, <3, 1>, <11, 1>, <6824071673648741, 1> ]

Total time: 2.949 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 09:58:01 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2( 3560841906445833920513,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 09:57:58 on modular  [Seed = 3364610919]
   -------------------------------------

[ <2, 2>, <3, 1>, <79, 1>, <10169, 1>, <10805359, 1>, <34184317, 1> ]

Total time: 3.059 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 09:59:23 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2( 3560841906445833920513,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 09:59:20 on modular  [Seed = 3280005554]
   -------------------------------------

[ <2, 2>, <3, 1>, <79, 1>, <10169, 1>, <10805359, 1>, <34184317, 1> ]

Total time: 3.059 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 09:59:59 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2( 3560841906445833920513,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 09:59:56 on modular  [Seed = 3667521743]
   -------------------------------------

[ <2, 2>, <3, 1>, <79, 1>, <10169, 1>, <10805359, 1>, <34184317, 1> ]

Total time: 3.069 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 10:00:28 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2( 5704689200685129054721,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 10:00:25 on modular  [Seed = 3886337495]
   -------------------------------------

[ <2, 2>, <3, 2>, <158463588910810193711, 1> ]

Total time: 3.369 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 10:01:06 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(319546020820551643220672513,3501693870747166);

Output: Magma V2.10-22    Sat Jul 24 2004 10:01:03 on modular  [Seed = 4290565417]
   -------------------------------------

[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]

Total time: 3.479 seconds, Total memory usage: 3.81MB


************** MAGMA *****************
Host pD9FAB6E3.dip.t-dialin.net. (217.250.182.227)
Time: Sat Jul 24 10:24:24 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L1:=LatticeWithGram(EHUT1);
M1:=Dual(L1);
L1 eq M1;
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
IsPositiveDefinite(EHUT3);
L3:=LatticeWithGram(EHUT3);
M3:=Dual(L3);
L3 eq M3; 
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
IsPositiveDefinite(EHUT2);
L2:=LatticeWithGram(EHUT2);
M2:=Dual(L2);
L2 eq M2; 

Output: Magma V2.10-22    Sat Jul 24 2004 10:24:21 on modular  [Seed = 2867436278]
   -------------------------------------

true
true
true
true
true
true

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9FAB6E3.dip.t-dialin.net. (217.250.182.227)
Time: Sat Jul 24 10:24:51 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
IsPositiveDefinite(EHUT1);
L1:=LatticeWithGram(EHUT1);
M1:=Dual(L1);
L1 eq M1;
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
IsPositiveDefinite(EHUT3);
L3:=LatticeWithGram(EHUT3);
M3:=Dual(L3);
L3 eq M3; 
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
IsPositiveDefinite(EHUT2);
L2:=LatticeWithGram(EHUT2);
M2:=Dual(L2);
L2 eq M2;
IsIsometric(L1,L3);
IsIsometric(L1,L2);

Output: Magma V2.10-22    Sat Jul 24 2004 10:24:43 on modular  [Seed = 2732692160]
   -------------------------------------

true
true
true
true
true
true
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
false

Total time: 8.469 seconds, Total memory usage: 2.10MB


************** MAGMA *****************
Host pD9FAB6E3.dip.t-dialin.net. (217.250.182.227)
Time: Sat Jul 24 10:26:04 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
IsIsometric(L1,L2);

Output: Magma V2.10-22    Sat Jul 24 2004 10:25:59 on modular  [Seed = 3187576195]
   -------------------------------------

false

Total time: 5.199 seconds, Total memory usage: 2.00MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:12:15 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i=4 to 10 do FindGroupOrder2(319546020820551643220672513,3501693870747166);


Output: Magma V2.10-22    Sat Jul 24 2004 11:12:12 on modular  [Seed = 425337885]
   -------------------------------------


>> for i=4 to 10 do FindGroupOrder2(319546020820551643220672513,35016938707471
        ^
User error: bad syntax

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:12:26 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=4 to 10 do FindGroupOrder2(319546020820551643220672513,3501693870747166);


Output: Magma V2.10-22    Sat Jul 24 2004 11:12:23 on modular  [Seed = 290597902]
   -------------------------------------


User error: syntax error at end of input

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:13:19 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=4 to 10 do 
FindGroupOrder2(319546020820551643220672513,3501693870747166);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 11:13:10 on modular  [Seed = 694818023]
   -------------------------------------

[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]
[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]
[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]
[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]
[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]
[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]
[ <2, 4>, <3, 1>, <37, 1>, <89849, 1>, <2002521578123757211, 1> ]

Total time: 9.029 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:13:37 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=4 to 10 do 
FindGroupOrder2(319546020820551643220672513,i);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 11:13:33 on modular  [Seed = 576790519]
   -------------------------------------

[ <2, 3>, <3, 1>, <7, 1>, <29, 1>, <65588263715222608239697, 1> ]

[<main>:3](
    p: 319546020820551643220672513,
    s: 5
)
>>    E := EllipticCurve([0,b*A,0,b^2,0]);
                        ^
Runtime error in 'EllipticCurve': Curve is singular

Total time: 3.489 seconds, Total memory usage: 3.83MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:14:05 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=10 to 20 do 
FindGroupOrder2(319546020820551643220672513,i);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 11:13:52 on modular  [Seed = 981010370]
   -------------------------------------

[ <2, 2>, <3, 1>, <29, 1>, <83, 1>, <443, 1>, <24973093965378171439, 1> ]
[ <2, 3>, <3, 2>, <11257, 1>, <394255945461748102769, 1> ]
[ <2, 3>, <3, 1>, <1321, 1>, <10079044310514955142971, 1> ]
[ <2, 4>, <3, 4>, <5, 1>, <23, 1>, <53, 1>, <3517, 1>, <45641, 1>, 
<252015459497, 1> ]
[ <2, 2>, <3, 1>, <2383, 1>, <602713, 1>, <18540334550860691, 1> ]
[ <2, 2>, <3, 1>, <27943, 1>, <77591, 1>, <12281963089824023, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <149, 1>, <3923, 1>, <4327, 1>, <1528939, 1>, 
<1377211159, 1> ]
[ <2, 2>, <3, 1>, <7, 1>, <3804119295482931902604349, 1> ]
[ <2, 2>, <3, 1>, <221401, 1>, <91990309, 1>, <1307466324841, 1> ]
[ <2, 2>, <3, 1>, <277, 1>, <503, 1>, <191119241722062987331, 1> ]
[ <2, 3>, <3, 2>, <13, 2>, <31, 1>, <61, 1>, <1873, 1>, <7414551850101419, 1> ]

Total time: 12.289 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:53:27 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=10 to 20 do 
FindGroupOrder2(3560841906445833920513,i);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 11:53:19 on modular  [Seed = 2783338754]
   -------------------------------------

[ <2, 2>, <3, 1>, <53, 1>, <61, 1>, <431, 1>, <212955308997581, 1> ]
[ <2, 5>, <3, 1>, <389, 1>, <1471, 1>, <64821516223223, 1> ]
[ <2, 2>, <3, 1>, <17, 1>, <240315011, 1>, <72634278281, 1> ]
[ <2, 4>, <3, 1>, <5, 1>, <311, 1>, <1911289, 1>, <24960581647, 1> ]
[ <2, 2>, <3, 1>, <13, 1>, <541, 1>, <644729, 1>, <65441557003, 1> ]
[ <2, 3>, <3, 1>, <17, 1>, <89, 1>, <296165741, 1>, <331106497, 1> ]
[ <2, 6>, <3, 1>, <18546051595666082647, 1> ]
[ <2, 4>, <3, 2>, <1039, 1>, <31344497, 1>, <759299909, 1> ]
[ <2, 2>, <3, 1>, <23, 1>, <89399, 1>, <144314825786717, 1> ]
[ <2, 3>, <3, 3>, <29, 1>, <442991011, 1>, <1283234507, 1> ]
[ <2, 4>, <3, 3>, <499, 1>, <16518416028849589, 1> ]

Total time: 7.989 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 11:56:02 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=21 to 30 do 
FindGroupOrder2(3560841906445833920513,i);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 11:55:55 on modular  [Seed = 2985457266]
   -------------------------------------

[ <2, 3>, <3, 3>, <41, 1>, <402082419437290321, 1> ]
[ <2, 6>, <3, 1>, <17, 1>, <1090944211526310949, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <59347365107109290543, 1> ]
[ <2, 6>, <3, 1>, <532391, 1>, <1840871, 1>, <18923323, 1> ]
[ <2, 2>, <3, 2>, <5, 1>, <151, 1>, <1753, 1>, <74734532802497, 1> ]
[ <2, 4>, <3, 1>, <5, 2>, <8009609, 1>, <370476043891, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <127, 1>, <1753, 1>, <266572782345497, 1> ]
[ <2, 3>, <3, 1>, <11, 1>, <139, 1>, <337, 1>, <49201, 1>, <5852347889, 1> ]
[ <2, 4>, <3, 1>, <11, 1>, <23, 1>, <1123, 1>, <261102588643823, 1> ]
[ <2, 2>, <3, 1>, <13, 1>, <2939, 1>, <28862987, 1>, <269083603, 1> ]

Total time: 7.509 seconds, Total memory usage: 4.16MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 12:38:12 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=1 to 1 do 
FindGroupOrder2(2663848877152141313,3501693870747166);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 12:38:09 on modular  [Seed = 3549430505]
   -------------------------------------

[ <2, 3>, <3, 2>, <5, 1>, <11, 1>, <53, 1>, <2419127, 1>, <5246623, 1> ]

Total time: 2.819 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 12:41:08 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=1 to 1 do 
FindGroupOrder2(6487031809,3501693870747166);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 12:41:05 on modular  [Seed = 4273811092]
   -------------------------------------

[ <2, 2>, <3, 4>, <83, 1>, <241229, 1> ]

Total time: 2.689 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 12:44:10 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=1 to 1 do 
FindGroupOrder2(167988556341760475137,3501693870747166);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 12:44:07 on modular  [Seed = 4139066986]
   -------------------------------------

[ <2, 4>, <3, 2>, <7, 1>, <107, 1>, <1103, 1>, <140557, 1>, <10046329, 1> ]

Total time: 3.179 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 12:53:49 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=1 to 1 do 
FindGroupOrder2(59649589127497217,3501693870747166);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 12:53:46 on modular  [Seed = 2277790422]
   -------------------------------------

[ <2, 3>, <3, 1>, <17, 1>, <10061, 1>, <14531356027, 1> ]

Total time: 2.789 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sat Jul 24 13:00:00 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=1 to 1 do 
FindGroupOrder2(59649589127497217,3501693870747166);
end for;


Output: Magma V2.10-22    Sat Jul 24 2004 12:59:57 on modular  [Seed = 2429764694]
   -------------------------------------

[ <2, 3>, <3, 1>, <17, 1>, <10061, 1>, <14531356027, 1> ]

Total time: 2.779 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Sat Jul 24 16:20:09 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
n:=2;
a[1]:=t;
a[2]:=t^2;
l:=[z-a[i]:i in [1..n]];
l;

quit;


Output: Magma V2.10-22    Sat Jul 24 2004 16:20:07 on modular  [Seed = 4189748419]
   -------------------------------------


>> a[1]:=t;
    ^
User error: Identifier 'a' has not been declared or assigned

>> a[2]:=t^2;
    ^
User error: Identifier 'a' has not been declared or assigned

>> l:=[z-a[i]:i in [1..n]];
         ^
User error: Identifier 'a' has not been declared or assigned

>> l;
   ^
User error: Identifier 'l' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host stats-dhcp-114.uchicago.edu. (128.135.149.114)
Time: Sat Jul 24 16:20:32 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
n:=2;
a_[1]:=t;
a_[2]:=t^2;
l:=[z-a_[i]:i in [1..n]];
l;

quit;

Output: Magma V2.10-22    Sat Jul 24 2004 16:20:29 on modular  [Seed = 4088428083]
   -------------------------------------


>> a_[1]:=t;
     ^
User error: Identifier 'a_' has not been declared or assigned

>> a_[2]:=t^2;
     ^
User error: Identifier 'a_' has not been declared or assigned

>> l:=[z-a_[i]:i in [1..n]];
         ^
User error: Identifier 'a_' has not been declared or assigned

>> l;
   ^
User error: Identifier 'l' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 06:41:10 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(2710954639361, 13)

Output: Magma V2.10-22    Sun Jul 25 2004 06:41:07 on modular  [Seed = 2884199615]
   -------------------------------------

[ <2, 3>, <3, 1>, <11, 1>, <34171, 1>, <300511, 1> ]

Total time: 2.769 seconds, Total memory usage: 2.96MB


************** MAGMA *****************
Host p508E5C4B.dip0.t-ipconnect.de. (80.142.92.75)
Time: Sun Jul 25 08:48:18 2004

Input: (a+b+a^2)^3

Output: Magma V2.10-22    Sun Jul 25 2004 08:48:15 on modular  [Seed = 1242081053]
   -------------------------------------


>> (a+b+a^2)^3;
    ^
User error: Identifier 'a' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 13:21:27 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
n:=2;
a[1]:=t;
a[2]:=t^2;
l:=[z-a[i]:i in [1..n]];
l;

quit;



Output: Magma V2.10-22    Sun Jul 25 2004 13:21:22 on modular  [Seed = 3768733096]
   -------------------------------------


>> a[1]:=t;
    ^
User error: Identifier 'a' has not been declared or assigned

>> a[2]:=t^2;
    ^
User error: Identifier 'a' has not been declared or assigned

>> l:=[z-a[i]:i in [1..n]];
         ^
User error: Identifier 'a' has not been declared or assigned

>> l;
   ^
User error: Identifier 'l' has not been declared or assigned

Total time: 2.599 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 13:26:14 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
a:=[t,t^2];
l:=[z-i : i in a];
l;

quit;


Output: Magma V2.10-22    Sun Jul 25 2004 13:26:11 on modular  [Seed = 2682074102]
   -------------------------------------

[
    z - t,
    -t^2 + z
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 13:26:48 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
a:=[t,t^2];
l:=[z-i : i in a];
l;
I:=ideal<R|l>;
I;

quit;

Output: Magma V2.10-22    Sun Jul 25 2004 13:26:45 on modular  [Seed = 2497067163]
   -------------------------------------

[
    z - t,
    -t^2 + z
]
Ideal of Polynomial ring of rank 4 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t, delz, delt
Basis:
[
    z - t,
    -t^2 + z
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 13:27:55 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i : i in a];
l;

I:=ideal<R|l>;
I;



Output: Magma V2.10-22    Sun Jul 25 2004 13:27:52 on modular  [Seed = 2362318926]
   -------------------------------------

[
    z - t,
    -t^2 + z,
    -t^3 + z
]
Ideal of Polynomial ring of rank 4 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t, delz, delt
Basis:
[
    z - t,
    -t^2 + z,
    -t^3 + z
]

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 13:28:27 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i : i in a];
l;

I:=ideal<R|l>;
I;
eliminate(I,t);


Output: Magma V2.10-22    Sun Jul 25 2004 13:28:24 on modular  [Seed = 2244421991]
   -------------------------------------

[
    z - t,
    -t^2 + z,
    -t^3 + z
]
Ideal of Polynomial ring of rank 4 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t, delz, delt
Basis:
[
    z - t,
    -t^2 + z,
    -t^3 + z
]

>> eliminate(I,t);
   ^
User error: Identifier 'eliminate' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 13:28:49 2004

Input: C:=RationalField();
R<z,t,delz,delt>:=PolynomialRing(C,4,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i : i in a];
I:=ideal<R|l>;
Eliminate(I,t);

Output: Magma V2.10-22    Sun Jul 25 2004 13:28:46 on modular  [Seed = 3187609897]
   -------------------------------------


>> Eliminate(I,t);;
            ^
Runtime error in 'Eliminate': Bad argument types
Argument types given: RngMPol, RngMPolElt

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:05:25 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prodt*:=i; end for;
complements:=[prod div i : i in l];
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal(R|[gen1,gen2]);
I;



Output: Magma V2.10-22    Sun Jul 25 2004 14:05:22 on modular  [Seed = 1932641356]
   -------------------------------------


>> prod:=1; for i in l do prodt*:=i; end for;
                               ^
Runtime error in '*:=': Argument 1 has not been initialized
Argument types given: *nothing ~, RngMPolElt

>> complements:=[prod div i : i in l];
                      ^
Runtime error in 'div': Argument 2 does not divide argument 1

>> gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
                                      ^
User error: Identifier 'complements' has not been declared or assigned

>> gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
                                      ^
User error: Identifier 'complements' has not been declared or assigned

>> I:=ideal(R|[gen1,gen2]);
             ^
User error: bad syntax

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:05:51 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal(R|[gen1,gen2]);
I;


Output: Magma V2.10-22    Sun Jul 25 2004 14:05:48 on modular  [Seed = 1797905482]
   -------------------------------------


>> I:=ideal(R|[gen1,gen2]);
             ^
User error: bad syntax

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:06:22 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:06:20 on modular  [Seed = 1663161506]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t
Basis:
[
    t^5 - 2*z*t^3 + t^4 - 2*z*t^2 + t^3 + 3*z^2 - 2*z*t,
    5*z*t^4 - 6*t^5 - 3*z^2*t^2 + 4*z*t^3 - 2*z^2*t + 3*z*t^2 - z^2
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:06:54 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2,"grevlex");
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:06:51 on modular  [Seed = 391487729]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t
Basis:
[
    t^5 - 2*z*t^3 + t^4 - 2*z*t^2 + t^3 + 3*z^2 - 2*z*t,
    5*z*t^4 - 6*t^5 - 3*z^2*t^2 + 4*z*t^3 - 2*z^2*t + 3*z*t^2 - z^2
]
Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^3*t^2 - 61/21*z^3*t + 2687/735*z^2*t^2 - 781/245*z*t^3 + 352/245*t^4 + 
        22/147*z^3 - 872/735*z^2*t - 353/245*z*t^2 + 362/245*t^3 + 969/245*z^2 -
        724/245*z*t,
    z^2*t^3 + 1/35*z^2*t^2 - 114/35*z*t^3 + 78/35*t^4 - 15/7*z^3 + 109/35*z^2*t 
        - 117/35*z*t^2 + 48/35*t^3 + 131/35*z^2 - 96/35*z*t,
    z*t^4 - 3/5*z^2*t^2 - 8/5*z*t^3 + 6/5*t^4 - 2/5*z^2*t - 9/5*z*t^2 + 6/5*t^3 
        + 17/5*z^2 - 12/5*z*t,
    t^5 - 2*z*t^3 + t^4 - 2*z*t^2 + t^3 + 3*z^2 - 2*z*t,
    z^4 - 1013/189*z^3*t + 29119/6615*z^2*t^2 + 4693/2205*z*t^3 - 4786/2205*t^4 
        + 7106/1323*z^3 - 63214/6615*z^2*t + 9314/2205*z*t^2 - 86/2205*t^3 - 
        172/2205*z^2 + 172/2205*z*t
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:20:56 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2,"grevlex");
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:20:53 on modular  [Seed = 627547773]
   -------------------------------------


>> gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
   ^
User error: bad syntax

>> I:=ideal<R|[gen1,gen2]>;
               ^
User error: Identifier 'gen1' has not been declared or assigned

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:21:13 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2,"grevlex");
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:21:10 on modular  [Seed = 3718211222]
   -------------------------------------

[
    -t^2 + z,
    z - t
]
Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t
Basis:
[
    -t^2 + 2*z - t,
    -2*z*t + 3*t^2 - z
]
Ideal of Polynomial ring of rank 2 over Rational Field
Graded Reverse Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 23/8*z + 15/8*t,
    z*t - 5/2*z + 3/2*t,
    t^2 - 2*z + t
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:27:14 2004

Input: C:=RationalField();
S<t>:=PolynomialRing(C,1,"grevlex");
R<z>:=PolynomialRing(S,1,"grevlex");
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;


Output: Magma V2.10-22    Sun Jul 25 2004 14:27:12 on modular  [Seed = 3532679183]
   -------------------------------------


>> difftl:=[Derivative(i,t):i in l];
                      ^
Runtime error in 'Derivative': Argument 2 is not a variable

>> complements:=[prod div i : i in l];
                      ^
Runtime error in 'div': Algorithm is not available for this kind of coefficient 
ring

>> complements;
   ^
User error: Identifier 'complements' has not been declared or assigned

>> gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
                                      ^
User error: Identifier 'complements' has not been declared or assigned

>> gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
                                      ^
User error: Identifier 'complements' has not been declared or assigned

>> I:=ideal<R|[gen1,gen2]>;
           ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:27:48 2004

Input: C:=RationalField();
S<t>:=PolynomialRing(C,1,"grevlex");
R<z>:=PolynomialRing(S,1,"grevlex");
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[-Derivative(i,t):i in a];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:27:46 on modular  [Seed = 3397939253]
   -------------------------------------


>> complements:=[prod div i : i in l];
                      ^
Runtime error in 'div': Algorithm is not available for this kind of coefficient 
ring

>> complements;
   ^
User error: Identifier 'complements' has not been declared or assigned

>> gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
                                      ^
User error: Identifier 'complements' has not been declared or assigned

>> gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
                                      ^
User error: Identifier 'complements' has not been declared or assigned

>> I:=ideal<R|[gen1,gen2]>;
           ^
Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:28:43 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:28:41 on modular  [Seed = 4257171321]
   -------------------------------------

[
    z - t^2,
    z - t
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: z, t
Basis:
[
    2*z - t^2 - t,
    -2*z*t - z + 3*t^2
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:29:06 2004

Input: C:=RationalField();
R<z,t>:=PolynomialRing(C,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;


Output: Magma V2.10-22    Sun Jul 25 2004 14:29:03 on modular  [Seed = 4122431303]
   -------------------------------------

[
    z - t^2,
    z - t
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: z, t
Basis:
[
    2*z - t^2 - t,
    -2*z*t - z + 3*t^2
]
Ideal of Polynomial ring of rank 2 over Rational Field
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z - 1/2*t^2 - 1/2*t,
    t^3 - 3/2*t^2 + 1/2*t
]

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:34:32 2004

Input: A:=AlgebraicClosure(RationalField());
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:34:29 on modular  [Seed = 3970846852]
   -------------------------------------


>> A:=AlgebraicClosure(RationalField());
                      ^
Runtime error in 'AlgebraicClosure': Bad argument types
Argument types given: FldRat

>> R<z,t>:=PolynomialRing(A,2);
                          ^
User error: Identifier 'A' has not been declared or assigned

>> a:=[t,t^2];
       ^
User error: Identifier 't' has not been declared or assigned

>> l:=[z-i:i in a];
                ^
User error: Identifier 'a' has not been declared or assigned

>> n:=#l;
       ^
User error: Identifier 'l' has not been declared or assigned

>> difftl:=[Derivative(i,t):i in l];
                                 ^
User error: Identifier 'l' has not been declared or assigned

>> diffzl:=[Derivative(i,z):i in l];
                                 ^
User error: Identifier 'l' has not been declared or assigned

>> prod:=1; for i in l do prod*:=i; end for;
                     ^
User error: Identifier 'l' has not been declared or assigned

>> complements:=[prod div i : i in l];
                                   ^
User error: Identifier 'l' has not been declared or assigned

>> complements;
   ^
User error: Identifier 'complements' has not been declared or assigned

>> gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
                         ^
User error: Identifier 'n' has not been declared or assigned

>> gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
                         ^
User error: Identifier 'n' has not been declared or assigned

>> I:=ideal<R|[gen1,gen2]>;
            ^
User error: Identifier 'R' has not been declared or assigned

>> I;
   ^
User error: Identifier 'I' has not been declared or assigned

>> GB:=GroebnerBasis(I);
                     ^
User error: Identifier 'I' has not been declared or assigned

>> I;;
   ^
User error: Identifier 'I' has not been declared or assigned

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:35:25 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:35:22 on modular  [Seed = 3886373840]
   -------------------------------------

[
    z - t^2,
    z - t
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    2*z - t^2 - t,
    -2*z*t - z + 3*t^2
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z - 1/2*t^2 - 1/2*t,
    t^3 - 3/2*t^2 + 1/2*t
]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:35:43 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;

Output: Magma V2.10-22    Sun Jul 25 2004 14:35:41 on modular  [Seed = 2682069951]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:36:30 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
RadicalDecomposition(I);


Output: Magma V2.10-22    Sun Jul 25 2004 14:36:27 on modular  [Seed = 2547329889]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r3^2 - 5/9*r3 - 5/9,
        t - r3
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r2^2 - 5/9*r2 - 5/9,
        t - r2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r1^2 - 5/9*r1 - 5/9,
        t - r1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 1,
        t + 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:41:18 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
RadicalDecomposition(I);
r1;

Output: Magma V2.10-22    Sun Jul 25 2004 14:41:15 on modular  [Seed = 3036023586]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r3^2 - 5/9*r3 - 5/9,
        t - r3
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r2^2 - 5/9*r2 - 5/9,
        t - r2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r1^2 - 5/9*r1 - 5/9,
        t - r1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 1,
        t + 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]

>> r1;;
   ^
User error: Identifier 'r1' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:41:48 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
RadicalDecomposition(I);
A.r2;

Output: Magma V2.10-22    Sun Jul 25 2004 14:41:46 on modular  [Seed = 2951548952]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r3^2 - 5/9*r3 - 5/9,
        t - r3
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r2^2 - 5/9*r2 - 5/9,
        t - r2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r1^2 - 5/9*r1 - 5/9,
        t - r1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 1,
        t + 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]

>> A.r2;;
     ^
User error: Identifier 'r2' has not been declared or assigned

Total time: 2.549 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:42:06 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
RadicalDecomposition(I);
r2;

Output: Magma V2.10-22    Sun Jul 25 2004 14:42:03 on modular  [Seed = 2816808961]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r3^2 - 5/9*r3 - 5/9,
        t - r3
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r2^2 - 5/9*r2 - 5/9,
        t - r2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r1^2 - 5/9*r1 - 5/9,
        t - r1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 1,
        t + 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]

>> r2;;
   ^
User error: Identifier 'r2' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:43:34 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
P:=RadicalDecomposition(I);
A.1;A.2;A.3;

Output: Magma V2.10-22    Sun Jul 25 2004 14:43:31 on modular  [Seed = 1578950737]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]
r1
r2
r3

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:43:52 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
P:=RadicalDecomposition(I);
describe(A.1);A.2;A.3;

Output: Magma V2.10-22    Sun Jul 25 2004 14:43:50 on modular  [Seed = 1444210796]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    3*z^2 - 2*z*t^3 - 2*z*t^2 - 2*z*t + t^5 + t^4 + t^3,
    -3*z^2*t^2 - 2*z^2*t - z^2 + 5*z*t^4 + 4*z*t^3 + 3*z*t^2 - 6*t^5
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z^2 - 2*z*t + 2513/24*t^11 - 14279/72*t^10 - 531/8*t^9 + 2665/9*t^8 - 
        5677/72*t^7 - 2395/24*t^6 + 2845/72*t^5 + 3*t^4 + t^3,
    z*t^2 - z*t + 973/16*t^11 - 5527/48*t^10 - 1835/48*t^9 + 2051/12*t^8 - 
        2177/48*t^7 - 2713/48*t^6 + 1021/48*t^5 + 7/4*t^4 + 1/2*t^3,
    t^12 - 52/21*t^11 + 10/21*t^10 + 67/21*t^9 - 17/7*t^8 - 10/21*t^7 + 
        20/21*t^6 - 5/21*t^5
]

>> describe(A.1);A.2;A.3;;
   ^
User error: Identifier 'describe' has not been declared or assigned
r2
r3

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:45:49 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
P:=RadicalDecomposition(I);
A;
A.1;A.2;A.3;

Output: Magma V2.10-22    Sun Jul 25 2004 14:45:46 on modular  [Seed = 1326313929]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
Algebraically closed field with 3 variables
Defining relations:
[
    r3^3 - 10/21*r3^2 - 10/21*r3 + 5/21,
    r2^3 - 10/21*r2^2 - 10/21*r2 + 5/21,
    r1^3 - 10/21*r1^2 - 10/21*r1 + 5/21
]
r1
r2
r3

Total time: 2.529 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:46:29 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2,t^3];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
P:=RadicalDecomposition(I);
P;
A;

Output: Magma V2.10-22    Sun Jul 25 2004 14:46:26 on modular  [Seed = 1191314969]
   -------------------------------------

[
    z^2 - z*t^3 - z*t^2 + t^5,
    z^2 - z*t^3 - z*t + t^4,
    z^2 - z*t^2 - z*t + t^3
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r3^2 - 5/9*r3 - 5/9,
        t - r3
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r2^2 - 5/9*r2 - 5/9,
        t - r2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 13/9*r1^2 - 5/9*r1 - 5/9,
        t - r1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z + 1,
        t + 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]
Algebraically closed field with 3 variables
Defining relations:
[
    r3^3 - 10/21*r3^2 - 10/21*r3 + 5/21,
    r2^3 - 10/21*r2^2 - 10/21*r2 + 5/21,
    r1^3 - 10/21*r1^2 - 10/21*r1 + 5/21
]

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 14:59:26 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[1,t];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
P:=RadicalDecomposition(I);
P;
A;

Output: Magma V2.10-22    Sun Jul 25 2004 14:59:23 on modular  [Seed = 1713579057]
   -------------------------------------

[
    z - t,
    z - 1
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ]
]
Algebraically closed field with no variables

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 15:00:22 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[1,t];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
gen1;
gen2;

I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
P:=RadicalDecomposition(I);
P;
A;

Output: Magma V2.10-22    Sun Jul 25 2004 15:00:20 on modular  [Seed = 172967954]
   -------------------------------------

[
    z - t,
    z - 1
]
2*z - t - 1
-z + 1
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ]
]
Algebraically closed field with no variables

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 15:09:37 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
gen1;
gen2;

I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
P:=RadicalDecomposition(I);
P;
A;

Output: Magma V2.10-22    Sun Jul 25 2004 15:09:34 on modular  [Seed = 1048279564]
   -------------------------------------

[
    z - t^2,
    z - t
]
2*z - t^2 - t
-2*z*t - z + 3*t^2
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 3/8,
        t - 1/2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]
Algebraically closed field with no variables

Total time: 2.509 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 15:10:55 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
gen1;
gen2;

I:=ideal<R|[gen1,gen2]>;
I;
GB:=GroebnerBasis(I);
I;
P:=RadicalDecomposition(I);
P;
A;

Output: Magma V2.10-22    Sun Jul 25 2004 15:10:52 on modular  [Seed = 930247639]
   -------------------------------------

[
    z - t^2,
    z - t
]
2*z - t^2 - t
-2*z*t - z + 3*t^2
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Basis:
[
    2*z - t^2 - t,
    -2*z*t - z + 3*t^2
]
Ideal of Polynomial ring of rank 2 over A
Lexicographical Order
Variables: z, t
Dimension 0
Groebner basis:
[
    z - 1/2*t^2 - 1/2*t,
    t^3 - 3/2*t^2 + 1/2*t
]
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 1,
        t - 1
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z - 3/8,
        t - 1/2
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Dimension 0, Radical, Prime
    Size of variety over algebraically closed field: 1
    Groebner basis:
    [
        z,
        t
    ]
]
Algebraically closed field with no variables

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 15:15:04 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
gen1;
gen2;
PrincIdealList:=[ideal<R|i> : i in l];
I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
WeGet:=[I meet i : i in PtincIdealList];
WeGet;


Output: Magma V2.10-22    Sun Jul 25 2004 15:15:01 on modular  [Seed = 694972096]
   -------------------------------------

[
    z - t^2,
    z - t
]
2*z - t^2 - t
-2*z*t - z + 3*t^2

>> WeGet:=[I meet i : i in PtincIdealList];
                           ^
User error: Identifier 'PtincIdealList' has not been declared or assigned

>> WeGet;
   ^
User error: Identifier 'WeGet' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-253-195-233.dsl.emhril.ameritech.net. (68.253.195.233)
Time: Sun Jul 25 15:15:41 2004

Input: A:=AlgebraicClosure();
R<z,t>:=PolynomialRing(A,2);
a:=[t,t^2];
l:=[z-i:i in a];
n:=#l;
difftl:=[Derivative(i,t):i in l];
diffzl:=[Derivative(i,z):i in l];
prod:=1; for i in l do prod*:=i; end for;
complements:=[prod div i : i in l];
complements;
gen1:=0; for i in [1..n] do gen1+:=complements[i]*diffzl[i]; end for;
gen2:=0; for i in [1..n] do gen2+:=complements[i]*difftl[i]; end for;
gen1;
gen2;
PrincIdealList:=[ideal<R|i> : i in l];
I:=ideal<R|[gen1,gen2]>;
GB:=GroebnerBasis(I);
WeGet:=[I meet i : i in PrincIdealList];
WeGet;

Output: Magma V2.10-22    Sun Jul 25 2004 15:15:38 on modular  [Seed = 560228006]
   -------------------------------------

[
    z - t^2,
    z - t
]
2*z - t^2 - t
-2*z*t - z + 3*t^2
[
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Basis:
    [
        z^2 - 7/8*z - t^2 + 7/8*t,
        z*t - 1/2*z - t^2 + 1/2*t
    ],
    Ideal of Polynomial ring of rank 2 over A
    Lexicographical Order
    Variables: z, t
    Basis:
    [
        -z^2 + z*t^2 + 3/8*z - 3/8*t^2,
        -z*t + 1/2*z + t^3 - 1/2*t^2
    ]
]

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 15:22:10 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for (i:=7 to 20) do
 FindGroupOrder2(2663848877152141313 , i)
end for

Output: Magma V2.10-22    Sun Jul 25 2004 15:22:08 on modular  [Seed = 4240029120]
   -------------------------------------


>> for (i:=7 to 20) do
       ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 15:22:25 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 20 do
 FindGroupOrder2(2663848877152141313 , i)
end for

Output: Magma V2.10-22    Sun Jul 25 2004 15:22:22 on modular  [Seed = 4105289159]
   -------------------------------------


>> end for;
   ^
User error: bad syntax

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 15:24:22 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 20 do
 FindGroupOrder2(2663848877152141313 , i);
end for;

Output: Magma V2.10-22    Sun Jul 25 2004 15:24:14 on modular  [Seed = 4004226924]
   -------------------------------------

[ <2, 2>, <3, 2>, <7, 1>, <29, 1>, <59, 1>, <2801, 1>, <15101, 1>, <146063, 1> ]
[ <2, 3>, <3, 2>, <5279, 1>, <6719, 1>, <1043087603, 1> ]
[ <2, 5>, <3, 2>, <23, 1>, <402151098850511, 1> ]
[ <2, 2>, <3, 1>, <5309, 1>, <41813412386717, 1> ]
[ <2, 3>, <3, 1>, <73, 1>, <379, 1>, <97429, 1>, <41176367, 1> ]
[ <2, 2>, <3, 2>, <7, 1>, <10570828869116387, 1> ]
[ <2, 3>, <3, 1>, <229703, 1>, <483205283647, 1> ]
[ <2, 2>, <3, 1>, <19, 1>, <1153, 1>, <10133172340481, 1> ]
[ <2, 3>, <3, 1>, <5, 1>, <2383, 1>, <9315459775213, 1> ]
[ <2, 4>, <3, 2>, <19, 1>, <36277, 1>, <26838740143, 1> ]
[ <2, 3>, <3, 1>, <11, 1>, <17, 1>, <379, 1>, <839, 1>, <26371, 1>, <70783, 1> ]
[ <2, 4>, <3, 1>, <19, 1>, <318749, 1>, <9163595587, 1> ]
[ <2, 3>, <3, 2>, <5, 1>, <19, 1>, <229, 1>, <659, 1>, <2580670661, 1> ]
[ <2, 2>, <3, 1>, <7, 2>, <1993, 1>, <859297, 1>, <2645341, 1> ]

Total time: 6.869 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 16:40:33 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 7 do
 FindGroupOrder2(4659775785220018543264560743076778192897 , i);
end for;

Output: Magma V2.10-22    Sun Jul 25 2004 16:40:24 on modular  [Seed = 324421876]
   -------------------------------------

[ <2, 2>, <3, 1>, <7, 1>, <11, 1>, <2837629, 1>, <55887879433, 1>, 
<31799464290970311203, 1> ]

Total time: 9.059 seconds, Total memory usage: 4.00MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 16:41:42 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=8 to 9 do
 FindGroupOrder2(4659775785220018543264560743076778192897 , i);
end for;

Output: Magma V2.10-22    Sun Jul 25 2004 16:41:25 on modular  [Seed = 155996835]
   -------------------------------------

[ <2, 6>, <3, 1>, <67, 1>, <389, 1>, <3337848793, 1>, <278979780703308733835053,
1> ]
[ <2, 2>, <3, 2>, <23, 1>, <5627748532874418530423904299981266433, 1> ]

Total time: 16.949 seconds, Total memory usage: 4.17MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 16:43:10 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=10 to 11 do
 FindGroupOrder2(4659775785220018543264560743076778192897 , i);
end for;

Output: Magma V2.10-22    Sun Jul 25 2004 16:42:57 on modular  [Seed = 4545038]
   -------------------------------------

[ <2, 4>, <3, 2>, <13, 1>, <67, 1>, <191, 1>, <499, 1>, 
<389807741835736037089745043961, 1> ]
[ <2, 2>, <3, 3>, <5, 1>, <31, 1>, <283, 1>, <41051, 1>, 
<23960693846006029746418084759, 1> ]

Total time: 12.759 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Sun Jul 25 16:48:52 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=12 to 13 do
 FindGroupOrder2(4659775785220018543264560743076778192897 , i);
end for;

Output: Magma V2.10-22    Sun Jul 25 2004 16:48:38 on modular  [Seed = 913533903]
   -------------------------------------

[ <2, 2>, <3, 3>, <7, 1>, <17, 1>, <59, 1>, <727, 1>, <43319737469, 1>, 
<195129110506794337343, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <53, 1>, <269, 1>, <2297, 1>, <2370392901973, 1>, 
<1000470498921487757, 1> ]

Total time: 13.979 seconds, Total memory usage: 4.53MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:01:04 2004

Input:  C := HyperellipticCurve(x^6+x^2+1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:01:01 on modular  [Seed = 3481964829]
   -------------------------------------


>>  C := HyperellipticCurve(x^6+x^2+1);;
                            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:01:30 2004

Input:  P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^6+x^2+1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:01:27 on modular  [Seed = 3330512958]
   -------------------------------------


Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:01:58 2004

Input:  P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^6+x^2+1);
Points(C : Bound := 1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:01:55 on modular  [Seed = 4273709154]
   -------------------------------------

{@ (1 : -1 : 0), (1 : 1 : 0), (0 : -1 : 1), (0 : 1 : 1) @}

Total time: 2.599 seconds, Total memory usage: 29.49MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:02:31 2004

Input:  P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^5+x^2+1);
Points(C : Bound := 1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:02:29 on modular  [Seed = 4138969164]
   -------------------------------------

{@ (1 : 0 : 0), (-1 : -1 : 1), (-1 : 1 : 1), (0 : -1 : 1), (0 : 1 : 1) @}

Total time: 2.579 seconds, Total memory usage: 29.49MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:02:44 2004

Input:  P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^3+x^2+1);
Points(C : Bound := 1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:02:42 on modular  [Seed = 4004229187]
   -------------------------------------

{@ (1 : 0 : 0), (-1 : -1 : 1), (-1 : 1 : 1), (0 : -1 : 1), (0 : 1 : 1) @}

Total time: 2.589 seconds, Total memory usage: 29.49MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:02:53 2004

Input:  P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^3+x^2-1);
Points(C : Bound := 1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:02:50 on modular  [Seed = 3852516160]
   -------------------------------------

{@ (1 : 0 : 0), (1 : -1 : 1), (1 : 1 : 1) @}

Total time: 2.599 seconds, Total memory usage: 29.49MB


************** MAGMA *****************
Host d235-148-13.home1.cgocable.net. (24.235.148.13)
Time: Sun Jul 25 17:03:00 2004

Input:  P<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^3+x^2-31);
Points(C : Bound := 1);

Output: Magma V2.10-22    Sun Jul 25 2004 17:02:58 on modular  [Seed = 2648243392]
   -------------------------------------

{@ (1 : 0 : 0) @}

Total time: 2.579 seconds, Total memory usage: 29.49MB


************** MAGMA *****************
Host pD9EB6AE0.dip0.t-ipconnect.de. (217.235.106.224)
Time: Sun Jul 25 18:03:14 2004

Input: Factorization(120);

Output: Magma V2.10-22    Sun Jul 25 2004 18:03:11 on modular  [Seed = 863394930]
   -------------------------------------

[ <2, 3>, <3, 1>, <5, 1> ]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pD9EB6AE0.dip0.t-ipconnect.de. (217.235.106.224)
Time: Sun Jul 25 18:08:43 2004

Input: R<x>:=PolynomialRing(RationalField());
C:=HyperellipticCurve(x^5+1);
J:=Jacobian(C);
N:=Conductor(J);
N;

Output: Magma V2.10-22    Sun Jul 25 2004 18:08:40 on modular  [Seed = 577195028]
   -------------------------------------


>> N:=Conductor(J);
               ^
Runtime error in 'Conductor': Bad argument types
Argument types given: JacHyp

>> N;;
   ^
User error: Identifier 'N' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9EB6AE0.dip0.t-ipconnect.de. (217.235.106.224)
Time: Sun Jul 25 18:09:03 2004

Input: R<x>:=PolynomialRing(RationalField());
C:=HyperellipticCurve(x^5+1);
J:=Jacobian(C);
N:=Conductor(C);
N;

Output: Magma V2.10-22    Sun Jul 25 2004 18:09:01 on modular  [Seed = 3667899641]
   -------------------------------------


>> N:=Conductor(C);
               ^
Runtime error in 'Conductor': Bad argument types
Argument types given: CrvHyp

>> N;;
   ^
User error: Identifier 'N' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9EB6AE0.dip0.t-ipconnect.de. (217.235.106.224)
Time: Sun Jul 25 18:09:35 2004

Input: ?Conductor

Output: Magma V2.10-22    Sun Jul 25 2004 18:09:32 on modular  [Seed = 3533159440]
   -------------------------------------

13 matches:
     1   I   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:brandt-modules/Elementary-Invariants/Conductor
     2   I   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             database/ConductorRange
     3   I   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             database/LargestConductor
     4   I   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             rational_curves/rational_curves-local/Conductor
     5   I   /magma/module-lattice/quadratic/invariants/Conductor
     6   I   /magma/ring-field-algebra/abelian-extension/invariants/Conductor
     7   I   /magma/ring-field-algebra/algebraic-field/operation/invariant/\
             Conductor
     8   I   /magma/ring-field-algebra/cyclotomic/structure/invariant/Conductor
     9   I   /magma/ring-field-algebra/function-field/class-fields/properties/\
             Conductor
    10   I   /magma/ring-field-algebra/function-field/class-fields/properties/\
             Conductor
    11   I   /magma/ring-field-algebra/quadratic/structure_ops/Conductor
    12   I   /magma/ring-field-algebra/quadratic/structure_ops/Conductor
    13   I   /magma/ring-field-algebra/rational/operation/invariant/Conductor
To view an entry, type ? followed by the number next to it

Total time: 2.509 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 18:58:18 2004

Input: JustesenCode(1, 2)

Output: Magma V2.10-22    Sun Jul 25 2004 18:58:15 on modular  [Seed = 2050949148]
   -------------------------------------


>> JustesenCode(1, 2);
               ^
Runtime error in 'JustesenCode': Argument 2 (2) should be in the range [1 .. 0]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 18:58:30 2004

Input: JustesenCode(2,1)

Output: Magma V2.10-22    Sun Jul 25 2004 18:58:28 on modular  [Seed = 1157644080]
   -------------------------------------


>> JustesenCode(2,1);
               ^
Runtime error in 'JustesenCode':  N must be of the form 2^k-1

Total time: 2.499 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 18:58:49 2004

Input: JustesenCode(3,1)

Output: Magma V2.10-22    Sun Jul 25 2004 18:58:47 on modular  [Seed = 1292384011]
   -------------------------------------

[12, 2, 7] Linear Code over GF(2)
Generator matrix:
[1 0 1 0 1 0 0 1 1 0 1 1]
[0 1 0 1 0 1 1 1 0 1 1 0]

Total time: 2.509 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 18:59:02 2004

Input: JustesenCode(3,1)

Output: Magma V2.10-22    Sun Jul 25 2004 18:59:00 on modular  [Seed = 1427123968]
   -------------------------------------

[12, 2, 7] Linear Code over GF(2)
Generator matrix:
[1 0 1 0 1 0 0 1 1 0 1 1]
[0 1 0 1 0 1 1 1 0 1 1 0]

Total time: 2.499 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 18:59:30 2004

Input: JustesenCode(3,2)

Output: Magma V2.10-22    Sun Jul 25 2004 18:59:28 on modular  [Seed = 1545152109]
   -------------------------------------

[12, 4, 4] Linear Code over GF(2)
Generator matrix:
[1 0 1 0 0 0 0 0 0 1 1 0]
[0 1 0 1 0 0 0 0 1 1 0 1]
[0 0 0 0 1 0 0 1 1 1 0 1]
[0 0 0 0 0 1 1 1 1 0 1 1]

Total time: 2.489 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:00:09 2004

Input: JustesenCode(1,0)

Output: Magma V2.10-22    Sun Jul 25 2004 19:00:07 on modular  [Seed = 947733038]
   -------------------------------------


>> JustesenCode(1,0);
               ^
Runtime error in 'JustesenCode': Argument 2 (0) should be in the range [1 .. 0]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:00:29 2004

Input: JustesenCode(1,1)

Output: Magma V2.10-22    Sun Jul 25 2004 19:00:26 on modular  [Seed = 4553451]
   -------------------------------------


>> JustesenCode(1,1);
               ^
Runtime error in 'JustesenCode': Argument 2 (1) should be in the range [1 .. 0]

Total time: 2.479 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:00:51 2004

Input: JustesenCode(3,1)

Output: Magma V2.10-22    Sun Jul 25 2004 19:00:49 on modular  [Seed = 139293384]
   -------------------------------------

[12, 2, 7] Linear Code over GF(2)
Generator matrix:
[1 0 1 0 1 0 0 1 1 0 1 1]
[0 1 0 1 0 1 1 1 0 1 1 0]

Total time: 2.499 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:03:16 2004

Input: JustesenCode(3,2)

Output: Magma V2.10-22    Sun Jul 25 2004 19:03:13 on modular  [Seed = 274033984]
   -------------------------------------

[12, 4, 4] Linear Code over GF(2)
Generator matrix:
[1 0 1 0 0 0 0 0 0 1 1 0]
[0 1 0 1 0 0 0 0 1 1 0 1]
[0 0 0 0 1 0 0 1 1 1 0 1]
[0 0 0 0 0 1 1 1 1 0 1 1]

Total time: 2.499 seconds, Total memory usage: 1.90MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:03:42 2004

Input: JustesenCode(3,3)

Output: Magma V2.10-22    Sun Jul 25 2004 19:03:40 on modular  [Seed = 408773941]
   -------------------------------------


>> JustesenCode(3,3);
               ^
Runtime error in 'JustesenCode': Argument 2 (3) should be in the range [1 .. 2]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:04:00 2004

Input: JustesenCode(4,1)

Output: Magma V2.10-22    Sun Jul 25 2004 19:03:58 on modular  [Seed = 3768950239]
   -------------------------------------


>> JustesenCode(4,1);
               ^
Runtime error in 'JustesenCode':  N must be of the form 2^k-1

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:04:10 2004

Input: JustesenCode(7,1)

Output: Magma V2.10-22    Sun Jul 25 2004 19:04:07 on modular  [Seed = 3903690222]
   -------------------------------------

[42, 3, 19] Linear Code over GF(2)
Generator matrix:
[1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1
    0 1]
[0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1
    0 0]
[0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0
    1 0]

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:04:45 2004

Input: JustesenCode(7,2)

Output: Magma V2.10-22    Sun Jul 25 2004 19:04:42 on modular  [Seed = 4038429979]
   -------------------------------------

[42, 6, 17] Linear Code over GF(2)
Generator matrix:
[1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0
    1 0]
[0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0
    0 1]
[0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1
    1 0]
[0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1
    1 1]
[0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1
    0 1]
[0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1
    0 0]

Total time: 2.479 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:05:13 2004

Input: JustesenCode(7,3)

Output: Magma V2.10-22    Sun Jul 25 2004 19:05:11 on modular  [Seed = 4223567421]
   -------------------------------------

[42, 9, 12] Linear Code over GF(2)
Generator matrix:
[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0
    0 1]
[0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1
    1 0]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0
    1 1]
[0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0
    1 0]
[0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0
    0 1]
[0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1
    1 1]

Total time: 2.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:05:35 2004

Input: JustesenCode(7,4)

Output: Magma V2.10-22    Sun Jul 25 2004 19:05:32 on modular  [Seed = 3280387614]
   -------------------------------------

[42, 12, 9] Linear Code over GF(2)
Generator matrix:
[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1
    1 1]
[0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1
    0 1]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1
    0 0]
[0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1
    1 1]
[0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1
    0 1]
[0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1
    0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0
    0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1
    0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0
    0 1]

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:06:01 2004

Input: JustesenCode(7,5)

Output: Magma V2.10-22    Sun Jul 25 2004 19:05:58 on modular  [Seed = 3415127676]
   -------------------------------------

[42, 15, 7] Linear Code over GF(2)
Generator matrix:
[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1
    1 0]
[0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0
    1 1]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1
    1 1]
[0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1
    0 1]
[0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1
    0 0]
[0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1
    0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1
    0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1
    1 1]

Total time: 2.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pu84.wroclaw.sdi.tpnet.pl. (217.98.142.84)
Time: Sun Jul 25 19:06:14 2004

Input: JustesenCode(7,4)

Output: Magma V2.10-22    Sun Jul 25 2004 19:06:12 on modular  [Seed = 3549867606]
   -------------------------------------

[42, 12, 9] Linear Code over GF(2)
Generator matrix:
[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1
    1 1]
[0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1
    0 1]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1
    0 0]
[0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1
    1 1]
[0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1
    0 1]
[0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1
    0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0
    0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0
    1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1
    0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0
    1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0
    0 1]

Total time: 2.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host cflow1.csv.warwick.ac.uk. (137.205.8.2)
Time: Mon Jul 26 05:11:07 2004

Input: Factorization(12344567);

Output: Magma V2.10-22    Mon Jul 26 2004 05:11:04 on modular  [Seed = 2117858748]
   -------------------------------------

[ <17, 1>, <41, 1>, <89, 1>, <199, 1> ]

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host cflow1.csv.warwick.ac.uk. (137.205.8.2)
Time: Mon Jul 26 05:11:25 2004

Input: Factorization(12344567);

D := K3Database();
#D;


Output: Magma V2.10-22    Mon Jul 26 2004 05:11:22 on modular  [Seed = 1983118758]
   -------------------------------------

[ <17, 1>, <41, 1>, <89, 1>, <199, 1> ]
391

Total time: 2.959 seconds, Total memory usage: 2.84MB


************** MAGMA *****************
Host cflow1.csv.warwick.ac.uk. (137.205.8.2)
Time: Mon Jul 26 05:11:49 2004

Input: Factorization(12344567);

D := K3Database();
#D;

D;

Output: Magma V2.10-22    Mon Jul 26 2004 05:11:46 on modular  [Seed = 1309394422]
   -------------------------------------

[ <17, 1>, <41, 1>, <89, 1>, <199, 1> ]
391
[
    Codimension 2 K3 surface, number 1, Fletcher2(82), with data
      Weights: [ 3, 4, 7, 10, 17 ]
      Numerator: $.1^41 - $.1^21 - $.1^20 + 1
      Basket: [ 2, 1 ], [ 17, 7 ],
    Codimension 3 K3 surface, number 2, Altinok3(48), with data
      Weights: [ 2, 3, 5, 5, 7, 12 ]
      Numerator: -$.1^34 + $.1^24 + $.1^22 + $.1^20 + $.1^19 - $.1^15 - $.1^14 -
    $.1^12 - $.1^10 + 1
      Basket: [ 5, 2 ], [ 12, 5 ],
    Codimension 2 K3 surface, number 3, Fletcher2(81), with data
      Weights: [ 2, 5, 9, 11, 13 ]
      Numerator: $.1^40 - $.1^22 - $.1^18 + 1
      Basket: [ 5, 1 ], [ 13, 2 ],
    Codimension 1 K3 surface, number 4, Reid1(79), with data
      Weights: [ 3, 5, 11, 14 ]
      Numerator: -$.1^33 + 1
      Basket: [ 5, 1 ], [ 14, 3 ],
    Codimension 2 K3 surface, number 5, Fletcher2(79), with data
      Weights: [ 4, 5, 7, 9, 13 ]
      Numerator: $.1^38 - $.1^20 - $.1^18 + 1
      Basket: [ 7, 2 ], [ 13, 4 ],
    Codimension 3 K3 surface, number 6, Altinok3(47), with data
      Weights: [ 2, 3, 5, 7, 8, 9 ]
      Numerator: -$.1^34 + $.1^24 + $.1^22 + $.1^20 + $.1^19 - $.1^15 - $.1^14 -
    $.1^12 - $.1^10 + 1
      Basket: [ 8, 3 ], [ 9, 2 ],
    Codimension 3 K3 surface, number 7, Altinok3(46), with data
      Weights: [ 3, 4, 5, 7, 8, 11 ]
      Numerator: -$.1^38 + $.1^26 + $.1^24 + $.1^23 + $.1^22 - $.1^16 - $.1^15 -
    $.1^14 - $.1^12 + 1
      Basket: [ 8, 3 ], [ 11, 4 ],
    Codimension 2 K3 surface, number 8, Fletcher2(71), with data
      Weights: [ 2, 3, 5, 8, 13 ]
      Numerator: $.1^31 - $.1^16 - $.1^15 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 13, 5 ],
    Codimension 2 K3 surface, number 9, Fletcher2(64), with data
      Weights: [ 2, 3, 5, 7, 12 ]
      Numerator: $.1^29 - $.1^15 - $.1^14 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 12, 5 ],
    Codimension 1 K3 surface, number 10, Reid1(74), with data
      Weights: [ 3, 4, 10, 13 ]
      Numerator: -$.1^30 + 1
      Basket: [ 2, 1 ], [ 4, 1 ], [ 13, 3 ],
    Codimension 1 K3 surface, number 11, Reid1(65), with data
      Weights: [ 2, 5, 9, 11 ]
      Numerator: -$.1^27 + 1
      Basket: [ 2, 1 ], [ 5, 1 ], [ 11, 2 ],
    Codimension 1 K3 surface, number 12, Reid1(91), with data
      Weights: [ 4, 5, 13, 22 ]
      Numerator: -$.1^44 + 1
      Basket: [ 2, 1 ], [ 5, 2 ], [ 13, 4 ],
    Codimension 3 K3 surface, number 13, Altinok3(51), with data
      Weights: [ 2, 5, 6, 7, 9, 11 ]
      Numerator: -$.1^40 + $.1^26 + $.1^25 + $.1^24 + $.1^23 + $.1^22 - $.1^18 -
    $.1^17 - $.1^16 - $.1^15 - $.1^14 + 1
      Basket: [ 2, 1 ], [ 6, 1 ], [ 11, 2 ],
    Codimension 2 K3 surface, number 14, Fletcher2(52), with data
      Weights: [ 2, 3, 5, 7, 8 ]
      Numerator: $.1^25 - $.1^15 - $.1^10 + 1
      Basket: [ 2, 1 ], [ 7, 2 ], [ 8, 3 ],
    Codimension 1 K3 surface, number 15, Reid1(58), with data
      Weights: [ 3, 4, 7, 10 ]
      Numerator: -$.1^24 + 1
      Basket: [ 2, 1 ], [ 7, 3 ], [ 10, 3 ],
    Codimension 1 K3 surface, number 16, Reid1(76), with data
      Weights: [ 5, 6, 8, 11 ]
      Numerator: -$.1^30 + 1
      Basket: [ 2, 1 ], [ 8, 3 ], [ 11, 5 ],
    Codimension 2 K3 surface, number 17, Fletcher2(73), with data
      Weights: [ 2, 3, 7, 9, 11 ]
      Numerator: $.1^32 - $.1^18 - $.1^14 + 1
      Basket: [ 3, 1 ], [ 3, 1 ], [ 11, 2 ],
    Codimension 2 K3 surface, number 18, Fletcher2(57), with data
      Weights: [ 2, 3, 5, 7, 9 ]
      Numerator: $.1^26 - $.1^14 - $.1^12 + 1
      Basket: [ 3, 1 ], [ 5, 2 ], [ 9, 2 ],
    Codimension 1 K3 surface, number 19, Reid1(85), with data
      Weights: [ 3, 5, 11, 19 ]
      Numerator: -$.1^38 + 1
      Basket: [ 3, 1 ], [ 5, 1 ], [ 11, 3 ],
    Codimension 2 K3 surface, number 20, Fletcher2(69), with data
      Weights: [ 3, 4, 5, 7, 11 ]
      Numerator: $.1^30 - $.1^16 - $.1^14 + 1
      Basket: [ 3, 1 ], [ 5, 2 ], [ 11, 4 ],
    Codimension 3 K3 surface, number 21, Altinok3(60), with data
      Weights: [ 3, 5, 6, 7, 8, 11 ]
      Numerator: -$.1^40 + $.1^26 + $.1^25 + $.1^24 + $.1^23 + $.1^22 - $.1^18 -
    $.1^17 - $.1^16 - $.1^15 - $.1^14 + 1
      Basket: [ 3, 1 ], [ 6, 1 ], [ 11, 3 ],
    Codimension 2 K3 surface, number 22, Fletcher2(50), with data
      Weights: [ 2, 3, 5, 7, 7 ]
      Numerator: $.1^24 - $.1^14 - $.1^10 + 1
      Basket: [ 3, 1 ], [ 7, 2 ], [ 7, 2 ],
    Codimension 2 K3 surface, number 23, Fletcher2(80), with data
      Weights: [ 5, 6, 7, 9, 11 ]
      Numerator: $.1^38 - $.1^20 - $.1^18 + 1
      Basket: [ 3, 1 ], [ 7, 2 ], [ 11, 5 ],
    Codimension 2 K3 surface, number 24, Fletcher2(72), with data
      Weights: [ 3, 4, 5, 8, 11 ]
      Numerator: $.1^31 - $.1^16 - $.1^15 + 1
      Basket: [ 4, 1 ], [ 4, 1 ], [ 11, 3 ],
    Codimension 2 K3 surface, number 25, Fletcher2(66), with data
      Weights: [ 3, 4, 5, 7, 10 ]
      Numerator: $.1^29 - $.1^15 - $.1^14 + 1
      Basket: [ 4, 1 ], [ 5, 2 ], [ 10, 3 ],
    Codimension 2 K3 surface, number 26, Fletcher2(62), with data
      Weights: [ 3, 4, 5, 7, 8 ]
      Numerator: $.1^27 - $.1^15 - $.1^12 + 1
      Basket: [ 4, 1 ], [ 7, 3 ], [ 8, 3 ],
    Codimension 1 K3 surface, number 27, Reid1(61), with data
      Weights: [ 4, 5, 7, 9 ]
      Numerator: -$.1^25 + 1
      Basket: [ 4, 1 ], [ 7, 2 ], [ 9, 4 ],
    Codimension 2 K3 surface, number 28, Fletcher2(44), with data
      Weights: [ 2, 3, 5, 5, 7 ]
      Numerator: $.1^22 - $.1^12 - $.1^10 + 1
      Basket: [ 5, 2 ], [ 5, 2 ], [ 7, 2 ],
    Codimension 2 K3 surface, number 29, Fletcher2(58), with data
      Weights: [ 3, 4, 5, 7, 7 ]
      Numerator: $.1^26 - $.1^14 - $.1^12 + 1
      Basket: [ 5, 2 ], [ 7, 3 ], [ 7, 3 ],
    Codimension 1 K3 surface, number 30, Reid1(56), with data
      Weights: [ 2, 3, 8, 11 ]
      Numerator: -$.1^24 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 2, 1 ], [ 11, 3 ],
    Codimension 2 K3 surface, number 31, Fletcher2(78), with data
      Weights: [ 4, 5, 6, 9, 14 ]
      Numerator: $.1^38 - $.1^20 - $.1^18 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 3, 1 ], [ 14, 5 ],
    Codimension 1 K3 surface, number 32, Reid1(38), with data
      Weights: [ 2, 3, 5, 8 ]
      Numerator: -$.1^18 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 5, 2 ], [ 8, 3 ],
    Codimension 1 K3 surface, number 33, Reid1(77), with data
      Weights: [ 2, 5, 9, 16 ]
      Numerator: -$.1^32 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 5, 1 ], [ 9, 2 ],
    Codimension 2 K3 surface, number 34, Fletcher2(65), with data
      Weights: [ 2, 5, 6, 7, 9 ]
      Numerator: $.1^29 - $.1^15 - $.1^14 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 6, 1 ], [ 9, 2 ],
    Codimension 1 K3 surface, number 35, Reid1(69), with data
      Weights: [ 4, 6, 7, 11 ]
      Numerator: -$.1^28 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 6, 1 ], [ 11, 4 ],
    Codimension 3 K3 surface, number 36, Altinok3(52), with data
      Weights: [ 2, 3, 4, 5, 7, 7 ]
      Numerator: -$.1^28 + $.1^19 + $.1^18 + $.1^17 + $.1^16 - $.1^12 - $.1^11 -
    $.1^10 - $.1^9 + 1
      Basket: [ 2, 1 ], [ 2, 1 ], [ 7, 2 ], [ 7, 3 ],
    Codimension 1 K3 surface, number 37, Reid1(48), with data
      Weights: [ 2, 3, 7, 9 ]
      Numerator: -$.1^21 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 3, 1 ], [ 9, 2 ],
    Codimension 1 K3 surface, number 38, Reid1(83), with data
      Weights: [ 3, 4, 11, 18 ]
      Numerator: -$.1^36 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 3, 1 ], [ 11, 4 ],
    Codimension 3 K3 surface, number 39, Altinok3(67), with data
      Weights: [ 2, 3, 4, 5, 7, 9 ]
      Numerator: -$.1^30 + $.1^20 + $.1^19 + $.1^18 + $.1^17 + $.1^16 - $.1^14 -
    $.1^13 - $.1^12 - $.1^11 - $.1^10 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 4, 1 ], [ 9, 2 ],
    Codimension 1 K3 surface, number 40, Reid1(80), with data
      Weights: [ 3, 4, 10, 17 ]
      Numerator: -$.1^34 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 4, 1 ], [ 10, 3 ],
    Codimension 1 K3 surface, number 41, Reid1(33), with data
      Weights: [ 2, 3, 5, 7 ]
      Numerator: -$.1^17 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 5, 2 ], [ 7, 2 ],
    Codimension 3 K3 surface, number 42, Altinok3(63), with data
      Weights: [ 3, 4, 5, 6, 7, 10 ]
      Numerator: -$.1^35 + $.1^23 + $.1^22 + $.1^21 + $.1^20 + $.1^19 - $.1^16 -
    $.1^15 - $.1^14 - $.1^13 - $.1^12 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 5, 1 ], [ 10, 3 ],
    Codimension 1 K3 surface, number 43, Reid1(95), with data
      Weights: [ 5, 6, 22, 33 ]
      Numerator: -$.1^66 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 5, 2 ], [ 11, 5 ],
    Codimension 1 K3 surface, number 44, Reid1(68), with data
      Weights: [ 3, 4, 7, 14 ]
      Numerator: -$.1^28 + 1
      Basket: [ 2, 1 ], [ 3, 1 ], [ 7, 3 ], [ 7, 3 ],
    Codimension 3 K3 surface, number 45, Altinok3(68), with data
      Weights: [ 2, 3, 4, 5, 5, 7 ]
      Numerator: -$.1^26 + $.1^17 + 2*$.1^16 + $.1^15 + $.1^14 - $.1^12 - $.1^11
    - 2*$.1^10 - $.1^9 + 1
      Basket: [ 2, 1 ], [ 4, 1 ], [ 5, 2 ], [ 7, 2 ],
    Codimension 1 K3 surface, number 46, Reid1(94), with data
      Weights: [ 4, 5, 18, 27 ]
      Numerator: -$.1^54 + 1
      Basket: [ 2, 1 ], [ 4, 1 ], [ 5, 2 ], [ 9, 4 ],
    Codimension 1 K3 surface, number 47, Reid1(27), with data
      Weights: [ 2, 3, 5, 5 ]
      Numerator: -$.1^15 + 1
      Basket: [ 2, 1 ], [ 5, 2 ], [ 5, 2 ], [ 5, 2 ],
    Codimension 1 K3 surface, number 48, Reid1(86), with data
      Weights: [ 5, 6, 8, 19 ]
      Numerator: -$.1^38 + 1
      Basket: [ 2, 1 ], [ 5, 1 ], [ 6, 1 ], [ 8, 3 ],
    Codimension 1 K3 surface, number 49, Reid1(93), with data
      Weights: [ 7, 8, 10, 25 ]
      Numerator: -$.1^50 + 1
      Basket: [ 2, 1 ], [ 5, 2 ], [ 7, 3 ], [ 8, 1 ],
    Codimension 3 K3 surface, number 50, Altinok3(45), with data
      Weights: [ 3, 3, 4, 5, 7, 10 ]
      Numerator: -$.1^32 + $.1^22 + $.1^20 + $.1^19 + $.1^18 + $.1^17 - $.1^15 -
    $.1^14 - $.1^13 - $.1^12 - $.1^10 + 1
      Basket: [ 3, 1 ], [ 3, 1 ], [ 3, 1 ], [ 10, 3 ],
    Codi
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host cflow1.csv.warwick.ac.uk. (137.205.8.2)
Time: Mon Jul 26 05:12:10 2004

Input: Factorization(12344567);

D := K3Database();
#D;

D;

%ls

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host cflow1.csv.warwick.ac.uk. (137.205.8.2)
Time: Mon Jul 26 05:12:28 2004

Input: Factorization(12344567);

D := K3Database();
#D;

D;
Cputime();

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.

************** MAGMA *****************
Host schneider.ruf.uni-freiburg.de. (132.230.9.119)
Time: Mon Jul 26 06:55:30 2004

Input: g=symmetric(5);


Output: Magma V2.10-22    Mon Jul 26 2004 06:55:27 on modular  [Seed = 3330499764]
   -------------------------------------


>> g=symmetric(5);
     ^
User error: Identifier 'symmetric' has not been declared or assigned

Total time: 2.529 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Mon Jul 26 09:29:00 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=31 to 40 do
  FindGroupOrder2(3560841906445833920513, i);
end for;

Output: Magma V2.10-22    Mon Jul 26 2004 09:28:51 on modular  [Seed = 2260910329]
   -------------------------------------

[ <2, 8>, <3, 1>, <197, 1>, <271, 1>, <86847226835459, 1> ]
[ <2, 5>, <3, 1>, <19, 1>, <67, 1>, <8712713, 1>, <3344257019, 1> ]
[ <2, 3>, <3, 2>, <43, 1>, <107, 1>, <10748997519980141, 1> ]
[ <2, 5>, <3, 1>, <7, 1>, <570251441, 1>, <9292167461, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <59347365107828826451, 1> ]
[ <2, 2>, <3, 1>, <11, 1>, <37, 1>, <1627, 1>, <193183, 1>, <2319639941, 1> ]
[ <2, 13>, <3, 1>, <5, 1>, <11, 1>, <37, 1>, <5683, 1>, <65287, 1>, <191899, 1> 
]
[ <2, 2>, <3, 4>, <17, 1>, <646485458701624511, 1> ]
[ <2, 3>, <3, 1>, <148368412771380330013, 1> ]
[ <2, 5>, <3, 1>, <5, 1>, <24118331, 1>, <307584328217, 1> ]

Total time: 7.849 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Mon Jul 26 09:39:37 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;2319639941
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=41 to 50 do
  FindGroupOrder2(3560841906445833920513, i);
end for;

Output: Magma V2.10-22    Mon Jul 26 2004 09:39:34 on modular  [Seed = 2615137121]
   -------------------------------------


>>    x := x/v^3;
      ^
User error: bad syntax

>>    b := x^3 + A*x^2 + x;
           ^
User error: Identifier 'x' has not been declared or assigned

>>    E := EllipticCurve([0,b*A,0,b^2,0]);
                            ^
User error: Identifier 'b' has not been declared or assigned

>>    return FactoredOrder(E);
      ^
User error: A 'return' can only be used inside a procedure or function

>> end function;
   ^
User error: bad syntax

>>   FindGroupOrder2(3560841906445833920513, i);
     ^
User error: Identifier 'FindGroupOrder2' has not been declared or assigned

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Mon Jul 26 09:40:02 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;2319639941
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=31 to 40 do
  FindGroupOrder2(3560841906445833920513, i);
end for;

Output: Magma V2.10-22    Mon Jul 26 2004 09:39:59 on modular  [Seed = 1865099183]
   -------------------------------------


>>    x := x/v^3;
      ^
User error: bad syntax

>>    b := x^3 + A*x^2 + x;
           ^
User error: Identifier 'x' has not been declared or assigned

>>    E := EllipticCurve([0,b*A,0,b^2,0]);
                            ^
User error: Identifier 'b' has not been declared or assigned

>>    return FactoredOrder(E);
      ^
User error: A 'return' can only be used inside a procedure or function

>> end function;
   ^
User error: bad syntax

>>   FindGroupOrder2(3560841906445833920513, i);
     ^
User error: Identifier 'FindGroupOrder2' has not been declared or assigned

Total time: 2.519 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Mon Jul 26 09:41:00 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=41 to 50 do
  FindGroupOrder2(3560841906445833920513, i);
end for;

Output: Magma V2.10-22    Mon Jul 26 2004 09:40:53 on modular  [Seed = 1949318398]
   -------------------------------------

[ <2, 6>, <3, 1>, <13, 1>, <1426619353590814307, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <7, 1>, <109, 1>, <149, 1>, <12437, 1>, <41973482267, 
1> ]
[ <2, 2>, <3, 1>, <5, 1>, <173, 1>, <12821, 1>, <26756754794083, 1> ]
[ <2, 4>, <3, 3>, <13, 1>, <103, 1>, <6155854815905117, 1> ]
[ <2, 3>, <3, 2>, <487, 1>, <101552643920870687, 1> ]
[ <2, 2>, <3, 2>, <5, 1>, <1346658721, 1>, <14690028533, 1> ]
[ <2, 2>, <3, 3>, <109, 1>, <302484021955936091, 1> ]
[ <2, 4>, <3, 1>, <43, 1>, <63907, 1>, <26995698468061, 1> ]
[ <2, 4>, <3, 1>, <13, 1>, <227, 1>, <22783, 1>, <1103395822429, 1> ]
[ <2, 2>, <3, 1>, <23, 1>, <12901601110215347633, 1> ]

Total time: 7.369 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host adsl-68-75-189-24.dsl.emhril.ameritech.net. (68.75.189.24)
Time: Tue Jul 27 01:57:42 2004

Input: 2(3 + 18/5)^2/(2*18/5 + 5)

Output: Magma V2.10-22    Tue Jul 27 2004 01:57:39 on modular  [Seed = 947689360]
   -------------------------------------


>> 2(3 + 18/5)^2/(2*18/5 + 5);
    ^
Runtime error: Bad argument types
Argument types given: FldRatElt, RngIntElt

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host adsl-68-75-189-24.dsl.emhril.ameritech.net. (68.75.189.24)
Time: Tue Jul 27 01:57:52 2004

Input: 2*(3 + 18/5)^2/(2*18/5 + 5)

Output: Magma V2.10-22    Tue Jul 27 2004 01:57:49 on modular  [Seed = 812949398]
   -------------------------------------

2178/305

Total time: 2.489 seconds, Total memory usage: 1.70MB


************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Tue Jul 27 05:00:19 2004

Input: 2+2


Output: Magma V2.11-2     Tue Jul 27 2004 05:00:18 on modular  [Seed = 610499834]
   -------------------------------------

4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d213-101-243-193.cust.tele2.fr. (213.101.243.193)
Time: Tue Jul 27 05:20:08 2004

Input: 16549549541

Output: Magma V2.11-2     Tue Jul 27 2004 05:20:07 on modular  [Seed = 4038569931]
   -------------------------------------

16549549541

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d213-101-243-193.cust.tele2.fr. (213.101.243.193)
Time: Tue Jul 27 05:20:32 2004

Input: 16549549541^54


Output: Magma V2.11-2     Tue Jul 27 2004 05:20:31 on modular  [Seed = 3785801410]
   -------------------------------------

6523093054045631925198431928066288888069324018054277748439425752110209835082592\
3902960923754957905131977423218123618770831414842914899229104884753804456546648\
7765285849120028446624032232159030427454756435386489118083618522030075060023750\
5212033058652014085782510698625970903759461159067348890945884527039400318909925\
7117000677911649977576620182296715270763846424907668088865114475057122941494020\
7634633759750813299135478649576665431049974482096242043927620540748523709545781\
058094293262317770942927372932606943086905480425590249924981893727128388890761

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d213-101-243-193.cust.tele2.fr. (213.101.243.193)
Time: Tue Jul 27 05:20:58 2004

Input: 16549549556498498498498468549846513651465849878878979887984654198765416541^254


Output: Magma V2.11-2     Tue Jul 27 2004 05:20:57 on modular  [Seed = 3651045084]
   -------------------------------------

3729830845145153163301640113313177119944231013450303914436310168269275442704777\
0946320641733550588657397987534855522207497763816741959960366472280910030938656\
2513074518409440863818688016727341437674336703655792287941317961321414974359741\
0215573163132751721322579734089660893598897722079745667336716719045408667183774\
1675055744994070659183127769197722423140205781529596282642608862111992934479463\
5942493459337211425113747661891603959448757340834533819090756786952085836671087\
7500640855689462362568712896906307853683346120623215462184964130363845368261432\
3722955651016439116390420215193373151993178877405452843545746683956978172444630\
1771402660098823328543513459004983416087708702741259223556958112081871376903484\
9872239816401966664988012378067170792407825205481576262499402985947884798759225\
9453450730245238003800596705607235386275542331644430813779541907255057396857719\
9200892965188838028504585400152007460459564902261762321938734432379803163783725\
9120093367891491085578903174509165470792105895223138513990124687468009527282401\
5548289214447655331950573853106093858727083157595977087978570685526084566753973\
2357358269270593495555689082524395689682356921052818732298945440810582701675856\
6180671791152363901532691506976782986798745810614876802744135710558218297574177\
4257846157056584021024315414788481824781371905040870966670749274240326193539022\
2894364318010697447230376397213118619482701567148197570699960353415602042669773\
0677581449495703257091803061743877444792372409904530324733265250902076730525238\
9037135436882973056455191343498480813040980401209682517830671421700961501462013\
5993551696863220539550298629138757104567876222886653507919101501632621224585114\
6142113901666679374885909370401738589091043901418098604618869713785130571842801\
4874835275246175125032888097936838718713340462684026401273939702228205330512586\
1675082145125866372261045627742567565057499214276918952668492654192762664768394\
7850496945296861670476900365216474738170947005858112089596039755876152538402659\
5903773629134433082759848957720922758774898646224402309367579913070710431716426\
2782757521582376689956932803185906215373614136501931510215823852093643615601784\
3012137588070453580253980325392909114468646082520197165550570174617160364651654\
7967343687329701478429033184422671150953844530832893384048593869336833215777666\
7826534243318343161657128224330953932323644546761124446177151408565029421547333\
5514744806405507227699299801816036162048012494652301880719375618092368390092169\
1248717578119012234913299974281296500370511555307595512768055750516489325961543\
9283889381237850000381360630365516154718123164420468915835616675965656774319562\
0591191701972067626955467687637621221515783248467518040862494418953687802627527\
9561531957574424332776056803287646570053639482540913031481335966463033731162418\
6825303446017127461132097794781930866078365438691593115389043840977623911481073\
7729434282338589518253866826487193871835819625780513556812304142043794190895131\
5994320328949080530398610720669054103484119375544217430316402084440612829112251\
2081725109822835055684613395592310785313240067982004803741801991539007108080786\
5991395618391690310999688104385537523248461404378412088821985732429357635169886\
7703432808759552483308038536855166243096586027284964275146418565244892212662804\
0741028194008148452868578466046323218616256608374685865126959196543896831534534\
3896751470636315774318595125438748784617149978461615850948459890779691732679719\
4866625023294685559547875200057414096249980715732699467312246628489571504027635\
6069185026972524234597573189800965204718981115496403909349336084417432197988711\
4929525859220624060136918533861397010089341810130663150267528132420224369567286\
4599464317469581185732208862756682945911973974337671988271773955126450265429219\
0390027464444341530235317942838286650940345855829597038154050751361824398433812\
3735489930884143743803446311464426127046272326207521241717298399640423987599887\
2672727928281552516163628569537591114722774007776222343344977165795057747074083\
6238944621641275640023468759904277851894038108197197173925061765770617306617440\
3620788008338606260895004789223346707860821415664894444435651317440319825390297\
4935376565448609180566032958979754288145502546527139344585001119413194240234519\
3334967062202484532723540308797314571168591726814785666822268012804433461196292\
8234050914890207838092182705532272930500320448928778000517398977706431521162116\
0617260971908694639233846417407433651473601217228904819228478260379446958849847\
8366466236246685501651293352829158848884897359658861731399167939549211346382746\
1509059547063414824178439028910646424321466073136867586348896040809687240087448\
3965094950584135561507150397636816898967341553859550102226472950341603016897285\
4175625538003188621471660260623060614005961905731500900943774338168648373574168\
0441043023198810459427653059061569716683741335930754111269676596673983740469207\
4660186655064849047958349995452787505370716683829983144996530693710129837820247\
4810294580813633255811552764355900134727457613059310682228109711424754597628665\
6907241447796562360285389183707781457443284117650609123295381320650229570698310\
1089348905843074598444265830096951408570987070972362382426753028346855560987304\
1862756697317653956744346673515337287710626089349691085088152158808701481301956\
6945681134202738177451915155693564556414303718225795071678235913277232091561054\
5948655028314962649761630059615895780790646368919817581123962842281978108227583\
3259069557961237171972635971071194498738208484959821881219165010889381306589630\
9868838454485620207270048838152750147899908108062982097092241664786054495906326\
7235832488380896152844554143369585726446381916232119185279708787764186469847743\
9352426525357523667768827767870382365293387982316430296861580292904696456815630\
1969331857386055351301364802126300430949191108009339522387995797361587219221167\
4060698853907705532425924870567346267948040491307146068396145122101298875380016\
4445366167572093852960027823300732190541496583643417076405951795936227441432298\
7310872349170542082165059564150848397802183646249993343558114262748737079745154\
7268981746537617788337673801281129979919387937734436624144187310074802903565165\
8299712816800824229849477855396436623996104664832073057048989609474915156733045\
1964089812671397618657785344986416001053914602274177290550650655897054438971931\
1709436936924484912261451452910882449852289252878050946327297282773367594303133\
5502939628979096099798945593100748529908331075508003869178994875533928775280352\
0839306462045976004616329197067303188607151624411220102081640381718704677586892\
0978094085113807227651863806268752464375383674056288766735110661342276151775812\
2747990987182037853869883304171213575261345275299587772936363459407591182326240\
4172147442098773670503497452959968622218146505014505114830315808050856721125614\
0394757475484583049391505039304734909559035804090332216292780855894982046517305\
0284481661313178212806548732663037410124663147426469133692272827392990495181581\
0333184685844662721046359262259440375393792445818403898248034862812055423761687\
5068284692064892026766103877139206857751331985598622611041009467838027193907855\
2361511483009607511403183335336213682575278404891605340166782819808069611127408\
5899986228530884993226350919480525870548694344644725148529469616097128382849846\
6344278357480416264599488693864252857700552904872194556939300289736837289329364\
9807281335442756224904150058988708348488102960375430002266276868431331315977442\
6544462110959463827374245382644411788284481477364683284881321816973198072591332\
7017315237238994354477527015422276232115619319147688095217674326766388986284891\
3675683847392995337936840274851500721224791092498835547110818880794453510516538\
6144554138337427234948637742298592755657898723896813465927276951004923018618901\
1058435473317281164987797268104787917313187686398274830668010524012905901798356\
2761254301143723329302522039820734386811444685689084141938132807540899177341319\
3109883932827609611935705972230302082789453720356146907026313404664992485487203\
1296777238501874305480357474755341473535687067453473089644331101484631009090205\
0479153983055441491579102610870046656537179957361535786927070826074820644859908\
7890808085289513601321522982270044631082389860936802579471165251435695476623257\
9902519782501115476843934574234300045710312052784976393281006779598299256439756\
6348177957480862567598217366353353757469681586330698915012805128554278512474449\
0185366411958079690214172640283425187214222348479278592496893975594708133178095\
4704221709264994088892762112533720972551775120630993273692044621025414933893121\
2065849002509393131969952292377434739405408577857649781090793114211029164259707\
6658742329083785582495301120062846167027671484397296600441504800227958371024690\
0595251298275989026307629488354076536174363187058377868100384769689103493534040\
1794427148740550692236476170360178660492164834735689948561695830098021334004278\
9743421372634874583707581959771145238097106102873238690673974178655326933971418\
7938421173203741186915163621493388800667220265648066074666329052435256418959966\
9235718688051731421245910596745800506051856506332286313738619768688761531324299\
9701446092963430658537032129954195150069298324147005761099794824687283957911566\
3689807796240476242974722115585496472498917585789250440960175409100125405298568\
7900635529376221313131318410354711233220467863479917628862650034813597625677425\
5151720580181775807053794933002104830011506632066162093257477220761306671031909\
0770439174693288092718406162925347183512421760885728637919557479355626357468527\
8338303214693604605729866375188635453575288632762663387288018303278534314370126\
0048981273478718847013821725301439342315447686307757593386677181493654716278755\
8317130798988214971367943782874744219043188580202424234761458019569835807740654\
1
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 05:55:05 2004

Input: 2;


Output: Magma V2.11-2     Tue Jul 27 2004 05:55:04 on modular  [Seed = 2395597194]
   -------------------------------------

2

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 05:55:20 2004

Input: 2;


3;


Output: Magma V2.11-2     Tue Jul 27 2004 05:55:19 on modular  [Seed = 2260853117]
   -------------------------------------

2
3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 05:55:35 2004

Input: 2;


3;
5;

Output: Magma V2.11-2     Tue Jul 27 2004 05:55:34 on modular  [Seed = 2100959892]
   -------------------------------------

2
3
5

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 05:57:26 2004

Input: 2+2;

Output: Magma V2.11-2     Tue Jul 27 2004 05:57:25 on modular  [Seed = 1966215951]
   -------------------------------------

4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:02:56 2004

Input: 2+2;

CoxeterGroup:Maximal;

Output: Magma V2.11-2     Tue Jul 27 2004 06:02:54 on modular  [Seed = 1031427085]
   -------------------------------------

4
Intrinsic 'CoxeterGroup'

Signatures:

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 804, column
    3:
    (Cat[GrpMat], <RootSys> R) -> GrpMat

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 814, column
    3:
    (Cat[GrpPermCox], <RootSys> R) -> GrpPermCox

        The permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 819, column
    3:
    (Cat[GrpPerm], <RootSys> R) -> GrpPermCox

        The plain permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 824, column
    5:
    (Cat[GrpFPCox], <RootSys> R) -> GrpFPCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 831, column
    3:
    (Cat[GrpFP], <RootSys> R) -> GrpFPCox

        The Coxeter group of R without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 836, column
    3:
    (<RootSys> R) -> GrpPermCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 846, column
    3:
    (Cat[GrpMat], <RootDtm> R) -> GrpMat

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 856, column
    3:
    (Cat[GrpPermCox], <RootDtm> R) -> GrpPermCox

        The permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 861, column
    3:
    (Cat[GrpPerm], <RootDtm> R) -> GrpPermCox

        The plain permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 866, column
    5:
    (Cat[GrpFPCox], <RootDtm> R) -> GrpFPCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 873, column
    3:
    (Cat[GrpFP], <RootDtm> R) -> GrpFPCox

        The Coxeter group of R without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 878, column
    3:
    (<RootDtm> R) -> GrpPermCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 908, column
    5:
    (Cat[GrpMat], <AlgMatElt> M) -> GrpMat

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 926, column
    3:
    (Cat[GrpPermCox], <AlgMatElt> M) -> GrpPermCox

        The permutation Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 934, column
    3:
    (Cat[GrpPerm], <AlgMatElt> M) -> GrpPerm

        The plain permutation Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 940, column
    5:
    (Cat[GrpFPCox], <AlgMatElt> M) -> GrpFPCox

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 947, column
    3:
    (Cat[GrpFP], <AlgMatElt> M) -> GrpFP

        The Coxeter group of the Coxeter (Cartan) matrix M without 
        normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 952, column
    3:
    (<AlgMatElt> M) -> Grp

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 963, column
    5:
    (Cat[GrpMat], <GrphUnd> G) -> GrpMat

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 976, column
    3:
    (Cat[GrpPermCox], <GrphUnd> G) -> GrpPermCox

        The permutation Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 985, column
    3:
    (Cat[GrpPerm], <GrphUnd> G) -> GrpPerm

        The plain permutation Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 991, column
    5:
    (Cat[GrpFPCox], <GrphUnd> G) -> GrpFPCox

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 999, column
    3:
    (Cat[GrpFP], <GrphUnd> G) -> GrpFP

        The Coxeter group of the Coxeter graph G without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1004, 
    column 3:
    (<GrphUnd> G) -> Grp

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1016, 
    column 5:
    (Cat[GrpMat], <GrphDir> D) -> Grp

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1029, 
    column 3:
    (Cat[GrpPermCox], <GrphDir> D) -> GrpPermCox

        The permutation Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1038, 
    column 3:
    (Cat[GrpPerm], <GrphDir> D) -> GrpPerm

        The plain permutation Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1044, 
    column 3:
    (Cat[GrpFPCox], <GrphDir> D) -> GrpPermCox

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1051, 
    column 3:
    (Cat[GrpFP], <GrphDir> D) -> GrpFP

        The Coxeter group of the Coxeter graph G without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1056, 
    column 3:
    (<GrphDir> D) -> Grp

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1068, 
    column 3:
    (Cat[GrpMat], <Mtrx> A, <Mtrx> B) -> GrpMat

        The Coxeter group with simple (co)roots given by the matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1073, 
    column 3:
    (Cat[GrpPermCox], <Mtrx> A, <Mtrx> B) -> GrpPermCox

        The permutation Coxeter group with simple (co)roots given by the matrix 
        A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1078, 
    column 3:
    (Cat[GrpPerm], <Mtrx> A, <Mtrx> B) -> GrpPermCox

        The plain permutation Coxeter group with simple (co)roots given by the 
        matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1083, 
    column 3:
    (<Mtrx> A, <Mtrx> B) -> Grp

        The Coxeter group with simple (co)roots given by the matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1095, 
    column 8:
    (Cat[GrpMat], <MonStgElt> N) -> GrpMat

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1110, 
    column 8:
    (Cat[GrpPermCox], <MonStgElt> N) -> GrpPermCox

        The permutation Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1117, 
    column 8:
    (Cat[GrpPerm], <MonStgElt> N) -> GrpPermCox

        The plain permutation Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1124, 
    column 8:
    (Cat[GrpFPCox], <MonStgElt> N) -> GrpFPCox

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1130, 
    column 3:
    (Cat[GrpFP], <MonStgElt> N) -> GrpFPCox

        The Coxeter group with Cartan name N without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1135, 
    column 8:
    (<MonStgElt> N) -> GrpPermCox

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1204, 
    column 5:
    (Cat[GrpMat], <GrpPermCox> W) -> GrpMat

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1215, 
    column 5:
    (Cat[GrpFPCox], <GrpPermCox> W) -> GrpFPCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1221, 
    column 5:
    (Cat[GrpFP], <GrpPermCox> W) -> GrpFP

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1233, 
    column 3:
    (Cat[GrpPermCox], <GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1238, 
    column 6:
    (Cat[GrpPerm], <GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1244, 
    column 3:
    (<GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1256, 
    column 5:
    (Cat[GrpMat], <GrpFPCox> W) -> GrpMat
    [
        A,
        B,
        C
    ]

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1276, 
    column 3:
    (Cat[GrpFPCox], <GrpFPCox> W) -> GrpFPCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1281, 
    column 6:
    (Cat[GrpFP], <GrpFPCox> W) -> GrpFP

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1288, 
    column 3:
    (Cat[GrpPermCox], <GrpFPCox> W) -> GrpPermCox
    [
        A,
        B,
        C
    ]

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1297, 
    column 3:
    (Cat[GrpPerm], <GrpFPCox> W) -> GrpPerm
    [
        A,
        B,
   
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:03:44 2004

Input: 2+2;

CoxeterGroup:Maximal;

x := 3;


Output: Magma V2.11-2     Tue Jul 27 2004 06:03:44 on modular  [Seed = 896687306]
   -------------------------------------

4
Intrinsic 'CoxeterGroup'

Signatures:

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 804, column
    3:
    (Cat[GrpMat], <RootSys> R) -> GrpMat

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 814, column
    3:
    (Cat[GrpPermCox], <RootSys> R) -> GrpPermCox

        The permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 819, column
    3:
    (Cat[GrpPerm], <RootSys> R) -> GrpPermCox

        The plain permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 824, column
    5:
    (Cat[GrpFPCox], <RootSys> R) -> GrpFPCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 831, column
    3:
    (Cat[GrpFP], <RootSys> R) -> GrpFPCox

        The Coxeter group of R without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 836, column
    3:
    (<RootSys> R) -> GrpPermCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 846, column
    3:
    (Cat[GrpMat], <RootDtm> R) -> GrpMat

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 856, column
    3:
    (Cat[GrpPermCox], <RootDtm> R) -> GrpPermCox

        The permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 861, column
    3:
    (Cat[GrpPerm], <RootDtm> R) -> GrpPermCox

        The plain permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 866, column
    5:
    (Cat[GrpFPCox], <RootDtm> R) -> GrpFPCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 873, column
    3:
    (Cat[GrpFP], <RootDtm> R) -> GrpFPCox

        The Coxeter group of R without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 878, column
    3:
    (<RootDtm> R) -> GrpPermCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 908, column
    5:
    (Cat[GrpMat], <AlgMatElt> M) -> GrpMat

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 926, column
    3:
    (Cat[GrpPermCox], <AlgMatElt> M) -> GrpPermCox

        The permutation Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 934, column
    3:
    (Cat[GrpPerm], <AlgMatElt> M) -> GrpPerm

        The plain permutation Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 940, column
    5:
    (Cat[GrpFPCox], <AlgMatElt> M) -> GrpFPCox

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 947, column
    3:
    (Cat[GrpFP], <AlgMatElt> M) -> GrpFP

        The Coxeter group of the Coxeter (Cartan) matrix M without 
        normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 952, column
    3:
    (<AlgMatElt> M) -> Grp

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 963, column
    5:
    (Cat[GrpMat], <GrphUnd> G) -> GrpMat

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 976, column
    3:
    (Cat[GrpPermCox], <GrphUnd> G) -> GrpPermCox

        The permutation Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 985, column
    3:
    (Cat[GrpPerm], <GrphUnd> G) -> GrpPerm

        The plain permutation Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 991, column
    5:
    (Cat[GrpFPCox], <GrphUnd> G) -> GrpFPCox

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 999, column
    3:
    (Cat[GrpFP], <GrphUnd> G) -> GrpFP

        The Coxeter group of the Coxeter graph G without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1004, 
    column 3:
    (<GrphUnd> G) -> Grp

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1016, 
    column 5:
    (Cat[GrpMat], <GrphDir> D) -> Grp

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1029, 
    column 3:
    (Cat[GrpPermCox], <GrphDir> D) -> GrpPermCox

        The permutation Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1038, 
    column 3:
    (Cat[GrpPerm], <GrphDir> D) -> GrpPerm

        The plain permutation Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1044, 
    column 3:
    (Cat[GrpFPCox], <GrphDir> D) -> GrpPermCox

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1051, 
    column 3:
    (Cat[GrpFP], <GrphDir> D) -> GrpFP

        The Coxeter group of the Coxeter graph G without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1056, 
    column 3:
    (<GrphDir> D) -> Grp

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1068, 
    column 3:
    (Cat[GrpMat], <Mtrx> A, <Mtrx> B) -> GrpMat

        The Coxeter group with simple (co)roots given by the matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1073, 
    column 3:
    (Cat[GrpPermCox], <Mtrx> A, <Mtrx> B) -> GrpPermCox

        The permutation Coxeter group with simple (co)roots given by the matrix 
        A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1078, 
    column 3:
    (Cat[GrpPerm], <Mtrx> A, <Mtrx> B) -> GrpPermCox

        The plain permutation Coxeter group with simple (co)roots given by the 
        matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1083, 
    column 3:
    (<Mtrx> A, <Mtrx> B) -> Grp

        The Coxeter group with simple (co)roots given by the matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1095, 
    column 8:
    (Cat[GrpMat], <MonStgElt> N) -> GrpMat

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1110, 
    column 8:
    (Cat[GrpPermCox], <MonStgElt> N) -> GrpPermCox

        The permutation Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1117, 
    column 8:
    (Cat[GrpPerm], <MonStgElt> N) -> GrpPermCox

        The plain permutation Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1124, 
    column 8:
    (Cat[GrpFPCox], <MonStgElt> N) -> GrpFPCox

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1130, 
    column 3:
    (Cat[GrpFP], <MonStgElt> N) -> GrpFPCox

        The Coxeter group with Cartan name N without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1135, 
    column 8:
    (<MonStgElt> N) -> GrpPermCox

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1204, 
    column 5:
    (Cat[GrpMat], <GrpPermCox> W) -> GrpMat

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1215, 
    column 5:
    (Cat[GrpFPCox], <GrpPermCox> W) -> GrpFPCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1221, 
    column 5:
    (Cat[GrpFP], <GrpPermCox> W) -> GrpFP

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1233, 
    column 3:
    (Cat[GrpPermCox], <GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1238, 
    column 6:
    (Cat[GrpPerm], <GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1244, 
    column 3:
    (<GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1256, 
    column 5:
    (Cat[GrpMat], <GrpFPCox> W) -> GrpMat
    [
        A,
        B,
        C
    ]

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1276, 
    column 3:
    (Cat[GrpFPCox], <GrpFPCox> W) -> GrpFPCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1281, 
    column 6:
    (Cat[GrpFP], <GrpFPCox> W) -> GrpFP

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1288, 
    column 3:
    (Cat[GrpPermCox], <GrpFPCox> W) -> GrpPermCox
    [
        A,
        B,
        C
    ]

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1297, 
    column 3:
    (Cat[GrpPerm], <GrpFPCox> W) -> GrpPerm
    [
        A,
        B,
    
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:03:55 2004

Input: 2+2;

CoxeterGroup:Maximal;

x := 3;


Output: Magma V2.11-2     Tue Jul 27 2004 06:03:55 on modular  [Seed = 761939161]
   -------------------------------------

4
Intrinsic 'CoxeterGroup'

Signatures:

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 804, column
    3:
    (Cat[GrpMat], <RootSys> R) -> GrpMat

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 814, column
    3:
    (Cat[GrpPermCox], <RootSys> R) -> GrpPermCox

        The permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 819, column
    3:
    (Cat[GrpPerm], <RootSys> R) -> GrpPermCox

        The plain permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 824, column
    5:
    (Cat[GrpFPCox], <RootSys> R) -> GrpFPCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 831, column
    3:
    (Cat[GrpFP], <RootSys> R) -> GrpFPCox

        The Coxeter group of R without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 836, column
    3:
    (<RootSys> R) -> GrpPermCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 846, column
    3:
    (Cat[GrpMat], <RootDtm> R) -> GrpMat

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 856, column
    3:
    (Cat[GrpPermCox], <RootDtm> R) -> GrpPermCox

        The permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 861, column
    3:
    (Cat[GrpPerm], <RootDtm> R) -> GrpPermCox

        The plain permutation Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 866, column
    5:
    (Cat[GrpFPCox], <RootDtm> R) -> GrpFPCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 873, column
    3:
    (Cat[GrpFP], <RootDtm> R) -> GrpFPCox

        The Coxeter group of R without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 878, column
    3:
    (<RootDtm> R) -> GrpPermCox

        The Coxeter group of R.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 908, column
    5:
    (Cat[GrpMat], <AlgMatElt> M) -> GrpMat

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 926, column
    3:
    (Cat[GrpPermCox], <AlgMatElt> M) -> GrpPermCox

        The permutation Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 934, column
    3:
    (Cat[GrpPerm], <AlgMatElt> M) -> GrpPerm

        The plain permutation Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 940, column
    5:
    (Cat[GrpFPCox], <AlgMatElt> M) -> GrpFPCox

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 947, column
    3:
    (Cat[GrpFP], <AlgMatElt> M) -> GrpFP

        The Coxeter group of the Coxeter (Cartan) matrix M without 
        normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 952, column
    3:
    (<AlgMatElt> M) -> Grp

        The Coxeter group of the Coxeter (Cartan) matrix M.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 963, column
    5:
    (Cat[GrpMat], <GrphUnd> G) -> GrpMat

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 976, column
    3:
    (Cat[GrpPermCox], <GrphUnd> G) -> GrpPermCox

        The permutation Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 985, column
    3:
    (Cat[GrpPerm], <GrphUnd> G) -> GrpPerm

        The plain permutation Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 991, column
    5:
    (Cat[GrpFPCox], <GrphUnd> G) -> GrpFPCox

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 999, column
    3:
    (Cat[GrpFP], <GrphUnd> G) -> GrpFP

        The Coxeter group of the Coxeter graph G without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1004, 
    column 3:
    (<GrphUnd> G) -> Grp

        The Coxeter group of the Coxeter graph G.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1016, 
    column 5:
    (Cat[GrpMat], <GrphDir> D) -> Grp

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1029, 
    column 3:
    (Cat[GrpPermCox], <GrphDir> D) -> GrpPermCox

        The permutation Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1038, 
    column 3:
    (Cat[GrpPerm], <GrphDir> D) -> GrpPerm

        The plain permutation Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1044, 
    column 3:
    (Cat[GrpFPCox], <GrphDir> D) -> GrpPermCox

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1051, 
    column 3:
    (Cat[GrpFP], <GrphDir> D) -> GrpFP

        The Coxeter group of the Coxeter graph G without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1056, 
    column 3:
    (<GrphDir> D) -> Grp

        The Coxeter group of the Dynkin digraph D.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1068, 
    column 3:
    (Cat[GrpMat], <Mtrx> A, <Mtrx> B) -> GrpMat

        The Coxeter group with simple (co)roots given by the matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1073, 
    column 3:
    (Cat[GrpPermCox], <Mtrx> A, <Mtrx> B) -> GrpPermCox

        The permutation Coxeter group with simple (co)roots given by the matrix 
        A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1078, 
    column 3:
    (Cat[GrpPerm], <Mtrx> A, <Mtrx> B) -> GrpPermCox

        The plain permutation Coxeter group with simple (co)roots given by the 
        matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1083, 
    column 3:
    (<Mtrx> A, <Mtrx> B) -> Grp

        The Coxeter group with simple (co)roots given by the matrix A (B).

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1095, 
    column 8:
    (Cat[GrpMat], <MonStgElt> N) -> GrpMat

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1110, 
    column 8:
    (Cat[GrpPermCox], <MonStgElt> N) -> GrpPermCox

        The permutation Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1117, 
    column 8:
    (Cat[GrpPerm], <MonStgElt> N) -> GrpPermCox

        The plain permutation Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1124, 
    column 8:
    (Cat[GrpFPCox], <MonStgElt> N) -> GrpFPCox

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1130, 
    column 3:
    (Cat[GrpFP], <MonStgElt> N) -> GrpFPCox

        The Coxeter group with Cartan name N without normalisation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1135, 
    column 8:
    (<MonStgElt> N) -> GrpPermCox

        The Coxeter group with Cartan name N.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1204, 
    column 5:
    (Cat[GrpMat], <GrpPermCox> W) -> GrpMat

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1215, 
    column 5:
    (Cat[GrpFPCox], <GrpPermCox> W) -> GrpFPCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1221, 
    column 5:
    (Cat[GrpFP], <GrpPermCox> W) -> GrpFP

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1233, 
    column 3:
    (Cat[GrpPermCox], <GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1238, 
    column 6:
    (Cat[GrpPerm], <GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1244, 
    column 3:
    (<GrpPermCox> W) -> GrpPermCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1256, 
    column 5:
    (Cat[GrpMat], <GrpFPCox> W) -> GrpMat
    [
        A,
        B,
        C
    ]

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1276, 
    column 3:
    (Cat[GrpFPCox], <GrpFPCox> W) -> GrpFPCox

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1281, 
    column 6:
    (Cat[GrpFP], <GrpFPCox> W) -> GrpFP

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1288, 
    column 3:
    (Cat[GrpPermCox], <GrpFPCox> W) -> GrpPermCox
    [
        A,
        B,
        C
    ]

        The Coxeter group W in a different representation.

    Defined in file: /usr/local/magma/package/LieThry/GrpCox.m, line 1297, 
    column 3:
    (Cat[GrpPerm], <GrpFPCox> W) -> GrpPerm
    [
        A,
        B,
    
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:04:18 2004

Input: x := 3;

Output: Magma V2.11-2     Tue Jul 27 2004 06:04:17 on modular  [Seed = 627199227]
   -------------------------------------


Total time: 0.770 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:04:27 2004

Input: x := 3;

x+1;


Output: Magma V2.11-2     Tue Jul 27 2004 06:04:26 on modular  [Seed = 459043534]
   -------------------------------------

4

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:04:53 2004

Input: time x := Factorization(14018573495721094857209462);


Output: Magma V2.11-2     Tue Jul 27 2004 06:04:52 on modular  [Seed = 307592105]
   -------------------------------------

Time: 0.200

Total time: 0.760 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:05:06 2004

Input: time x := Factorization(14018573495721094857209462);
x;

Output: Magma V2.11-2     Tue Jul 27 2004 06:05:05 on modular  [Seed = 172843940]
   -------------------------------------

Time: 0.190
[ <2, 1>, <43, 1>, <185489897, 1>, <878790010621961, 1> ]

Total time: 0.750 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:05:13 2004

Input: time x := Factorization(14018573495721094852354621567324573457209462);
x;

Output: Magma V2.11-2     Tue Jul 27 2004 06:05:12 on modular  [Seed = 38103973]
   -------------------------------------

Time: 1.050
[ <2, 1>, <3980549991531654949, 1>, <1760883989090030433124319, 1> ]

Total time: 1.659 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:05:27 2004

Input: time x := Factorization(14018573495752457245624624245221094852354621567324573457209462);
x;

Output: Magma V2.11-2     Tue Jul 27 2004 06:05:23 on modular  [Seed = 4206728038]
   -------------------------------------

Time: 3.500
[ <2, 1>, <3, 1>, <443, 1>, <499, 1>, <231559, 1>, <815206369, 1>, 
<6386364010889, 1>, <8767290609033359654315528119, 1> ]

Total time: 4.089 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:06:10 2004

Input: time x := Factorization(14018573495752457245624624245221094852354621567324573457209462);
x;
x+1;

Output: Magma V2.11-2     Tue Jul 27 2004 06:06:04 on modular  [Seed = 4020799388]
   -------------------------------------

Time: 3.960
[ <2, 1>, <3, 1>, <443, 1>, <499, 1>, <231559, 1>, <815206369, 1>, 
<6386364010889, 1>, <8767290609033359654315528119, 1> ]

>> x+1;;
    ^
Runtime error in '+': Bad argument types
Argument types given: RngIntEltFact[Tup], RngIntElt

Total time: 4.620 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:06:34 2004

Input: time x := Factorization(14018573495752457245624624245221094852354621567324573457209462);
x;
x[1]+1;

Output: Magma V2.11-2     Tue Jul 27 2004 06:06:29 on modular  [Seed = 3852635583]
   -------------------------------------

Time: 3.910
[ <2, 1>, <3, 1>, <443, 1>, <499, 1>, <231559, 1>, <815206369, 1>, 
<6386364010889, 1>, <8767290609033359654315528119, 1> ]

>> x[1]+1;;
       ^
Runtime error in '+': Bad argument types
Argument types given: Tup, RngIntElt

Total time: 4.549 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:06:47 2004

Input: time x := Factorization(14018573495752457245624624245221094852354621567324573457209462);
x;
x[1][1]+1;

Output: Magma V2.11-2     Tue Jul 27 2004 06:06:40 on modular  [Seed = 3717903762]
   -------------------------------------

Time: 5.760
[ <2, 1>, <3, 1>, <443, 1>, <499, 1>, <231559, 1>, <815206369, 1>, 
<6386364010889, 1>, <8767290609033359654315528119, 1> ]
3

Total time: 6.719 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host narmada.maths.warwick.ac.uk. (137.205.234.203)
Time: Tue Jul 27 06:07:11 2004

Input: time x := Factorization(14018573495752457245624624245221094852354621567324573457209462);
x;
x[1][1]+1;

Output: Magma V2.11-2     Tue Jul 27 2004 06:07:05 on modular  [Seed = 3549740005]
   -------------------------------------

Time: 4.690
[ <2, 1>, <3, 1>, <443, 1>, <499, 1>, <231559, 1>, <815206369, 1>, 
<6386364010889, 1>, <8767290609033359654315528119, 1> ]
3

Total time: 5.240 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:41:19 2004

Input: time x := Factorization(140185723462562562625623495752457245624624245221094852354621567324573457209462);
x;
x[1][1]+1;

Output: Magma V2.11-2     Tue Jul 27 2004 06:40:52 on modular  [Seed = 1360404836]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:42:01 2004

Input: time x := Factorization(140185723462562562625623495752457245624624245221094852354621567324573457209462);
x;
x[1][1]+1;

Output: Magma V2.11-2     Tue Jul 27 2004 06:41:41 on modular  [Seed = 1495148861]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:42:47 2004

Input: Factorization(140185723462562562625623495745624624245221094852354621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:42:27 on modular  [Seed = 1629884915]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:42:59 2004

Input: Factorization(14018624624245221094852354621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:42:58 on modular  [Seed = 1764628954]
   -------------------------------------

[ <2, 1>, <1153049, 1>, <292392053, 1>, <9471657239137, 1>, 
<2195008011256384679, 1> ]

Total time: 0.860 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:43:07 2004

Input: Factorization(140186246242452210948523542456246621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:43:05 on modular  [Seed = 1899364809]
   -------------------------------------

[ <2, 1>, <3, 1>, <13, 1>, <193, 1>, <138371, 1>, <3465367, 1>, <1290506196139, 
1>, <15048703520548372722034811, 1> ]

Total time: 2.429 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:43:29 2004

Input: Factorization(140186246242452210948523542456242456266621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:43:12 on modular  [Seed = 2067532730]
   -------------------------------------

[ <2, 1>, <19, 1>, <241, 1>, <18451, 1>, <149872182227, 1>, <1086900329674447, 
1>, <5093005056530176862089231, 1> ]

Total time: 16.740 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:43:38 2004

Input: Factorization(1401862462424522109485235424566242456266621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:43:37 on modular  [Seed = 2227434588]
   -------------------------------------

[ <2, 1>, <5009, 1>, <81899, 1>, <185408231, 1>, 
<9215454733751156702197620349975446140283511, 1> ]

Total time: 1.129 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host serv.math.metu.edu.tr. (144.122.136.16)
Time: Tue Jul 27 06:44:03 2004

Input: 2^123

Output: Magma V2.11-2     Tue Jul 27 2004 06:44:00 on modular  [Seed = 2446778720]
   -------------------------------------

10633823966279326983230456482242756608

Total time: 0.679 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:44:06 2004

Input: Factorization(1401862462424522109485235424566242456245266621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:43:46 on modular  [Seed = 2362178671]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (137.205.234.203)
Time: Tue Jul 27 06:45:37 2004

Input: Factorization(1401862462424522109485235424566242456245266621567324573457209462);



Output: Magma V2.11-2     Tue Jul 27 2004 06:45:16 on modular  [Seed = 2783106712]
   -------------------------------------



************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Tue Jul 27 14:15:53 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 + 90*x^14 + 2775*x^12 + 40230*x^10 + 304380*x^8 + 1255500*x^6 + 2784375*x^4 + 3037500*x^2 + 1265625));


Output: Magma V2.11-2     Tue Jul 27 2004 14:15:44 on modular  [Seed = 3599830019]
   -------------------------------------

70 16

Total time: 7.100 seconds, Total memory usage: 6.94MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Tue Jul 27 14:17:46 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 57*x^14 + 1212*x^12 - 12385*x^10 + 64261*x^8 - 162395*x^6 + 159448*x^4 - 6131*x^2 + 1));


Output: Magma V2.11-2     Tue Jul 27 2004 14:17:41 on modular  [Seed = 3634300313]
   -------------------------------------

77 16

Total time: 5.390 seconds, Total memory usage: 6.23MB


************** MAGMA *****************
Host adsl-68-75-189-24.dsl.emhril.ameritech.net. (68.75.189.24)
Time: Tue Jul 27 17:09:45 2004

Input: arctan(40i);

Output: Magma V2.11-2     Tue Jul 27 2004 17:09:42 on modular  [Seed = 2564758814]
   -------------------------------------


>> arctan(40i);;
            ^
User error: bad syntax

Total time: 0.669 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-189-24.dsl.emhril.ameritech.net. (68.75.189.24)
Time: Tue Jul 27 17:09:51 2004

Input: arctan(40*i);

Output: Magma V2.11-2     Tue Jul 27 2004 17:09:51 on modular  [Seed = 2177238030]
   -------------------------------------


>> arctan(40*i);;
             ^
User error: Identifier 'i' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-189-24.dsl.emhril.ameritech.net. (68.75.189.24)
Time: Tue Jul 27 17:10:00 2004

Input: arctan(40*I);

Output: Magma V2.11-2     Tue Jul 27 2004 17:09:59 on modular  [Seed = 2328694589]
   -------------------------------------


>> arctan(40*I);;
             ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 03:56:23 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2(4659775785220018543264560743076778192897,14152267);


Output: Magma V2.11-2     Wed Jul 28 2004 03:56:16 on modular  [Seed = 3230064118]
   -------------------------------------

[ <2, 2>, <3, 2>, <5, 1>, <149, 1>, <163, 1>, <197, 1>, <7187, 1>, <18311, 1>, 
<123677, 1>, <226133, 1>, <314263, 1>, <4677853, 1> ]

Total time: 6.110 seconds, Total memory usage: 4.45MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:42:13 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;



NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le 2k+1 then return x0;
	end if;
	
	w := Cieling(m/2)+k;

	x1 := NewtonLift(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x); mod (p^m);

	Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;

	


Output: Magma V2.11-2     Wed Jul 28 2004 04:42:12 on modular  [Seed = 1157849784]
   -------------------------------------


>>         if x0 le 2k+1 then return x0;
                     ^
User error: bad syntax

>>         end if;
           ^
User error: bad syntax

>>         w := Cieling(m/2)+k;
                ^
User error: Identifier 'Cieling' has not been declared or assigned

>>         x1 := NewtonLift(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 
                            ^
User error: Identifier 'x0' has not been declared or assigned

>>         x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq
                                 ^
User error: Identifier 'x1' has not been declared or assigned

>>         y := Sigma(x); mod (p^m);
                      ^
User error: Identifier 'x' has not been declared or assigned

>>         y := Sigma(x); mod (p^m);
                          ^
User error: bad syntax

>>         Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
                                   ^
User error: Identifier 'x0' has not been declared or assigned

>>         Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
                                   ^
User error: Identifier 'x0' has not been declared or assigned

>>         V := F(x,y) mod (p^m);
                  ^
User error: Identifier 'x' has not been declared or assigned

>>         C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
                                   ^
User error: Identifier 'V' has not been declared or assigned

>>         a := C[1]; b := C[2];
                ^
User error: Identifier 'C' has not been declared or assigned

>>         a := C[1]; b := C[2];
                           ^
User error: Identifier 'C' has not been declared or assigned

>>         return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );
           ^
User error: A 'return' can only be used inside a procedure or function

>> end function;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:42:51 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;



NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le (2*k+1) then return x0;
	end if;
	
	w := Cieling(m/2)+k;

	x1 := NewtonLift(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x); mod (p^m);

	Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;



Output: Magma V2.11-2     Wed Jul 28 2004 04:42:50 on modular  [Seed = 2101042030]
   -------------------------------------


>>         y := Sigma(x); mod (p^m);
                          ^
User error: bad syntax

>>         Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
                                   ^
User error: Identifier 'x0' has not been declared or assigned

>>         Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
                                   ^
User error: Identifier 'x0' has not been declared or assigned

>>         V := F(x,y) mod (p^m);
                  ^
User error: Identifier 'x' has not been declared or assigned

>>         C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
                                   ^
User error: Identifier 'V' has not been declared or assigned

>>         a := C[1]; b := C[2];
                ^
User error: Identifier 'C' has not been declared or assigned

>>         a := C[1]; b := C[2];
                           ^
User error: Identifier 'C' has not been declared or assigned

>>         return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );
           ^
User error: A 'return' can only be used inside a procedure or function

>> end function;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:43:22 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;



NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le (2*k+1) then return x0;
	end if;
	
	w := Cieling(m/2)+k;

	x1 := NewtonLift(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x) mod (p^m);

	Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;

	


Output: Magma V2.11-2     Wed Jul 28 2004 04:43:21 on modular  [Seed = 1966297926]
   -------------------------------------


>>         w := Cieling(m/2)+k;
                ^
User error: Identifier 'Cieling' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:44:05 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;



NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le (2*k+1) then return x0;
	end if;
	
	w := Ceiling(m/2)+k;

	x1 := NewtonLift(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x) mod (p^m);

	Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;

	


Output: Magma V2.11-2     Wed Jul 28 2004 04:44:04 on modular  [Seed = 1831553824]
   -------------------------------------


>>         x1 := NewtonLift(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 
                 ^
User error: Identifier 'NewtonLift' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:44:53 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;



NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le (2*k+1) then return x0;
	end if;
	
	w := Ceiling(m/2)+k;

	x1 := $$(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x) mod (p^m);

	Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;

	


Output: Magma V2.11-2     Wed Jul 28 2004 04:44:52 on modular  [Seed = 1679966969]
   -------------------------------------


>>         Dx := (Derivative(F,1))(x0,sigma(x0)) mod p^(w-k); 
                                      ^
User error: Identifier 'sigma' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:45:17 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;



NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le (2*k+1) then return x0;
	end if;
	
	w := Ceiling(m/2)+k;

	x1 := $$(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x) mod (p^m);

	Dx := (Derivative(F,1))(x0,Sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,Sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;

	


Output: Magma V2.11-2     Wed Jul 28 2004 04:45:16 on modular  [Seed = 2631580185]
   -------------------------------------


>>         C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
                ^
User error: Identifier 'ArtinSchreierRoot' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (132.72.45.174)
Time: Wed Jul 28 04:46:58 2004

Input: 
//=================================================
//        NewtonLift Algorithm
//=================================================

//p := NextPrime(10);
p := 5;
Precision:=10;
n := 3;
m := 6;
q := p^n;


Qp := pAdicRing(p,Precision);

Zq := UnramifiedExtension(Qp,n);

ppm := Zq!(p^m);

R:= quo<Zq|ppm>;

// =======================A S R ============================//

ArtinSchreierRoot := function(a,b,m,v)

	if v eq 1 then
		return [GaloisImage(a,n-1) , 
			GaloisImage(b,n-1) ];
	end if;

	AB := $$(a,b,m,Floor(v/2));

	A := AB[1]; B := AB[2];

	AB := [( A * GaloisImage(A,n-Floor(v/2)) ), 
	      ( A * GaloisImage(B,n-Floor(v/2)) + B )];

	A := AB[1]; B := AB[2];

	if v mod 2 eq 1 then
	
		AB := [( A * GaloisImage(a,n-v) ) , 
		      ( A * GaloisImage(b,n-v) + B )];

	end if;
	
	return AB;

end function;
//===========================================================//


NewtonLift := function(x0,k,m,F,Sigma,n)

//xo is in ( Zq/p^(2k+1)Zq ), m is in N //
//F is a 2 variable function //
//Sigma is a power of Frq //

	if x0 le (2*k+1) then return x0;
	end if;
	
	w := Ceiling(m/2)+k;

	x1 := $$(x0,k,w,F,Sigma,n); // x1 is in Zq / (p^w)Zq 

	
	x := quo<Zq|Zq!(p^m)>!x1; // x is now in Zq / (p^m)Zq

	y := Sigma(x) mod (p^m);

	Dx := (Derivative(F,1))(x0,Sigma(x0)) mod p^(w-k); 
	Dy := (Derivative(F,2))(x0,Sigma(x0)) mod p^(w-k);
	
	V := F(x,y) mod (p^m);
	
	C := ArtinSchreierRoot(-V / ((p^(w-k))*Dy) , 
			        -Dx/Dy, w-k, n );

	a := C[1]; b := C[2];

	return (x + ( (p^(w-k)) * ((1-a)^(-1)) * b) );

end function;

	


Output: Magma V2.11-2     Wed Jul 28 2004 04:46:57 on modular  [Seed = 2496839052]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host tolman.mat.unimi.it. (159.149.2.7)
Time: Wed Jul 28 06:49:47 2004

Input: A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^2-y^3);
p := Origin(A);
IsCusp(C,p);

Output: Magma V2.11-2     Wed Jul 28 2004 06:49:42 on modular  [Seed = 1932900015]
   -------------------------------------

true

Total time: 0.770 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host anelise.capfed2.sinectis.com.ar. (216.244.232.3)
Time: Wed Jul 28 10:41:03 2004

Input: 2+2

Output: Magma V2.11-2     Wed Jul 28 2004 10:40:55 on modular  [Seed = 4038462234]
   -------------------------------------

4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:55:26 2004

Input: 
  F:=FiniteField(5^2); s:=0;
        for x in F do for y in F do         if tt y^2+x*y-x^3=0 then
            s:=s+1
                     end if;
         end for;
               end for;
       end for;

Output: Magma V2.11-2     Wed Jul 28 2004 13:55:26 on modular  [Seed = 2244160555]
   -------------------------------------


>>         for x in F do for y in F do         if tt y^2+x*y-x^3=0 then
                                                     ^
User error: bad syntax

>>                      end if;
                        ^
User error: bad syntax

>>          end for;
            ^
User error: bad syntax

>>                end for;
                  ^
User error: bad syntax

>>        end for;;
          ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:55:40 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do for y in F do         if tt y^2+x*y-x^3=0 then
            s:=s+1
                     end if;
         end for;
               end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:55:39 on modular  [Seed = 2378900534]
   -------------------------------------


>>         for x in F do for y in F do         if tt y^2+x*y-x^3=0 then
                                                     ^
User error: bad syntax

>>                      end if;
                        ^
User error: bad syntax

>>          end for;
            ^
User error: bad syntax

>>                end for;
                  ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:55:47 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do for y in F do         if  y^2+x*y-x^3=0 then
            s:=s+1
                     end if;
         end for;
               end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:55:46 on modular  [Seed = 2513648663]
   -------------------------------------


>>                      end if;
                        ^
User error: bad syntax

>>          end for;
            ^
User error: bad syntax

>>                end for;
                  ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:56:07 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do for y in F do         
           if  y^2+x*y-x^3=0 then
            s:=s+1;
           end if;
         end for;
               end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:56:07 on modular  [Seed = 2664969993]
   -------------------------------------


>>            if  y^2+x*y-x^3=0 then
              ^
Runtime error in if: Logical expected

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:57:10 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do         
           if  y^2+x*y-x^3=0 then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:57:09 on modular  [Seed = 3869265715]
   -------------------------------------


>>            if  y^2+x*y-x^3=0 then
              ^
Runtime error in if: Logical expected

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:57:19 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do         
           if  (y^2+x*y-x^3=0) then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:57:18 on modular  [Seed = 4004005680]
   -------------------------------------


>>            if  (y^2+x*y-x^3=0) then
              ^
Runtime error in if: Logical expected

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:57:21 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do         
           if  (y^2+x*y-x^3=0) then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:57:20 on modular  [Seed = 4138753750]
   -------------------------------------


>>            if  (y^2+x*y-x^3=0) then
              ^
Runtime error in if: Logical expected

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:58:58 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3=0);      
           if  (t) then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:58:58 on modular  [Seed = 3280300929]
   -------------------------------------


>>         t:=F!(y^2+x*y-x^3=0);      
               ^
Runtime error in '!': Illegal coercion
LHS: FldFin
RHS: RelElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:59:11 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t=0) then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:59:11 on modular  [Seed = 3415040900]
   -------------------------------------


>>            if  (t=0) then
              ^
Runtime error in if: Logical expected

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 13:59:52 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t ne 0) then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 13:59:51 on modular  [Seed = 3566369891]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:00:08 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
       

Output: Magma V2.11-2     Wed Jul 28 2004 14:00:07 on modular  [Seed = 863345591]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:00:34 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
return(s);
       

Output: Magma V2.11-2     Wed Jul 28 2004 14:00:34 on modular  [Seed = 947818713]
   -------------------------------------


>> return(s);
   ^
User error: A 'return' can only be used inside a procedure or function

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:00:47 2004

Input:   F:=FiniteField(5^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
return s;
       

Output: Magma V2.11-2     Wed Jul 28 2004 14:00:46 on modular  [Seed = 121745386]
   -------------------------------------


>> return s;
   ^
User error: A 'return' can only be used inside a procedure or function

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:01:39 2004

Input: function count3(p) 
 F:=FiniteField(p^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  

Output: Magma V2.11-2     Wed Jul 28 2004 14:01:38 on modular  [Seed = 290961968]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:01:52 2004

Input: function count3(p) 
 F:=FiniteField(p^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  
count3(5);


Output: Magma V2.11-2     Wed Jul 28 2004 14:01:50 on modular  [Seed = 408859445]
   -------------------------------------

24

Total time: 1.329 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:02:23 2004

Input: function count3(p) 
 F:=FiniteField(p^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  
count3(5);
count3(11);

Output: Magma V2.11-2     Wed Jul 28 2004 14:02:20 on modular  [Seed = 1613155183]
   -------------------------------------

24
120

Total time: 3.029 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:03:10 2004

Input: function count3(p) 
 F:=FiniteField(p^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  
count3(5);
count3(11);
count3(17);

Output: Magma V2.11-2     Wed Jul 28 2004 14:03:09 on modular  [Seed = 1747895062]
   -------------------------------------

24
120
288

Total time: 1.109 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:03:48 2004

Input: function count3(p) 
 F:=FiniteField(p^2); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  
count3(5);
count3(11);
count3(17);
count3(7);

Output: Magma V2.11-2     Wed Jul 28 2004 14:03:42 on modular  [Seed = 1966333480]
   -------------------------------------

24
120
288
48

Total time: 5.689 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:04:21 2004

Input: function count3(p,e) 
 F:=FiniteField(p^e); s:=0;
        for x in F do 
        for y in F do   
        t:=F!(y^2+x*y-x^3);      
           if  (t eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  
count3(5,2);
count3(7,1);

Output: Magma V2.11-2     Wed Jul 28 2004 14:04:15 on modular  [Seed = 2101073601]
   -------------------------------------

24
6

Total time: 5.699 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:15:24 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
        for x in F do 
        for y in F do   
        s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
           if  (s eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  

count3(7,1,1);

Output: Magma V2.11-2     Wed Jul 28 2004 14:15:15 on modular  [Seed = 1275781212]
   -------------------------------------

1

Total time: 5.040 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:15:46 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
        for x in F do 
        for y in F do   
        s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
           if  (s eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  

count3(7,2,1);

Output: Magma V2.11-2     Wed Jul 28 2004 14:15:34 on modular  [Seed = 1528690494]
   -------------------------------------

1

Total time: 11.779 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:16:11 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
        for x in F do 
        for y in F do   
        s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
           if  (s eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  

count3(5,2,1);

Output: Magma V2.11-2     Wed Jul 28 2004 14:15:57 on modular  [Seed = 2749698013]
   -------------------------------------

1

Total time: 13.180 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:16:33 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
        for x in F do 
        for y in F do   
        s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
           if  (s eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  

count3(5,2,2);

Output: Magma V2.11-2     Wed Jul 28 2004 14:16:19 on modular  [Seed = 2884438011]
   -------------------------------------

1

Total time: 13.420 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:16:56 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
        for x in F do 
        for y in F do   
        s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
           if  (s eq 0) then
            s:=s+1;
           end if;
         end for;
         end for;
         return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:16:42 on modular  [Seed = 3019185946]
   -------------------------------------

1

Total time: 13.570 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:18:42 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
       
E:=EllipticCurve(
               [FiniteField(p^e)|(1-t^3, -t^3, -t^30,0]);
               sum:=sum-p^e+#E;
        s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:18:29 on modular  [Seed = 3103659118]
   -------------------------------------


>>                [FiniteField(p^e)|(1-t^3, -t^3, -t^30,0]);
                                                         ^
User error: bad syntax

>>                sum:=sum-p^e+#E;
                       ^
User error: Identifier 'sum' has not been declared or assigned

>>         s:=F!(y^2+(1-t^3)*x*y-t^3*(y-x^3));      
              ^
User error: Identifier 'F' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 12.830 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:19:27 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
       
E:=EllipticCurve(
               [FiniteField(p^e)|(1-t^3, -t^3, -t^30,0]);
               s:=-p^e+#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:19:15 on modular  [Seed = 2160471936]
   -------------------------------------


>>                [FiniteField(p^e)|(1-t^3, -t^3, -t^30,0]);
                                                         ^
User error: bad syntax

>>                s:=-p^e+#E;
                      ^
User error: Identifier 'p' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 10.639 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:19:37 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
       
E:=EllipticCurve(
               [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0]);
               s:=-p^e+#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:19:25 on modular  [Seed = 2260740488]
   -------------------------------------


>>                [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0]);
                                                        ^
User error: bad syntax

>>                s:=-p^e+#E;
                      ^
User error: Identifier 'p' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 10.720 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:20:33 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
       
E:=EllipticCurve(
               [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0,0]);
               s:=-p^e+#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:20:17 on modular  [Seed = 4155594933]
   -------------------------------------


>>                [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0,0]);
                                                          ^
User error: bad syntax

>>                s:=-p^e+#E;
                      ^
User error: Identifier 'p' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 15.269 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:21:07 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
       
E:=EllipticCurve(
               [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0,0]);
               s:=E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:20:51 on modular  [Seed = 4290334815]
   -------------------------------------


>>                [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0,0]);
                                                          ^
User error: bad syntax

>>                s:=E;
                     ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 15.810 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:21:31 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
       
E:=EllipticCurve(
               [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:21:16 on modular  [Seed = 3347146872]
   -------------------------------------


>>                [FiniteField(p^e)|(1-t^3, -t^3, -t^3,0,0]);
                                                          ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 14.800 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:23:30 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:+F!;   
E:=EllipticCurve(
               [F|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:23:24 on modular  [Seed = 3448464370]
   -------------------------------------


>>     t:+F!;   
         ^
User error: bad syntax

>>                [F|(1-t^3, -t^3, -t^3,0,0]);
                                           ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 4.759 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:24:12 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!;   
E:=EllipticCurve(
               [F|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:24:06 on modular  [Seed = 3583212464]
   -------------------------------------


>>     t:=F!;   
            ^
User error: bad syntax

>>                [F|(1-t^3, -t^3, -t^3,0,0]);
                                           ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 5.419 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:24:41 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!  
E:=EllipticCurve(
               [F|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:24:34 on modular  [Seed = 3701109405]
   -------------------------------------


>> E:=EllipticCurve(
    ^
User error: bad syntax

>>                [F|(1-t^3, -t^3, -t^3,0,0]);
                                           ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 5.720 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:24:59 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!  
E:=EllipticCurve(
               [F|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:24:52 on modular  [Seed = 627280755]
   -------------------------------------


>> E:=EllipticCurve(
    ^
User error: bad syntax

>>                [F|(1-t^3, -t^3, -t^3,0,0]);
                                           ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 6.710 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:25:16 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!(t)  
E:=EllipticCurve(
               [F|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:25:08 on modular  [Seed = 846503061]
   -------------------------------------


>> E:=EllipticCurve(
   ^
User error: bad syntax

>>                [F|(1-t^3, -t^3, -t^3,0,0]);
                                           ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 6.749 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:25:30 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!(t);  
E:=EllipticCurve(
               [F|(1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:25:22 on modular  [Seed = 981243018]
   -------------------------------------


>>                [F|(1-t^3, -t^3, -t^3,0,0]);
                                           ^
User error: bad syntax

>>                s:=#E;
                      ^
User error: Identifier 'E' has not been declared or assigned

>>               return s;
                 ^
User error: A 'return' can only be used inside a procedure or function

>>       end function;  
         ^
User error: bad syntax

>> count3(5,2,3);;
   ^
User error: Identifier 'count3' has not been declared or assigned

Total time: 7.090 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:26:50 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!(t);  
E:=EllipticCurve([F|1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);

Output: Magma V2.11-2     Wed Jul 28 2004 14:26:49 on modular  [Seed = 38055113]
   -------------------------------------

20

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Jul 28 14:27:09 2004

Input: function count3(p,e,t) 
 F:=FiniteField(p^e); s:=0;
    t:=F!(t);  
E:=EllipticCurve([F|1-t^3, -t^3, -t^3,0,0]);
               s:=#E;
        
              return s;
      end function;  

count3(5,2,3);
count3(5,2,4);

Output: Magma V2.11-2     Wed Jul 28 2004 14:27:08 on modular  [Seed = 172795092]
   -------------------------------------

20
35

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:39:43 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2( 641, 3501693870747166);
FindGroupOrder2( 6700417, 3501693870747166);
FindGroupOrder2( 274177, 3501693870747166);
FindGroupOrder2( 67280421310721, 3501693870747166);
FindGroupOrder2( 5704689200685129054721, 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:39:41 on modular  [Seed = 408857559]
   -------------------------------------

[ <2, 5>, <3, 1>, <7, 1> ]
[ <2, 2>, <3, 4>, <5, 1>, <4139, 1> ]
[ <2, 2>, <3, 1>, <22783, 1> ]
[ <2, 2>, <3, 1>, <13, 1>, <625267, 1>, <689761, 1> ]
[ <2, 2>, <3, 2>, <158463588910810193711, 1> ]

Total time: 1.570 seconds, Total memory usage: 5.18MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:43:43 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:43:42 on modular  [Seed = 1949484680]
   -------------------------------------

[ <2, 3>, <3, 1>, <17, 1>, <127, 1>, <23910112363, 1> ]

Total time: 0.829 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:45:17 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print FactoredOrder(E);
   return;
end function;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:45:16 on modular  [Seed = 2101069923]
   -------------------------------------


>>    return;
      ^
User error: functions must return a value

>> FindGroupOrder2( 1238926361552897 , 3501693870747166);
   ^
User error: Identifier 'FindGroupOrder2' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:45:29 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print FactoredOrder(E);
   return;
end function;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:45:29 on modular  [Seed = 1242365729]
   -------------------------------------


>> end function;
       ^
User error: bad syntax

>> FindGroupOrder2( 1238926361552897 , 3501693870747166);
   ^
User error: Identifier 'FindGroupOrder2' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:45:39 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:45:39 on modular  [Seed = 1343677729]
   -------------------------------------

[ <2, 3>, <3, 1>, <17, 1>, <127, 1>, <23910112363, 1> ]

Total time: 0.809 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:46:00 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print "sigma=",s," order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:45:59 on modular  [Seed = 1478421789]
   -------------------------------------

sigma= 3501693870747166  order  [ <2, 3>, <3, 1>, <17, 1>, <127, 1>, 
<23910112363, 1> ]

Total time: 0.809 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:46:16 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p," : sigma=",s," order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:46:15 on modular  [Seed = 2699433461]
   -------------------------------------

1238926361552897  : sigma= 3501693870747166  order  [ <2, 3>, <3, 1>, <17, 1>, 
<127, 1>, <23910112363, 1> ]

Total time: 0.829 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:46:38 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p,": sigma=",s,", order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 1238926361552897 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:46:37 on modular  [Seed = 2834177287]
   -------------------------------------

1238926361552897 : sigma= 3501693870747166 , order  [ <2, 3>, <3, 1>, <17, 1>, 
<127, 1>, <23910112363, 1> ]

Total time: 0.819 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:48:44 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p,": sigma=",s,", order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 2424833 , 3501693870747166);
FindGroupOrder2( 7455602825647884208337395736200454918783366342657 , 3501693870747166);
FindGroupOrder2( 45592577 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:48:33 on modular  [Seed = 2985756050]
   -------------------------------------

2424833 : sigma= 3501693870747166 , order  [ <2, 6>, <3, 1>, <5, 1>, <7, 1>, 
<19, 2> ]
7455602825647884208337395736200454918783366342657 : sigma= 3501693870747166 , 
order  [ <2, 2>, <3, 1>, <47, 1>, <373, 1>, <5851, 1>, <38402733857, 1>, 
<157725745151679759107803467607, 1> ]
45592577 : sigma= 3501693870747166 , order  [ <2, 4>, <3, 1>, <5, 2>, <37987, 1>
]

Total time: 10.979 seconds, Total memory usage: 5.32MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:53:50 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p,": sigma=",s,", order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 319489 , 3501693870747166);
FindGroupOrder2( 974849 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:53:49 on modular  [Seed = 3170503587]
   -------------------------------------

319489 : sigma= 3501693870747166 , order  [ <2, 2>, <3, 4>, <5, 1>, <197, 1> ]
974849 : sigma= 3501693870747166 , order  [ <2, 2>, <3, 1>, <29, 1>, <2803, 1> ]

Total time: 0.639 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:55:14 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p,": sigma=",s,", order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 114689 , 3501693870747166);
FindGroupOrder2( 26017793 , 3501693870747166);
FindGroupOrder2( 63766529 , 3501693870747166);
FindGroupOrder2( 190274191361 , 3501693870747166);
FindGroupOrder2( 1256132134125569 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:55:13 on modular  [Seed = 2244162102]
   -------------------------------------

114689 : sigma= 3501693870747166 , order  [ <2, 2>, <3, 3>, <7, 1>, <151, 1> ]
26017793 : sigma= 3501693870747166 , order  [ <2, 3>, <3, 1>, <7, 1>, <149, 1>, 
<1039, 1> ]
63766529 : sigma= 3501693870747166 , order  [ <2, 2>, <3, 2>, <1771387, 1> ]
190274191361 : sigma= 3501693870747166 , order  [ <2, 4>, <3, 4>, <11, 1>, <197,
1>, <67751, 1> ]
1256132134125569 : sigma= 3501693870747166 , order  [ <2, 5>, <3, 2>, <13, 2>, 
<17, 1>, <1518123839, 1> ]

Total time: 0.960 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 14:56:50 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p,": sigma=",s,", order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 2710954639361 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 14:56:50 on modular  [Seed = 2547064903]
   -------------------------------------

2710954639361 : sigma= 3501693870747166 , order  [ <2, 4>, <3, 1>, <787, 1>, 
<71763997, 1> ]

Total time: 0.750 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Wed Jul 28 15:06:31 2004

Input: FindGroupOrder2 := procedure (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   print p,": sigma=",s,", order ",FactoredOrder(E);
   return;
end procedure;
FindGroupOrder2( 59649589127497217 , 3501693870747166);


Output: Magma V2.11-2     Wed Jul 28 2004 15:06:30 on modular  [Seed = 4105325792]
   -------------------------------------

59649589127497217 : sigma= 3501693870747166 , order  [ <2, 3>, <3, 1>, <17, 1>, 
<10061, 1>, <14531356027, 1> ]

Total time: 0.819 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host maclaurin.math.lsu.edu. (130.39.168.211)
Time: Wed Jul 28 15:11:15 2004

Input: $VERSION


Output: Magma V2.11-2     Wed Jul 28 2004 15:11:15 on modular  [Seed = 3347152054]
   -------------------------------------


>> $VERSION
    ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host maclaurin.math.lsu.edu. (130.39.168.211)
Time: Wed Jul 28 15:12:19 2004

Input: C<z> := PolynomialRing(ComplexField(100));
f := z^5-z^4+2;
A := AnalyticJacobian(f);


Output: Magma V2.11-2     Wed Jul 28 2004 15:12:12 on modular  [Seed = 3481891937]
   -------------------------------------


Total time: 7.159 seconds, Total memory usage: 3.66MB


************** MAGMA *****************
Host maclaurin.math.lsu.edu. (130.39.168.211)
Time: Wed Jul 28 15:13:34 2004

Input: C<z> := PolynomialRing(ComplexField(100));
f := z^5-z^4+2;
A := AnalyticJacobian(f);
M := EndomorphismRing(A);
M;


Output: Magma V2.11-2     Wed Jul 28 2004 15:13:27 on modular  [Seed = 3566366497]
   -------------------------------------

Matrix Algebra of degree 4 with 1 generator over Integer Ring

Total time: 7.379 seconds, Total memory usage: 3.76MB


************** MAGMA *****************
Host sjcd-dmzweb-ce3.cisco.com. (128.107.253.39)
Time: Wed Jul 28 15:26:09 2004

Input: 13#

Output: Magma V2.11-2     Wed Jul 28 2004 15:26:08 on modular  [Seed = 21478901]
   -------------------------------------


>> 13#;
     ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pD9FAB084.dip.t-dialin.net. (217.250.176.132)
Time: Wed Jul 28 17:22:29 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
IsIsometric(L1,L2);
N:=Lattice("Lambda",16);
IsIsometric(L1,N);

Output: Magma V2.11-2     Wed Jul 28 2004 17:22:25 on modular  [Seed = 1763717469]
   -------------------------------------

false
false

Total time: 3.229 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pD9FAB084.dip.t-dialin.net. (217.250.176.132)
Time: Wed Jul 28 17:26:56 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
IsIsometric(L1,L2);
N:=Lattice("Lambda",16);
IsIsometric(L1,N);
M:=Lattice("E",8);
E88:=OrthogonalSum(M,M);
IsIsometric(L1;E88);

Output: Magma V2.11-2     Wed Jul 28 2004 17:26:53 on modular  [Seed = 2614280352]
   -------------------------------------

false
false

>> IsIsometric(L1;E88);;
                 ^
User error: bad syntax

Total time: 3.250 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pD9FAB084.dip.t-dialin.net. (217.250.176.132)
Time: Wed Jul 28 17:27:55 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
IsIsometric(L1,L2);
N:=Lattice("Lambda",16);
IsIsometric(L1,N);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);

Output: Magma V2.11-2     Wed Jul 28 2004 17:27:49 on modular  [Seed = 4055411330]
   -------------------------------------

false
false
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]

Total time: 6.400 seconds, Total memory usage: 3.13MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 02:55:10 2004

Input: F2 := FiniteField(2);


Output: Magma V2.11-2     Thu Jul 29 2004 02:55:10 on modular  [Seed = 543817310]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 02:55:18 2004

Input: F2 := FiniteField(2):


Output: Magma V2.11-2     Thu Jul 29 2004 02:55:18 on modular  [Seed = 677508686]
   -------------------------------------


>> F2 := FiniteField(2):
                       ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 02:56:40 2004

Input: F2 := FiniteField(2);
R := F2[x,y]/(y^2+y-x^3);



Output: Magma V2.11-2     Thu Jul 29 2004 02:56:39 on modular  [Seed = 408012431]
   -------------------------------------


>> R := F2[x,y]/(y^2+y-x^3);
           ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 03:01:27 2004

Input: F2 := FiniteField(2);
R<x,y> := PolynomialRing(F2,2);
I := ideal<R| y^2+y-x^3>;
S := R/I;
S

Output: Magma V2.11-2     Thu Jul 29 2004 03:01:27 on modular  [Seed = 1966904450]
   -------------------------------------

Affine Algebra of rank 2 over GF(2)
Lexicographical Order
Variables: x, y
Quotient relations:
[
    x^3 + y^2 + y
]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 03:09:11 2004

Input: F2 := FiniteField(2);
R<x,y> := PolynomialRing(F2,2);
I := ideal<R| y^2+y-x^3>;
S := R/I;
ClassGroup(S);


Output: Magma V2.11-2     Thu Jul 29 2004 03:09:10 on modular  [Seed = 1377546740]
   -------------------------------------


>> ClassGroup(S);
             ^
Runtime error in 'ClassGroup': Bad argument types
Argument types given: RngMPolRes

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host proxy.westpac.com.au. (203.24.6.121)
Time: Thu Jul 29 03:34:43 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Jul 29 2004 03:34:42 on modular  [Seed = 2750040577]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host proxy.westpac.com.au. (203.24.6.121)
Time: Thu Jul 29 03:35:15 2004

Input: RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;


Output: Magma V2.11-2     Thu Jul 29 2004 03:35:14 on modular  [Seed = 2900706606]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host proxy.westpac.com.au. (203.24.6.121)
Time: Thu Jul 29 03:35:36 2004

Input: RandomHEC_3_2:=procedure();
 K:=GF(2);
 P<x>:=PolynomialRing(K);
 S4:=car<K,K,K,K>;
 S7:=car<K,K,K,K,K,K,K>;
 a:=Random(S4);
 b:=Random(S7);
 h:=P!(a[1]+a[2]*x+a[3]*x^2+a[4]*x^3);
 f:=P!(b[1]+b[2]*x+b[3]*x^2+b[4]*x^3+b[5]*x^4+b[6]*x^5
 +b[7]*x^6+x^7);
 print IsHyperellipticCurve([f,h]);
 end procedure;


Output: Magma V2.11-2     Thu Jul 29 2004 03:35:35 on modular  [Seed = 2497543523]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pallas.matha.RWTH-Aachen.DE. (134.130.164.47)
Time: Thu Jul 29 05:54:25 2004

Input: Q := Rationals();
g1 := [ 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0,
        0, 0,-1, 0, 0, 0,
        0, 0, 0,-1, 0, 0,
        0, 0, 0, 0,-1, 0,
        0, 0, 0, 0, 0,-1];
g2 := [ 1, 0, 0, 0, 0, 0,
        0,-1, 0, 0, 0, 0,
        0, 0, 1, 0, 0, 0,
        0, 0, 0,-1, 0, 0,
        0, 0, 0, 0,-1, 0,
        0, 0, 0, 0, 0,-1];
g3 := [ 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0,
        0, 0, 1, 0, 0, 0,
        0, 0, 0, 1, 0, 0,
        0, 0, 0, 0,-1, 0,
        0, 0, 0, 0, 0,-1];
g4 := [ 1/4, 3/4, 3/4, 3/4, 3/4, 3/4,
        1/4,-1/4, 3/4,-1/4,-1/4,-1/4,
        1/4, 3/4,-1/4,-1/4,-1/4,-1/4,
        1/4,-1/4,-1/4, 3/4,-1/4,-1/4,
        1/4,-1/4,-1/4,-1/4, 3/4,-1/4,
        1/4,-1/4,-1/4,-1/4,-1/4, 3/4];
G := MatrixGroup< 6, Q | g1,g2,g3,g4 >;
Order(G);
G;
IR := InvariantRing(G);
PI := PrimaryInvariants(IR);
PI;
SI := SecondaryInvariants(IR);
SI;


Output: Magma V2.11-2     Thu Jul 29 2004 05:54:04 on modular  [Seed = 1680731242]
   -------------------------------------

720
MatrixGroup(6, Rational Field) of order 720 = 2^4 * 3^2 * 5
Generators:
    [ 1  0  0  0  0  0]
    [ 0  1  0  0  0  0]
    [ 0  0 -1  0  0  0]
    [ 0  0  0 -1  0  0]
    [ 0  0  0  0 -1  0]
    [ 0  0  0  0  0 -1]

    [ 1  0  0  0  0  0]
    [ 0 -1  0  0  0  0]
    [ 0  0  1  0  0  0]
    [ 0  0  0 -1  0  0]
    [ 0  0  0  0 -1  0]
    [ 0  0  0  0  0 -1]

    [ 1  0  0  0  0  0]
    [ 0  1  0  0  0  0]
    [ 0  0  1  0  0  0]
    [ 0  0  0  1  0  0]
    [ 0  0  0  0 -1  0]
    [ 0  0  0  0  0 -1]

    [ 1/4  3/4  3/4  3/4  3/4  3/4]
    [ 1/4 -1/4  3/4 -1/4 -1/4 -1/4]
    [ 1/4  3/4 -1/4 -1/4 -1/4 -1/4]
    [ 1/4 -1/4 -1/4  3/4 -1/4 -1/4]
    [ 1/4 -1/4 -1/4 -1/4  3/4 -1/4]
    [ 1/4 -1/4 -1/4 -1/4 -1/4  3/4]
[
    x1^2 + 3*x2^2 + 3*x3^2 + 3*x4^2 + 6*x5*x6,
    x5^2 - 2*x5*x6 + x6^2,
    x1^3 - 9*x1*x2^2 - 9*x1*x3^2 - 9*x1*x4^2 + 9*x1*x5^2 + 18*x1*x5*x6 + 
        9*x1*x6^2 + 54*x2*x3*x4,
    x1^4 + 6*x1^2*x2^2 + 6*x1^2*x3^2 + 6*x1^2*x4^2 + 24*x1*x2*x3*x4 + 9*x2^4 + 
        6*x2^2*x3^2 + 6*x2^2*x4^2 + 12*x2^2*x5^2 + 24*x2^2*x5*x6 + 12*x2^2*x6^2 
        + 9*x3^4 + 6*x3^2*x4^2 + 12*x3^2*x5^2 + 24*x3^2*x5*x6 + 12*x3^2*x6^2 + 
        9*x4^4 + 12*x4^2*x5^2 + 24*x4^2*x5*x6 + 12*x4^2*x6^2 + 12*x5^3*x6 + 
        12*x5*x6^3,
    x1^5 - 6*x1^3*x2^2 - 6*x1^3*x3^2 - 6*x1^3*x4^2 + 12*x1^2*x2*x3*x4 - 
        27*x1*x2^4 + 30*x1*x2^2*x3^2 + 30*x1*x2^2*x4^2 + 24*x1*x2^2*x5^2 + 
        48*x1*x2^2*x5*x6 + 24*x1*x2^2*x6^2 - 27*x1*x3^4 + 30*x1*x3^2*x4^2 + 
        24*x1*x3^2*x5^2 + 48*x1*x3^2*x5*x6 + 24*x1*x3^2*x6^2 - 27*x1*x4^4 + 
        24*x1*x4^2*x5^2 + 48*x1*x4^2*x5*x6 + 24*x1*x4^2*x6^2 + 3*x1*x5^4 + 
        12*x1*x5^3*x6 + 18*x1*x5^2*x6^2 + 12*x1*x5*x6^3 + 3*x1*x6^4 + 
        36*x2^3*x3*x4 + 36*x2*x3^3*x4 + 36*x2*x3*x4^3 + 144*x2*x3*x4*x5^2 + 
        288*x2*x3*x4*x5*x6 + 144*x2*x3*x4*x6^2,
    x1^6 + 45*x1^2*x2^4 + 45*x1^2*x3^4 + 45*x1^2*x4^4 + 90*x1^2*x5^2*x6^2 + 
        360*x1*x2*x3*x4*x5^2 + 360*x1*x2*x3*x4*x5*x6 + 360*x1*x2*x3*x4*x6^2 + 
        18*x2^6 + 270*x2^2*x3^2*x4^2 + 90*x2^2*x3^2*x5^2 + 360*x2^2*x3^2*x5*x6 +
        90*x2^2*x3^2*x6^2 + 90*x2^2*x4^2*x5^2 + 360*x2^2*x4^2*x5*x6 + 
        90*x2^2*x4^2*x6^2 + 45*x2^2*x5^4 + 180*x2^2*x5^2*x6^2 + 45*x2^2*x6^4 + 
        18*x3^6 + 90*x3^2*x4^2*x5^2 + 360*x3^2*x4^2*x5*x6 + 90*x3^2*x4^2*x6^2 + 
        45*x3^2*x5^4 + 180*x3^2*x5^2*x6^2 + 45*x3^2*x6^4 + 18*x4^6 + 
        45*x4^2*x5^4 + 180*x4^2*x5^2*x6^2 + 45*x4^2*x6^4 + 18*x5^5*x6 - 
        90*x5^4*x6^2 + 180*x5^3*x6^3 - 90*x5^2*x6^4 + 18*x5*x6^5
]


************** MAGMA *****************
Host pallas.matha.RWTH-Aachen.DE. (134.130.164.47)
Time: Thu Jul 29 05:57:43 2004

Input: Q := Rationals();
g1 := [ 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0,
        0, 0,-1, 0, 0, 0,
        0, 0, 0,-1, 0, 0,
        0, 0, 0, 0,-1, 0,
        0, 0, 0, 0, 0,-1];
g2 := [ 1, 0, 0, 0, 0, 0,
        0,-1, 0, 0, 0, 0,
        0, 0, 1, 0, 0, 0,
        0, 0, 0,-1, 0, 0,
        0, 0, 0, 0,-1, 0,
        0, 0, 0, 0, 0,-1];
g3 := [ 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0,
        0, 0, 1, 0, 0, 0,
        0, 0, 0, 1, 0, 0,
        0, 0, 0, 0,-1, 0,
        0, 0, 0, 0, 0,-1];
g4 := [ 1/4, 3/4, 3/4, 3/4, 3/4, 3/4,
        1/4,-1/4, 3/4,-1/4,-1/4,-1/4,
        1/4, 3/4,-1/4,-1/4,-1/4,-1/4,
        1/4,-1/4,-1/4, 3/4,-1/4,-1/4,
        1/4,-1/4,-1/4,-1/4, 3/4,-1/4,
        1/4,-1/4,-1/4,-1/4,-1/4, 3/4];
g5 := [ 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0,
        0, 0, 1, 0, 0, 0,
        0, 0, 0, 0, 0, 1,
        0, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 1, 0];
G := MatrixGroup< 6, Q | g1,g2,g3,g4,g5 >;
Order(G);
G;
IR := InvariantRing(G);
PI := PrimaryInvariants(IR);
PI;


Output: Magma V2.11-2     Thu Jul 29 2004 05:57:23 on modular  [Seed = 1831134812]
   -------------------------------------

25920
MatrixGroup(6, Rational Field) of order 25920 = 2^6 * 3^4 * 5
Generators:
    [ 1  0  0  0  0  0]
    [ 0  1  0  0  0  0]
    [ 0  0 -1  0  0  0]
    [ 0  0  0 -1  0  0]
    [ 0  0  0  0 -1  0]
    [ 0  0  0  0  0 -1]

    [ 1  0  0  0  0  0]
    [ 0 -1  0  0  0  0]
    [ 0  0  1  0  0  0]
    [ 0  0  0 -1  0  0]
    [ 0  0  0  0 -1  0]
    [ 0  0  0  0  0 -1]

    [ 1  0  0  0  0  0]
    [ 0  1  0  0  0  0]
    [ 0  0  1  0  0  0]
    [ 0  0  0  1  0  0]
    [ 0  0  0  0 -1  0]
    [ 0  0  0  0  0 -1]

    [ 1/4  3/4  3/4  3/4  3/4  3/4]
    [ 1/4 -1/4  3/4 -1/4 -1/4 -1/4]
    [ 1/4  3/4 -1/4 -1/4 -1/4 -1/4]
    [ 1/4 -1/4 -1/4  3/4 -1/4 -1/4]
    [ 1/4 -1/4 -1/4 -1/4  3/4 -1/4]
    [ 1/4 -1/4 -1/4 -1/4 -1/4  3/4]

    [1 0 0 0 0 0]
    [0 1 0 0 0 0]
    [0 0 1 0 0 0]
    [0 0 0 0 0 1]
    [0 0 0 1 0 0]
    [0 0 0 0 1 0]


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:47:36 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
N:=Lattice("Lambda",16);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L1,N);
IsIsometric(L2,K);
IsIsometric(L2,N);

Output: Magma V2.11-2     Thu Jul 29 2004 09:47:24 on modular  [Seed = 3970257462]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false
false
false

Total time: 12.199 seconds, Total memory usage: 3.16MB


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:50:27 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
N:=Lattice("Lambda",16);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L1,N);
IsIsometric(L2,K);
IsIsometric(L2,N);
P:=Dual(N);
IsIsometric(P,N);


Output: Magma V2.11-2     Thu Jul 29 2004 09:50:06 on modular  [Seed = 3533345642]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false
false
false


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:51:46 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
N:=Lattice("Lambda",16);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L1,N);
IsIsometric(L2,K);
IsIsometric(L2,N);
P:=Dual(N);
P eq N;


Output: Magma V2.11-2     Thu Jul 29 2004 09:51:34 on modular  [Seed = 3667041034]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false
false
false

>> P eq N;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 12.199 seconds, Total memory usage: 3.16MB


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:54:50 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
N:=Lattice("D",16);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L1,N);
IsIsometric(L2,K);
IsIsometric(L2,N);
P:=Dual(N);
P eq N;


Output: Magma V2.11-2     Thu Jul 29 2004 09:54:32 on modular  [Seed = 3431238754]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false
false


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 3431238754
Time to this point: 17.97
Segmentation fault

>> P eq N;
     ^
Runtime error in 'eq': Arguments are not compatible
Argument types given: Lat, Lat

Total time: 17.940 seconds, Total memory usage: 3.28MB


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:55:52 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
N:=Lattice("D",16);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L1,N);
IsIsometric(L2,K);
IsIsometric(L2,N);
P:=Dual(N);
IsIsometric(P,N);


Output: Magma V2.11-2     Thu Jul 29 2004 09:55:34 on modular  [Seed = 1064796112]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false
false


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1064796112
Time to this point: 17.97
Segmentation fault
false

Total time: 17.949 seconds, Total memory usage: 3.28MB


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:56:31 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
N:=Lattice("D",16);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L1,N);
IsIsometric(L2,K);
IsIsometric(L2,N);
P:=Dual(N);
IsIsometric(P,N);


Output: Magma V2.11-2     Thu Jul 29 2004 09:56:13 on modular  [Seed = 677406956]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false
false


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 677406956
Time to this point: 17.97
Segmentation fault
false

Total time: 17.930 seconds, Total memory usage: 3.28MB


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:57:44 2004

Input: N:=Lattice("D",16);
P:=Dual(N);
IsIsometric(P,N);


Output: Magma V2.11-2     Thu Jul 29 2004 09:57:44 on modular  [Seed = 543712065]
   -------------------------------------

false

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:58:22 2004

Input: N:=Lattice("Lambda",16);
P:=Dual(N);
IsIsometric(P,N);


Output: Magma V2.11-2     Thu Jul 29 2004 09:58:01 on modular  [Seed = 407919432]
   -------------------------------------



************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 09:58:50 2004

Input: N:=Lattice("Lambda",16);
P:=Dual(N);
IsIsometric(P,N);


Output: Magma V2.11-2     Thu Jul 29 2004 09:58:30 on modular  [Seed = 324751532]
   -------------------------------------



************** MAGMA *****************
Host pD9FABBD1.dip.t-dialin.net. (217.250.187.209)
Time: Thu Jul 29 10:05:35 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
EHUT2:=Matrix(RationalField(),16,16,[2,0,-1,0,0,0,-1,0,-1,0,-1,0,0,-1,1,1, 0,2,0,-1,0,0,0,-1,0,-1,0,-1,1,0,-1,1, -1,0,2,0,1,-1,0,0,0,0,0,0,0,0,0,-1, 0,-1,0,2,1,1,0,0,0,0,0,0,0,0,1,0, 0,0,1,1,2,0,0,0,0,0,0,0,0,0,1,0, 0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,1, -1,0,0,0,0,0,2,0,1,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,2,0,1,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,2,0,1,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,2,0,1,-1,0,0,-1, -1,0,0,0,0,0,1,0,1,0,2,0,0,1,-1,0, 0,-1,0,0,0,0,0,1,0,1,0,2,-1,0,0,-1, 0,1,0,0,0,0,0,-1,0,-1,0,-1,2,0,0,1, -1,0,0,0,0,0,1,0,1,0,1,0,0,2,-1,0, 1,-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,4,0, 1,1,-1,0,0,1,0,-1,0,-1,0,-1,1,0,0,4]);
L2:=LatticeWithGram(EHUT2);
EHUT3:=Matrix(RationalField(),16,16,[2,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0, 0,2,-1,1,-1,0,0,1,0,0,0,0,0,0,0,0, 1,-1,2,0,1,1,1,0,0,0,0,0,0,0,0,0, 1,1,0,2,-1,1,0,1,0,0,0,0,0,0,0,0, 0,-1,1,-1,2,0,1,0,0,0,0,0,0,0,0,0, 1,0,1,1,0,2,0,1,0,0,0,0,0,0,0,0, 1,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0, 0,1,0,1,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,2,0,1,1,1,0,0,1, 0,0,0,0,0,0,0,0,0,2,-1,1,0,1,-1,0, 0,0,0,0,0,0,0,0,1,-1,2,0,1,0,1,1, 0,0,0,0,0,0,0,0,1,1,0,2,0,1,-1,1, 0,0,0,0,0,0,0,0,1,0,1,0,2,0,1,1, 0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,1, 0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,2,0, 0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,2]);
L3:=LatticeWithGram(EHUT3);
IsIsometric(L1,L2);
IsIsometric(L1,L3);
M:=Lattice("E",8);
K:=OrthogonalSum(M,M);
IsIsometric(L1,K);
IsIsometric(L2,K);


Output: Magma V2.11-2     Thu Jul 29 2004 10:05:23 on modular  [Seed = 2117483364]
   -------------------------------------

false
true 
[-1  0  0 -2  1  0  0  0 -1  0 -1  0 -1  0  0  0]
[-1  0  0 -1  0  0 -1  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0]
[ 0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  1  0]
[ 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0 -1  0  1  0  0  0  0  0  0]
true 
[ 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  0]
[-1  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 -1]
[ 0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0 -1  0  0 -2  0  1  0  1  0  0  0  1  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0 -1  0  0]
[ 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0 -1  2  0  0  1  0  0  0 -1  0  0  0 -1  1  0]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]
false

Total time: 12.160 seconds, Total memory usage: 3.06MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Jul 29 11:56:29 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
B:=Scheme(P,[
    1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
    -1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW,
    XX^2*YY - u^3*XX^2*WW + YY^3 - u*WW^3,
    1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
    -1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW
];


Output: Magma V2.11-2     Thu Jul 29 2004 11:56:28 on modular  [Seed = 1377439045]
   -------------------------------------


>> ];
    ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Jul 29 11:56:39 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
B:=Scheme(P,[
    1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
    -1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW,
    XX^2*YY - u^3*XX^2*WW + YY^3 - u*WW^3,
    1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
    -1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW
]);


Output: Magma V2.11-2     Thu Jul 29 2004 11:56:38 on modular  [Seed = 1241650503]
   -------------------------------------


Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Jul 29 11:56:50 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
B:=Scheme(P,[
    1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
    -1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW,
    XX^2*YY - u^3*XX^2*WW + YY^3 - u*WW^3,
    1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
    -1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW
]);
B;
Points(B);


Output: Magma V2.11-2     Thu Jul 29 2004 11:56:49 on modular  [Seed = 1107959096]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
-1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW,
XX^2*YY - u^3*XX^2*WW + YY^3 - u*WW^3,
1/2*XX + 1/2*YY + 1/2*z^3*ZZ - 1/2*z^3*WW,
-1/2*XX + 1/2*YY + 1/2*z^3*ZZ + 1/2*z^3*WW


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1107959096
Time to this point: 0.66
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.610 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Jul 29 11:58:12 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<XX,YY,ZZ,WW>:=ProjectiveSpace(cu,3);
B:=Scheme(P,[
    1/2*XX + 1/2*YY - 1/2*z^3*ZZ + 1/2*z^3*WW,
    -1/2*XX + 1/2*YY - 1/2*z^3*ZZ - 1/2*z^3*WW,
    XX^2*YY - u^3*XX^2*WW + YY^3 - u*WW^3,
    1/2*XX + 1/2*YY - 1/2*z^3*ZZ + 1/2*z^3*WW,
    -1/2*XX + 1/2*YY - 1/2*z^3*ZZ - 1/2*z^3*WW
]);
B;
Points(B);


Output: Magma V2.11-2     Thu Jul 29 2004 11:58:11 on modular  [Seed = 3136480530]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
1/2*XX + 1/2*YY - 1/2*z^3*ZZ + 1/2*z^3*WW,
-1/2*XX + 1/2*YY - 1/2*z^3*ZZ - 1/2*z^3*WW,
XX^2*YY - u^3*XX^2*WW + YY^3 - u*WW^3,
1/2*XX + 1/2*YY - 1/2*z^3*ZZ + 1/2*z^3*WW,
-1/2*XX + 1/2*YY - 1/2*z^3*ZZ - 1/2*z^3*WW


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 3136480530
Time to this point: 0.65
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.600 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:09:45 2004

Input: IrreducibleSparseGF2Polynomial(5)

Output: Magma V2.11-2     Thu Jul 29 2004 14:09:44 on modular  [Seed = 3053308391]
   -------------------------------------

$.1^5 + $.1^2 + 1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:09:57 2004

Input: IrreducibleSparseGF2Polynomial(2456)

Output: Magma V2.11-2     Thu Jul 29 2004 14:09:57 on modular  [Seed = 2733301485]
   -------------------------------------

$.1^2456 + $.1^12 + $.1^5 + $.1^3 + 1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:10:11 2004

Input: IrreducibleSparseGF2Polynomial(2)

Output: Magma V2.11-2     Thu Jul 29 2004 14:10:10 on modular  [Seed = 2580669729]
   -------------------------------------


>> IrreducibleSparseGF2Polynomial(2);
                                 ^
Runtime error in 'IrreducibleSparseGF2Polynomial': No polynomial known for this 
degree

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:10:23 2004

Input: IrreducibleSparseGF2Polynomial(3)

Output: Magma V2.11-2     Thu Jul 29 2004 14:10:22 on modular  [Seed = 2446978341]
   -------------------------------------


>> IrreducibleSparseGF2Polynomial(3);
                                 ^
Runtime error in 'IrreducibleSparseGF2Polynomial': No polynomial known for this 
degree

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:10:27 2004

Input: IrreducibleSparseGF2Polynomial(4)

Output: Magma V2.11-2     Thu Jul 29 2004 14:10:26 on modular  [Seed = 2311189793]
   -------------------------------------

$.1^4 + $.1 + 1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:12:11 2004

Input: IrreducibleSparseGF2Polynomial(4);
IrreduciblePolynomail(FiniteField(2), 2)


Output: Magma V2.11-2     Thu Jul 29 2004 14:12:10 on modular  [Seed = 2177498433]
   -------------------------------------

$.1^4 + $.1 + 1

>> IrreduciblePolynomail(FiniteField(2), 2)
   ^
User error: Identifier 'IrreduciblePolynomail' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:12:23 2004

Input: IrreducibleSparseGF2Polynomial(4);
IrreduciblePolynomial(FiniteField(2), 2)


Output: Magma V2.11-2     Thu Jul 29 2004 14:12:22 on modular  [Seed = 4189161157]
   -------------------------------------

$.1^4 + $.1 + 1
$.1^2 + $.1 + 1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:12:30 2004

Input: IrreducibleSparseGF2Polynomial(4);
IrreduciblePolynomial(FiniteField(2), 3)


Output: Magma V2.11-2     Thu Jul 29 2004 14:12:30 on modular  [Seed = 4055469765]
   -------------------------------------

$.1^4 + $.1 + 1
$.1^3 + $.1 + 1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:12:48 2004

Input: IrreducibleSparseGF2Polynomial(5);

Output: Magma V2.11-2     Thu Jul 29 2004 14:12:48 on modular  [Seed = 3919681267]
   -------------------------------------

$.1^5 + $.1^2 + 1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:13:04 2004

Input: IrreducibleSparseGF2Polynomial(6);

Output: Magma V2.11-2     Thu Jul 29 2004 14:13:04 on modular  [Seed = 3785989867]
   -------------------------------------

$.1^6 + $.1 + 1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host GLORFINDEL.MIT.EDU. (18.243.1.196)
Time: Thu Jul 29 14:13:15 2004

Input: IrreducibleSparseGF2Polynomial(7);

Output: Magma V2.11-2     Thu Jul 29 2004 14:13:14 on modular  [Seed = 3650201304]
   -------------------------------------

$.1^7 + $.1 + 1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pD9FF9F6C.dip.t-dialin.net. (217.255.159.108)
Time: Thu Jul 29 14:53:11 2004

Input: 7635763^4576943*876865^145+564*8765387^32675

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Thu Jul 29 2004 14:53:00 on modular  [Seed = 441588907]
   -------------------------------------


Current total memory usage: 71.4MB, failed memory request: 31.2MB
System Error: User memory limit has been reached

Total time: 11.540 seconds, Total memory usage: 74.91MB


************** MAGMA *****************
Host pD9FF9F6C.dip.t-dialin.net. (217.255.159.108)
Time: Thu Jul 29 14:53:37 2004

Input: 7635763^457*876865^145+564*8765387^32

Output: Magma V2.11-2     Thu Jul 29 2004 14:53:36 on modular  [Seed = 256313730]
   -------------------------------------

1544585119083598687461721009988375527061226737280781602539132068518387762347016\
1808507329465967971439468107735609990188657500756821368114840991610807556558518\
7571865549372196830892270788944355205140306023182914046284364969930430201718988\
0063815136199185257987155221355402358996677629516859996684168624242767193140815\
9917645431117004067661392383843777864539634629966381569585192102850665078841765\
0232772825574983275420574700108230521107836600786450059752728031128927537061117\
1228226541786367451147666000077601563223503128299924246702959801614685249709904\
8986867075161436868033944748661919214770773568429805466362911052351760657910247\
9542020229605026425718059805864053688338144789022369591007447545455202121842221\
8782200707119411161933932232911923991032819442918219147303667896867211833861577\
4971614549504000639774208146080125407606356964910996787322490713120814112169126\
8743844588880590655085209888539619634382469531689144907913578038539768375916966\
4067909222966418267962160971389619188420281512596140119251271468677716787442793\
6814326340566705670287791584284458949772694524286480056574411975147044979123863\
0706312349966875395689632380227681737307893715897300860061064204905553009608691\
4733431358799226582966206413359337287996899317143996147793059522556218694025622\
4255629274319982591109233158315623313923634583662630775089033925938524994265046\
7697326045515907060839503424773468245686706849722018129448566509669580585972703\
4541721957683473348477076547138696531927118891950995442430358682542861291344268\
9388305196281722491809931705648492994001489440363910471797075364609554097159439\
7994056152170967771487891391599538284753000685867451734149516229861176438741409\
4818580061818389218146483601795301512220837724518477343187001479544092015966223\
4010100447426811588056690548665127684330032512188145121980896023859491255499832\
8365627164742356702686355013635479487037323524678424057512492018129451994389819\
0802400210960697955067692592820351571587659722642659788880657085643405962447660\
1457534892204787443106044638706661326267479322997062382652257123766434215582679\
0855765827403536507928274163759627357531982408036715007259656223276358426971522\
8723536949561663253636276488515593007383381735308572881428058443840815696503231\
4513109150931924477625466893954474085512751061776780939719148483814252661548626\
7788430112115703965020439240430659764065737017359258624613657380287429965468296\
9889173729902486585892564328156906188578367916679986677447607424683291455070668\
7148248469842495729660548491849381037818965805965950567695046812689937815837420\
8041001330332927631145691688167335531933593754314964014941352542094276190357135\
8007466178117449976247170229165599792384551652323394857661922724700325793931763\
4532664034255129431188080917971993127166860649588911658406931982108325293548381\
7126461025881089867791493498546521874565652772220103370531084927308897536792062\
3877430520835910082286312351841482710216609075332934924468620329033144467375680\
6078299266710738797418235606791795284809182314093087938287025719751556296822991\
9697842886069082844408491060589752621583546524916984713299132310644352307532685\
8830651028696224554055033731700914607209487072495284004389899410822544046278583\
1996141901665176766441369238336629440682603607840159085711426076093879080159931\
4218553290804355929661396665294592834385929764041901549432465393094724817765850\
4236713070978315163024577304364204369986543481957601039129217374662677404795670\
8058515194374501304823764749367294666524092170752331257510472636392477376181245\
9476421392657330509321145955705667497492430477384974060287114042561512073925550\
7912948166769329528926313044177258424541507898286484200794184234088867861176055\
0401529710653626588465528723919496064453031300574985287354057615133064406158954\
1551908088649272733458360642258235748900064815782733996829011716480245078069931\
4020446739321930269061281411417420645290895532914739894741027815521016610417868\
6673072059239625356057612294916075124607643158782261288066806561190264313102071\
5600904367271651182132936375935617313443513713815605709959

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Thu Jul 29 15:11:17 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i=7 to 20 do
FindGroupOrder2(167988556341760475137 , i);
end for;

Output: Magma V2.11-2     Thu Jul 29 2004 15:11:16 on modular  [Seed = 1731161486]
   -------------------------------------


>> for i=7 to 20 do
        ^
User error: bad syntax

>> FindGroupOrder2(167988556341760475137 , i);
                                           ^
User error: Identifier 'i' has not been declared or assigned

>> end for;;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Thu Jul 29 15:11:32 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 20 do
FindGroupOrder2(167988556341760475137 , i);
end for;

Output: Magma V2.11-2     Thu Jul 29 2004 15:11:24 on modular  [Seed = 1595364798]
   -------------------------------------

[ <2, 2>, <3, 2>, <7, 1>, <67, 1>, <211, 1>, <20063, 1>, <2350314749, 1> ]
[ <2, 3>, <3, 1>, <13, 1>, <107, 1>, <3354613, 1>, <1500026393, 1> ]
[ <2, 2>, <3, 2>, <4666348787144631341, 1> ]
[ <2, 6>, <3, 1>, <19, 1>, <196967059, 1>, <233792873, 1> ]
[ <2, 3>, <3, 1>, <43, 1>, <3197839, 1>, <50903003209, 1> ]
[ <2, 2>, <3, 1>, <13999046363012653321, 1> ]
[ <2, 2>, <3, 2>, <4666348787468915089, 1> ]
[ <2, 3>, <3, 2>, <13, 1>, <179474953357274849, 1> ]
[ <2, 4>, <3, 2>, <2203, 1>, <21187, 1>, <24993854771, 1> ]
[ <2, 3>, <3, 1>, <11, 1>, <227399, 1>, <2798254561847, 1> ]
[ <2, 4>, <3, 1>, <17, 1>, <757, 1>, <16463989, 1>, <16518043, 1> ]
[ <2, 5>, <3, 3>, <73, 1>, <2663441088653333, 1> ]
[ <2, 2>, <3, 2>, <7, 2>, <29, 1>, <3761, 1>, <128159, 1>, <6812879, 1> ]
[ <2, 4>, <3, 1>, <7, 2>, <11, 1>, <288247, 1>, <22526042509, 1> ]

Total time: 6.910 seconds, Total memory usage: 5.18MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Thu Jul 29 15:12:47 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 8 do
p := 167988556341760475137;
print "p = ",p," sigma = ",i," : ",FindGroupOrder2(p , i);
end for;

Output: Magma V2.11-2     Thu Jul 29 2004 15:12:45 on modular  [Seed = 1343774019]
   -------------------------------------

p =  167988556341760475137  sigma =  7  :  [ <2, 2>, <3, 2>, <7, 1>, <67, 1>, 
<211, 1>, <20063, 1>, <2350314749, 1> ]
p =  167988556341760475137  sigma =  8  :  [ <2, 3>, <3, 1>, <13, 1>, <107, 1>, 
<3354613, 1>, <1500026393, 1> ]

Total time: 1.419 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Thu Jul 29 15:13:26 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 8 do
p := 167988556341760475137;
print " sigma=",i,", order ",FindGroupOrder2(p , i);
end for;

Output: Magma V2.11-2     Thu Jul 29 2004 15:13:24 on modular  [Seed = 1207977249]
   -------------------------------------

 sigma= 7 , order  [ <2, 2>, <3, 2>, <7, 1>, <67, 1>, <211, 1>, <20063, 1>, 
<2350314749, 1> ]
 sigma= 8 , order  [ <2, 3>, <3, 1>, <13, 1>, <107, 1>, <3354613, 1>, 
<1500026393, 1> ]

Total time: 1.419 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Thu Jul 29 15:13:42 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 20 do
p := 167988556341760475137;
print " sigma=",i,", order ",FindGroupOrder2(p , i);
end for;

Output: Magma V2.11-2     Thu Jul 29 2004 15:13:35 on modular  [Seed = 1074285858]
   -------------------------------------

 sigma= 7 , order  [ <2, 2>, <3, 2>, <7, 1>, <67, 1>, <211, 1>, <20063, 1>, 
<2350314749, 1> ]
 sigma= 8 , order  [ <2, 3>, <3, 1>, <13, 1>, <107, 1>, <3354613, 1>, 
<1500026393, 1> ]
 sigma= 9 , order  [ <2, 2>, <3, 2>, <4666348787144631341, 1> ]
 sigma= 10 , order  [ <2, 6>, <3, 1>, <19, 1>, <196967059, 1>, <233792873, 1> ]
 sigma= 11 , order  [ <2, 3>, <3, 1>, <43, 1>, <3197839, 1>, <50903003209, 1> ]
 sigma= 12 , order  [ <2, 2>, <3, 1>, <13999046363012653321, 1> ]
 sigma= 13 , order  [ <2, 2>, <3, 2>, <4666348787468915089, 1> ]
 sigma= 14 , order  [ <2, 3>, <3, 2>, <13, 1>, <179474953357274849, 1> ]
 sigma= 15 , order  [ <2, 4>, <3, 2>, <2203, 1>, <21187, 1>, <24993854771, 1> ]
 sigma= 16 , order  [ <2, 3>, <3, 1>, <11, 1>, <227399, 1>, <2798254561847, 1> ]
 sigma= 17 , order  [ <2, 4>, <3, 1>, <17, 1>, <757, 1>, <16463989, 1>, 
<16518043, 1> ]
 sigma= 18 , order  [ <2, 5>, <3, 3>, <73, 1>, <2663441088653333, 1> ]
 sigma= 19 , order  [ <2, 2>, <3, 2>, <7, 2>, <29, 1>, <3761, 1>, <128159, 1>, 
<6812879, 1> ]
 sigma= 20 , order  [ <2, 4>, <3, 1>, <7, 2>, <11, 1>, <288247, 1>, 
<22526042509, 1> ]

Total time: 6.949 seconds, Total memory usage: 4.82MB


************** MAGMA *****************
Host dual.math.mun.ca. (134.153.205.224)
Time: Thu Jul 29 17:29:05 2004

Input: mwrank[0,1,0,0,-23]

Output: Magma V2.11-2     Thu Jul 29 2004 17:29:04 on modular  [Seed = 3314411738]
   -------------------------------------


>> mwrank[0,1,0,0,-23];
   ^
User error: Identifier 'mwrank' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host dual.math.mun.ca. (134.153.205.224)
Time: Thu Jul 29 17:29:17 2004

Input: mwrank([0,1,0,0,-23])

Output: Magma V2.11-2     Thu Jul 29 2004 17:29:17 on modular  [Seed = 1014239535]
   -------------------------------------


>> mwrank([0,1,0,0,-23]);
   ^
User error: Identifier 'mwrank' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host dual.math.mun.ca. (134.153.205.224)
Time: Thu Jul 29 17:29:31 2004

Input: mwrank(0,1,0,0,-23)


Output: Magma V2.11-2     Thu Jul 29 2004 17:29:31 on modular  [Seed = 880548145]
   -------------------------------------


>> mwrank(0,1,0,0,-23)
   ^
User error: Identifier 'mwrank' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 195-23-150-24.net.novis.pt. (195.23.150.24)
Time: Thu Jul 29 18:38:05 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Jul 29 2004 18:38:04 on modular  [Seed = 3499683234]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:17:46 2004

Input: Factorization(24192);
Factorization(3779382983);
Factorization(13716864);

Output: Magma V2.11-2     Fri Jul 30 2004 00:17:46 on modular  [Seed = 1411178229]
   -------------------------------------

[ <2, 7>, <3, 3>, <7, 1> ]
[ <51941, 1>, <72763, 1> ]
[ <2, 7>, <3, 7>, <7, 2> ]

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:23:53 2004

Input: Factorization(3779382983);
Factorization(13716864);
Factorization(24192);


Output: Magma V2.11-2     Fri Jul 30 2004 00:23:52 on modular  [Seed = 2647986574]
   -------------------------------------

[ <51941, 1>, <72763, 1> ]
[ <2, 7>, <3, 7>, <7, 2> ]
[ <2, 7>, <3, 3>, <7, 1> ]

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:25:50 2004

Input: 3779382983/13716864
Factorization(24192);

Output: Magma V2.11-2     Fri Jul 30 2004 00:25:49 on modular  [Seed = 2497452050]
   -------------------------------------


>> Factorization(24192);;
   ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:25:55 2004

Input: 3779382983/13716864;
Factorization(24192);

Output: Magma V2.11-2     Fri Jul 30 2004 00:25:54 on modular  [Seed = 2900631605]
   -------------------------------------

3779382983/13716864
[ <2, 7>, <3, 3>, <7, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:27:02 2004

Input: 567/275.5

Output: Magma V2.11-2     Fri Jul 30 2004 00:27:02 on modular  [Seed = 3153278182]
   -------------------------------------

2.0580762250453720508166969146954

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:27:13 2004

Input: 567/2

Output: Magma V2.11-2     Fri Jul 30 2004 00:27:13 on modular  [Seed = 3019586777]
   -------------------------------------

567/2

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:27:19 2004

Input: 567/2.0

Output: Magma V2.11-2     Fri Jul 30 2004 00:27:18 on modular  [Seed = 1258538023]
   -------------------------------------

283.50000000000000000000000000000

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:32:01 2004

Input: 3+7+7+9+3+8+2+9+8+3;
1+3+7+1+6+8+6+4;
2+4+1+9+2; 

Output: Magma V2.11-2     Fri Jul 30 2004 00:32:00 on modular  [Seed = 1175373900]
   -------------------------------------

59
36
18

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:33:09 2004

Input: 3+7+7+9+3+8+2+9+8+3;
1*3*7*1*6*8*6*4;
2*4*1*9*2; 

Output: Magma V2.11-2     Fri Jul 30 2004 00:33:08 on modular  [Seed = 1578553488]
   -------------------------------------

59
24192
144

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 00:33:29 2004

Input: 3*7*7*9*3*8*2*9*8*3;
1*3*7*1*6*8*6*4;
2*4*1*9*2; 

Output: Magma V2.11-2     Fri Jul 30 2004 00:33:29 on modular  [Seed = 1444862085]
   -------------------------------------

13716864
24192
144

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Fri Jul 30 00:57:52 2004

Input: factor(200)






Output: Magma V2.11-2     Fri Jul 30 2004 00:57:51 on modular  [Seed = 997437246]
   -------------------------------------


>> factor(200)
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 01:25:18 2004

Input: 640320^[9/(3.141592*sqrt(163)]

Output: Magma V2.11-2     Fri Jul 30 2004 01:25:17 on modular  [Seed = 307923170]
   -------------------------------------


>> 640320^[9/(3.141592*sqrt(163)];
                                ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 01:25:24 2004

Input: 640320^[9/(pi*sqrt(163)]

Output: Magma V2.11-2     Fri Jul 30 2004 01:25:23 on modular  [Seed = 711110820]
   -------------------------------------


>> 640320^[9/(pi*sqrt(163)];
                          ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 01:25:39 2004

Input: 640320^[9/(Pi*(163)^(1/2)]

Output: Magma V2.11-2     Fri Jul 30 2004 01:25:39 on modular  [Seed = 577419452]
   -------------------------------------


>> 640320^[9/(Pi*(163)^(1/2)];
                            ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 01:25:47 2004

Input: 640320^(9/(Pi*(163)^(1/2))

Output: Magma V2.11-2     Fri Jul 30 2004 01:25:47 on modular  [Seed = 980590764]
   -------------------------------------


>> 640320^(9/(Pi*(163)^(1/2));
                             ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-50-108.dsl.emhril.ameritech.net. (68.75.50.108)
Time: Fri Jul 30 01:25:58 2004

Input: 640320^(9/((163)^(1/2))

Output: Magma V2.11-2     Fri Jul 30 2004 01:25:57 on modular  [Seed = 846899354]
   -------------------------------------


>> 640320^(9/((163)^(1/2));
                          ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:04:52 2004

Input: c:=2^31;
c:=c-1;
if isprime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:04:51 on modular  [Seed = 222674769]
   -------------------------------------


>> if isprime(c) then
      ^
User error: Identifier 'isprime' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:05:26 2004

Input: c:=2^31;
c:=c-1;
if isprimitive(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:05:25 on modular  [Seed = 72136318]
   -------------------------------------


>> if isprimitive(c) then
      ^
User error: Identifier 'isprimitive' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:06:01 2004

Input: c:=2^31;
c:=c-1;
c;
if IsPrime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:06:00 on modular  [Seed = 475311627]
   -------------------------------------

2147483647
2147483647

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:06:16 2004

Input: c:=2^31;
c:=c-1;
if IsPrime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:06:15 on modular  [Seed = 341616188]
   -------------------------------------

2147483647

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:06:40 2004

Input: c:=2^10000;
c:=c-1;
c;
if IsPrime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:06:39 on modular  [Seed = 744791580]
   -------------------------------------

1995063116880758384883742162683585083823496831886192454852008949852943883022194\
6631919961684036194597899331129423209124271556491349413781117593785932096323957\
8557300467937945267652465512660598955205500869181933115425086084606181046855090\
7486608962488809048989483800925394163325785062156830947390255691238806522509664\
3874441046759871626985453222868538161694315775629640762836880760732228535091641\
4761839563814589694638994108409605362678210646214273333940365255656495306031426\
8023496940033593431665145929777327966577560617258203140799419817960737824568376\
2280037302885487251900834464581454650557929601414833921615734588139257095379769\
1192778008269577356744441230620187578363255027283237892707103738028663930314281\
3324140162419567169057406141965434232463880124885614730520743199225961179625013\
0992860241708340807605932320161268492288496255841312844061536738951487114256315\
1110897455142033138202029316409575964647560104058458415660720449628670165150619\
2063100418642227590867090057460641785695191145605506825125040600751984226189805\
9237118054444788072906395242548339221982707404473162376760846613033778706039803\
4131971334936546227005631699374555082417809728109832913144035718775247685098572\
7693792643322159939987688666080836883783802764328277517227365757274478411229438\
9733810861607423253291974813120197604178281965697475898164531258434135959862784\
1301281854062834766490886905210475808826158239619857701224070443305830758690393\
1960460340497315658320867210591330090375282341553974539439771525745529051021231\
0947321610753474825740775273986348298498340756937955646638621874569499279016572\
1037013644331358172143117913982229838458473344402709641828510050729277483645505\
7863450110085298781238947392869954083434615880704395911898581514577917714361969\
8728131459483783202081474982171858011389071228250905826817436220577475921417653\
7156877256149045829049924610286300815355833081301019876758562343435389554091756\
2340084488752616264356864883351946372037729324009445624692325435040067802727383\
7755376406726898636241037491410966718557050759098100246789880178271925953381282\
4219540283027594084489550146766683896979968862416363133763939033734558014076367\
4187771105538422573949911018646821969658165148513049422236994771476306915546821\
7682876200362777257723781365331611196811280792669481887201298643660768551639860\
5346022978715575179473852463694469230878942659482170080511203223654962881690357\
3912136833839359175641873385051097027161391543959099159815465441733631165693603\
1122249937969999226781732358023111862644575299135758175008199839236284615249881\
0889602322443621737716180863570154684840586223297928538756234865564405369626220\
1896357102881236156751254333830327002909766865056855715750551672751889919412971\
1337690149916181315171544007728650573189557450920330185304847113818315407324053\
3190384620840364217637039115506397890007428536721962809034779745333204683687958\
6858023795221862912008074281955131794815762444829851846150970488802727472157468\
8131594750409732115080498190455803416826949787141316063210686391511681774304792\
596709375

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:07:00 2004

Input: c:=2^10000;
c:=c-1;
if IsPrime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:07:00 on modular  [Seed = 611096319]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:07:30 2004

Input: c:=2^1025;
c:=c-1;
c;
if IsPrime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:07:30 on modular  [Seed = 1014271681]
   -------------------------------------

3595386269724631815458610381578049467235953957884613145468601623154653516110019\
2626541695464481507204224022775974278671531757953762883324498569486127894824875\
5535786849730970552604439202492188238906165904170011537676301364684925762947826\
221081654474326701021369172596479894491876959432609670712659248448274431

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:08:15 2004

Input: c:=2^1024;
c:=c-1;
c;
if IsPrime(c) then
   c;
end if


Output: Magma V2.11-2     Fri Jul 30 2004 03:08:14 on modular  [Seed = 846889123]
   -------------------------------------

1797693134862315907729305190789024733617976978942306572734300811577326758055009\
6313270847732240753602112011387987139335765878976881441662249284743063947412437\
7767893424865485276302219601246094119453082952085005768838150682342462881473913\
110540827237163350510684586298239947245938479716304835356329624224137215

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:10:46 2004

Input: for i:= 1 to 1024 do
c:=2^i;
c:=c-1;
if IsPrime(c) then
   c;
end if;
end for;

Output: Magma V2.11-2     Fri Jul 30 2004 03:10:42 on modular  [Seed = 3734399971]
   -------------------------------------

3
7
31
127
8191
131071
524287
2147483647
2305843009213693951
618970019642690137449562111
162259276829213363391578010288127
170141183460469231731687303715884105727
6864797660130609714981900799081393217269435300143305409394463459185543183397656\
052122559640661454554977296311391480858037121987999716643812574028291115057151
5311379928167670986895882065524686273295931177270319231994441382004035598608522\
4273916250226522928566888932948624650101534657933765270723940951997876658735194\
3831270835393219031728127

Total time: 3.179 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:11:09 2004

Input: for i:= 1 to 1024 do
c:=2^i;
c:=c-1;
if IsPrime(c) then
   i;
end if;
end for;

Output: Magma V2.11-2     Fri Jul 30 2004 03:11:06 on modular  [Seed = 3600704275]
   -------------------------------------

2
3
5
7
13
17
19
31
61
89
107
127
521
607

Total time: 3.190 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:11:43 2004

Input: for i:= 1 to 10024 do
c:=2^i;
c:=c-1;
if IsPrime(c) then
   i;
end if;
end for;

Output: Magma V2.11-2     Fri Jul 30 2004 03:11:22 on modular  [Seed = 4003879739]
   -------------------------------------

2
3
5
7
13
17
19
31
61
89
107
127
521
607
1279


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:14:13 2004

Input: 

c:=2^1024;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:13:52 on modular  [Seed = 3853341082]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:16:35 2004

Input: 
c:=2^1024;
c:=c-1;
Factorization(64);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:16:34 on modular  [Seed = 4089137006]
   -------------------------------------

[ <2, 6> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:16:57 2004

Input: c:=2^1024;
c:=c-1;
Factorization(10002);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:16:56 on modular  [Seed = 2344828716]
   -------------------------------------

[ <2, 1>, <3, 1>, <1667, 1> ]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:17:18 2004

Input: c:=2^1024;
c:=c-1;
Factorization(81);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:17:18 on modular  [Seed = 2177447216]
   -------------------------------------

[ <3, 4> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:17:43 2004

Input: c:=2^1024;
c:=c-1;
Factorization(76986786786876876876876987698767876565456434543453453453453);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:17:38 on modular  [Seed = 2580623044]
   -------------------------------------

[ <229, 1>, <547, 1>, <12007, 1>, <8995247, 1>, <821422717441649, 1>, 
<6927540472524289571297478811, 1> ]

Total time: 4.680 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:18:13 2004

Input: c:=2^1024;
c:=c-1;
Factorization((2^521)-1);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:18:12 on modular  [Seed = 2951157972]
   -------------------------------------

[ <6864797660130609714981900799081393217269435300143305409394463459185543183397\
6560521225596406614545549772963113914808580371219879997166438125740282911150571\
51, 1> ]

Total time: 1.139 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:18:54 2004

Input: c:=2^1024;
c:=987
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:18:53 on modular  [Seed = 2800619956]
   -------------------------------------


>> Factorization(c);
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:19:05 2004

Input: c:=2^1024;
c:=987;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:19:05 on modular  [Seed = 3203795352]
   -------------------------------------

[ <3, 1>, <7, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:19:36 2004

Input: c:=2^512;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:19:35 on modular  [Seed = 3070099838]
   -------------------------------------

[ <3, 1>, <5, 1>, <17, 1>, <257, 1>, <641, 1>, <65537, 1>, <274177, 1>, 
<6700417, 1>, <67280421310721, 1>, <1238926361552897, 1>, <59649589127497217, 
1>, <5704689200685129054721, 1>, <934616397153579777691635581996068965840512375\
41638188580280321, 1> ]

Total time: 1.020 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:19:55 2004

Input: c:=2^600;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:19:54 on modular  [Seed = 1325922459]
   -------------------------------------

[ <3, 2>, <5, 3>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <31, 1>, <41, 1>, <61, 1>, 
<101, 1>, <151, 1>, <241, 1>, <251, 1>, <331, 1>, <401, 1>, <601, 1>, <1201, 1>,
<1321, 1>, <1801, 1>, <4051, 1>, <8101, 1>, <61681, 1>, <63901, 1>, <100801, 1>,
<268501, 1>, <340801, 1>, <2787601, 1>, <10567201, 1>, <13334701, 1>, 
<1182468601, 1>, <3173389601, 1>, <4562284561, 1>, <1133836730401, 1>, 
<1461503031127477825099979369543473122548042956801, 1> ]

Total time: 0.909 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:20:10 2004

Input: c:=2^900;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:20:09 on modular  [Seed = 1394336948]
   -------------------------------------

[ <3, 3>, <5, 3>, <7, 1>, <11, 1>, <13, 1>, <19, 1>, <31, 1>, <37, 1>, <41, 1>, 
<61, 1>, <73, 1>, <101, 1>, <109, 1>, <151, 1>, <181, 1>, <251, 1>, <331, 1>, 
<601, 1>, <631, 1>, <1201, 1>, <1321, 1>, <1801, 1>, <4051, 1>, <8101, 1>, 
<23311, 1>, <54001, 1>, <63901, 1>, <100801, 1>, <115201, 1>, <268501, 1>, 
<617401, 1>, <695701, 1>, <10567201, 1>, <13334701, 1>, <18837001, 1>, 
<29247661, 1>, <1182468601, 1>, <1348206751, 1>, <4714696801, 1>, 
<1133836730401, 1>, <307116398490301, 1>, <413150254353901, 1>, 
<6269989892198401, 1>, <13861369826299351, 1>, <3192261504216112476901, 1>, 
<281941472953710177758647201, 1> ]

Total time: 0.720 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:20:44 2004

Input: c:=2^1024;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:20:23 on modular  [Seed = 1797512338]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:21:18 2004

Input: c:=2^1004;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:20:58 on modular  [Seed = 1663816951]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:21:41 2004

Input: c:=2^950;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:21:40 on modular  [Seed = 1882768954]
   -------------------------------------

[ <3, 1>, <11, 1>, <31, 1>, <191, 1>, <251, 1>, <601, 1>, <1801, 1>, <2281, 1>, 
<4051, 1>, <4751, 1>, <174763, 1>, <524287, 1>, <18020551, 1>, <420778751, 1>, 
<30327152671, 1>, <3011347479614249131, 1>, <1369738735713888876695951, 1>, 
<113709467433878120743807151, 1>, <3145393391123750039342489201, 1>, 
<23352531315412606928823082635851, 1>, <170617159758027087771086981194610206694\
353113401, 1>, <32972619777851117988625390165531124382269394491251, 1> ]

Total time: 1.250 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:22:00 2004

Input: c:=2^990;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:21:57 on modular  [Seed = 138460755]
   -------------------------------------

[ <3, 3>, <7, 1>, <11, 2>, <19, 1>, <23, 1>, <31, 1>, <67, 1>, <73, 1>, <89, 1>,
<151, 1>, <199, 1>, <331, 1>, <631, 1>, <683, 1>, <881, 1>, <991, 1>, <2971, 1>,
<3191, 1>, <5347, 1>, <20857, 1>, <23311, 1>, <153649, 1>, <201961, 1>, <599479,
1>, <18837001, 1>, <48912491, 1>, <415365721, 1>, <33057806959, 1>, 
<242099935645987, 1>, <2252127523412251, 1>, <2048568835297380486760231, 1>, 
<334202934764737951438594746151, 1>, <6084777159537635796550536863741698483921, 
1>, <1573646189656401207486767880720222624035301340663285632613380740307779641, 
1> ]

Total time: 2.500 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:22:20 2004

Input: c:=2^999;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:22:15 on modular  [Seed = 4765289]
   -------------------------------------

[ <7, 1>, <73, 1>, <223, 1>, <1999, 1>, <7993, 1>, <10657, 1>, <169831, 1>, 
<262657, 1>, <321679, 1>, <1238761, 1>, <26295457, 1>, <36085879, 1>, 
<199381087, 1>, <319020217, 1>, <473589937, 1>, <616318177, 1>, <698962539799, 
1>, <4096460559560875111, 1>, <610750585993378533918571366551132613003293697, 
1>, <50421058836714133724261887847592742328031614097175170107712789048567396887\
7718991187197029450161772747335442226187851047716605340725373913, 1> ]

Total time: 4.280 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:22:40 2004

Input: c:=2^1000;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:22:39 on modular  [Seed = 407940713]
   -------------------------------------

[ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401, 
1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>,
<61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>, 
<2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>, 
<269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>, 
<47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251, 
1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\
10181938001, 1> ]

Total time: 0.939 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:23:23 2004

Input: c:=2^1002;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:23:03 on modular  [Seed = 778475575]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:23:55 2004

Input: c:=2^1001;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:23:35 on modular  [Seed = 644780063]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:25:06 2004

Input: c:=2^11;
c:=c-1;
Factorization(179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137215
);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:24:45 on modular  [Seed = 1047955661]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:25:47 2004

Input: c:=2^11;
c:=c-1;
Factorization(17976931348623159077293051907890247336179769789423065727343008115773267580550096313270847732240753602112011387987139335765878976881441662249284743063947412437776789342486548527630221960124609411945308295208500576883815068234246288147391311054082723716335051068458629823994724593847971630483535632962);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:25:26 on modular  [Seed = 931103135]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:26:22 2004

Input: c:=2^11;
c:=c-1;
Factorization(1797693134862315907729305190789024733617976978942306572734300811577326758055009631327084773224075360211201138798713933576587897688144166224928474306394741243777678934248654852763022196012460941194530829520850057688381506823424628814739131105408272371633505106845862982399472459384797163048);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:26:01 on modular  [Seed = 3481761419]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:26:55 2004

Input: c:=2^11;
c:=c-1;
Factorization(17976931348623159077293051907890247336179769789423065727343008115773267580550096313270847732240753602112011387987139335765878976881441662249284743063947412437776789342486548527630221960124609411945308295208500576883815068234246288147391311054082723716);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:26:35 on modular  [Seed = 3348070050]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:27:33 2004

Input: c:=2^11;
c:=c-1;
Factorization(179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:27:12 on modular  [Seed = 3751241409]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:28:08 2004

Input: c:=2^11;
c:=c-1;
Factorization(17976931348623159077293051907890247336179769789423065727343008115773267580550096313270847732240753602112011387987139335765878);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:27:47 on modular  [Seed = 3617550058]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:28:33 2004

Input: c:=2^11;
c:=c-1;
Factorization(1797693134862315907729305190789024733617976978942306572734300811577326758055009);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:28:32 on modular  [Seed = 3970192642]
   -------------------------------------

[ <7, 3>, <127, 1>, <6096329, 1>, <67693866785730864899874430465741330866404382\
06075992413321483635761, 1> ]

Total time: 1.089 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:29:08 2004

Input: c:=2^11;
c:=c-1;
Factorization(17976931348623159077293051907890247336179769789423065727343008115773267580550093454534543534543534657567657567);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:28:48 on modular  [Seed = 3853343771]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:29:39 2004

Input: c:=2^11;
c:=c-1;
Factorization(17976931348623159077293051907890247336179769789423065727343008115773267580550093454534543534543);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:29:18 on modular  [Seed = 4256515197]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:30:07 2004

Input: c:=2^11;
c:=c-1;
Factorization(1797693134862315907729305190789024733617976978942306572734300811577326758055009345453);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:29:47 on modular  [Seed = 4122823760]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:30:19 2004

Input: c:=2^11;
c:=c-1;
Factorization(17976931348623159077293051907890247336179769789423065727343008115773267580550093);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:30:18 on modular  [Seed = 2327982798]
   -------------------------------------

[ <1013, 1>, <17746230354020887539282380955469148406890197225491673965787767142\
915367799161, 1> ]

Total time: 1.429 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:30:49 2004

Input: c:=2^11;
c:=c-1;
Factorization(65727343008115773267580550093);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:30:48 on modular  [Seed = 2194291428]
   -------------------------------------

[ <61, 1>, <227, 1>, <241, 1>, <4177, 1>, <4507, 1>, <1046215881730081, 1> ]

Total time: 0.590 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:31:17 2004

Input: c:=2^521;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:31:16 on modular  [Seed = 2597462672]
   -------------------------------------

[ <6864797660130609714981900799081393217269435300143305409394463459185543183397\
6560521225596406614545549772963113914808580371219879997166438125740282911150571\
51, 1> ]
6864797660130609714981900799081393217269435300143305409394463459185543183397656\
052122559640661454554977296311391480858037121987999716643812574028291115057151

Total time: 1.710 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:31:50 2004

Input: c:=2^1001;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:31:29 on modular  [Seed = 2463771277]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:31:59 2004

Input: c:=2^1000;
c:=c-1;
Factorization(c);
if IsPrime(c) then
   c;
end if;


Output: Magma V2.11-2     Fri Jul 30 2004 03:31:57 on modular  [Seed = 2866942601]
   -------------------------------------

[ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401, 
1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>,
<61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>, 
<2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>, 
<269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>, 
<47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251, 
1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\
10181938001, 1> ]

Total time: 1.939 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:32:25 2004

Input: c:=2^1000;
c:=c-1;
c;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:32:24 on modular  [Seed = 2733251172]
   -------------------------------------

1071508607186267320948425049060001810561404811705533607443750388370351051124936\
1224931983788156958581275946729175531468251871452856923140435984577574698574803\
9345677748242309854210746050623711418779541821530464749835819412673987675591655\
43946077062914571196477686542167660429831652624386837205668069375
[ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401, 
1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>,
<61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>, 
<2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>, 
<269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>, 
<47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251, 
1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\
10181938001, 1> ]

Total time: 0.909 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:33:16 2004

Input: c:=2^1000;
c:=c-1;
c:=10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069375;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:33:13 on modular  [Seed = 3136422477]
   -------------------------------------

[ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401, 
1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>,
<61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>, 
<2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>, 
<269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>, 
<47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251, 
1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\
10181938001, 1> ]

Total time: 2.180 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:34:06 2004

Input: c:=2^1000;
c:=c-1;
c:=1071508607186267320948425049060001810561404811705533607443750388370351051124936122493198378815695858127594672917553146825187145285692314043598457757469857480393456777482423098542107460506237114187795418215304647498358194126739876755916554394607706291457119647768654216766042983165262438683720566806937556;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:33:45 on modular  [Seed = 3002731045]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:34:36 2004

Input: c:=2^1000;
c:=c-1;
c:=107150860718626732094842504906000181056140481170553360744375038837035105112493612249319837881569585812759467291755314682518714528569231404359845775746985748039345677748242309854210746050623711418779541821530464749835819412673987675591655439460770629145711964776865421676604298316526243868372056680693755;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:34:15 on modular  [Seed = 1428024819]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:35:10 2004

Input: c:=2^1000;
c:=c-1;
c:=10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069377;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:34:49 on modular  [Seed = 1561716245]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:35:21 2004

Input: c:=2^1000;
c:=c-1;
c:=10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069375;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:35:20 on modular  [Seed = 1141702445]
   -------------------------------------

[ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401, 
1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>,
<61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>, 
<2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>, 
<269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>, 
<47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251, 
1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\
10181938001, 1> ]

Total time: 1.449 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:35:53 2004

Input: c:=2^1000;
c:=c-1;
c:=10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069373;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:35:33 on modular  [Seed = 1275393880]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:36:30 2004

Input: c:=2^1000;
c:=c-1;
c:=1071508607186267320948425049060001810561404811705533607443750388370351051124936122493198378815695858127594672917553146825187145285692314043598457757469857480393456777482423098542107460506237114187795418215304647498358194126739876755916554394607706291457119647768654216766042983165262438683720566806937;
Factorization(c);


Output: Magma V2.11-2     Fri Jul 30 2004 03:36:10 on modular  [Seed = 1950142287]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:37:52 2004

Input: for i:= 1 to 100000 do
    if IsPrime(i) then
       i;
    end if;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:37:52 on modular  [Seed = 424780440]
   -------------------------------------

2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
113
127
131
137
139
149
151
157
163
167
173
179
181
191
193
197
199
211
223
227
229
233
239
241
251
257
263
269
271
277
281
283
293
307
311
313
317
331
337
347
349
353
359
367
373
379
383
389
397
401
409
419
421
431
433
439
443
449
457
461
463
467
479
487
491
499
503
509
521
523
541
547
557
563
569
571
577
587
593
599
601
607
613
617
619
631
641
643
647
653
659
661
673
677
683
691
701
709
719
727
733
739
743
751
757
761
769
773
787
797
809
811
821
823
827
829
839
853
857
859
863
877
881
883
887
907
911
919
929
937
941
947
953
967
971
977
983
991
997
1009
1013
1019
1021
1031
1033
1039
1049
1051
1061
1063
1069
1087
1091
1093
1097
1103
1109
1117
1123
1129
1151
1153
1163
1171
1181
1187
1193
1201
1213
1217
1223
1229
1231
1237
1249
1259
1277
1279
1283
1289
1291
1297
1301
1303
1307
1319
1321
1327
1361
1367
1373
1381
1399
1409
1423
1427
1429
1433
1439
1447
1451
1453
1459
1471
1481
1483
1487
1489
1493
1499
1511
1523
1531
1543
1549
1553
1559
1567
1571
1579
1583
1597
1601
1607
1609
1613
1619
1621
1627
1637
1657
1663
1667
1669
1693
1697
1699
1709
1721
1723
1733
1741
1747
1753
1759
1777
1783
1787
1789
1801
1811
1823
1831
1847
1861
1867
1871
1873
1877
1879
1889
1901
1907
1913
1931
1933
1949
1951
1973
1979
1987
1993
1997
1999
2003
2011
2017
2027
2029
2039
2053
2063
2069
2081
2083
2087
2089
2099
2111
2113
2129
2131
2137
2141
2143
2153
2161
2179
2203
2207
2213
2221
2237
2239
2243
2251
2267
2269
2273
2281
2287
2293
2297
2309
2311
2333
2339
2341
2347
2351
2357
2371
2377
2381
2383
2389
2393
2399
2411
2417
2423
2437
2441
2447
2459
2467
2473
2477
2503
2521
2531
2539
2543
2549
2551
2557
2579
2591
2593
2609
2617
2621
2633
2647
2657
2659
2663
2671
2677
2683
2687
2689
2693
2699
2707
2711
2713
2719
2729
2731
2741
2749
2753
2767
2777
2789
2791
2797
2801
2803
2819
2833
2837
2843
2851
2857
2861
2879
2887
2897
2903
2909
2917
2927
2939
2953
2957
2963
2969
2971
2999
3001
3011
3019
3023
3037
3041
3049
3061
3067
3079
3083
3089
3109
3119
3121
3137
3163
3167
3169
3181
3187
3191
3203
3209
3217
3221
3229
3251
3253
3257
3259
3271
3299
3301
3307
3313
3319
3323
3329
3331
3343
3347
3359
3361
3371
3373
3389
3391
3407
3413
3433
3449
3457
3461
3463
3467
3469
3491
3499
3511
3517
3527
3529
3533
3539
3541
3547
3557
3559
3571
3581
3583
3593
3607
3613
3617
3623
3631
3637
3643
3659
3671
3673
3677
3691
3697
3701
3709
3719
3727
3733
3739
3761
3767
3769
3779
3793
3797
3803
3821
3823
3833
3847
3851
3853
3863
3877
3881
3889
3907
3911
3917
3919
3923
3929
3931
3943
3947
3967
3989
4001
4003
4007
4013
4019
4021
4027
4049
4051
4057
4073
4079
4091
4093
4099
4111
4127
4129
4133
4139
4153
4157
4159
4177
4201
4211
4217
4219
4229
4231
4241
4243
4253
4259
4261
4271
4273
4283
4289
4297
4327
4337
4339
4349
4357
4363
4373
4391
4397
4409
4421
4423
4441
4447
4451
4457
4463
4481
4483
4493
4507
4513
4517
4519
4523
4547
4549
4561
4567
4583
4591
4597
4603
4621
4637
4639
4643
4649
4651
4657
4663
4673
4679
4691
4703
4721
4723
4729
4733
4751
4759
4783
4787
4789
4793
4799
4801
4813
4817
4831
4861
4871
4877
4889
4903
4909
4919
4931
4933
4937
4943
4951
4957
4967
4969
4973
4987
4993
4999
5003
5009
5011
5021
5023
5039
5051
5059
5077
5081
5087
5099
5101
5107
5113
5119
5147
5153
5167
5171
5179
5189
5197
5209
5227
5231
5233
5237
5261
5273
5279
5281
5297
5303
5309
5323
5333
5347
5351
5381
5387
5393
5399
5407
5413
5417
5419
5431
5437
5441
5443
5449
5471
5477
5479
5483
5501
5503
5507
5519
5521
5527
5531
5557
5563
5569
5573
5581
5591
5623
5639
5641
5647
5651
5653
5657
5659
5669
5683
5689
5693
5701
5711
5717
5737
5741
5743
5749
5779
5783
5791
5801
5807
5813
5821
5827
5839
5843
5849
5851
5857
5861
5867
5869
5879
5881
5897
5903
5923
5927
5939
5953
5981
5987
6007
6011
6029
6037
6043
6047
6053
6067
6073
6079
6089
6091
6101
6113
6121
6131
6133
6143
6151
6163
6173
6197
6199
6203
6211
6217
6221
6229
6247
6257
6263
6269
6271
6277
6287
6299
6301
6311
6317
6323
6329
6337
6343
6353
6359
6361
6367
6373
6379
6389
6397
6421
6427
6449
6451
6469
6473
6481
6491
6521
6529
6547
6551
6553
6563
6569
6571
6577
6581
6599
6607
6619
6637
6653
6659
6661
6673
6679
6689
6691
6701
6703
6709
6719
6733
6737
6761
6763
6779
6781
6791
6793
6803
6823
6827
6829
6833
6841
6857
6863
6869
6871
6883
6899
6907
6911
6917
6947
6949
6959
6961
6967
6971
6977
6983
6991
6997
7001
7013
7019
7027
7039
7043
7057
7069
7079
7103
7109
7121
7127
7129
7151
7159
7177
7187
7193
7207
7211
7213
7219
7229
7237
7243
7247
7253
7283
7297
7307
7309
7321
7331
7333
7349
7351
7369
7393
7411
7417
7433
7451
7457
7459
7477
7481
7487
7489
7499
7507
7517
7523
7529
7537
7541
7547
7549
7559
7561
7573
7577
7583
7589
7591
7603
7607
7621
7639
7643
7649
7669
7673
7681
7687
7691
7699
7703
7717
7723
7727
7741
7753
7757
7759
7789
7793
7817
7823
7829
7841
7853
7867
7873
7877
7879
7883
7901
7907
7919
7927
7933
7937
7949
7951
7963
7993
8009
8011
8017
8039
8053
8059
8069
8081
8087
8089
8093
8101
8111
8117
8123
8147
8161
8167
8171
8179
8191
8209
8219
8221
8231
8233
8237
8243
8263
8269
8273
8287
8291
8293
8297
8311
8317
8329
8353
8363
8369
8377
8387
8389
8419
8423
8429
8431
8443
8447
8461
8467
8501
8513
8521
8527
8537
8539
8543
8563
8573
8581
8597
8599
8609
8623
8627
8629
8641
8647
8663
8669
8677
8681
8689
8693
8699
8707
8713
8719
8731
8737
8741
8747
8753
8761
8779
8783
8803
8807
8819
8821
8831
8837
8839
8849
8861
8863
8867
8887
8893
8923
8929
8933
8941
8951
8963
8969
8971
8999
9001
9007
9011
9013
9029
9041
9043
9049
9059
9067
9091
9103
9109
9127
9133
9137
9151
9157
9161
9173
9181
9187
9199
9203
9209
9221
9227
9239
9241
9257
9277
9281
9283
9293
9311
9319
9323
9337
9341
9343
9349
9371
9377
9391
9397
9403
9413
9419
9421
9431
9433
9437
9439
9461
9463
9467
9473
9479
9491
9497
9511
9521
9533
9539
9547
9551
9587
9601
9613
9619
9623
9629
9631
9643
9649
9661
9677
9679
9689
9697
9719
9721
9733
9739
9743
9749
9767
9769
9781
9787
9791
9803
9811
9817
9829
9833
9839
9851
9857
9859
9871
9883
9887
9901
9907
9923
9929
9931
9941
9949
9967
9973
10007
10009
10037
10039
10061
10067
10069
10079
10091
10093
10099
10103
10111
10133
10139
10141
10151
10159
10163
10169
10177
10181
10193
10211
10223
10243
10247
10253
10259
10267
10271
10273
10289
10301
10303
10313
10321
10331
10333
10337
10343
10357
10369
10391
10399
10427
10429
10433
10453
10457
10459
10463
10477
10487
10499
10501
10513
10529
10531
10559
10567
10589
10597
10601
10607
10613
10627
10631
10639
10651
10657
10663
10667
10687
10691
10709
10711
10723
10729
10733
10739
10753
10771
10781
10789
10799
10831
10837
10847
10853
10859
10861
10867
10883
10889
10891
10903
10909
10937
10939
10949
10957
10973
10979
10987
10993
11003
11027
11047
11057
11059
11069
11071
11083
11087
11093
11113
11117
11119
11131
11149
11159
11161
11171
11173
11177
11197
11213
11239
11243
11251
11257
11261
11273
11279
11287
11299
11311
11317
11321
11329
11351
11353
11369
11383
11393
11399
11411
11423
11437
11443
11447
11467
11471
11483
11489
11491
11497
11503
11519
11527
11549
11551
11579
11587
11593
11597
11617
11621
11633
11657
11677
11681
11689
11699
11701
11717
11719
11731
11743
11777
11779
11783
11789
11801
11807
11813
11821
11827
11831
11833
11839
11863
11867
11887
11897
11903
11909
11923
11927
11933
11939
11941
11953
11959
11969
11971
11981
11987
12007
12011
12037
12041
12043
12049
12071
12073
12097
12101
12107
12109
12113
12119
12143
12149
12157
12161
12163
12197
12203
12211
12227
12239
12241
12251
12253
12263
12269
12277
12281
12289
12301
12323
12329
12343
12347
12373
12377
12379
12391
12401
12409
12413
12421
12433
12437
12451
12457
12473
12479
12487
12491
12497
12503
12511
12517
12527
12539
12541
12547
12553
12569
12577
12583
12589
12601
12611
12613
12619
12637
12641
12647
12653
12659
12671
12689
12697
12703
12713
12721
12739
12743
12757
12763
12781
12791
12799
12809
12821
12823
12829
12841
12853
12889
12893
12899
12907
12911
12917
12919
12923
12941
12953
12959
12967
12973
12979
12983
13001
13003
13007
13009
13033
13037
13043
13049
13063
13093
13099
13103
13109
13121
13127
13147
13151
13159
13163
13171
13177
13183
13187
13217
13219
13229
13241
13249
13259
13267
13291
13297
13309
13313
13327
13331
13337
13339
13367
13381
13397
13399
13411
13417
13421
13441
13451
13457
13463
13469
13477
13487
13499
13513
13523
13537
13553
13567
13577
13591
13597
13613
13619
13627
13633
13649
13669
13679
13681
13687
13691
13693
13697
13709
13711
13721
13723
13729
13751
13757
13759
13763
13781
13789
13799
13807
13829
13831
13841
13859
13873
13877
13879
13883
13901
13903
13907
13913
13921
13931
13933
13963
13967
13997
13999
14009
14011
14029
14033
14051
14057
14071
14081
14083
14087
14107
14143
14149
14153
14159
14173
14177
14197
14207
14221
14243
14249
14251
14281
14293
14303
14321
14323
14327
14341
14347
14369
14387
14389
14401
14407
14411
14419
14423
14431
14437
14447
14449
14461
14479
14489
14503
14519
14533
14537
14543
14549
14551
14557
14561
14563
14591
14593
14621
14627
14629
14633
14639
14653
14657
14669
14683
14699
14713
14717
14723
14731
14737
14741
14747
14753
14759
14767
14771
14779
14783
14797
14813
14821
14827
14831
14843
14851
14867
14869
14879
14887
14891
14897
14923
14929
14939
14947
14951
14957
14969
14983
15013
15017
15031
15053
15061
15073
15077
15083
15091
15101
15107
15121
15131
15137
15139
15149
15161
15173
15187
15193
15199
15217
15227
15233
15241
15259
15263
15269
15271
15277
15287
15289
15299
15307
15313
15319
15329
15331
15349
15359
15361
15373
15377
15383
15391
15401
15413
15427
15439
15443
15451
15461
15467
15473
15493
15497
15511
15527
15541
15551
15559
15569
15581
15583
15601
15607
15619
15629
15641
15643
15647
15649
15661
15667
15671
15679
15683
15727
15731
15733
15737
15739
15749
15761
15767
15773
15787
15791
15797
15803
15809
15817
15823
15859
15877
15881
15887
15889
15901
15907
15913
15919
15923
15937
15959
15971
15973
15991
16001
16007
16033
16057
16061
16063
16067
16069
16073
16087
16091
16097
16103
16111
16127
16139
16141
16183
16187
16189
16193
16217
16223

 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:38:38 2004

Input: for i:= 16223 to 100000 do
    if IsPrime(i) then
       i;
    end if;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:38:37 on modular  [Seed = 38451630]
   -------------------------------------

16223
16229
16231
16249
16253
16267
16273
16301
16319
16333
16339
16349
16361
16363
16369
16381
16411
16417
16421
16427
16433
16447
16451
16453
16477
16481
16487
16493
16519
16529
16547
16553
16561
16567
16573
16603
16607
16619
16631
16633
16649
16651
16657
16661
16673
16691
16693
16699
16703
16729
16741
16747
16759
16763
16787
16811
16823
16829
16831
16843
16871
16879
16883
16889
16901
16903
16921
16927
16931
16937
16943
16963
16979
16981
16987
16993
17011
17021
17027
17029
17033
17041
17047
17053
17077
17093
17099
17107
17117
17123
17137
17159
17167
17183
17189
17191
17203
17207
17209
17231
17239
17257
17291
17293
17299
17317
17321
17327
17333
17341
17351
17359
17377
17383
17387
17389
17393
17401
17417
17419
17431
17443
17449
17467
17471
17477
17483
17489
17491
17497
17509
17519
17539
17551
17569
17573
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30757
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30841
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30869
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31013
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31079
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31121
31123
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31193
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31469
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31511
31513
31517
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31547
31567
31573
31583
31601
31607
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31643
31649
31657
31663
31667
31687
31699
31721
31723
31727
31729
31741
31751
31769
31771
31793
31799
31817
31847
31849
31859
31873
31883
31891
31907
31957
31963
31973
31981
31991
32003
32009
32027
32029
32051
32057
32059
32063
32069
32077
32083
32089
32099
32117
32119
32141
32143
32159
32173
32183
32189
32191
32203
32213
32233
32237
32251
32257
32261
32297
32299
32303
32309
32321
32323
32327
32341
32353
32359
32363
32369
32371
32377
32381
32401
32411
32413
32423
32429
32441
32443
32467
32479
32491
32497
32503
32507
32531
32533
32537
32561
32563
32569
32573
32579
32587
32603
32609
32611
32621
32633
32647
32653
32687
32693
32707
32713
32717
32719
32749
32771
32779
32783
32789
32797
32801
32803
32831
32833
32839
32843
32869
32887
32909
32911
32917
32933
32939
32941
329
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:39:26 2004

Input: for i:= 16223 to 100000 step 2 do
    if IsPrime(i) then
       i;
    end if;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:39:25 on modular  [Seed = 172142710]
   -------------------------------------


>> for i:= 16223 to 100000 step 2 do
                           ^
User error: bad syntax

>>     if IsPrime(i) then
                  ^
User error: Identifier 'i' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
[ <2, 3> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:39:52 2004

Input: for i:= 16223 to 100000 i:=i+2 do
    if IsPrime(i) then
       i;
    end if;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:39:52 on modular  [Seed = 846891051]
   -------------------------------------


>> for i:= 16223 to 100000 i:=i+2 do
                           ^
User error: bad syntax

>>     if IsPrime(i) then
                  ^
User error: Identifier 'i' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
[ <2, 3> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:40:26 2004

Input: for i:= 16223 to 100000 do
    if IsPrime(i) then
       i;
    end if;
    i:=i+1
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:40:25 on modular  [Seed = 3516492777]
   -------------------------------------


>> end for;
   ^
User error: bad syntax
[ <2, 3> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:40:40 2004

Input: for i:= 16223 to 100000 do
    if IsPrime(i) then
       i;
    end if;
    i:=i+1;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:40:39 on modular  [Seed = 3650184191]
   -------------------------------------


>>     i:=i+1;
       ^
User error: Bad use of identifier 'i'
[ <2, 3> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:41:56 2004

Input: for i:= 1655758658657657657656756223879786878787 to 1076567576576567576576567834434345334656457757587   do
    if IsPrime(i) then
       i;
    end if;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:41:35 on modular  [Seed = 3247012671]
   -------------------------------------

1655758658657657657656756223879786878963
1655758658657657657656756223879786879053
1655758658657657657656756223879786879059
1655758658657657657656756223879786879143
1655758658657657657656756223879786879179
1655758658657657657656756223879786879191
1655758658657657657656756223879786879209
1655758658657657657656756223879786879299
1655758658657657657656756223879786879321
1655758658657657657656756223879786879389
1655758658657657657656756223879786879459
1655758658657657657656756223879786879561
1655758658657657657656756223879786879597
1655758658657657657656756223879786879893
1655758658657657657656756223879786879927
1655758658657657657656756223879786879989
1655758658657657657656756223879786880109
1655758658657657657656756223879786880119
1655758658657657657656756223879786880793
1655758658657657657656756223879786880839
1655758658657657657656756223879786880847
1655758658657657657656756223879786880983
1655758658657657657656756223879786880989
1655758658657657657656756223879786881001
1655758658657657657656756223879786881049
1655758658657657657656756223879786881061
1655758658657657657656756223879786881111
1655758658657657657656756223879786881469
1655758658657657657656756223879786881487
1655758658657657657656756223879786881493
1655758658657657657656756223879786881661
1655758658657657657656756223879786881687
1655758658657657657656756223879786881867
1655758658657657657656756223879786881949
1655758658657657657656756223879786881951
1655758658657657657656756223879786882011
1655758658657657657656756223879786882023
1655758658657657657656756223879786882039
1655758658657657657656756223879786882173
1655758658657657657656756223879786882189
1655758658657657657656756223879786882221
1655758658657657657656756223879786882281
1655758658657657657656756223879786882329
1655758658657657657656756223879786882629
1655758658657657657656756223879786882663
1655758658657657657656756223879786882693
1655758658657657657656756223879786882777
1655758658657657657656756223879786882861
1655758658657657657656756223879786882917
1655758658657657657656756223879786882993
1655758658657657657656756223879786883017
1655758658657657657656756223879786883349
1655758658657657657656756223879786883503
1655758658657657657656756223879786883511
1655758658657657657656756223879786883607
1655758658657657657656756223879786883731
1655758658657657657656756223879786883799
1655758658657657657656756223879786883983
1655758658657657657656756223879786884027
1655758658657657657656756223879786884193
1655758658657657657656756223879786884279
1655758658657657657656756223879786884399
1655758658657657657656756223879786884423
1655758658657657657656756223879786884591
1655758658657657657656756223879786884657
1655758658657657657656756223879786884717
1655758658657657657656756223879786884919
1655758658657657657656756223879786884937
1655758658657657657656756223879786884987
1655758658657657657656756223879786884991
1655758658657657657656756223879786885063
1655758658657657657656756223879786885101
1655758658657657657656756223879786885137
1655758658657657657656756223879786885143
1655758658657657657656756223879786885173
1655758658657657657656756223879786885333
1655758658657657657656756223879786885387
1655758658657657657656756223879786885519
1655758658657657657656756223879786885627
1655758658657657657656756223879786885807
1655758658657657657656756223879786885917
1655758658657657657656756223879786886097
1655758658657657657656756223879786886401
1655758658657657657656756223879786886451
1655758658657657657656756223879786886599
1655758658657657657656756223879786886797
1655758658657657657656756223879786886901
1655758658657657657656756223879786887153
1655758658657657657656756223879786887273
1655758658657657657656756223879786887367
1655758658657657657656756223879786887451
1655758658657657657656756223879786887513
1655758658657657657656756223879786887651
1655758658657657657656756223879786887741
1655758658657657657656756223879786887759
1655758658657657657656756223879786887763
1655758658657657657656756223879786887777
1655758658657657657656756223879786887793
1655758658657657657656756223879786888101
1655758658657657657656756223879786888123
1655758658657657657656756223879786888153
1655758658657657657656756223879786888329
1655758658657657657656756223879786888431
1655758658657657657656756223879786888491
1655758658657657657656756223879786888591
1655758658657657657656756223879786888743
1655758658657657657656756223879786888789
1655758658657657657656756223879786888923
1655758658657657657656756223879786888993
1655758658657657657656756223879786889007
1655758658657657657656756223879786889061
1655758658657657657656756223879786889179
1655758658657657657656756223879786889257
1655758658657657657656756223879786889271
1655758658657657657656756223879786889373
1655758658657657657656756223879786889433
1655758658657657657656756223879786889527
1655758658657657657656756223879786889569
1655758658657657657656756223879786889583
1655758658657657657656756223879786889719
1655758658657657657656756223879786889769
1655758658657657657656756223879786889853
1655758658657657657656756223879786889989
1655758658657657657656756223879786890097
1655758658657657657656756223879786890147
1655758658657657657656756223879786890283
1655758658657657657656756223879786890327
1655758658657657657656756223879786890429
1655758658657657657656756223879786890433
1655758658657657657656756223879786890537
1655758658657657657656756223879786890553
1655758658657657657656756223879786890673
1655758658657657657656756223879786890733
1655758658657657657656756223879786890777
1655758658657657657656756223879786890793
1655758658657657657656756223879786890819
1655758658657657657656756223879786890891
1655758658657657657656756223879786891063
1655758658657657657656756223879786891459
1655758658657657657656756223879786891521
1655758658657657657656756223879786891671
1655758658657657657656756223879786891897
1655758658657657657656756223879786891933
1655758658657657657656756223879786891981


************** MAGMA *****************
Host 3(NXDOMAIN) (213.165.116.4)
Time: Fri Jul 30 03:43:16 2004

Input: for i:= 16557586586576576576567562238797868787873453453454354353453453453453453453453453453454354354354354354353453454354354354354355645765756765765765765765756775675 to 1076567576576567576576567834434345334656457757587756756756989798327479237497289374897238947893278497839274897328947892374987329847983278947893274897328947893278947983274987239874892346676575213   do
    if IsPrime(i) then
       i;
    end if;
end for;
Factorization(8);


Output: Magma V2.11-2     Fri Jul 30 2004 03:42:56 on modular  [Seed = 3380704408]
   -------------------------------------



************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Jul 30 07:14:28 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=7 to 20 do
  print i, " ", FindGroupOrder2( 59649589127497217 , i);
end for;

Output: Magma V2.11-2     Fri Jul 30 2004 07:14:24 on modular  [Seed = 2716519780]
   -------------------------------------

7   [ <2, 2>, <3, 6>, <5, 1>, <1033, 1>, <3960496271, 1> ]
8   [ <2, 2>, <3, 1>, <7, 1>, <19, 1>, <3067, 1>, <12185989261, 1> ]
9   [ <2, 2>, <3, 1>, <45737, 1>, <108682227947, 1> ]
10   [ <2, 2>, <3, 1>, <7, 2>, <27061, 1>, <3748748389, 1> ]
11   [ <2, 4>, <3, 1>, <271, 1>, <4585608052517, 1> ]
12   [ <2, 2>, <3, 1>, <5, 1>, <227, 1>, <653, 1>, <42223, 1>, <158843, 1> ]
13   [ <2, 3>, <3, 1>, <7, 2>, <59, 1>, <78367, 1>, <10970209, 1> ]
14   [ <2, 2>, <3, 1>, <5, 1>, <7, 2>, <337, 1>, <60204676349, 1> ]
15   [ <2, 5>, <3, 1>, <5, 1>, <11, 1>, <22853, 1>, <494345191, 1> ]
16   [ <2, 2>, <3, 1>, <11, 1>, <59, 1>, <109, 1>, <10303, 1>, <6820109, 1> ]
17   [ <2, 2>, <3, 1>, <19, 1>, <852829, 1>, <306768419, 1> ]
18   [ <2, 5>, <3, 1>, <7, 1>, <67, 1>, <1324839850903, 1> ]
19   [ <2, 4>, <3, 1>, <53, 1>, <2371, 1>, <25303, 1>, <390829, 1> ]
20   [ <2, 2>, <3, 2>, <11, 1>, <2269, 1>, <66386194163, 1> ]

Total time: 3.599 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:11:39 2004

Input: ?ecm

Output: Magma V2.11-2     Fri Jul 30 2004 10:11:38 on modular  [Seed = 341770840]
   -------------------------------------

===============================================================================
PATH: /magma/ring-field-algebra/integer/factor/factorization-specific/ECM
KIND: Intrinsic
===============================================================================
ECM(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
ECM(n, B, r, c) : RngIntElt, RngIntElt, RngIntElt, RngIntElt -> RngIntEltFact, [
RngIntElt ], RngIntElt

        Proof: BoolElt                      Default: true

        Bases: RngIntElt                    Default: 20

    Given an integer n>1, an attempt to find its prime factorization is
    made using the Elliptic Curve Method ECM.  For at most c randomly
    chosen elliptic curves E modulo n a large multiple M, built up from
    the prime powers less than B, of a random point P on E is computed.
    If a prime divisor p of n has the property that the order of E
    modulo p divides M (i.e., is B-smooth), then this will be detected
    as a non-trivial greatest common divisor between n and a coordinate
    of the point M.P.  The initial smoothness bound B, and the maximum
    number of elliptic curves c may be specified by the user, as well as
    the growth rate r for the smoothness bound: with each new curve the
    smoothness is multiplied by r.  The rate r must be an integer,
    rational or real number greater than or equal to 1.  If only n is
    given as argument, default values B=500, r=1.2 and c=10 are used.
    When a factor is found, the function immediately returns.  The
    function returns three values: a factorization sequence, a sequence
    containing unfactored composite factors and the number of steps
    performed.
===============================================================================

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:12:22 2004

Input: ?ecmcurve

Output: Magma V2.11-2     Fri Jul 30 2004 10:12:21 on modular  [Seed = 475466255]
   -------------------------------------

No references for word "ecmcurve"

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:12:31 2004

Input: ?ellcurve

Output: Magma V2.11-2     Fri Jul 30 2004 10:12:31 on modular  [Seed = 72290845]
   -------------------------------------

No references for word "ellcurve"

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:12:40 2004

Input: ?elliptic

Output: Magma V2.11-2     Fri Jul 30 2004 10:12:39 on modular  [Seed = 205986317]
   -------------------------------------

33 matches:
     1   O   /magma/combinatorial-geometrical-incidence
     2   S   /magma/geometry/elliptic-curve
     3   S   /magma/geometry/modular-symbol/elliptic-curves
     4   S   /magma/group/GrpPSL2/structure-of-congruence-groups/\
             cusps-and-elliptic-points
     5   S   /magma/ring-field-algebra/real-complex/elliptic-modular
     6   I   /magma/geometry/algebraic-curve/global-curvepl/global-special/\
             EllipticCurve
     7   I   /magma/geometry/algebraic-curve/global-curvepl/global-special/\
             IsEllipticWeierstrass
     8   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             EllipticCurve
     9   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             EllipticCurve
    10   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             EllipticCurve
    11   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             EllipticCurve
    12   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             EllipticCurve
    13   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             EllipticCurveFromjInvariant
    14   I   /magma/geometry/elliptic-curve/creation/creation-curve/\
             SupersingularEllipticCurve
    15   I   /magma/geometry/elliptic-curve/creation/creation-predicates/\
             IsEllipticCurve
    16   I   /magma/geometry/elliptic-curve/creation/creation-predicates/\
             IsEllipticCurve
    17   I   /magma/geometry/elliptic-curve/database/CremonaDatabase
    18   I   /magma/geometry/elliptic-curve/database/EllipticCurve
    19   I   /magma/geometry/elliptic-curve/database/EllipticCurve
    20   I   /magma/geometry/elliptic-curve/database/EllipticCurves
    21   I   /magma/geometry/elliptic-curve/database/EllipticCurves
    22   I   /magma/geometry/elliptic-curve/database/EllipticCurves
    23   I   /magma/geometry/elliptic-curve/database/EllipticCurves
    24   I   /magma/geometry/elliptic-curve/rational_curves/four-descent/\
             EllipticCurve
    25   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-elliptic_logs/EllipticExponential
    26   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-elliptic_logs/EllipticLogarithm
    27   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-elliptic_logs/pAdicEllipticLogarithm
    28   I   /magma/geometry/hyperelliptic-curve/creation/quadratic-twists/\
             IsEllipticCurve
    29   I   /magma/geometry/modular-forms/abelian-varieties/EllipticCurve
    30   I   /magma/geometry/modular-forms/ellcrv/subsec_creation/EllipticCurve
    31   I   /magma/geometry/modular-forms/ellcrv/subsec_invariants/\
             EllipticInvariants
    32   I   /magma/geometry/modular-forms/ellcrv/subsec_invariants/\
             EllipticPeriods
    33   I   /magma/group/GrpPSL2/structure-of-congruence-groups/\
             cusps-and-elliptic-points/EllipticPoints
To view an entry, type ? followed by the number next to it

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:12:59 2004

Input: ?elliptic-curve

Output: Magma V2.11-2     Fri Jul 30 2004 10:12:58 on modular  [Seed = 880747016]
   -------------------------------------

===============================================================================
PATH: /magma/geometry/elliptic-curve
KIND: Section
===============================================================================
ELLIPTIC CURVES.

Subsections:

    [+1] introduction
    [+2] creation
    [+3] operations_curve
    [+4] subgroup_schemes
    [+5] pointset
    [+6] point
    [+7] function_field
    [+8] rational_curves
    [+9] integral_points
    [+10] database
    [+11] over_anf
    [+12] alff-curves
    [+13] ff_curves
    [+14] morphism
===============================================================================

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:13:31 2004

Input: ?elliptic-curve+1

Output: Magma V2.11-2     Fri Jul 30 2004 10:13:30 on modular  [Seed = 1014442720]
   -------------------------------------

No references for word "elliptic-curve+1"

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:14:03 2004

Input: ?grouporder

Output: Magma V2.11-2     Fri Jul 30 2004 10:14:02 on modular  [Seed = 611267288]
   -------------------------------------

No references for word "grouporder"

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:14:07 2004

Input: ?group

Output: Magma V2.11-2     Fri Jul 30 2004 10:14:07 on modular  [Seed = 744962773]
   -------------------------------------

662 matches:
     1   O   /magma/group
     2   O   /system/database
     3   O   /system/database/galpols
     4   S   /magma/combinatorial-geometrical-incidence/alg_sym/\
             operation-element/Symmetric-Group-Character
     5   S   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action
     6   S   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action/automorphism-group
     7   S   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action/group-actions
     8   S   /magma/combinatorial-geometrical-incidence/graph/\
             automorphism-group-graph
     9   S   /magma/combinatorial-geometrical-incidence/graph/group-code-design
    10   S   /magma/combinatorial-geometrical-incidence/graph/\
             group-code-design/group
    11   S   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-design/automorphism-group
    12   S   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group
    13   S   /magma/geometry/algebraic-curve/divisors/divisor-group
    14   S   /magma/geometry/algebraic-curve/linear-equivalence/class-group
    15   S   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-group
    16   S   /magma/geometry/hyperelliptic-curve/2-selmer-group
    17   S   /magma/group/abelian/group-Boolean
    18   S   /magma/group/databases-overview/ATLAS-database/atlas-group-access
    19   S   /magma/group/finitely-presented/fp-group-construction
    20   S   /magma/group/finitely-presented/fp-group-construction/\
             fp-group-constructor
    21   S   /magma/group/finitely-presented/fp-group-construction/\
             fp-group-constructor
    22   S   /magma/group/finitely-presented/fp-group-construction/\
             fp-group-conversion
    23   S   /magma/group/finitely-presented/fp-group-construction/\
             fp-group-conversion-coxeter-group
    24   S   /magma/group/finitely-presented/fp-group-construction/\
             fp-group-conversion-coxeter-group
    25   S   /magma/group/finitely-presented/fp-group-construction/\
             fp-group-quotient
    26   S   /magma/group/finitely-presented/group-identification
    27   S   /magma/group/fiurg/create-group-refl
    28   S   /magma/group/fiurg/create-group-refl-complex
    29   S   /magma/group/fiurg/create-group-refl-real
    30   S   /magma/group/group-overview
    31   S   /magma/group/group-overview/extension-standard-group
    32   S   /magma/group/group-overview/operation-subgroup/abstract-group
    33   S   /magma/group/GrpPSL2/group-action
    34   S   /magma/group/matrix/creation-general-linear-group
    35   S   /magma/group/matrix/creation-general-linear-group/\
             creation-general-matrix-group
    36   S   /magma/group/matrix/properties/abstract-group
    37   S   /magma/group/matrix/properties/group-order
    38   S   /magma/group/matrix/soluble-matrix-group
    39   S   /magma/group/matrix/soluble-matrix-group/abelian-group
    40   S   /magma/group/matrix/soluble-matrix-group/p-group
    41   S   /magma/group/p-groups/p-group
    42   S   /magma/group/p-groups/p-group
    43   S   /magma/group/p-groups/standard-presentation/automorphism-group
    44   S   /magma/group/permutation/linear-group
    45   S   /magma/group/permutation/operation/abstract-group-properties
    46   S   /magma/group/permutation/operation/group-order
    47   S   /magma/group/permutation/presentations/fp-group
    48   S   /magma/group/permutation/presentations/word-group
    49   S   /magma/group/polycyclic/group-boolean
    50   S   /magma/group/polycyclic/power-group
    51   S   /magma/group/polycyclic/subgroup-quotient-homomorphism-extension/\
             standard-group
    52   S   /magma/group/soluble/automorphism-group
    53   S   /magma/group/soluble/group-properties
    54   S   /magma/group/soluble/more-presentations/conditioned-presentation/\
             operation-group
    55   S   /magma/group/soluble/optimization/power-group
    56   S   /magma/lie-theory/coxeter-groups/group-braid
    57   S   /magma/lie-theory/coxeter-groups/group-elt-op
    58   S   /magma/lie-theory/coxeter-groups/group-op
    59   S   /magma/lie-theory/coxeter-groups/group-prop
    60   S   /magma/lie-theory/finite-coxeter-groups/group-elt-op
    61   S   /magma/lie-theory/finite-coxeter-groups/group-op
    62   S   /magma/lie-theory/finite-coxeter-groups/group-op
    63   S   /magma/module-lattice/quadratic/class-group
    64   S   /magma/ring-field-algebra/abelian-extension/creation/\
             ray-class-group
    65   S   /magma/ring-field-algebra/abelian-extension/group-theory
    66   S   /magma/ring-field-algebra/alg_quat/unit-group
    67   S   /magma/ring-field-algebra/algebraic-field/ideal-class-group
    68   S   /magma/ring-field-algebra/algebraic-field/unit-group
    69   S   /magma/ring-field-algebra/function-field/Divisors/\
             divisor-class-group
    70   S   /magma/ring-field-algebra/invariant-ring/group-action
    71   S   /magma/ring-field-algebra/quadratic/structure_ops/class-group
    72   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action/automorphism-group/\
             AutomorphismGroup
    73   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action/automorphism-group/\
             AutomorphismGroupStabilizer
    74   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action/automorphism-group/\
             AutomorphismGroupStabilizer
    75   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/group-action/automorphism-group/\
             PermutationGroup
    76   I   /magma/combinatorial-geometrical-incidence/graph/\
             automorphism-group-graph/creation/AutomorphismGroup
    77   I   /magma/combinatorial-geometrical-incidence/graph/\
             automorphism-group-graph/variant/EdgeGroup
    78   I   /magma/combinatorial-geometrical-incidence/incidence-geometry/\
             access/Group
    79   I   /magma/combinatorial-geometrical-incidence/incidence-geometry/\
             automorphisms/AutomorphismGroup
    80   I   /magma/combinatorial-geometrical-incidence/incidence-geometry/\
             automorphisms/CorrelationGroup
    81   I   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-design/automorphism-group/creation/\
             AutomorphismGroup
    82   I   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-design/automorphism-group/creation/\
             AutomorphismGroupStabilizer
    83   I   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-design/automorphism-group/creation/BlockGroup
    84   I   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-design/automorphism-group/creation/PointGroup
    85   I   /magma/combinatorial-geometrical-incidence/\
             incidence-structure-hadamard/hadamard-misc/\
             HadamardAutomorphismGroup
    86   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/central/CentralCollineationGroup
    87   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/central/CentralCollineationGroup
    88   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/central/CentralCollineationGroup
    89   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/creation/CollineationGroup
    90   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/creation/CollineationGroup
    91   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/creation/CollineationGroup
    92   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/creation/CollineationGroupStabilizer
    93   I   /magma/combinatorial-geometrical-incidence/plane/\
             collineation-group/creation/LineGroup
    94   I   /magma/geometry/algebraic-curve/divisors/divisor-creation/\
             DivisorGroup
    95   I   /magma/geometry/algebraic-curve/divisors/divisor-group/\
             DivisorGroup
    96   I   /magma/geometry/algebraic-curve/linear-equivalence/class-group/\
             ClassGroup
    97   I   /magma/geometry/algebraic-curve/linear-equivalence/class-group/\
             GlobalUnitGroup
    98   I   /magma/geometry/elliptic-curve/ff_curves/abelian_group/\
             AbelianGroup
    99   I   /magma/geometry/elliptic-curve/ff_curves/abelian_group/\
             AbelianGroup
   100   I   /magma/geometry/elliptic-curve/over_anf/over_anf-selmer/\
             over_anf-selmer-etale/pSelmerGroup
   101   I   /magma/geometry/elliptic-curve/over_anf/over_anf-selmer/\
             over_anf-selmer-selmer/PseudoMordellWeilGroup
   102   I   /magma/geometry/elliptic-curve/over_anf/over_anf-selmer/\
             over_anf-selmer-selmer/SelmerGroup
   103   I   /magma/geometry/elliptic-curve/over_anf/over_anf-selmer/\
             over_anf-selmer-selmer/TwoSelmerGroup
   104   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-group/AbelianGroup
   105   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-group/AbelianGroup
   106   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-group/AbelianGroup
   107   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-group/AbelianGroup
   108   I   /magma/geometry/hyperelliptic-curve/2-selmer-group/SelmerGroup
   109   I   /magma/geometry/hyperelliptic-curve/2
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host it023180.massey.ac.nz. (130.123.128.114)
Time: Fri Jul 30 10:14:26 2004

Input: ?groupo

Output: Magma V2.11-2     Fri Jul 30 2004 10:14:25 on modular  [Seed = 3550004548]
   -------------------------------------

No references for word "groupo"

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host alb-24-194-121-197.nycap.rr.com. (24.194.121.197)
Time: Fri Jul 30 10:47:53 2004

Input: x=4;


Output: Magma V2.11-2     Fri Jul 30 2004 10:47:52 on modular  [Seed = 1578451103]
   -------------------------------------


>> x=4;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:57:26 2004

Input: 5 mod 3

Output: Magma V2.11-2     Fri Jul 30 2004 12:57:26 on modular  [Seed = 980485780]
   -------------------------------------

2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:57:34 2004

Input: 10 mod 5

Output: Magma V2.11-2     Fri Jul 30 2004 12:57:34 on modular  [Seed = 846794388]
   -------------------------------------

0

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:58:05 2004

Input: 2 mod 13


Output: Magma V2.11-2     Fri Jul 30 2004 12:58:05 on modular  [Seed = 594025574]
   -------------------------------------

2

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:58:14 2004

Input: 2^100 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 12:58:14 on modular  [Seed = 3683706021]
   -------------------------------------

3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:58:24 2004

Input: 2^200 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 12:58:24 on modular  [Seed = 3567250364]
   -------------------------------------

9

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:58:32 2004

Input: 2^300 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 12:58:32 on modular  [Seed = 3431461804]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:58:37 2004

Input: 2^400 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 12:58:37 on modular  [Seed = 3297770401]
   -------------------------------------

3

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:58:43 2004

Input: 2^500 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 12:58:43 on modular  [Seed = 4239901671]
   -------------------------------------

9

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:59:36 2004

Input: 2^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 12:59:36 on modular  [Seed = 3987133133]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 12:59:51 2004

Input: 2^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 12:59:50 on modular  [Seed = 3853441595]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:00:05 2004

Input: 3^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:00:04 on modular  [Seed = 2177547853]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:00:53 2004

Input: 4^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:00:52 on modular  [Seed = 3119679013]
   -------------------------------------

45956

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:01:02 2004

Input: 3^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:01:01 on modular  [Seed = 2985987620]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:02:36 2004

Input: 2^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:02:36 on modular  [Seed = 2850199517]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:02:48 2004

Input: 3^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:02:47 on modular  [Seed = 2716508110]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:02:53 2004

Input: 5^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:02:52 on modular  [Seed = 1511089213]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:02:58 2004

Input: 6^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:02:58 on modular  [Seed = 1377397835]
   -------------------------------------

6532

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:03:05 2004

Input: 9^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:03:05 on modular  [Seed = 1241609304]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:03:10 2004

Input: 10^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:03:10 on modular  [Seed = 1107917911]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:03:16 2004

Input: 11^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:03:15 on modular  [Seed = 2050049141]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:03:21 2004

Input: 12^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:03:20 on modular  [Seed = 1916357745]
   -------------------------------------

45956

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:04:21 2004

Input: 2^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:04:21 on modular  [Seed = 1780569252]
   -------------------------------------

1

Total time: 0.569 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:04:31 2004

Input: 3^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:04:29 on modular  [Seed = 1646877860]
   -------------------------------------

1

Total time: 2.160 seconds, Total memory usage: 14.07MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:04:39 2004

Input: 4^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:04:35 on modular  [Seed = 441525474]
   -------------------------------------

1

Total time: 3.099 seconds, Total memory usage: 18.89MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:04:48 2004

Input: 5^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:04:45 on modular  [Seed = 307834084]
   -------------------------------------

18954689

Total time: 3.359 seconds, Total memory usage: 20.19MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:05:00 2004

Input: 6^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:04:56 on modular  [Seed = 155334634]
   -------------------------------------

1

Total time: 3.369 seconds, Total memory usage: 20.40MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:05:26 2004

Input: 9^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:05:21 on modular  [Seed = 963774387]
   -------------------------------------

1

Total time: 4.339 seconds, Total memory usage: 25.36MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:05:40 2004

Input: 10^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:05:35 on modular  [Seed = 897452977]
   -------------------------------------

18954689

Total time: 4.909 seconds, Total memory usage: 26.53MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:05:50 2004

Input: 11^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:05:45 on modular  [Seed = 761664415]
   -------------------------------------

1

Total time: 4.890 seconds, Total memory usage: 26.64MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:06:02 2004

Input: 12^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:05:57 on modular  [Seed = 627973003]
   -------------------------------------

1

Total time: 4.929 seconds, Total memory usage: 26.73MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:06:12 2004

Input: 13^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:06:06 on modular  [Seed = 3717653368]
   -------------------------------------

1

Total time: 5.230 seconds, Total memory usage: 27.88MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:06:22 2004

Input: 14^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:06:17 on modular  [Seed = 3583906951]
   -------------------------------------

177187

Total time: 5.230 seconds, Total memory usage: 27.96MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:06:35 2004

Input: 15^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:06:30 on modular  [Seed = 3448114304]
   -------------------------------------

18954689

Total time: 5.509 seconds, Total memory usage: 28.05MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:06:48 2004

Input: 16^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:06:42 on modular  [Seed = 3314418876]
   -------------------------------------

1

Total time: 5.839 seconds, Total memory usage: 31.46MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:06:59 2004

Input: 13^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:06:54 on modular  [Seed = 4256578696]
   -------------------------------------

1

Total time: 5.209 seconds, Total memory usage: 27.88MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:07:13 2004

Input: 17^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:07:07 on modular  [Seed = 4122883221]
   -------------------------------------

18954689

Total time: 5.669 seconds, Total memory usage: 31.52MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:07:25 2004

Input: 18^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:07:19 on modular  [Seed = 3970379248]
   -------------------------------------

1

Total time: 5.659 seconds, Total memory usage: 31.59MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:07:37 2004

Input: 19^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:07:31 on modular  [Seed = 3836683756]
   -------------------------------------

1

Total time: 5.660 seconds, Total memory usage: 31.66MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:07:52 2004

Input: 20^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:07:46 on modular  [Seed = 2631359909]
   -------------------------------------

18954689

Total time: 5.879 seconds, Total memory usage: 32.76MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:08:05 2004

Input: 21^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:07:59 on modular  [Seed = 2497664416]
   -------------------------------------

177187

Total time: 5.890 seconds, Total memory usage: 32.82MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:08:16 2004

Input: 22^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:08:10 on modular  [Seed = 2194228131]
   -------------------------------------

1

Total time: 5.909 seconds, Total memory usage: 32.87MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:08:30 2004

Input: 23^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:08:24 on modular  [Seed = 3119675498]
   -------------------------------------

177187

Total time: 5.910 seconds, Total memory usage: 32.93MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:08:43 2004

Input: 24^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:08:36 on modular  [Seed = 2985980031]
   -------------------------------------

1

Total time: 6.219 seconds, Total memory usage: 32.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:08:55 2004

Input: 25^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:08:49 on modular  [Seed = 2850187347]
   -------------------------------------

177187

Total time: 6.419 seconds, Total memory usage: 34.06MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:09:13 2004

Input: 24^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:09:06 on modular  [Seed = 2716491849]
   -------------------------------------

1

Total time: 6.230 seconds, Total memory usage: 32.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:09:28 2004

Input: 28^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:09:21 on modular  [Seed = 1477679552]
   -------------------------------------

177187

Total time: 6.450 seconds, Total memory usage: 34.19MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:09:39 2004

Input: 29^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:09:32 on modular  [Seed = 1343984070]
   -------------------------------------

177187

Total time: 6.430 seconds, Total memory usage: 34.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:09:53 2004

Input: 30^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:09:47 on modular  [Seed = 1208191433]
   -------------------------------------

18954689

Total time: 6.440 seconds, Total memory usage: 34.28MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:10:06 2004

Input: 29^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:10:00 on modular  [Seed = 1091207411]
   -------------------------------------

177187

Total time: 6.440 seconds, Total memory usage: 34.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:10:21 2004

Input: 28^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:10:14 on modular  [Seed = 2033367253]
   -------------------------------------

177187

Total time: 6.449 seconds, Total memory usage: 34.19MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:12:44 2004

Input: 2^157464 mod 472392

Output: Magma V2.11-2     Fri Jul 30 2004 13:12:43 on modular  [Seed = 1899671968]
   -------------------------------------

413344

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:12:51 2004

Input: 3^157464 mod 472392

Output: Magma V2.11-2     Fri Jul 30 2004 13:12:50 on modular  [Seed = 1763879329]
   -------------------------------------

59049

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:12:58 2004

Input: 4^157464 mod 472392

Output: Magma V2.11-2     Fri Jul 30 2004 13:12:57 on modular  [Seed = 1630183842]
   -------------------------------------

413344

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:22:23 2004

Input: 2^6 mod 19

Output: Magma V2.11-2     Fri Jul 30 2004 13:22:22 on modular  [Seed = 727771583]
   -------------------------------------

7

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:22:27 2004

Input: 3^6 mod 19

Output: Magma V2.11-2     Fri Jul 30 2004 13:22:26 on modular  [Seed = 594076074]
   -------------------------------------

7

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:23:00 2004

Input: 2^54 mod 163

Output: Magma V2.11-2     Fri Jul 30 2004 13:22:59 on modular  [Seed = 3683654002]
   -------------------------------------

104

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:23:05 2004

Input: 3^54 mod 163

Output: Magma V2.11-2     Fri Jul 30 2004 13:23:04 on modular  [Seed = 3516535667]
   -------------------------------------

58

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:23:31 2004

Input: 2^162 mod 487

Output: Magma V2.11-2     Fri Jul 30 2004 13:23:30 on modular  [Seed = 3380743297]
   -------------------------------------

232

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:23:37 2004

Input: 3^162 mod 487

Output: Magma V2.11-2     Fri Jul 30 2004 13:23:37 on modular  [Seed = 3247047810]
   -------------------------------------

232

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:24:13 2004

Input: 2^486 mod 1459

Output: Magma V2.11-2     Fri Jul 30 2004 13:24:13 on modular  [Seed = 4189207710]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:24:25 2004

Input: 11^486 mod 1459

Output: Magma V2.11-2     Fri Jul 30 2004 13:24:24 on modular  [Seed = 4055512291]
   -------------------------------------

339

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:24:29 2004

Input: 12^486 mod 1459

Output: Magma V2.11-2     Fri Jul 30 2004 13:24:28 on modular  [Seed = 3919719679]
   -------------------------------------

339

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:24:34 2004

Input: 13^486 mod 1459

Output: Magma V2.11-2     Fri Jul 30 2004 13:24:33 on modular  [Seed = 3786024170]
   -------------------------------------

339

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:12 2004

Input: 2^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:12 on modular  [Seed = 2664782780]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:19 2004

Input: 5^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:18 on modular  [Seed = 2531087282]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:26 2004

Input: 9^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:25 on modular  [Seed = 2395294545]
   -------------------------------------

17300

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:31 2004

Input: 10^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:30 on modular  [Seed = 2261599062]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:36 2004

Input: 11^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:36 on modular  [Seed = 3203758964]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:41 2004

Input: 12^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:40 on modular  [Seed = 3070063480]
   -------------------------------------

22066

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:45 2004

Input: 13^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:45 on modular  [Seed = 2934270829]
   -------------------------------------

17300

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:25:50 2004

Input: 14^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:25:50 on modular  [Seed = 2800575330]
   -------------------------------------

22066

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:26:03 2004

Input: 13^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:26:02 on modular  [Seed = 1477680559]
   -------------------------------------

17300

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:26:07 2004

Input: 12^13122 mod 39367

Output: Magma V2.11-2     Fri Jul 30 2004 13:26:06 on modular  [Seed = 1343985059]
   -------------------------------------

22066

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:26:28 2004

Input: 2^4 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 13:26:28 on modular  [Seed = 1208192465]
   -------------------------------------

3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:26:33 2004

Input: 3^4 mod 13

Output: Magma V2.11-2     Fri Jul 30 2004 13:26:33 on modular  [Seed = 1074496980]
   -------------------------------------

3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:26:57 2004

Input: 2^12 mod 37

Output: Magma V2.11-2     Fri Jul 30 2004 13:26:56 on modular  [Seed = 1899672780]
   -------------------------------------

26

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:27:00 2004

Input: 3^12 mod 37

Output: Magma V2.11-2     Fri Jul 30 2004 13:27:00 on modular  [Seed = 1747168721]
   -------------------------------------

10

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:28:07 2004

Input: 5^36 mod 109

Output: Magma V2.11-2     Fri Jul 30 2004 13:28:07 on modular  [Seed = 525654885]
   -------------------------------------

63

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:28:13 2004

Input: 6^36 mod 109

Output: Magma V2.11-2     Fri Jul 30 2004 13:28:12 on modular  [Seed = 391959398]
   -------------------------------------

63

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:28:17 2004

Input: 7^36 mod 109

Output: Magma V2.11-2     Fri Jul 30 2004 13:28:16 on modular  [Seed = 256166754]
   -------------------------------------

63

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:28:50 2004

Input: 5^972 mod 2917

Output: Magma V2.11-2     Fri Jul 30 2004 13:28:50 on modular  [Seed = 105759241]
   -------------------------------------

247

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:28:56 2004

Input: 6^972 mod 2917

Output: Magma V2.11-2     Fri Jul 30 2004 13:28:56 on modular  [Seed = 1047919163]
   -------------------------------------

247

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:29:01 2004

Input: 7^972 mod 2917

Output: Magma V2.11-2     Fri Jul 30 2004 13:29:00 on modular  [Seed = 914223671]
   -------------------------------------

2669

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:30:25 2004

Input: 28^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:30:19 on modular  [Seed = 694349279]
   -------------------------------------

177187

Total time: 6.449 seconds, Total memory usage: 34.19MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:30:36 2004

Input: 29^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:30:29 on modular  [Seed = 560653769]
   -------------------------------------

177187

Total time: 6.440 seconds, Total memory usage: 34.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:30:48 2004

Input: 30^6377292 mod 19131877

Output: Magma V2.11-2     Fri Jul 30 2004 13:30:42 on modular  [Seed = 3650231622]
   -------------------------------------

18954689

Total time: 6.440 seconds, Total memory usage: 34.28MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:36:02 2004

Input: 2^24 mod 73

Output: Magma V2.11-2     Fri Jul 30 2004 13:36:01 on modular  [Seed = 3481536915]
   -------------------------------------

64

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:36:08 2004

Input: 3^24 mod 73

Output: Magma V2.11-2     Fri Jul 30 2004 13:36:07 on modular  [Seed = 3347841437]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:36:16 2004

Input: 5^24 mod 73

Output: Magma V2.11-2     Fri Jul 30 2004 13:36:15 on modular  [Seed = 4290001325]
   -------------------------------------

8

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:36:21 2004

Input: 4^24 mod 73

Output: Magma V2.11-2     Fri Jul 30 2004 13:36:21 on modular  [Seed = 4156305855]
   -------------------------------------

8

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:36:26 2004

Input: 5^24 mod 73

Output: Magma V2.11-2     Fri Jul 30 2004 13:36:26 on modular  [Seed = 4020513192]
   -------------------------------------

8

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:36:31 2004

Input: 6^24 mod 73

Output: Magma V2.11-2     Fri Jul 30 2004 13:36:30 on modular  [Seed = 3886817700]
   -------------------------------------

64

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:37:09 2004

Input: 4^5832 mod 17497

Output: Magma V2.11-2     Fri Jul 30 2004 13:37:09 on modular  [Seed = 2681493895]
   -------------------------------------

12777

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:37:15 2004

Input: 5^5832 mod 17497

Output: Magma V2.11-2     Fri Jul 30 2004 13:37:15 on modular  [Seed = 2547798401]
   -------------------------------------

4719

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:37:20 2004

Input: 6^5832 mod 17497

Output: Magma V2.11-2     Fri Jul 30 2004 13:37:20 on modular  [Seed = 2412005762]
   -------------------------------------

4719

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:38:40 2004

Input: 10^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:38:40 on modular  [Seed = 2194228351]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:38:45 2004

Input: 11^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:38:44 on modular  [Seed = 3136388163]
   -------------------------------------

6532

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:38:49 2004

Input: 12^17496 mod 52489

Output: Magma V2.11-2     Fri Jul 30 2004 13:38:48 on modular  [Seed = 3002692679]
   -------------------------------------

45956

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:39:30 2004

Input: 2^157464 mod 472393

Output: Magma V2.11-2     Fri Jul 30 2004 13:39:30 on modular  [Seed = 2800574505]
   -------------------------------------

206113

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:39:34 2004

Input: 3^157464 mod 472393

Output: Magma V2.11-2     Fri Jul 30 2004 13:39:34 on modular  [Seed = 1477680850]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:39:58 2004

Input: 4^157464 mod 472393

Output: Magma V2.11-2     Fri Jul 30 2004 13:39:57 on modular  [Seed = 1377408227]
   -------------------------------------

266279

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:40:02 2004

Input: 5^157464 mod 472393

Output: Magma V2.11-2     Fri Jul 30 2004 13:40:02 on modular  [Seed = 1967043547]
   -------------------------------------

206113

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:40:07 2004

Input: 6^157464 mod 472393

Output: Magma V2.11-2     Fri Jul 30 2004 13:40:06 on modular  [Seed = 1831250887]
   -------------------------------------

206113

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:46:45 2004

Input: 2^144 mod 433

Output: Magma V2.11-2     Fri Jul 30 2004 13:46:44 on modular  [Seed = 138658000]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:46:50 2004

Input: 5^144 mod 433

Output: Magma V2.11-2     Fri Jul 30 2004 13:46:50 on modular  [Seed = 4966614]
   -------------------------------------

198

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:46:55 2004

Input: 6^144 mod 433

Output: Magma V2.11-2     Fri Jul 30 2004 13:46:54 on modular  [Seed = 947122410]
   -------------------------------------

198

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:47:02 2004

Input: 7^144 mod 433

Output: Magma V2.11-2     Fri Jul 30 2004 13:47:01 on modular  [Seed = 813431033]
   -------------------------------------

234

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:49:09 2004

Input: 2^432 mod 1297

Output: Magma V2.11-2     Fri Jul 30 2004 13:49:09 on modular  [Seed = 577366379]
   -------------------------------------

365

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:49:17 2004

Input: 3^432 mod 1297

Output: Magma V2.11-2     Fri Jul 30 2004 13:49:17 on modular  [Seed = 3567198101]
   -------------------------------------

931

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:49:22 2004

Input: 4^432 mod 1297

Output: Magma V2.11-2     Fri Jul 30 2004 13:49:21 on modular  [Seed = 3448112816]
   -------------------------------------

931

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:49:54 2004

Input: 2^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:49:53 on modular  [Seed = 3314421464]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:49:58 2004

Input: 3^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:49:58 on modular  [Seed = 4273288676]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:06 2004

Input: 6^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:05 on modular  [Seed = 4139597287]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:10 2004

Input: 9^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:09 on modular  [Seed = 4003800544]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:15 2004

Input: 10^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:14 on modular  [Seed = 2648069783]
   -------------------------------------

1998

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:18 2004

Input: 11^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:18 on modular  [Seed = 2514378387]
   -------------------------------------

1890

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:23 2004

Input: 12^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:22 on modular  [Seed = 2378581647]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:27 2004

Input: 13^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:27 on modular  [Seed = 2244890298]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:31 2004

Input: 14^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:31 on modular  [Seed = 3187046022]
   -------------------------------------

1890

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:36 2004

Input: 15^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:35 on modular  [Seed = 3053354626]
   -------------------------------------

1998

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:41 2004

Input: 16^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:41 on modular  [Seed = 2917557888]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:47 2004

Input: 17^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:47 on modular  [Seed = 2783866510]
   -------------------------------------

1998

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:52 2004

Input: 18^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:51 on modular  [Seed = 1578472826]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:50:56 2004

Input: 19^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:50:56 on modular  [Seed = 1444781449]
   -------------------------------------

1890

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:51:02 2004

Input: 20^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:51:01 on modular  [Seed = 1308984724]
   -------------------------------------

1998

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:51:07 2004

Input: 21^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:51:06 on modular  [Seed = 1175293331]
   -------------------------------------

1890

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:51:11 2004

Input: 20^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:51:10 on modular  [Seed = 2117449135]
   -------------------------------------

1998

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:51:16 2004

Input: 19^1296 mod 3889

Output: Magma V2.11-2     Fri Jul 30 2004 13:51:15 on modular  [Seed = 1983757754]
   -------------------------------------

1890

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:52:28 2004

Input: 2^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:52:27 on modular  [Seed = 1780589038]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 3.11MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:52:34 2004

Input: 3
^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:52:32 on modular  [Seed = 1646897628]
   -------------------------------------

2694502

Total time: 1.179 seconds, Total memory usage: 7.82MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:52:43 2004

Input: 3^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:52:42 on modular  [Seed = 441569711]
   -------------------------------------

2694502

Total time: 1.179 seconds, Total memory usage: 7.82MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:52:49 2004

Input: 5^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:52:47 on modular  [Seed = 307878306]
   -------------------------------------

5808554

Total time: 1.669 seconds, Total memory usage: 10.99MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:03 2004

Input: 6^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:01 on modular  [Seed = 155370155]
   -------------------------------------

2694502

Total time: 1.750 seconds, Total memory usage: 11.08MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:08 2004

Input: 7^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:06 on modular  [Seed = 1031206752]
   -------------------------------------

1

Total time: 1.750 seconds, Total memory usage: 11.16MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:17 2004

Input: 9^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:14 on modular  [Seed = 880803425]
   -------------------------------------

5808554

Total time: 2.090 seconds, Total memory usage: 13.40MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:24 2004

Input: 10^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:22 on modular  [Seed = 745006689]
   -------------------------------------

5808554

Total time: 2.159 seconds, Total memory usage: 13.45MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:30 2004

Input: 11^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:28 on modular  [Seed = 594078052]
   -------------------------------------

5808554

Total time: 2.139 seconds, Total memory usage: 13.50MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:39 2004

Input: 10^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:37 on modular  [Seed = 3683652005]
   -------------------------------------

5808554

Total time: 2.139 seconds, Total memory usage: 13.45MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:53:45 2004

Input: 9^2834352 mod 8503057

Output: Magma V2.11-2     Fri Jul 30 2004 13:53:43 on modular  [Seed = 3549960619]
   -------------------------------------

5808554

Total time: 2.070 seconds, Total memory usage: 13.40MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:54:46 2004

Input: 2^32 mod 97

Output: Magma V2.11-2     Fri Jul 30 2004 13:54:45 on modular  [Seed = 3414163953]
   -------------------------------------

35

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:54:51 2004

Input: 3^32 mod 97

Output: Magma V2.11-2     Fri Jul 30 2004 13:54:51 on modular  [Seed = 3280472567]
   -------------------------------------

35

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:55:18 2004

Input: 3^864 mod 2593

Output: Magma V2.11-2     Fri Jul 30 2004 13:55:17 on modular  [Seed = 4205916192]
   -------------------------------------

1137

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:55:30 2004

Input: 2^864 mod 2593

Output: Magma V2.11-2     Fri Jul 30 2004 13:55:30 on modular  [Seed = 4072224831]
   -------------------------------------

1137

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:56:33 2004

Input: 2^69984 mod 209953

Output: Magma V2.11-2     Fri Jul 30 2004 13:56:33 on modular  [Seed = 3936428132]
   -------------------------------------

197649

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:56:39 2004

Input: 3^69984 mod 209953

Output: Magma V2.11-2     Fri Jul 30 2004 13:56:38 on modular  [Seed = 3802736747]
   -------------------------------------

12303

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:30 2004

Input: 3^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:29 on modular  [Seed = 2597410764]
   -------------------------------------

591310

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:34 2004

Input: 2^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:33 on modular  [Seed = 2463719360]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:40 2004

Input: 5^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:39 on modular  [Seed = 2327922630]
   -------------------------------------

591310

Total time: 0.590 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:44 2004

Input: 6^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:43 on modular  [Seed = 2194231242]
   -------------------------------------

591310

Total time: 0.590 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:48 2004

Input: 7^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:47 on modular  [Seed = 3136387070]
   -------------------------------------

38546

Total time: 0.600 seconds, Total memory usage: 3.28MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:52 2004

Input: 7^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:51 on modular  [Seed = 3002695666]
   -------------------------------------

38546

Total time: 0.590 seconds, Total memory usage: 3.28MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:57:57 2004

Input: 6^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:57:56 on modular  [Seed = 2866898897]
   -------------------------------------

591310

Total time: 0.580 seconds, Total memory usage: 3.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:58:02 2004

Input: 5^209952 mod 629857

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:01 on modular  [Seed = 2733207508]
   -------------------------------------

591310

Total time: 0.590 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:58:36 2004

Input: 2^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:36 on modular  [Seed = 1477678410]
   -------------------------------------

84

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:58:40 2004

Input: 3^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:40 on modular  [Seed = 1343987038]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:58:47 2004

Input: 5^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:46 on modular  [Seed = 1208190272]
   -------------------------------------

84

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:58:52 2004

Input: 6^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:51 on modular  [Seed = 1074498885]
   -------------------------------------

84

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:58:56 2004

Input: 4^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:55 on modular  [Seed = 2016654713]
   -------------------------------------

108

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:59:00 2004

Input: 5^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:58:59 on modular  [Seed = 1882963277]
   -------------------------------------

84

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:59:04 2004

Input: 6^64 mod 193

Output: Magma V2.11-2     Fri Jul 30 2004 13:59:03 on modular  [Seed = 1747166545]
   -------------------------------------

84

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:59:40 2004

Input: 2^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 13:59:40 on modular  [Seed = 525652685]
   -------------------------------------

363

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:59:47 2004

Input: 3^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 13:59:46 on modular  [Seed = 341826008]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:59:52 2004

Input: 5^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 13:59:51 on modular  [Seed = 206029253]
   -------------------------------------

363

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 13:59:56 2004

Input: 6^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 13:59:55 on modular  [Seed = 72337857]
   -------------------------------------

363

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:00:02 2004

Input: 4^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 14:00:01 on modular  [Seed = 1031205058]
   -------------------------------------

213

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:00:02 2004

Input: 4^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 14:00:02 on modular  [Seed = 644738010]
   -------------------------------------

213

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:00:07 2004

Input: 5^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 14:00:06 on modular  [Seed = 3633517856]
   -------------------------------------

363

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:00:11 2004

Input: 6^192 mod 577

Output: Magma V2.11-2     Fri Jul 30 2004 14:00:10 on modular  [Seed = 3499826468]
   -------------------------------------

363

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:00:48 2004

Input: 2^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:00:48 on modular  [Seed = 3364029766]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:00:53 2004

Input: 3^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:00:53 on modular  [Seed = 3230338379]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:12 2004

Input: 10^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:11 on modular  [Seed = 4172494145]
   -------------------------------------

70308

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:16 2004

Input: 11^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:16 on modular  [Seed = 4038802754]
   -------------------------------------

69660

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:20 2004

Input: 12^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:19 on modular  [Seed = 3903006041]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:25 2004

Input: 13^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:24 on modular  [Seed = 3769314634]
   -------------------------------------

69660

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:31 2004

Input: 14^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:30 on modular  [Seed = 2563986748]
   -------------------------------------

70308

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:34 2004

Input: 15^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:34 on modular  [Seed = 2430295344]
   -------------------------------------

70308

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:39 2004

Input: 14^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:38 on modular  [Seed = 2294498516]
   -------------------------------------

70308

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:01:42 2004

Input: 13^46656 mod 139969

Output: Magma V2.11-2     Fri Jul 30 2004 14:01:42 on modular  [Seed = 2160807128]
   -------------------------------------

69660

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:02:42 2004

Input: 2^3779136 mod 11337409

Output: Magma V2.11-2     Fri Jul 30 2004 14:02:42 on modular  [Seed = 3102962852]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 3.23MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:02:48 2004

Input: 3^3779136 mod 11337409

Output: Magma V2.11-2     Fri Jul 30 2004 14:02:46 on modular  [Seed = 2969271465]
   -------------------------------------

1

Total time: 1.359 seconds, Total memory usage: 9.41MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:03:00 2004

Input: 13^3779136 mod 11337409

Output: Magma V2.11-2     Fri Jul 30 2004 14:02:57 on modular  [Seed = 2833474727]
   -------------------------------------

5665788

Total time: 3.039 seconds, Total memory usage: 17.54MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:03:07 2004

Input: 14^3779136 mod 11337409

Output: Magma V2.11-2     Fri Jul 30 2004 14:03:04 on modular  [Seed = 2699783334]
   -------------------------------------

5671620

Total time: 3.019 seconds, Total memory usage: 17.59MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:03:14 2004

Input: 15^3779136 mod 11337409

Output: Magma V2.11-2     Fri Jul 30 2004 14:03:11 on modular  [Seed = 1730980697]
   -------------------------------------

5665788

Total time: 3.360 seconds, Total memory usage: 18.68MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:03:40 2004

Input: 2^384 mod 1153

Output: Magma V2.11-2     Fri Jul 30 2004 14:03:39 on modular  [Seed = 1864672117]
   -------------------------------------

650

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:03:45 2004

Input: 3^384 mod 1153

Output: Magma V2.11-2     Fri Jul 30 2004 14:03:44 on modular  [Seed = 2000468886]
   -------------------------------------

650

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:08 2004

Input: 3^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:08 on modular  [Seed = 1074498745]
   -------------------------------------

722

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:13 2004

Input: 2^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:12 on modular  [Seed = 1258325942]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:33 2004

Input: 9^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:32 on modular  [Seed = 1394122626]
   -------------------------------------

2734

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:37 2004

Input: 10^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:37 on modular  [Seed = 1527814031]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:48 2004

Input: 11^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:47 on modular  [Seed = 594079741]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:53 2004

Input: 12^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:52 on modular  [Seed = 727771022]
   -------------------------------------

722

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:04:57 2004

Input: 13^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:04:56 on modular  [Seed = 846855835]
   -------------------------------------

2734

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:05:01 2004

Input: 14^1152 mod 3457

Output: Magma V2.11-2     Fri Jul 30 2004 14:05:01 on modular  [Seed = 980547222]
   -------------------------------------

722

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:05:48 2004

Input: 2^3456 mod 10369

Output: Magma V2.11-2     Fri Jul 30 2004 14:05:47 on modular  [Seed = 38391448]
   -------------------------------------

833

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:05:52 2004

Input: 3^3456 mod 10369

Output: Magma V2.11-2     Fri Jul 30 2004 14:05:51 on modular  [Seed = 172082836]
   -------------------------------------

9535

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:06:58 2004

Input: 3^279936 mod 839809

Output: Magma V2.11-2     Fri Jul 30 2004 14:06:57 on modular  [Seed = 307879217]
   -------------------------------------

635782

Total time: 0.600 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:07:04 2004

Input: 2^279936 mod 839809

Output: Magma V2.11-2     Fri Jul 30 2004 14:07:03 on modular  [Seed = 441570620]
   -------------------------------------

635782

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:07:11 2004

Input: 3^279936 mod 839809

Output: Magma V2.11-2     Fri Jul 30 2004 14:07:10 on modular  [Seed = 3802738125]
   -------------------------------------

635782

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:07:50 2004

Input: 3^256 mod 769

Output: Magma V2.11-2     Fri Jul 30 2004 14:07:50 on modular  [Seed = 3936429565]
   -------------------------------------

408

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:07:56 2004

Input: 2^256 mod 769

Output: Magma V2.11-2     Fri Jul 30 2004 14:07:56 on modular  [Seed = 4072226287]
   -------------------------------------

408

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:09:13 2004

Input: 2^1679616 mod 5038849

Output: Magma V2.11-2     Fri Jul 30 2004 14:09:12 on modular  [Seed = 4289998934]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:09:17 2004

Input: 3^1679616 mod 5038849

Output: Magma V2.11-2     Fri Jul 30 2004 14:09:16 on modular  [Seed = 3364030309]
   -------------------------------------

1

Total time: 0.899 seconds, Total memory usage: 5.84MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:09:36 2004

Input: 13^1679616 mod 5038849

Output: Magma V2.11-2     Fri Jul 30 2004 14:09:35 on modular  [Seed = 3499827054]
   -------------------------------------

2517480

Total time: 1.409 seconds, Total memory usage: 9.12MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:09:43 2004

Input: 14^1679616 mod 5038849

Output: Magma V2.11-2     Fri Jul 30 2004 14:09:41 on modular  [Seed = 3633518428]
   -------------------------------------

2517480

Total time: 1.679 seconds, Total memory usage: 10.29MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:09:49 2004

Input: 15^1679616 mod 5038849

Output: Magma V2.11-2     Fri Jul 30 2004 14:09:47 on modular  [Seed = 2699783978]
   -------------------------------------

2521368

Total time: 1.669 seconds, Total memory usage: 10.32MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:10:53 2004

Input: 2^248832 mod 746497

Output: Magma V2.11-2     Fri Jul 30 2004 14:10:53 on modular  [Seed = 2900845280]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:10:58 2004

Input: 3^248832 mod 746497

Output: Magma V2.11-2     Fri Jul 30 2004 14:10:57 on modular  [Seed = 3036642020]
   -------------------------------------

388818

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:11:06 2004

Input: 5^248832 mod 746497

Output: Magma V2.11-2     Fri Jul 30 2004 14:11:05 on modular  [Seed = 3170333412]
   -------------------------------------

357678

Total time: 0.600 seconds, Total memory usage: 3.31MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:11:12 2004

Input: 6^248832 mod 746497

Output: Magma V2.11-2     Fri Jul 30 2004 14:11:11 on modular  [Seed = 2228177626]
   -------------------------------------

388818

Total time: 0.600 seconds, Total memory usage: 3.42MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:11:17 2004

Input: 7^248832 mod 746497

Output: Magma V2.11-2     Fri Jul 30 2004 14:11:16 on modular  [Seed = 2361868969]
   -------------------------------------

357678

Total time: 0.610 seconds, Total memory usage: 3.42MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:11:47 2004

Input: 2^6144 mod 18432

Output: Magma V2.11-2     Fri Jul 30 2004 14:11:46 on modular  [Seed = 2497665687]
   -------------------------------------

4096

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:11:52 2004

Input: 3^6144 mod 18432

Output: Magma V2.11-2     Fri Jul 30 2004 14:11:51 on modular  [Seed = 2631357082]
   -------------------------------------

14337

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:12:35 2004

Input: 3^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:12:34 on modular  [Seed = 1697557399]
   -------------------------------------

246889

Total time: 0.620 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:12:40 2004

Input: 2^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:12:40 on modular  [Seed = 1831248789]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:12:48 2004

Input: 5^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:12:47 on modular  [Seed = 1967045514]
   -------------------------------------

1

Total time: 0.659 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:12:59 2004

Input: 15^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:12:58 on modular  [Seed = 2100736951]
   -------------------------------------

246889

Total time: 0.769 seconds, Total memory usage: 4.71MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:05 2004

Input: 14^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:04 on modular  [Seed = 1158581141]
   -------------------------------------

246889

Total time: 0.770 seconds, Total memory usage: 4.70MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:10 2004

Input: 13^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:09 on modular  [Seed = 1292272536]
   -------------------------------------

1

Total time: 0.760 seconds, Total memory usage: 4.70MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:21 2004

Input: 16^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:20 on modular  [Seed = 1428069365]
   -------------------------------------

1

Total time: 0.770 seconds, Total memory usage: 4.90MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:28 2004

Input: 19^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:27 on modular  [Seed = 1561760762]
   -------------------------------------

246889

Total time: 0.829 seconds, Total memory usage: 5.18MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:34 2004

Input: 18^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:33 on modular  [Seed = 628026248]
   -------------------------------------

1246103

Total time: 0.819 seconds, Total memory usage: 5.17MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:39 2004

Input: 17^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:38 on modular  [Seed = 761717663]
   -------------------------------------

1246103

Total time: 0.769 seconds, Total memory usage: 4.91MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:44 2004

Input: 18^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:43 on modular  [Seed = 897514370]
   -------------------------------------

1246103

Total time: 0.819 seconds, Total memory usage: 5.17MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:13:48 2004

Input: 19^497664 mod 1492993

Output: Magma V2.11-2     Fri Jul 30 2004 14:13:47 on modular  [Seed = 1031205766]
   -------------------------------------

246889

Total time: 0.819 seconds, Total memory usage: 5.18MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:14:28 2004

Input: 2^4096 mod 12289

Output: Magma V2.11-2     Fri Jul 30 2004 14:14:27 on modular  [Seed = 89052262]
   -------------------------------------

6240

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:14:32 2004

Input: 3^4096 mod 12289

Output: Magma V2.11-2     Fri Jul 30 2004 14:14:32 on modular  [Seed = 222747749]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:14:41 2004

Input: 5^4096 mod 12289

Output: Magma V2.11-2     Fri Jul 30 2004 14:14:40 on modular  [Seed = 391956071]
   -------------------------------------

6240

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:14:45 2004

Input: 6^4096 mod 12289

Output: Magma V2.11-2     Fri Jul 30 2004 14:14:44 on modular  [Seed = 3769315732]
   -------------------------------------

6240

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:14:49 2004

Input: 4^4096 mod 12289

Output: Magma V2.11-2     Fri Jul 30 2004 14:14:48 on modular  [Seed = 3936435090]
   -------------------------------------

6048

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:15:33 2004

Input: 2^110592 mod 331777

Output: Magma V2.11-2     Fri Jul 30 2004 14:15:32 on modular  [Seed = 4088931031]
   -------------------------------------

239223

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:15:37 2004

Input: 3^110592 mod 331777

Output: Magma V2.11-2     Fri Jul 30 2004 14:15:36 on modular  [Seed = 4222626515]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:15:47 2004

Input: 5^110592 mod 331777

Output: Magma V2.11-2     Fri Jul 30 2004 14:15:47 on modular  [Seed = 3280474864]
   -------------------------------------

92553

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:15:52 2004

Input: 6^110592 mod 331777

Output: Magma V2.11-2     Fri Jul 30 2004 14:15:51 on modular  [Seed = 3414170364]
   -------------------------------------

239223

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:15:56 2004

Input: 4^110592 mod 331777

Output: Magma V2.11-2     Fri Jul 30 2004 14:15:55 on modular  [Seed = 3549954792]
   -------------------------------------

92553

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:16:38 2004

Input: 2^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:16:37 on modular  [Seed = 2699784517]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:16:43 2004

Input: 3^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:16:42 on modular  [Seed = 2833480002]
   -------------------------------------

1

Total time: 0.600 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:16:52 2004

Input: 5^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:16:51 on modular  [Seed = 2969264451]
   -------------------------------------

498528

Total time: 0.610 seconds, Total memory usage: 3.59MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:17:07 2004

Input: 12^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:17:06 on modular  [Seed = 3136383864]
   -------------------------------------

1

Total time: 0.669 seconds, Total memory usage: 3.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:17:11 2004

Input: 13^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:17:11 on modular  [Seed = 2194232133]
   -------------------------------------

498528

Total time: 0.669 seconds, Total memory usage: 3.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:17:15 2004

Input: 14^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:17:15 on modular  [Seed = 2361875783]
   -------------------------------------

496800

Total time: 0.669 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:17:19 2004

Input: 15^331776 mod 995329

Output: Magma V2.11-2     Fri Jul 30 2004 14:17:19 on modular  [Seed = 2547795544]
   -------------------------------------

498528

Total time: 0.689 seconds, Total memory usage: 4.05MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:18:10 2004

Input: 2^663558 mod 1990675

Output: Magma V2.11-2     Fri Jul 30 2004 14:18:09 on modular  [Seed = 1680848358]
   -------------------------------------

1513169

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:18:14 2004

Input: 3^663558 mod 1990675

Output: Magma V2.11-2     Fri Jul 30 2004 14:18:13 on modular  [Seed = 1814543850]
   -------------------------------------

42714

Total time: 0.669 seconds, Total memory usage: 3.88MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:18:56 2004

Input: 2^49152 mod 147457

Output: Magma V2.11-2     Fri Jul 30 2004 14:18:56 on modular  [Seed = 2066787080]
   -------------------------------------

78348

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:19:01 2004

Input: 3^49152 mod 147457

Output: Magma V2.11-2     Fri Jul 30 2004 14:19:01 on modular  [Seed = 1107923508]
   -------------------------------------

69108

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:19:42 2004

Input: 3^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:19:42 on modular  [Seed = 1224907028]
   -------------------------------------

1

Total time: 0.689 seconds, Total memory usage: 4.29MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:19:47 2004

Input: 2^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:19:46 on modular  [Seed = 1360691568]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:19:51 2004

Input: 5^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:19:50 on modular  [Seed = 1494387068]
   -------------------------------------

2167887

Total time: 0.769 seconds, Total memory usage: 4.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:00 2004

Input: 13^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:19:59 on modular  [Seed = 543944716]
   -------------------------------------

1

Total time: 1.050 seconds, Total memory usage: 6.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:01 2004

Input: 13^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:19:59 on modular  [Seed = 644740618]
   -------------------------------------

1

Total time: 1.070 seconds, Total memory usage: 6.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:06 2004

Input: 14^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:20:05 on modular  [Seed = 89052467]
   -------------------------------------

1

Total time: 1.000 seconds, Total memory usage: 6.25MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:10 2004

Input: 15^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:20:09 on modular  [Seed = 222747959]
   -------------------------------------

2167887

Total time: 1.000 seconds, Total memory usage: 6.26MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:16 2004

Input: 17^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:20:15 on modular  [Seed = 358532393]
   -------------------------------------

486321

Total time: 1.020 seconds, Total memory usage: 6.62MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:22 2004

Input: 19^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:20:20 on modular  [Seed = 492227866]
   -------------------------------------

2167887

Total time: 1.070 seconds, Total memory usage: 6.99MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:20:58 2004

Input: 18^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:20:57 on modular  [Seed = 3853399311]
   -------------------------------------

1

Total time: 1.089 seconds, Total memory usage: 6.99MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:04 2004

Input: 20^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:03 on modular  [Seed = 3987094785]
   -------------------------------------

2167887

Total time: 1.079 seconds, Total memory usage: 7.00MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:09 2004

Input: 21^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:08 on modular  [Seed = 4122879234]
   -------------------------------------

1

Total time: 1.080 seconds, Total memory usage: 7.01MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:14 2004

Input: 22^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:13 on modular  [Seed = 4256574727]
   -------------------------------------

2167887

Total time: 1.079 seconds, Total memory usage: 7.02MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:18 2004

Input: 23^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:17 on modular  [Seed = 3314423099]
   -------------------------------------

1

Total time: 1.080 seconds, Total memory usage: 7.03MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:22 2004

Input: 24^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:21 on modular  [Seed = 3448118543]
   -------------------------------------

1

Total time: 1.089 seconds, Total memory usage: 7.03MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:28 2004

Input: 25^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:26 on modular  [Seed = 3583902992]
   -------------------------------------

486321

Total time: 1.070 seconds, Total memory usage: 7.04MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:32 2004

Input: 26^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:31 on modular  [Seed = 3717598485]
   -------------------------------------

1

Total time: 1.129 seconds, Total memory usage: 7.04MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:37 2004

Input: 27^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:35 on modular  [Seed = 2783868278]
   -------------------------------------

1

Total time: 1.169 seconds, Total memory usage: 7.31MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:42 2004

Input: 28^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:41 on modular  [Seed = 2917563771]
   -------------------------------------

1

Total time: 1.169 seconds, Total memory usage: 7.32MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:47 2004

Input: 29^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:46 on modular  [Seed = 3053348204]
   -------------------------------------

2167887

Total time: 1.169 seconds, Total memory usage: 7.33MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:21:57 2004

Input: 30^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:21:56 on modular  [Seed = 3187043610]
   -------------------------------------

2167887

Total time: 1.169 seconds, Total memory usage: 7.33MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:22:02 2004

Input: 31^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:22:01 on modular  [Seed = 2244891951]
   -------------------------------------

2167887

Total time: 1.169 seconds, Total memory usage: 7.33MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:22:08 2004

Input: 30^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:22:07 on modular  [Seed = 2378587425]
   -------------------------------------

2167887

Total time: 1.189 seconds, Total memory usage: 7.33MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:22:14 2004

Input: 29^884736 mod 2654209

Output: Magma V2.11-2     Fri Jul 30 2004 14:22:13 on modular  [Seed = 2514371875]
   -------------------------------------

2167887

Total time: 1.179 seconds, Total memory usage: 7.33MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:24:01 2004

Input: 2^589824 mod 1769473

Output: Magma V2.11-2     Fri Jul 30 2004 14:24:00 on modular  [Seed = 1697560135]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:24:32 2004

Input: 3^589824 mod 1769473

Output: Magma V2.11-2     Fri Jul 30 2004 14:24:32 on modular  [Seed = 1831255663]
   -------------------------------------

883584

Total time: 0.640 seconds, Total memory usage: 3.75MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:24:40 2004

Input: 5^589824 mod 1769473

Output: Magma V2.11-2     Fri Jul 30 2004 14:24:39 on modular  [Seed = 1967040112]
   -------------------------------------

885888

Total time: 0.699 seconds, Total memory usage: 4.29MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:24:45 2004

Input: 6^589824 mod 1769473

Output: Magma V2.11-2     Fri Jul 30 2004 14:24:44 on modular  [Seed = 2100735603]
   -------------------------------------

883584

Total time: 0.699 seconds, Total memory usage: 4.31MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:24:49 2004

Input: 7^589824 mod 1769473

Output: Magma V2.11-2     Fri Jul 30 2004 14:24:48 on modular  [Seed = 1241618776]
   -------------------------------------

885888

Total time: 0.750 seconds, Total memory usage: 4.59MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:26:08 2004

Input: 2^1769472 mod 5308417

Output: Magma V2.11-2     Fri Jul 30 2004 14:26:08 on modular  [Seed = 1444775412]
   -------------------------------------

254182

Total time: 0.549 seconds, Total memory usage: 2.98MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:26:22 2004

Input: 3^1769472 mod 5308417

Output: Magma V2.11-2     Fri Jul 30 2004 14:26:21 on modular  [Seed = 1578470897]
   -------------------------------------

5054234

Total time: 0.909 seconds, Total memory usage: 5.92MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:27:08 2004

Input: 3^393216 mod 1179649

Output: Magma V2.11-2     Fri Jul 30 2004 14:27:07 on modular  [Seed = 661451966]
   -------------------------------------

881334

Total time: 0.600 seconds, Total memory usage: 3.37MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:27:14 2004

Input: 2^393216 mod 1179649

Output: Magma V2.11-2     Fri Jul 30 2004 14:27:13 on modular  [Seed = 795147596]
   -------------------------------------

298314

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:27:49 2004

Input: 2^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:27:49 on modular  [Seed = 980543613]
   -------------------------------------

392448

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:27:53 2004

Input: 3^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:27:52 on modular  [Seed = 21680971]
   -------------------------------------

1

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:28:03 2004

Input: 4^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:28:02 on modular  [Seed = 155376473]
   -------------------------------------

393984

Total time: 0.590 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:28:07 2004

Input: 6^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:28:06 on modular  [Seed = 291160900]
   -------------------------------------

392448

Total time: 0.600 seconds, Total memory usage: 3.44MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:28:12 2004

Input: 5^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:28:11 on modular  [Seed = 424856384]
   -------------------------------------

1

Total time: 0.590 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:28:27 2004

Input: 29^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:28:26 on modular  [Seed = 3870110927]
   -------------------------------------

393984

Total time: 0.669 seconds, Total memory usage: 3.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:28:32 2004

Input: 30^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:28:31 on modular  [Seed = 4003806403]
   -------------------------------------

392448

Total time: 0.679 seconds, Total memory usage: 3.97MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:28:38 2004

Input: 31^262144 mod 786433

Output: Magma V2.11-2     Fri Jul 30 2004 14:28:37 on modular  [Seed = 4139590849]
   -------------------------------------

393984

Total time: 0.689 seconds, Total memory usage: 4.04MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:29:39 2004

Input: 2^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:29:38 on modular  [Seed = 4273286158]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 3.35MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:29:44 2004

Input: 3^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:29:42 on modular  [Seed = 3331134514]
   -------------------------------------

6820451

Total time: 1.760 seconds, Total memory usage: 11.45MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:29:53 2004

Input: 5^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:29:50 on modular  [Seed = 3464830002]
   -------------------------------------

1

Total time: 2.479 seconds, Total memory usage: 15.75MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:30:02 2004

Input: 29^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:29:57 on modular  [Seed = 3617326352]
   -------------------------------------

6820451

Total time: 4.919 seconds, Total memory usage: 26.02MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:30:11 2004

Input: 30^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:30:06 on modular  [Seed = 3751021843]
   -------------------------------------

6820451

Total time: 5.200 seconds, Total memory usage: 27.11MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:30:20 2004

Input: 31^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:30:15 on modular  [Seed = 2817291634]
   -------------------------------------

1

Total time: 5.209 seconds, Total memory usage: 27.13MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:30:31 2004

Input: 28^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:30:26 on modular  [Seed = 2950987023]
   -------------------------------------

7335325

Total time: 4.900 seconds, Total memory usage: 26.00MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:30:41 2004

Input: 29^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:30:36 on modular  [Seed = 3086771481]
   -------------------------------------

6820451

Total time: 4.919 seconds, Total memory usage: 26.02MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:30:51 2004

Input: 30^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:30:46 on modular  [Seed = 3220466955]
   -------------------------------------

6820451

Total time: 5.209 seconds, Total memory usage: 27.11MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:31:12 2004

Input: 29^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:31:07 on modular  [Seed = 2278315278]
   -------------------------------------

6820451

Total time: 4.909 seconds, Total memory usage: 26.02MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:31:20 2004

Input: 28^4718592 mod 14155777

Output: Magma V2.11-2     Fri Jul 30 2004 14:31:15 on modular  [Seed = 2412010782]
   -------------------------------------

7335325

Total time: 4.919 seconds, Total memory usage: 26.00MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:32:38 2004

Input: 2^9437184 mod 28311553

Output: Magma V2.11-2     Fri Jul 30 2004 14:32:38 on modular  [Seed = 1831254094]
   -------------------------------------

1

Total time: 0.570 seconds, Total memory usage: 3.94MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:32:47 2004

Input: 3^9437184 mod 28311553

Output: Magma V2.11-2     Fri Jul 30 2004 14:32:43 on modular  [Seed = 1967038555]
   -------------------------------------

14151168

Total time: 3.349 seconds, Total memory usage: 20.12MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:32:58 2004

Input: 5^9437184 mod 28311553

Output: Magma V2.11-2     Fri Jul 30 2004 14:32:53 on modular  [Seed = 2100734030]
   -------------------------------------

14151168

Total time: 4.890 seconds, Total memory usage: 27.67MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:33:07 2004

Input: 7^9437184 mod 28311553

Output: Magma V2.11-2     Fri Jul 30 2004 14:33:02 on modular  [Seed = 1158582398]
   -------------------------------------

14160384

Total time: 5.650 seconds, Total memory usage: 30.24MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:33:17 2004

Input: 6^9437184 mod 28311553

Output: Magma V2.11-2     Fri Jul 30 2004 14:33:11 on modular  [Seed = 1292277824]
   -------------------------------------

14151168

Total time: 5.219 seconds, Total memory usage: 29.03MB


************** MAGMA *****************
Host d214.math.mtholyoke.edu. (138.110.3.214)
Time: Fri Jul 30 14:33:25 2004

Input: 5^9437184 mod 28311553

Output: Magma V2.11-2     Fri Jul 30 2004 14:33:20 on modular  [Seed = 1428062272]
   -------------------------------------

14151168

Total time: 4.919 seconds, Total memory usage: 27.67MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Fri Jul 30 16:20:56 2004

Input: y=Mod(1,3)*x  
a=y^3+3*y^2+2
a^2

Output: Magma V2.11-2     Fri Jul 30 2004 16:20:55 on modular  [Seed = 3203748477]
   -------------------------------------


>> a=y^3+3*y^2+2
   ^
User error: bad syntax

>> a^2;
   ^
User error: Identifier 'a' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-6-41-32.client.comcast.net. (24.6.41.32)
Time: Fri Jul 30 21:40:54 2004

Input: (2231^4721 + 2229)/2230/(2*67162747)


Output: Magma V2.11-2     Fri Jul 30 2004 21:40:53 on modular  [Seed = 1494409364]
   -------------------------------------

6166063608181991123530942252851242460696821245069411805807630052625511522336586\
3280758035230731863020186167922497121658060854121714221594559168762293002634775\
8692370672938867761671054562842281191501237073104321802578476319108534257533480\
1893947659906215037994545589079536467261909896006836014601901435029436846489691\
6440372271269983405804965341797341558426249256874736728816491644858982092758859\
9602619656394098862483833599714707543366236464073470896599713460215571903703061\
2979373880733297155049349402506858728823854194063644502049089528185550392195471\
2042759486052227965371866463512806852567455311407119223196854692054448630433263\
8143024617934688159892222005355949931397668240636350737039913942558995634010196\
2159571396853470298409038981917818680131154658384320796982336752222964341109595\
4875502215238766328348953325136957887109092197304163957847319336539266732233022\
8067877555818742225177767719310699141527159151676896922210483634702241487809289\
0066460092347561036709727640704164036464272407534324259672998943513032664445189\
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5239793226982299696527041668980388400524054031326833423253349366889509027887773\
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2868956331709291256397718020096009967670274737951792342122048411525532404732003\
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5656896312535707988145740231935756728751459964781649714813985708483454566283660\
5886874600299840991193206632722605876491101654672983604273960659678891027837935\
0955887601033874581048292143468552043885644613758387641437127870068878519340246\
4044934052895005699691617132867814700739945734854214017210127769637426567362121\
2050958060006010241737222382063670058371077992967875535312619170420920172600352\
8374681689315742232932527998530409951721047484741247226548806943622038649582070\
9431440909655013889799701272423573782740799443014486166719711705746977748753818\
3904242730750130528774694226490094848320956293424672825345680839560719883784077\
9319263786229610584670638337781671792293369170366046965041158084722550670504601\
5048137493111800789721899456582213886902802496527891159744478212781555450003801\
9098099396610337949417231388142115072192713755062130883252035216052252428826915\
6921560866597588182390066859463942916210179000662216941348580202068660819420248\
8250454488483600587038980744543752800916405953620214929466355996046731824912317\
4165904666201356792117871523795411050649540968567381591783226664607537220706222\
2782237404099688773049989371422447059970082735133086412460209135089387855875651\
8672320826911059665790090193632996019326941106591997272792295112217756453987591\
5297864221855360305307770830020654326015459472777777310988312419841422612447601\
8583305898632046956475545767630246312166227247120151741245694450148183282963425\
1448910855893558953479031841964780133291415964108363717926512009141779100857933\
7
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host evrtwa1-ar7-4-63-180-017.evrtwa1.dsl-verizon.net. (4.63.180.17)
Time: Sat Jul 31 12:48:30 2004

Input: x^2+2*x+1

Output: Magma V2.11-2     Sat Jul 31 2004 12:48:28 on modular  [Seed = 2395210403]
   -------------------------------------


>> x^2+2*x+1;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.720 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host evrtwa1-ar7-4-63-180-017.evrtwa1.dsl-verizon.net. (4.63.180.17)
Time: Sat Jul 31 12:48:46 2004

Input: x=1
x^2+2*x+1

Output: Magma V2.11-2     Sat Jul 31 2004 12:48:45 on modular  [Seed = 2000550762]
   -------------------------------------


>> x^2+2*x+1;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host evrtwa1-ar7-4-63-180-017.evrtwa1.dsl-verizon.net. (4.63.180.17)
Time: Sat Jul 31 12:50:01 2004

Input: factor(81)

Output: Magma V2.11-2     Sat Jul 31 2004 12:50:00 on modular  [Seed = 1377361562]
   -------------------------------------


>> factor(81);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ool-18bbf3f4.dyn.optonline.net. (24.187.243.244)
Time: Sat Jul 31 16:49:29 2004

Input: 55334343434+232322378787878*6

Output: Magma V2.11-2     Sat Jul 31 2004 16:49:28 on modular  [Seed = 694447490]
   -------------------------------------

1393989607070702

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ool-18bbf3f4.dyn.optonline.net. (24.187.243.244)
Time: Sat Jul 31 16:59:00 2004

Input: 34*2-100+1

Output: Magma V2.11-2     Sat Jul 31 2004 16:59:00 on modular  [Seed = 138756462]
   -------------------------------------

-31

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.152.8.176)
Time: Sat Jul 31 22:08:08 2004

Input: (6873635!)mod(721!)

Output: Magma V2.11-2     Sat Jul 31 2004 22:08:07 on modular  [Seed = 4206357254]
   -------------------------------------


>> (6873635!)mod(721!);
            ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.152.8.176)
Time: Sat Jul 31 22:08:42 2004

Input: 6873635mod721

Output: Magma V2.11-2     Sat Jul 31 2004 22:08:42 on modular  [Seed = 3566847242]
   -------------------------------------


>> 6873635mod721;
          ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.152.8.176)
Time: Sat Jul 31 22:08:56 2004

Input: 6873635 mod 721

Output: Magma V2.11-2     Sat Jul 31 2004 22:08:56 on modular  [Seed = 3700542736]
   -------------------------------------

342

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.152.8.176)
Time: Sat Jul 31 22:09:27 2004

Input: 6873635 mod 721

Output: Magma V2.11-2     Sat Jul 31 2004 22:09:26 on modular  [Seed = 3069945620]
   -------------------------------------

342

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.152.8.176)
Time: Sat Jul 31 22:09:55 2004

Input: 6873635^7646558 mod 721

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Sat Jul 31 2004 22:09:45 on modular  [Seed = 3203641123]
   -------------------------------------


Current total memory usage: 91.6MB, failed memory request: 26.2MB
System Error: User memory limit has been reached

Total time: 9.780 seconds, Total memory usage: 96.08MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.152.8.176)
Time: Sat Jul 31 22:10:10 2004

Input: 6873635^7646 mod 721

Output: Magma V2.11-2     Sat Jul 31 2004 22:10:09 on modular  [Seed = 2733617879]
   -------------------------------------

358

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:18:47 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Sun Aug  1 2004 00:18:47 on modular  [Seed = 2750320115]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:25:37 2004

Input: 1!

Output: Magma V2.11-2     Sun Aug  1 2004 00:25:36 on modular  [Seed = 2227811635]
   -------------------------------------


>> 1!;
     ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:25:44 2004

Input: 1!;

Output: Magma V2.11-2     Sun Aug  1 2004 00:25:43 on modular  [Seed = 2361507132]
   -------------------------------------


>> 1!;;
     ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:25:52 2004

Input: 5!


Output: Magma V2.11-2     Sun Aug  1 2004 00:25:52 on modular  [Seed = 1966621907]
   -------------------------------------


>> ;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:26:03 2004

Input: 5+5


Output: Magma V2.11-2     Sun Aug  1 2004 00:26:02 on modular  [Seed = 2100317393]
   -------------------------------------

10

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:26:16 2004

Input: 1-1


Output: Magma V2.11-2     Sun Aug  1 2004 00:26:16 on modular  [Seed = 1697142011]
   -------------------------------------

0

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pool-68-237-221-226.ny325.east.verizon.net. (68.237.221.226)
Time: Sun Aug  1 00:26:30 2004

Input: 10!

Output: Magma V2.11-2     Sun Aug  1 2004 00:26:29 on modular  [Seed = 1377788881]
   -------------------------------------


>> 10!;
      ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-73.mtholyoke.edu. (138.110.72.73)
Time: Sun Aug  1 00:59:36 2004

Input: 2^16 mod 7


Output: Magma V2.11-2     Sun Aug  1 2004 00:59:36 on modular  [Seed = 560732399]
   -------------------------------------

2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-73.mtholyoke.edu. (138.110.72.73)
Time: Sun Aug  1 00:59:42 2004

Input: 3^16 mod 7


Output: Magma V2.11-2     Sun Aug  1 2004 00:59:41 on modular  [Seed = 694423777]
   -------------------------------------

4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-73.mtholyoke.edu. (138.110.72.73)
Time: Sun Aug  1 00:59:47 2004

Input: 4^16 mod 7


Output: Magma V2.11-2     Sun Aug  1 2004 00:59:46 on modular  [Seed = 291252389]
   -------------------------------------

4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host HSE-Kitchener-ppp230668.sympatico.ca. (64.230.146.87)
Time: Sun Aug  1 12:13:24 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Sun Aug  1 2004 12:13:19 on modular  [Seed = 1544555518]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.799 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 18:31:59 2004

Input: E:=EllipticCurve([0, 1]);


Output: Magma V2.11-2     Sun Aug  1 2004 18:31:59 on modular  [Seed = 594480507]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 18:32:10 2004

Input: E:=EllipticCurve([0, 1]);E;

Output: Magma V2.11-2     Sun Aug  1 2004 18:32:10 on modular  [Seed = 728171846]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 1 over Rational Field

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 18:33:10 2004

Input: E:=EllipticCurve([0, 1]);
IsogenyFromKernel(E, DivisionPolynomial(E, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 18:33:10 on modular  [Seed = 863968658]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 729 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
729 over Rational Field
taking (x : y : 1) to ((x^9 - 96*x^6 + 48*x^3 + 64) / (x^8 + 8*x^5 + 16*x^2) : 
    (x^12*y + 220*x^9*y - 1776*x^6*y - 320*x^3*y - 512*y) / (x^12 + 12*x^9 + 
    48*x^6 + 64*x^3) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 18:33:26 2004

Input: E:=EllipticCurve([0, 2]);
IsogenyFromKernel(E, DivisionPolynomial(E, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 18:33:25 on modular  [Seed = 997660041]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 1458 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
1458 over Rational Field
taking (x : y : 1) to ((x^9 - 192*x^6 + 192*x^3 + 512) / (x^8 + 16*x^5 + 64*x^2)
: (x^12*y + 440*x^9*y - 7104*x^6*y - 2560*x^3*y - 8192*y) / (x^12 + 24*x^9 + 
    192*x^6 + 512*x^3) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 18:34:29 2004

Input: E:=EllipticCurve([96, -16]);
IsogenyFromKernel(E, DivisionPolynomial(E, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 18:34:28 on modular  [Seed = 1125084592]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 7776*x - 11664 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
7776*x - 11664 over Rational Field
taking (x : y : 1) to ((x^9 - 1152*x^7 + 1536*x^6 + 276480*x^5 + 36864*x^4 + 
    31862784*x^3 - 7077888*x^2 + 766771200*x - 113508352) / (x^8 + 384*x^6 - 
    128*x^5 + 30720*x^4 - 24576*x^3 - 1175552*x^2 + 393216*x + 9437184) : 
    (x^12*y + 2112*x^10*y - 3520*x^9*y - 1520640*x^8*y + 811008*x^7*y - 
    81850368*x^6*y - 38928384*x^5*y - 15736504320*x^4*y + 1133772800*x^3*y - 
    735307628544*x^2*y + 179734315008*x*y - 2370050195456*y) / (x^12 + 576*x^10 
    - 192*x^9 + 101376*x^8 - 73728*x^7 + 3551232*x^6 - 5898240*x^5 - 
    309067776*x^4 + 226230272*x^3 + 5398069248*x^2 - 1811939328*x - 28991029248)
: 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:06:15 2004

Input: E:=EllipticCurve([96, -16]);
S:=nTorsionSubgroup(E,3);
IsogenyFromKernel(E, S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:06:15 on modular  [Seed = 3280933186]
   -------------------------------------


>> S:=nTorsionSubgroup(E,3);
                      ^
Runtime error in 'nTorsionSubgroup': Bad argument types
Argument types given: CrvEll[FldRat], RngIntElt

>> IsogenyFromKernel(E, S);;
                        ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:07:24 2004

Input: E:=EllipticCurve([96, -16]);
DivisionPolynomial(E, 3);
S:=nTorsionSubgroup(E,3);
IsogenyFromKernel(E, S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:07:24 on modular  [Seed = 3414628609]
   -------------------------------------

3*$.1^4 + 576*$.1^2 - 192*$.1 - 9216
3*$.1^4 + 576*$.1^2 - 192*$.1 - 9216
1

>> S:=nTorsionSubgroup(E,3);
                      ^
Runtime error in 'nTorsionSubgroup': Bad argument types
Argument types given: CrvEll[FldRat], RngIntElt

>> IsogenyFromKernel(E, S);;
                        ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:09:52 2004

Input: E:=EllipticCurve([96, -16]);
DivisionPolynomial(E, 3);
S:=pPowerTorsion(E,3);
IsogenyFromKernel(E, S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:09:52 on modular  [Seed = 3700427194]
   -------------------------------------

3*$.1^4 + 576*$.1^2 - 192*$.1 - 9216
3*$.1^4 + 576*$.1^2 - 192*$.1 - 9216
1

>> IsogenyFromKernel(E, S);;
                    ^
Runtime error in 'IsogenyFromKernel': Bad argument types
Argument types given: CrvEll[FldRat], GrpAb

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:11:39 2004

Input: E:=EllipticCurve([96, -16]);
S:=TorsionSubgroupScheme(E, 9);
IsogenyFromKernel(E, S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:11:38 on modular  [Seed = 3853070377]
   -------------------------------------


>> IsogenyFromKernel(E, S);;
                    ^
Runtime error in 'IsogenyFromKernel': Bad argument types
Argument types given: CrvEll[FldRat], SchGrpEll

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:12:18 2004

Input: E:=EllipticCurve([96, -16]);
S:=TorsionSubgroup(E, 9);
IsogenyFromKernel(E, S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:12:17 on modular  [Seed = 3936763678]
   -------------------------------------


>> S:=TorsionSubgroup(E, 9);
                     ^
Runtime error in 'TorsionSubgroup': Bad argument types
Argument types given: CrvEll[FldRat], RngIntElt

>> IsogenyFromKernel(E, S);;
                        ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:12:28 2004

Input: E:=EllipticCurve([96, -16]);
S:=TorsionSubgroup(E);
IsogenyFromKernel(E, S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:12:28 on modular  [Seed = 4072548104]
   -------------------------------------


>> IsogenyFromKernel(E, S);;
                    ^
Runtime error in 'IsogenyFromKernel': Bad argument types
Argument types given: CrvEll[FldRat], GrpAb

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:12:54 2004

Input: E:=EllipticCurve([96, -16]);
S:=TorsionSubgroup(E);
IsogenyFromKernel(S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:12:53 on modular  [Seed = 4206243561]
   -------------------------------------


>> IsogenyFromKernel(S);;
                    ^
Runtime error in 'IsogenyFromKernel': Bad argument types
Argument types given: GrpAb

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:14:23 2004

Input: E:=EllipticCurve([96, -16]);
S:=TorsionSubgroupScheme(E,3);
IsogenyFromKernel(S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:14:23 on modular  [Seed = 71880802]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 7776*x - 11664 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
7776*x - 11664 over Rational Field
taking (x : y : 1) to ((x^9 - 1152*x^7 + 1536*x^6 + 276480*x^5 + 36864*x^4 + 
    31862784*x^3 - 7077888*x^2 + 766771200*x - 113508352) / (x^8 + 384*x^6 - 
    128*x^5 + 30720*x^4 - 24576*x^3 - 1175552*x^2 + 393216*x + 9437184) : 
    (x^12*y + 2112*x^10*y - 3520*x^9*y - 1520640*x^8*y + 811008*x^7*y - 
    81850368*x^6*y - 38928384*x^5*y - 15736504320*x^4*y + 1133772800*x^3*y - 
    735307628544*x^2*y + 179734315008*x*y - 2370050195456*y) / (x^12 + 576*x^10 
    - 192*x^9 + 101376*x^8 - 73728*x^7 + 3551232*x^6 - 5898240*x^5 - 
    309067776*x^4 + 226230272*x^3 + 5398069248*x^2 - 1811939328*x - 28991029248)
: 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:14:52 2004

Input: E:=EllipticCurve([96, -16]);
S:=TorsionSubgroupScheme(E,3);
S;
IsogenyFromKernel(S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:14:51 on modular  [Seed = 525585309]
   -------------------------------------

Subgroup scheme of E defined by x^4 + 192*x^2 - 64*x - 3072
Elliptic Curve defined by y^2 = x^3 + 7776*x - 11664 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
7776*x - 11664 over Rational Field
taking (x : y : 1) to ((x^9 - 1152*x^7 + 1536*x^6 + 276480*x^5 + 36864*x^4 + 
    31862784*x^3 - 7077888*x^2 + 766771200*x - 113508352) / (x^8 + 384*x^6 - 
    128*x^5 + 30720*x^4 - 24576*x^3 - 1175552*x^2 + 393216*x + 9437184) : 
    (x^12*y + 2112*x^10*y - 3520*x^9*y - 1520640*x^8*y + 811008*x^7*y - 
    81850368*x^6*y - 38928384*x^5*y - 15736504320*x^4*y + 1133772800*x^3*y - 
    735307628544*x^2*y + 179734315008*x*y - 2370050195456*y) / (x^12 + 576*x^10 
    - 192*x^9 + 101376*x^8 - 73728*x^7 + 3551232*x^6 - 5898240*x^5 - 
    309067776*x^4 + 226230272*x^3 + 5398069248*x^2 - 1811939328*x - 28991029248)
: 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:16:09 2004

Input: E:=EllipticCurve([96, -16]);
Roots(DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:16:08 on modular  [Seed = 375046855]
   -------------------------------------

[ <4, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:16:54 2004

Input: E:=EllipticCurve([96, -16]);
Roots(DivisionPolynomial(E,3));
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:16:53 on modular  [Seed = 778238242]
   -------------------------------------

[ <4, 1> ]
Elliptic Curve defined by y^2 = x^3 + 7776*x - 11664 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
7776*x - 11664 over Rational Field
taking (x : y : 1) to ((x^9 - 1152*x^7 + 1536*x^6 + 276480*x^5 + 36864*x^4 + 
    31862784*x^3 - 7077888*x^2 + 766771200*x - 113508352) / (x^8 + 384*x^6 - 
    128*x^5 + 30720*x^4 - 24576*x^3 - 1175552*x^2 + 393216*x + 9437184) : 
    (x^12*y + 2112*x^10*y - 3520*x^9*y - 1520640*x^8*y + 811008*x^7*y - 
    81850368*x^6*y - 38928384*x^5*y - 15736504320*x^4*y + 1133772800*x^3*y - 
    735307628544*x^2*y + 179734315008*x*y - 2370050195456*y) / (x^12 + 576*x^10 
    - 192*x^9 + 101376*x^8 - 73728*x^7 + 3551232*x^6 - 5898240*x^5 - 
    309067776*x^4 + 226230272*x^3 + 5398069248*x^2 - 1811939328*x - 28991029248)
: 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:19:29 2004

Input: E:=EllipticCurve([96, -16]);
Roots(DivisionPolynomial(E,3));
Points(E,4);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:19:28 on modular  [Seed = 864019610]
   -------------------------------------

[ <4, 1> ]
[]
Elliptic Curve defined by y^2 = x^3 + 7776*x - 11664 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 
7776*x - 11664 over Rational Field
taking (x : y : 1) to ((x^9 - 1152*x^7 + 1536*x^6 + 276480*x^5 + 36864*x^4 + 
    31862784*x^3 - 7077888*x^2 + 766771200*x - 113508352) / (x^8 + 384*x^6 - 
    128*x^5 + 30720*x^4 - 24576*x^3 - 1175552*x^2 + 393216*x + 9437184) : 
    (x^12*y + 2112*x^10*y - 3520*x^9*y - 1520640*x^8*y + 811008*x^7*y - 
    81850368*x^6*y - 38928384*x^5*y - 15736504320*x^4*y + 1133772800*x^3*y - 
    735307628544*x^2*y + 179734315008*x*y - 2370050195456*y) / (x^12 + 576*x^10 
    - 192*x^9 + 101376*x^8 - 73728*x^7 + 3551232*x^6 - 5898240*x^5 - 
    309067776*x^4 + 226230272*x^3 + 5398069248*x^2 - 1811939328*x - 28991029248)
: 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:19:57 2004

Input: E:=EllipticCurve([(-3)^2*96, (-3)^3*(-16)]);
Roots(DivisionPolynomial(E,3));
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:19:57 on modular  [Seed = 1258790143]
   -------------------------------------

[ <-12, 1> ]
Elliptic Curve defined by y^2 = x^3 - x^2 + 2593/3*x + 3887/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 
x^2 + 2593/3*x + 3887/27 over Rational Field
taking (x : y : 1) to ((1/9*x^9 + 1/3*x^8 - 1152*x^7 - 3456*x^6 + 2489472*x^5 - 
    165888*x^4 + 2582876160*x^3 + 1434267648*x^2 + 558689550336*x + 
    268881887232) / (x^8 + 3456*x^6 + 3456*x^5 + 2488320*x^4 + 5971968*x^3 - 
    856977408*x^2 - 859963392*x + 61917364224) : (1/27*x^12*y + 704*x^10*y + 
    3520*x^9*y - 4561920*x^8*y - 7299072*x^7*y - 2209959936*x^6*y + 
    3153199104*x^5*y - 3823970549760*x^4*y - 826520371200*x^3*y - 
    1608117783625728*x^2*y - 1179236840767488*x*y - 46649697997160448*y) / (x^12
    + 5184*x^10 + 5184*x^9 + 8211456*x^8 + 17915904*x^7 + 2588848128*x^6 + 
    12899450880*x^5 - 2027793678336*x^4 - 4452890443776*x^3 + 
    318750591025152*x^2 + 320979616137216*x - 15407021574586368) : 1)

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:20:11 2004

Input: E:=EllipticCurve([(-3)^2*96, (-3)^3*(-16)]);
Roots(DivisionPolynomial(E,3));
Pints(E, -12);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:20:11 on modular  [Seed = 1461420181]
   -------------------------------------

[ <-12, 1> ]

>> Pints(E, -12);
   ^
User error: Identifier 'Pints' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - x^2 + 2593/3*x + 3887/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 
x^2 + 2593/3*x + 3887/27 over Rational Field
taking (x : y : 1) to ((1/9*x^9 + 1/3*x^8 - 1152*x^7 - 3456*x^6 + 2489472*x^5 - 
    165888*x^4 + 2582876160*x^3 + 1434267648*x^2 + 558689550336*x + 
    268881887232) / (x^8 + 3456*x^6 + 3456*x^5 + 2488320*x^4 + 5971968*x^3 - 
    856977408*x^2 - 859963392*x + 61917364224) : (1/27*x^12*y + 704*x^10*y + 
    3520*x^9*y - 4561920*x^8*y - 7299072*x^7*y - 2209959936*x^6*y + 
    3153199104*x^5*y - 3823970549760*x^4*y - 826520371200*x^3*y - 
    1608117783625728*x^2*y - 1179236840767488*x*y - 46649697997160448*y) / (x^12
    + 5184*x^10 + 5184*x^9 + 8211456*x^8 + 17915904*x^7 + 2588848128*x^6 + 
    12899450880*x^5 - 2027793678336*x^4 - 4452890443776*x^3 + 
    318750591025152*x^2 + 320979616137216*x - 15407021574586368) : 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:20:21 2004

Input: E:=EllipticCurve([(-3)^2*96, (-3)^3*(-16)]);
Roots(DivisionPolynomial(E,3));
Points(E, -12);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:20:20 on modular  [Seed = 1864612018]
   -------------------------------------

[ <-12, 1> ]
[]
Elliptic Curve defined by y^2 = x^3 - x^2 + 2593/3*x + 3887/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 
x^2 + 2593/3*x + 3887/27 over Rational Field
taking (x : y : 1) to ((1/9*x^9 + 1/3*x^8 - 1152*x^7 - 3456*x^6 + 2489472*x^5 - 
    165888*x^4 + 2582876160*x^3 + 1434267648*x^2 + 558689550336*x + 
    268881887232) / (x^8 + 3456*x^6 + 3456*x^5 + 2488320*x^4 + 5971968*x^3 - 
    856977408*x^2 - 859963392*x + 61917364224) : (1/27*x^12*y + 704*x^10*y + 
    3520*x^9*y - 4561920*x^8*y - 7299072*x^7*y - 2209959936*x^6*y + 
    3153199104*x^5*y - 3823970549760*x^4*y - 826520371200*x^3*y - 
    1608117783625728*x^2*y - 1179236840767488*x*y - 46649697997160448*y) / (x^12
    + 5184*x^10 + 5184*x^9 + 8211456*x^8 + 17915904*x^7 + 2588848128*x^6 + 
    12899450880*x^5 - 2027793678336*x^4 - 4452890443776*x^3 + 
    318750591025152*x^2 + 320979616137216*x - 15407021574586368) : 1)

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:21:09 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E,3));
Points(E, -12);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:21:08 on modular  [Seed = 2134092146]
   -------------------------------------

[ <12, 1> ]
[]
Elliptic Curve defined by y^2 + y = x^3 + x^2 + 163/3*x + 298/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 + 163/3*x + 298/27 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 1/3*x^8 - 288*x^7 + 623232*x^5 - 580608*x^4 +
    647212032*x^3 - 144322560*x^2 + 139457396736*x - 82699812864) / (x^8 + 
    3456*x^6 - 3456*x^5 + 2488320*x^4 - 5971968*x^3 - 856977408*x^2 + 
    859963392*x + 61917364224) : (1/216*x^12*y - 1/2*x^12 + 88*x^10*y - 
    2592*x^10 - 440*x^9*y + 2592*x^9 - 570240*x^8*y - 4105728*x^8 + 912384*x^7*y
    + 8957952*x^7 - 276244992*x^6*y - 1294424064*x^6 - 394149888*x^5*y + 
    6449725440*x^5 - 477996318720*x^4*y + 1013896839168*x^4 + 103315046400*x^3*y
    - 2226445221888*x^3 - 201014722953216*x^2*y - 159375295512576*x^2 + 
    147404605095936*x*y + 160489808068608*x - 5831212249645056*y + 
    7703510787293184) / (x^12 + 5184*x^10 - 5184*x^9 + 8211456*x^8 - 
    17915904*x^7 + 2588848128*x^6 - 12899450880*x^5 - 2027793678336*x^4 + 
    4452890443776*x^3 + 318750591025152*x^2 - 320979616137216*x - 
    15407021574586368) : 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:22:09 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E,3));
Points(E, 12);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:22:09 on modular  [Seed = 2278248911]
   -------------------------------------

[ <12, 1> ]
[ (12 : -108 : 1), (12 : 108 : 1) ]
Elliptic Curve defined by y^2 + y = x^3 + x^2 + 163/3*x + 298/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 + 163/3*x + 298/27 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 1/3*x^8 - 288*x^7 + 623232*x^5 - 580608*x^4 +
    647212032*x^3 - 144322560*x^2 + 139457396736*x - 82699812864) / (x^8 + 
    3456*x^6 - 3456*x^5 + 2488320*x^4 - 5971968*x^3 - 856977408*x^2 + 
    859963392*x + 61917364224) : (1/216*x^12*y - 1/2*x^12 + 88*x^10*y - 
    2592*x^10 - 440*x^9*y + 2592*x^9 - 570240*x^8*y - 4105728*x^8 + 912384*x^7*y
    + 8957952*x^7 - 276244992*x^6*y - 1294424064*x^6 - 394149888*x^5*y + 
    6449725440*x^5 - 477996318720*x^4*y + 1013896839168*x^4 + 103315046400*x^3*y
    - 2226445221888*x^3 - 201014722953216*x^2*y - 159375295512576*x^2 + 
    147404605095936*x*y + 160489808068608*x - 5831212249645056*y + 
    7703510787293184) / (x^12 + 5184*x^10 - 5184*x^9 + 8211456*x^8 - 
    17915904*x^7 + 2588848128*x^6 - 12899450880*x^5 - 2027793678336*x^4 + 
    4452890443776*x^3 + 318750591025152*x^2 - 320979616137216*x - 
    15407021574586368) : 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:24:12 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
TorsionSubroup(E);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:24:12 on modular  [Seed = 2464039975]
   -------------------------------------


>> TorsionSubroup(E);
   ^
User error: Identifier 'TorsionSubroup' has not been declared or assigned
Elliptic Curve defined by y^2 + y = x^3 + x^2 + 163/3*x + 298/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 + 163/3*x + 298/27 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 1/3*x^8 - 288*x^7 + 623232*x^5 - 580608*x^4 +
    647212032*x^3 - 144322560*x^2 + 139457396736*x - 82699812864) / (x^8 + 
    3456*x^6 - 3456*x^5 + 2488320*x^4 - 5971968*x^3 - 856977408*x^2 + 
    859963392*x + 61917364224) : (1/216*x^12*y - 1/2*x^12 + 88*x^10*y - 
    2592*x^10 - 440*x^9*y + 2592*x^9 - 570240*x^8*y - 4105728*x^8 + 912384*x^7*y
    + 8957952*x^7 - 276244992*x^6*y - 1294424064*x^6 - 394149888*x^5*y + 
    6449725440*x^5 - 477996318720*x^4*y + 1013896839168*x^4 + 103315046400*x^3*y
    - 2226445221888*x^3 - 201014722953216*x^2*y - 159375295512576*x^2 + 
    147404605095936*x*y + 160489808068608*x - 5831212249645056*y + 
    7703510787293184) / (x^12 + 5184*x^10 - 5184*x^9 + 8211456*x^8 - 
    17915904*x^7 + 2588848128*x^6 - 12899450880*x^5 - 2027793678336*x^4 + 
    4452890443776*x^3 + 318750591025152*x^2 - 320979616137216*x - 
    15407021574586368) : 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:25:03 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
TorsionSubgroup(E);
IsogenyFromKernel(E, DivisionPolynomial(E,3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:25:02 on modular  [Seed = 2867231821]
   -------------------------------------

Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0
Elliptic Curve defined by y^2 + y = x^3 + x^2 + 163/3*x + 298/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 + 163/3*x + 298/27 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 1/3*x^8 - 288*x^7 + 623232*x^5 - 580608*x^4 +
    647212032*x^3 - 144322560*x^2 + 139457396736*x - 82699812864) / (x^8 + 
    3456*x^6 - 3456*x^5 + 2488320*x^4 - 5971968*x^3 - 856977408*x^2 + 
    859963392*x + 61917364224) : (1/216*x^12*y - 1/2*x^12 + 88*x^10*y - 
    2592*x^10 - 440*x^9*y + 2592*x^9 - 570240*x^8*y - 4105728*x^8 + 912384*x^7*y
    + 8957952*x^7 - 276244992*x^6*y - 1294424064*x^6 - 394149888*x^5*y + 
    6449725440*x^5 - 477996318720*x^4*y + 1013896839168*x^4 + 103315046400*x^3*y
    - 2226445221888*x^3 - 201014722953216*x^2*y - 159375295512576*x^2 + 
    147404605095936*x*y + 160489808068608*x - 5831212249645056*y + 
    7703510787293184) / (x^12 + 5184*x^10 - 5184*x^9 + 8211456*x^8 - 
    17915904*x^7 + 2588848128*x^6 - 12899450880*x^5 - 2027793678336*x^4 + 
    4452890443776*x^3 + 318750591025152*x^2 - 320979616137216*x - 
    15407021574586368) : 1)

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:25:16 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
S:=TorsionSubgroup(E);
IsogenyFromKernel(S);

Output: Magma V2.11-2     Sun Aug  1 2004 21:25:15 on modular  [Seed = 2783540055]
   -------------------------------------


>> IsogenyFromKernel(S);;
                    ^
Runtime error in 'IsogenyFromKernel': Bad argument types
Argument types given: GrpAb

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:27:58 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
IsogenyFromKernel(S, DivisionPolynomial(E, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:27:58 on modular  [Seed = 3186713642]
   -------------------------------------


>> IsogenyFromKernel(S, DivisionPolynomial(E, 3));;
                     ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:28:08 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
IsogenyFromKernel(E, DivisionPolynomial(E, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 21:28:08 on modular  [Seed = 3036179733]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 + x^2 + 163/3*x + 298/27 over Rational 
Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 + 163/3*x + 298/27 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 1/3*x^8 - 288*x^7 + 623232*x^5 - 580608*x^4 +
    647212032*x^3 - 144322560*x^2 + 139457396736*x - 82699812864) / (x^8 + 
    3456*x^6 - 3456*x^5 + 2488320*x^4 - 5971968*x^3 - 856977408*x^2 + 
    859963392*x + 61917364224) : (1/216*x^12*y - 1/2*x^12 + 88*x^10*y - 
    2592*x^10 - 440*x^9*y + 2592*x^9 - 570240*x^8*y - 4105728*x^8 + 912384*x^7*y
    + 8957952*x^7 - 276244992*x^6*y - 1294424064*x^6 - 394149888*x^5*y + 
    6449725440*x^5 - 477996318720*x^4*y + 1013896839168*x^4 + 103315046400*x^3*y
    - 2226445221888*x^3 - 201014722953216*x^2*y - 159375295512576*x^2 + 
    147404605095936*x*y + 160489808068608*x - 5831212249645056*y + 
    7703510787293184) / (x^12 + 5184*x^10 - 5184*x^9 + 8211456*x^8 - 
    17915904*x^7 + 2588848128*x^6 - 12899450880*x^5 - 2027793678336*x^4 + 
    4452890443776*x^3 + 318750591025152*x^2 - 320979616137216*x - 
    15407021574586368) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:29:02 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E, 3));
IsogenyFromKernel(E, );

Output: Magma V2.11-2     Sun Aug  1 2004 21:29:02 on modular  [Seed = 3264092949]
   -------------------------------------

[ <12, 1> ]

>> IsogenyFromKernel(E, );;
                        ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:29:48 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E, 3));
_<X>:=PolynomialRing(RationalField());
IsogenyFromKernel(E, );

Output: Magma V2.11-2     Sun Aug  1 2004 21:29:48 on modular  [Seed = 3667264223]
   -------------------------------------

[ <12, 1> ]

>> IsogenyFromKernel(E, );;
                        ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:30:02 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E, 3));
_<X>:=PolynomialRing(RationalField());
IsogenyFromKernel(E, X-12);

Output: Magma V2.11-2     Sun Aug  1 2004 21:30:01 on modular  [Seed = 3533572802]
   -------------------------------------

[ <12, 1> ]
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 - 9*x - 15 over Rational Field
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:31:32 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E, 3));
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
IsogenyFromKernel(E2, X-5);

Output: Magma V2.11-2     Sun Aug  1 2004 21:31:31 on modular  [Seed = 3836230814]
   -------------------------------------

[ <12, 1> ]
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Elliptic curve isogeny from: CrvEll: E2 to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 - 769*x - 8470 over Rational Field
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:34:12 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
Roots(DivisionPolynomial(E, 3));
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
Kernel(g(f));

Output: Magma V2.11-2     Sun Aug  1 2004 21:34:11 on modular  [Seed = 4289930469]
   -------------------------------------

[ <12, 1> ]

>> Kernel(g(f));;
           ^
Runtime error in map application: Element is not in the domain of the map

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:34:24 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
Kernel(g(f));

Output: Magma V2.11-2     Sun Aug  1 2004 21:34:24 on modular  [Seed = 4156239070]
   -------------------------------------


>> Kernel(g(f));;
           ^
Runtime error in map application: Element is not in the domain of the map

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:36:19 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;

Output: Magma V2.11-2     Sun Aug  1 2004 21:36:19 on modular  [Seed = 256103572]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:43:02 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticExtension(RationalField(), -3);
E2;E3;

Output: Magma V2.11-2     Sun Aug  1 2004 21:43:02 on modular  [Seed = 980870932]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)

>> K:=QuadraticExtension(RationalField(), -3);
      ^
User error: Identifier 'QuadraticExtension' has not been declared or assigned
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:44:49 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;

Output: Magma V2.11-2     Sun Aug  1 2004 21:44:48 on modular  [Seed = 864022187]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:46:34 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;
TorsionSubgroup(E);
TorsionSubgroup(E(K));

Output: Magma V2.11-2     Sun Aug  1 2004 21:46:34 on modular  [Seed = 1308791740]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0

>> TorsionSubgroup(E(K));;
                  ^
Runtime error in 'TorsionSubgroup': Bad argument types
Argument types given: SetPtEll[FldQuad]

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:47:56 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;
TorsionSubgroup(E);
E:=ChangeRing(E, K)
TorsionSubgroup(E);

Output: Magma V2.11-2     Sun Aug  1 2004 21:47:55 on modular  [Seed = 1175099909]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0

>> TorsionSubgroup(E);;
   ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:48:51 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;
TorsionSubgroup(E);
E:=ChangeRing(E, K)
pPowerTorsion(E,3);

Output: Magma V2.11-2     Sun Aug  1 2004 21:48:50 on modular  [Seed = 1595114453]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0

>> pPowerTorsion(E,3);;
   ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:49:05 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;
TorsionSubgroup(E);
E:=ChangeRing(E, K)
TorsionSubgroup(E);

Output: Magma V2.11-2     Sun Aug  1 2004 21:49:05 on modular  [Seed = 1461423054]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0

>> TorsionSubgroup(E);;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:49:55 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;
TorsionSubgroup(E);
E:=ChangeBase(E, K)
TorsionSubgroup(E);

Output: Magma V2.11-2     Sun Aug  1 2004 21:49:54 on modular  [Seed = 1864610725]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0

>> TorsionSubgroup(E);;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:53:14 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);
f;g;
K:=QuadraticField(-3);
E2;E3;
TorsionSubgroup(E);
E4:=EllipticCurve([K|(3)^2*96, (3^3*(-16))]);
TorsionSubgroup(E4);

Output: Magma V2.11-2     Sun Aug  1 2004 21:53:12 on modular  [Seed = 2050401786]
   -------------------------------------

Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((1/36*x^3 - x^2 + 84*x + 384) / (x^2 - 24*x + 144) : 
    (1/216*x^3*y - 1/2*x^3 - 1/6*x^2*y + 18*x^2 - 10*x*y - 216*x - 296*y + 864) 
/ (x^3 - 36*x^2 + 432*x - 1728) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 10*x^2 + 177*x - 399) / (x^2 - 10*x + 25) : (x^3*y
    - 15*x^2*y - 77*x*y - 76*x - 87*y + 19) / (x^3 - 15*x^2 + 75*x - 125) : 1)
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 9*x - 15 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0 to CrvEll: E4 given by a rule [no inverse]

Total time: 1.139 seconds, Total memory usage: 3.64MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:58:21 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X=12096));

Output: Magma V2.11-2     Sun Aug  1 2004 21:58:21 on modular  [Seed = 2311411516]
   -------------------------------------


>> IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X=12096));;
                              ^
Runtime error in '*': Bad argument types
Argument types given: RngUPolElt[FldRat], RelElt

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:58:46 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));

Output: Magma V2.11-2     Sun Aug  1 2004 21:58:45 on modular  [Seed = 2211405150]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 - 769*x - 8470 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 13*x^8 + 7692*x^7 - 1162800*x^6 + 
    77789376*x^5 - 2352665088*x^4 + 33935708160*x^3 - 206295662592*x^2 + 
    536366333952*x + 80693231616) / (x^8 - 456*x^7 + 71856*x^6 - 4731264*x^5 + 
    144716544*x^4 - 2057840640*x^3 + 12929310720*x^2 - 29095428096*x + 
    21069103104) : (1/216*x^12*y - 1/2*x^12 - 19/6*x^11*y + 342*x^11 - 64*x^10*y
    - 92880*x^10 + 5944*x^9*y + 12872736*x^9 + 628128*x^8*y - 991626624*x^8 + 
    28294272*x^7*y + 44665468416*x^7 + 733142016*x^6*y - 1202318401536*x^6 + 
    8002437120*x^5*y + 19307253104640*x^5 - 172995969024*x^4*y - 
    181185687060480*x^4 - 9471517360128*x^3*y + 944211425624064*x^3 - 
    183351934844928*x^2*y - 2501059051782144*x^2 - 1556458062741504*x*y + 
    3167444684242944*x + 15671573832794112*y - 1529111226875904) / (x^12 - 
    684*x^11 + 185760*x^10 - 25745472*x^9 + 1983253248*x^8 - 89330936832*x^7 + 
    2404636803072*x^6 - 38614506209280*x^5 + 362371374120960*x^4 - 
    1888422851248128*x^3 + 5002118103564288*x^2 - 6334889368485888*x + 
    3058222453751808) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:59:13 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

E3;
IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));

Output: Magma V2.11-2     Sun Aug  1 2004 21:59:13 on modular  [Seed = 2614576482]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 769*x - 8470 over Rational Field
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 + y = 
x^3 + x^2 - 769*x - 8470 over Rational Field
taking (x : y : 1) to ((1/36*x^9 - 13*x^8 + 7692*x^7 - 1162800*x^6 + 
    77789376*x^5 - 2352665088*x^4 + 33935708160*x^3 - 206295662592*x^2 + 
    536366333952*x + 80693231616) / (x^8 - 456*x^7 + 71856*x^6 - 4731264*x^5 + 
    144716544*x^4 - 2057840640*x^3 + 12929310720*x^2 - 29095428096*x + 
    21069103104) : (1/216*x^12*y - 1/2*x^12 - 19/6*x^11*y + 342*x^11 - 64*x^10*y
    - 92880*x^10 + 5944*x^9*y + 12872736*x^9 + 628128*x^8*y - 991626624*x^8 + 
    28294272*x^7*y + 44665468416*x^7 + 733142016*x^6*y - 1202318401536*x^6 + 
    8002437120*x^5*y + 19307253104640*x^5 - 172995969024*x^4*y - 
    181185687060480*x^4 - 9471517360128*x^3*y + 944211425624064*x^3 - 
    183351934844928*x^2*y - 2501059051782144*x^2 - 1556458062741504*x*y + 
    3167444684242944*x + 15671573832794112*y - 1529111226875904) / (x^12 - 
    684*x^11 + 185760*x^10 - 25745472*x^9 + 1983253248*x^8 - 89330936832*x^7 + 
    2404636803072*x^6 - 38614506209280*x^5 + 362371374120960*x^4 - 
    1888422851248128*x^3 + 5002118103564288*x^2 - 6334889368485888*x + 
    3058222453751808) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 21:59:38 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
Kernel(h);

Output: Magma V2.11-2     Sun Aug  1 2004 21:59:37 on modular  [Seed = 2480894610]
   -------------------------------------

Subgroup scheme of E defined by x^4 - 228*x^3 + 9936*x^2 - 100224*x + 145152

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:00:01 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
E(Kernel(h));

Output: Magma V2.11-2     Sun Aug  1 2004 22:00:00 on modular  [Seed = 2884061827]
   -------------------------------------


>> E(Kernel(h));;
    ^
Runtime error: Bad argument types
Argument types given: SchGrpEll, CrvEll[FldRat]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:00:12 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
Roots(Kernel(h));

Output: Magma V2.11-2     Sun Aug  1 2004 22:00:12 on modular  [Seed = 3380947181]
   -------------------------------------


>> Roots(Kernel(h));;
        ^
Runtime error in 'Roots': Bad argument types
Argument types given: SchGrpEll

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:00:27 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
Kernel(h);

Output: Magma V2.11-2     Sun Aug  1 2004 22:00:27 on modular  [Seed = 3247251698]
   -------------------------------------

Subgroup scheme of E defined by x^4 - 228*x^3 + 9936*x^2 - 100224*x + 145152

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:01:32 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
Degree(h);

Output: Magma V2.11-2     Sun Aug  1 2004 22:01:31 on modular  [Seed = 3667278761]
   -------------------------------------

9

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:03:39 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
TorsionSubgroupScheme(E, 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:03:38 on modular  [Seed = 3550425633]
   -------------------------------------

Subgroup scheme of E defined by x^4 + 1728*x^2 - 1728*x - 248832

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:04:02 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K=Kernel(h);
TorsionSubgroupScheme(K, 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:04:02 on modular  [Seed = 3953593329]
   -------------------------------------


>> K=Kernel(h);
   ^
User error: Identifier 'K' has not been declared or assigned

>> TorsionSubgroupScheme(K, 3);;
                         ^
User error: Identifier 'K' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:04:13 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K:=Kernel(h);
TorsionSubgroupScheme(K, 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:04:13 on modular  [Seed = 3819897846]
   -------------------------------------

Subgroup scheme of E defined by x - 12

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:04:28 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K:=Kernel(h);
TorsionSubgroupScheme(K, 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:04:28 on modular  [Seed = 4223081439]
   -------------------------------------

Subgroup scheme of E defined by x^4 - 228*x^3 + 9936*x^2 - 100224*x + 145152

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:05:27 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K:=Kernel(h);
TorsionSubgroupScheme(K, 5);

Output: Magma V2.11-2     Sun Aug  1 2004 22:05:27 on modular  [Seed = 4105704603]
   -------------------------------------

Subgroup scheme of E defined by 1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:05:40 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K:=Kernel(h);
TorsionSubgroupScheme(K, 27);

Output: Magma V2.11-2     Sun Aug  1 2004 22:05:40 on modular  [Seed = 256110448]
   -------------------------------------

Subgroup scheme of E defined by x^4 - 228*x^3 + 9936*x^2 - 100224*x + 145152

Total time: 0.720 seconds, Total memory usage: 3.41MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:07:34 2004

Input: E:=EllipticCurve([(3)^2*96, (3)^3*(-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K:=Kernel(h);
TorsionSubgroupScheme(K, 27);
Points(K);

Output: Magma V2.11-2     Sun Aug  1 2004 22:07:33 on modular  [Seed = 122415081]
   -------------------------------------

Subgroup scheme of E defined by x^4 - 228*x^3 + 9936*x^2 - 100224*x + 145152
{@ (12 : -108 : 1), (12 : 108 : 1), (0 : 1 : 0) @}

Total time: 0.750 seconds, Total memory usage: 3.41MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:10:42 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E3, g:=IsogenyFromKernel(E2, X-5);

_, h:= IsogenyFromKernel(E, (X-12)*(X^3-216*X^2+7344*X-12096));
K:=Kernel(h);
TorsionSubgroupScheme(K, 27);
Points();

Output: Magma V2.11-2     Sun Aug  1 2004 22:10:41 on modular  [Seed = 795069573]
   -------------------------------------

Subgroup scheme of E defined by 1

>> Points();;
         ^
Runtime error in 'Points': Bad argument types
Argument types given:

Total time: 0.819 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:11:10 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E2;

Output: Magma V2.11-2     Sun Aug  1 2004 22:11:09 on modular  [Seed = 661374097]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 5184*x - 168912 over F

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:11:24 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());
E2, f:=IsogenyFromKernel(E, X-12);
E2;f;

Output: Magma V2.11-2     Sun Aug  1 2004 22:11:23 on modular  [Seed = 1064557823]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 5184*x - 168912 over F
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^3 - 24*x^2 + 1200*x - 1216) / (x^2 - 24*x + 144) : 
    (x^3*y - 36*x^2*y - 624*x*y - 11968*y) / (x^3 - 36*x^2 + 432*x - 1728) : 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:11:48 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

TorsionSubgroup(E);


E2, f:=IsogenyFromKernel(E, X-12);


Output: Magma V2.11-2     Sun Aug  1 2004 22:11:47 on modular  [Seed = 930862303]
   -------------------------------------

Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0 to CrvEll: E given by a rule [no inverse]

Total time: 0.809 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:12:02 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());

TorsionSubgroup(E);


E2, f:=IsogenyFromKernel(E, X-12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:12:01 on modular  [Seed = 1325640885]
   -------------------------------------

Abelian Group of order 1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:12:34 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));


E2, f:=IsogenyFromKernel(E, X-12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:12:33 on modular  [Seed = 1191945565]
   -------------------------------------

[ <4, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:12:52 2004

Input: F:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Pints(E,4);

E2, f:=IsogenyFromKernel(E, X-4);

Output: Magma V2.11-2     Sun Aug  1 2004 22:12:51 on modular  [Seed = 1595129207]
   -------------------------------------

[ <4, 1> ]

>> Pints(E,4);
   ^
User error: Identifier 'Pints' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:13:05 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4);

Output: Magma V2.11-2     Sun Aug  1 2004 22:13:05 on modular  [Seed = 1461433709]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:13:19 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4);
E2;

Output: Magma V2.11-2     Sun Aug  1 2004 22:13:18 on modular  [Seed = 1864600922]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]
Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:13:36 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4);
E2; TorsionGubgrou(E2);

Output: Magma V2.11-2     Sun Aug  1 2004 22:13:35 on modular  [Seed = 1730905404]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]
Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F

>> E2; TorsionGubgrou(E2);;
       ^
User error: Identifier 'TorsionGubgrou' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:13:47 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4);
E2; TorsionGubgroup(E2);

Output: Magma V2.11-2     Sun Aug  1 2004 22:13:47 on modular  [Seed = 2134089007]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]
Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F

>> E2; TorsionGubgroup(E2);;
       ^
User error: Identifier 'TorsionGubgroup' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:14:01 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4);
E2; TorsionSubgroup(E2);

Output: Magma V2.11-2     Sun Aug  1 2004 22:14:00 on modular  [Seed = 2000393492]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]
Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0 to CrvEll: E2 given by a rule [no inverse]

Total time: 0.819 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:14:32 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4);
Roots(DivisionPolynomial(E2, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 22:14:31 on modular  [Seed = 2411949315]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]
[ <-12, 1>, <64, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:14:50 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());

Roots(DivisionPolynomial(E, 3));
Points(E,4);

E2, f:=IsogenyFromKernel(E, X-4); E2;
Roots(DivisionPolynomial(E2, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 22:14:49 on modular  [Seed = 2278253845]
   -------------------------------------

[ <4, 1> ]
[ (4 : -12*a : 1), (4 : 12*a : 1) ]
Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
[ <-12, 1>, <64, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:15:56 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
degree(f);
Roots(DivisionPolynomial(E2, 3));

points(E,-12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:15:56 on modular  [Seed = 2530899009]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F

>> degree(f);
   ^
User error: Identifier 'degree' has not been declared or assigned
[ <-12, 1>, <64, 1> ]

>> points(E,-12);;
   ^
User error: Identifier 'points' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:16:08 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
Degree(f);
Roots(DivisionPolynomial(E2, 3));

points(E,-12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:16:07 on modular  [Seed = 2934066242]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
3
[ <-12, 1>, <64, 1> ]

>> points(E,-12);;
   ^
User error: Identifier 'points' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:16:19 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
Degree(f);
Roots(DivisionPolynomial(E2, 3));

Points(E,-12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:16:18 on modular  [Seed = 2800370783]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
3
[ <-12, 1>, <64, 1> ]
[]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:16:34 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
Degree(f);
Roots(DivisionPolynomial(E2, 3));

Points(E,64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:16:33 on modular  [Seed = 3203554228]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
3
[ <-12, 1>, <64, 1> ]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:18:23 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-109);
E2:=EllipticCurve([F2|-1344,-20176]);
Roots(DivisionPolynomial(E2, 3));

Points(E,64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:18:22 on modular  [Seed = 3414634158]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
[ <-12, 1>, <64, 1> ]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:18:36 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-109);
E2:=EllipticCurve([F2|-1344,-20176]);
Roots(DivisionPolynomial(E2, 3));

Points(E,-12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:18:35 on modular  [Seed = 3280938675]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
[ <-12, 1>, <64, 1> ]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:19:21 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(10147);
E2:=EllipticCurve([F2|-1344,-20176]);
Roots(DivisionPolynomial(E2, 3));

Points(E,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:19:20 on modular  [Seed = 3684122232]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
[ <-12, 1>, <64, 1> ]
[]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:19:41 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(10147);
E2:=EllipticCurve([F2|-1344,-20176]);
TorsionSubgroup(E2);

Points(E,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:19:40 on modular  [Seed = 3550426724]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to CrvEll: E2 given by a rule [no 
inverse]
[]
[]

Total time: 0.750 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:20:19 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-109);
E2:=EllipticCurve([F2|-1344,-20176]);
TorsionSubgroup(E2);

Points(E,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:20:19 on modular  [Seed = 4289927703]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to CrvEll: E2 given by a rule [no 
inverse]
[]
[]

Total time: 0.789 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:21:26 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
TorsionSubgroup(E2);

Points(E,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:21:25 on modular  [Seed = 4156232665]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
    3*$.1 = 0 to CrvEll: E2 given by a rule [no inverse]
[]
[]

Total time: 0.809 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:22:10 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
Roots(DivisionPolynomial(E, 3));

Points(E,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:22:10 on modular  [Seed = 239266390]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
[ <4, 1> ]
[]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:22:48 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
IsogenyFromKernel(E2, X-4);

Points(E,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:22:47 on modular  [Seed = 105570939]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over F2
Elliptic curve isogeny from: CrvEll: E2 to Elliptic Curve defined by y^2 = x^3 +
11616*x + 766064 over F2
taking (x : y : 1) to ((x^3 - 8*x^2 - 2576*x - 91584) / (x^2 - 8*x + 16) : 
    (x^3*y - 12*x^2*y + 2640*x*y + 193472*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)
[]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:23:42 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
IsogenyFromKernel(E2, X-4);

Points(E2,-12); Points(E, 64);

Output: Magma V2.11-2     Sun Aug  1 2004 22:23:41 on modular  [Seed = 341373107]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over F2
Elliptic curve isogeny from: CrvEll: E2 to Elliptic Curve defined by y^2 = x^3 +
11616*x + 766064 over F2
taking (x : y : 1) to ((x^3 - 8*x^2 - 2576*x - 91584) / (x^2 - 8*x + 16) : 
    (x^3*y - 12*x^2*y + 2640*x*y + 193472*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)
[ (-12 : -76*b : 1), (-12 : 76*b : 1) ]
[]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:24:13 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
E3, g:=IsogenyFromKernel(E2, X-4);
f;g;

Output: Magma V2.11-2     Sun Aug  1 2004 22:24:13 on modular  [Seed = 744540395]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 
1344*x - 20176 over F
taking (x : y : 1) to ((x^3 - 8*x^2 + 304*x + 576) / (x^2 - 8*x + 16) : (x^3*y -
    12*x^2*y - 240*x*y - 2368*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 8*x^2 - 2576*x - 91584) / (x^2 - 8*x + 16) : 
    (x^3*y - 12*x^2*y + 2640*x*y + 193472*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:26:12 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
E3, g:=IsogenyFromKernel(E2, X-4);
f;g;

E4, h:=IsogenyFromKernel(E, (x-4)*(x^3-12*x^2+336*x+512));

Output: Magma V2.11-2     Sun Aug  1 2004 22:26:11 on modular  [Seed = 980868467]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 
1344*x - 20176 over F
taking (x : y : 1) to ((x^3 - 8*x^2 + 304*x + 576) / (x^2 - 8*x + 16) : (x^3*y -
    12*x^2*y - 240*x*y - 2368*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 8*x^2 - 2576*x - 91584) / (x^2 - 8*x + 16) : 
    (x^3*y - 12*x^2*y + 2640*x*y + 193472*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)

>> E4, h:=IsogenyFromKernel(E, (x-4)*(x^3-12*x^2+336*x+512));;
                                ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:26:31 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
E3, g:=IsogenyFromKernel(E2, X-4);
f;g;

E4, h:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));

Output: Magma V2.11-2     Sun Aug  1 2004 22:26:30 on modular  [Seed = 847172974]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 
1344*x - 20176 over F
taking (x : y : 1) to ((x^3 - 8*x^2 + 304*x + 576) / (x^2 - 8*x + 16) : (x^3*y -
    12*x^2*y - 240*x*y - 2368*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)
Elliptic curve isogeny from: CrvEll: E2 to CrvEll: E3
taking (x : y : 1) to ((x^3 - 8*x^2 - 2576*x - 91584) / (x^2 - 8*x + 16) : 
    (x^3*y - 12*x^2*y + 2640*x*y + 193472*y) / (x^3 - 12*x^2 + 48*x - 64) : 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:27:02 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());


E2, f:=IsogenyFromKernel(E, X-4); E2;
F2<b>:=QuadraticField(-1);
E2:=EllipticCurve([F2|-1344,-20176]);
E3, g:=IsogenyFromKernel(E2, X-4);

E3, h:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E3;
Degree(h);

Output: Magma V2.11-2     Sun Aug  1 2004 22:27:02 on modular  [Seed = 1241951542]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1344*x - 20176 over F
Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over F
9

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:28:01 2004

Input: F<a>:=QuadraticField(3);
E:=EllipticCurve([F|96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
nTorsionSubgroup(Kernel(f), 3);


Output: Magma V2.11-2     Sun Aug  1 2004 22:28:00 on modular  [Seed = 1108256248]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over F

>> nTorsionSubgroup(Kernel(f), 3);
                   ^
Runtime error in 'nTorsionSubgroup': Bad argument types
Argument types given: SchGrpEll, RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:28:29 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
nTorsionSubgroup(Kernel(f), 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:28:28 on modular  [Seed = 1528282269]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field

>> nTorsionSubgroup(Kernel(f), 3);;
                   ^
Runtime error in 'nTorsionSubgroup': Bad argument types
Argument types given: SchGrpEll, RngIntElt

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:29:13 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
Points(Kernel(f));

Output: Magma V2.11-2     Sun Aug  1 2004 22:29:13 on modular  [Seed = 1461432484]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
{@ (0 : 1 : 0) @}

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:30:17 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
TorsionSubGroupScheme(Kernel(f), 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:30:16 on modular  [Seed = 1814071902]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field

>> TorsionSubGroupScheme(Kernel(f), 3);;
   ^
User error: Identifier 'TorsionSubGroupScheme' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:30:26 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
TorsionSubgroupScheme(Kernel(f), 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:30:25 on modular  [Seed = 1680376367]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Subgroup scheme of E defined by x - 4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:30:42 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
TorsionSubgroupScheme(Kernel(f), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:30:41 on modular  [Seed = 2083559975]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Subgroup scheme of E defined by x - 4

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:31:11 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
TorsionSubgroupScheme(Kernel(f), 12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:31:10 on modular  [Seed = 1949864464]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Subgroup scheme of E defined by x - 4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:31:25 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
Degree(f);
TorsionSubgroupScheme(Kernel(f), 12);

Output: Magma V2.11-2     Sun Aug  1 2004 22:31:25 on modular  [Seed = 2361420539]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
9
Subgroup scheme of E defined by x - 4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:31:37 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);

Output: Magma V2.11-2     Sun Aug  1 2004 22:31:36 on modular  [Seed = 2227724806]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
9
Subgroup scheme of E defined by x - 4

Total time: 0.689 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:32:03 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);

Output: Magma V2.11-2     Sun Aug  1 2004 22:32:02 on modular  [Seed = 2630908468]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4

Total time: 0.689 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:33:14 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);

Output: Magma V2.11-2     Sun Aug  1 2004 22:33:13 on modular  [Seed = 2497213047]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4

Total time: 0.689 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:34:10 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
DivisionPolynomial(E, 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:34:09 on modular  [Seed = 2900379015]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4
3*X^4 + 576*X^2 - 192*X - 9216
3*X^4 + 576*X^2 - 192*X - 9216
1

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:34:42 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
DivisionPolynomial(E, 3);

Output: Magma V2.11-2     Sun Aug  1 2004 22:34:42 on modular  [Seed = 3119862001]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4
3*X^4 + 576*X^2 - 192*X - 9216
3*X^4 + 576*X^2 - 192*X - 9216
1

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:35:01 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
Roots(DivisionPolynomial(E, 3));

Output: Magma V2.11-2     Sun Aug  1 2004 22:35:01 on modular  [Seed = 2986170606]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4
[ <4, 1> ]

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:35:21 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
Roots(DivisionPolynomial(E, 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:35:20 on modular  [Seed = 3464636332]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4

>> Roots(DivisionPolynomial(E, 9);;
                                 ^
User error: bad syntax

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:35:34 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
Roots(DivisionPolynomial(E, 9));

Output: Magma V2.11-2     Sun Aug  1 2004 22:35:34 on modular  [Seed = 3330944954]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4
[ <4, 1> ]

Total time: 0.750 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:35:49 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-12*X^2+336*X+512));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
DivisionPolynomial(E, 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:35:48 on modular  [Seed = 3734124368]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 11616*x + 766064 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 32*x^8 - 1280*x^7 - 49664*x^6 + 1220608*x^5 - 
    10342400*x^4 + 83537920*x^3 - 127533056*x^2 + 1021050880*x - 606339072) / 
    (x^8 - 32*x^7 + 1024*x^6 - 13952*x^5 + 169984*x^4 - 573440*x^3 - 880640*x^2 
    + 3407872*x + 4194304) : (x^12*y - 48*x^11*y + 4224*x^10*y + 64832*x^9*y - 
    4995072*x^8*y + 28606464*x^7*y - 96301056*x^6*y + 2338652160*x^5*y - 
    42677305344*x^4*y + 199701561344*x^3*y - 1747716145152*x^2*y + 
    2303226544128*x*y - 3100060418048*y) / (x^12 - 48*x^11 + 1920*x^10 - 
    43456*x^9 + 811008*x^8 - 9437184*x^7 + 83079168*x^6 - 315555840*x^5 - 
    259522560*x^4 + 3148611584*x^3 + 578813952*x^2 - 10468982784*x - 8589934592)
: 1)
Subgroup scheme of E defined by x^4 - 16*x^3 + 384*x^2 - 832*x - 2048
9
Subgroup scheme of E defined by x - 4
9*X^40 + 100224*X^38 - 365184*X^37 - 295888896*X^36 + 128065536*X^35 - 
    383271063552*X^34 + 538390167552*X^33 - 131478189244416*X^32 - 
    82388352761856*X^31 - 110553217703608320*X^30 + 65159376666624000*X^29 - 
    38507629927402045440*X^28 + 60048882662476087296*X^27 - 
    4345035020156962603008*X^26 + 12764066201557562032128*X^25 + 
    331583177927863346135040*X^24 + 1140403313363202405826560*X^23 + 
    176751578802505608163491840*X^22 - 70539510715464872487813120*X^21 + 
    24364421426777736310067036160*X^20 - 25301165488675227302551879680*X^19 + 
    1687169756500655663572032946176*X^18 - 1821367182247958479561065234432*X^17 
    + 84727967467238783575303504527360*X^16 - 
    49780321741568463706140690087936*X^15 + 
    4960552277882164871558833970872320*X^14 - 
    2819923464177140811012036643258368*X^13 + 
    227292605048546553150906154673504256*X^12 - 
    244833794792890416320970895159984128*X^11 + 
    3936193473097542527059194751796379648*X^10 - 
    5668023400755313435099163155400491008*X^9 - 
    8508179940825060838741951509027618816*X^8 - 
    39986775878405556901404034261680390144*X^7 - 
    1350643762654277857973926298199986798592*X^6 + 
    1074576672903661103663880386853916901376*X^5 - 
    4123649420671238307952633217219404234752*X^4 + 
    1226098746935940286302635452784393060352*X^3 - 
    25235648790330883717100267313383778287616*X^2 + 
    8380538851543875202385890771352961417216*X + 
    3798981951832736916589500011299366502400
9*X^40 + 100224*X^38 - 365184*X^37 - 295888896*X^36 + 128065536*X^35 - 
    383271063552*X^34 + 538390167552*X^33 - 131478189244416*X^32 - 
    82388352761856*X^31 - 110553217703608320*X^30 + 65159376666624000*X^29 - 
    38507629927402045440*X^28 + 60048882662476087296*X^27 - 
    4345035020156962603008*X^26 + 12764066201557562032128*X^25 + 
    331583177927863346135040*X^24 + 1140403313363202405826560*X^23 + 
    176751578802505608163491840*X^22 - 70539510715464872487813120*X^21 + 
    24364421426777736310067036160*X^20 - 25301165488675227302551879680*X^19 + 
    1687169756500655663572032946176*X^18 - 1821367182247958479561065234432*X^17 
    + 84727967467238783575303504527360*X^16 - 
    49780321741568463706140690087936*X^15 + 
    4960552277882164871558833970872320*X^14 - 
    2819923464177140811012036643258368*X^13 + 
    227292605048546553150906154673504256*X^12 - 
    244833794792890416320970895159984128*X^11 + 
    3936193473097542527059194751796379648*X^10 - 
    5668023400755313435099163155400491008*X^9 - 
    8508179940825060838741951509027618816*X^8 - 
    39986775878405556901404034261680390144*X^7 - 
    1350643762654277857973926298199986798592*X^6 + 
    1074576672903661103663880386853916901376*X^5 - 
    4123649420671238307952633217219404234752*X^4 + 
    1226098746935940286302635452784393060352*X^3 - 
    25235648790330883717100267313383778287616*X^2 + 
    8380538851543875202385890771352961417216*X + 
    3798981951832736916589500011299366502400
1

Total time: 0.689 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:38:10 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X+448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);
DivisionPolynomial(E, 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:38:10 on modular  [Seed = 3583589837]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14004496 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1543552*x^6 + 34201856*x^5 -
    320465920*x^4 + 1297211392*x^3 - 1689878528*x^2 + 2746679296*x - 2217738240)
/ (x^8 - 152*x^7 + 7984*x^6 - 173440*x^5 + 1643264*x^4 - 5945344*x^3 + 
    3973120*x^2 + 10092544*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    104000*x^9*y - 163584*x^8*y + 50568192*x^7*y - 429785088*x^6*y + 
    33562460160*x^5*y - 466655772672*x^4*y + 3436884262912*x^3*y - 
    17082098909184*x^2*y + 23584705609728*x*y - 17412351066112*y) / (x^12 - 
    228*x^11 + 20640*x^10 - 950848*x^9 + 24065280*x^8 - 344521728*x^7 + 
    2744082432*x^6 - 11172151296*x^5 + 17419862016*x^4 + 10363863040*x^3 - 
    31995199488*x^2 - 27128758272*x - 5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 2816*x - 1792
9
Subgroup scheme of E defined by x - 4
9*X^40 + 100224*X^38 - 365184*X^37 - 295888896*X^36 + 128065536*X^35 - 
    383271063552*X^34 + 538390167552*X^33 - 131478189244416*X^32 - 
    82388352761856*X^31 - 110553217703608320*X^30 + 65159376666624000*X^29 - 
    38507629927402045440*X^28 + 60048882662476087296*X^27 - 
    4345035020156962603008*X^26 + 12764066201557562032128*X^25 + 
    331583177927863346135040*X^24 + 1140403313363202405826560*X^23 + 
    176751578802505608163491840*X^22 - 70539510715464872487813120*X^21 + 
    24364421426777736310067036160*X^20 - 25301165488675227302551879680*X^19 + 
    1687169756500655663572032946176*X^18 - 1821367182247958479561065234432*X^17 
    + 84727967467238783575303504527360*X^16 - 
    49780321741568463706140690087936*X^15 + 
    4960552277882164871558833970872320*X^14 - 
    2819923464177140811012036643258368*X^13 + 
    227292605048546553150906154673504256*X^12 - 
    244833794792890416320970895159984128*X^11 + 
    3936193473097542527059194751796379648*X^10 - 
    5668023400755313435099163155400491008*X^9 - 
    8508179940825060838741951509027618816*X^8 - 
    39986775878405556901404034261680390144*X^7 - 
    1350643762654277857973926298199986798592*X^6 + 
    1074576672903661103663880386853916901376*X^5 - 
    4123649420671238307952633217219404234752*X^4 + 
    1226098746935940286302635452784393060352*X^3 - 
    25235648790330883717100267313383778287616*X^2 + 
    8380538851543875202385890771352961417216*X + 
    3798981951832736916589500011299366502400
9*X^40 + 100224*X^38 - 365184*X^37 - 295888896*X^36 + 128065536*X^35 - 
    383271063552*X^34 + 538390167552*X^33 - 131478189244416*X^32 - 
    82388352761856*X^31 - 110553217703608320*X^30 + 65159376666624000*X^29 - 
    38507629927402045440*X^28 + 60048882662476087296*X^27 - 
    4345035020156962603008*X^26 + 12764066201557562032128*X^25 + 
    331583177927863346135040*X^24 + 1140403313363202405826560*X^23 + 
    176751578802505608163491840*X^22 - 70539510715464872487813120*X^21 + 
    24364421426777736310067036160*X^20 - 25301165488675227302551879680*X^19 + 
    1687169756500655663572032946176*X^18 - 1821367182247958479561065234432*X^17 
    + 84727967467238783575303504527360*X^16 - 
    49780321741568463706140690087936*X^15 + 
    4960552277882164871558833970872320*X^14 - 
    2819923464177140811012036643258368*X^13 + 
    227292605048546553150906154673504256*X^12 - 
    244833794792890416320970895159984128*X^11 + 
    3936193473097542527059194751796379648*X^10 - 
    5668023400755313435099163155400491008*X^9 - 
    8508179940825060838741951509027618816*X^8 - 
    39986775878405556901404034261680390144*X^7 - 
    1350643762654277857973926298199986798592*X^6 + 
    1074576672903661103663880386853916901376*X^5 - 
    4123649420671238307952633217219404234752*X^4 + 
    1226098746935940286302635452784393060352*X^3 - 
    25235648790330883717100267313383778287616*X^2 + 
    8380538851543875202385890771352961417216*X + 
    3798981951832736916589500011299366502400
1

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:38:26 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X+448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);

Output: Magma V2.11-2     Sun Aug  1 2004 22:38:26 on modular  [Seed = 3986752965]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14004496 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1543552*x^6 + 34201856*x^5 -
    320465920*x^4 + 1297211392*x^3 - 1689878528*x^2 + 2746679296*x - 2217738240)
/ (x^8 - 152*x^7 + 7984*x^6 - 173440*x^5 + 1643264*x^4 - 5945344*x^3 + 
    3973120*x^2 + 10092544*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    104000*x^9*y - 163584*x^8*y + 50568192*x^7*y - 429785088*x^6*y + 
    33562460160*x^5*y - 466655772672*x^4*y + 3436884262912*x^3*y - 
    17082098909184*x^2*y + 23584705609728*x*y - 17412351066112*y) / (x^12 - 
    228*x^11 + 20640*x^10 - 950848*x^9 + 24065280*x^8 - 344521728*x^7 + 
    2744082432*x^6 - 11172151296*x^5 + 17419862016*x^4 + 10363863040*x^3 - 
    31995199488*x^2 - 27128758272*x - 5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 2816*x - 1792
9
Subgroup scheme of E defined by x - 4

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:38:48 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 27);

Output: Magma V2.11-2     Sun Aug  1 2004 22:38:47 on modular  [Seed = 3853061592]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792

Total time: 0.699 seconds, Total memory usage: 3.60MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:39:55 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);
TorsionSubgroupScheme(Kernel(f), 9);
TorsionSubgroupScheme(Kernel(f), 720);

Output: Magma V2.11-2     Sun Aug  1 2004 22:39:34 on modular  [Seed = 4256241041]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:40:20 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);
TorsionSubgroupScheme(Kernel(f), 9);


Output: Magma V2.11-2     Sun Aug  1 2004 22:40:19 on modular  [Seed = 508753536]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 109344*x - 14172496 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^7 - 144*x^6 + 28704*x^5 - 1245632*x^4 + 21567744*x^3 -
    118751232*x^2 + 204722176*x + 2801664) / (x^6 - 144*x^5 + 6816*x^4 - 
    118400*x^3 + 730368*x^2 - 731136*x + 200704) : (x^9*y - 216*x^8*y - 
    3888*x^7*y - 48576*x^6*y + 5951232*x^5*y - 69285888*x^4*y + 1707663360*x^3*y
    + 15216132096*x^2*y - 59845312512*x*y - 96287850496*y) / (x^9 - 216*x^8 + 
    18000*x^7 - 727104*x^6 + 14881536*x^5 - 152985600*x^4 + 701865984*x^3 - 
    938262528*x^2 + 491323392*x - 89915392) : 1)
Subgroup scheme of E defined by x^3 - 72*x^2 + 816*x - 448
7
Subgroup scheme of E defined by 1
Subgroup scheme of E defined by x^3 - 72*x^2 + 816*x - 448

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:40:58 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);
TorsionSubgroupScheme(Kernel(f), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:40:57 on modular  [Seed = 325057447]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:42:34 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);

E:=EllipticCurve([0,-1]);
E2, f:=IsogenyFromKernel(E, (X-1)*(X+1)*X);
f; Degree(f); Kernel(f);
TorsionSubgroupScheme(Kernel(f), 2);
TorsionSubgroupScheme(Kernel(f), 4);
TorsionSubgroupScheme(Kernel(f), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:42:33 on modular  [Seed = 728219711]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4

>> E2, f:=IsogenyFromKernel(E, (X-1)*(X+1)*X);
                           ^
Runtime error in 'IsogenyFromKernel': Can't push polynomial through the isogeny
Elliptic curve isogeny from: Elliptic Curve defined by y^2 = x^3 + 96*x - 16 
over Rational Field to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
9
Subgroup scheme of Elliptic Curve defined by y^2 = x^3 + 96*x - 16 over Rational
Field defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
Subgroup scheme of Elliptic Curve defined by y^2 = x^3 + 96*x - 16 over Rational
Field defined by 1
Subgroup scheme of Elliptic Curve defined by y^2 = x^3 + 96*x - 16 over Rational
Field defined by 1
Subgroup scheme of Elliptic Curve defined by y^2 = x^3 + 96*x - 16 over Rational
Field defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:43:53 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);

e:=EllipticCurve([0,-1]);
e2, F:=IsogenyFromKernel(e, (X-1)*(X+1)*X);
F; Degree(F); Kernel(F);
TorsionSubgroupScheme(Kernel(F), 2);
TorsionSubgroupScheme(Kernel(F), 4);
TorsionSubgroupScheme(Kernel(F), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:43:52 on modular  [Seed = 577685831]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4

>> e2, F:=IsogenyFromKernel(e, (X-1)*(X+1)*X);
                           ^
Runtime error in 'IsogenyFromKernel': Can't push polynomial through the isogeny

>> F; Degree(F); Kernel(F);
   ^
User error: Identifier 'F' has not been declared or assigned

>> F; Degree(F); Kernel(F);
             ^
User error: Identifier 'F' has not been declared or assigned

>> F; Degree(F); Kernel(F);
                        ^
User error: Identifier 'F' has not been declared or assigned

>> TorsionSubgroupScheme(Kernel(F), 2);
                                ^
User error: Identifier 'F' has not been declared or assigned

>> TorsionSubgroupScheme(Kernel(F), 4);
                                ^
User error: Identifier 'F' has not been declared or assigned

>> TorsionSubgroupScheme(Kernel(F), 9);;
                                ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:44:04 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);

e:=EllipticCurve([0,-1]);
e2, F:=IsogenyFromKernel(e, (X-1)*(X+1)*X);
F; Degree(F); Kernel(F);
TorsionSubgroupScheme(Kernel(F), 2);
TorsionSubgroupScheme(Kernel(F), 4);
TorsionSubgroupScheme(Kernel(F), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:44:04 on modular  [Seed = 980865347]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4

>> e2, F:=IsogenyFromKernel(e, (X-1)*(X+1)*X);
                           ^
Runtime error in 'IsogenyFromKernel': Can't push polynomial through the isogeny

>> F; Degree(F); Kernel(F);
   ^
User error: Identifier 'F' has not been declared or assigned

>> F; Degree(F); Kernel(F);
             ^
User error: Identifier 'F' has not been declared or assigned

>> F; Degree(F); Kernel(F);
                        ^
User error: Identifier 'F' has not been declared or assigned

>> TorsionSubgroupScheme(Kernel(F), 2);
                                ^
User error: Identifier 'F' has not been declared or assigned

>> TorsionSubgroupScheme(Kernel(F), 4);
                                ^
User error: Identifier 'F' has not been declared or assigned

>> TorsionSubgroupScheme(Kernel(F), 9);;
                                ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:44:25 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);

e:=EllipticCurve([-1,0]);
e2, F:=IsogenyFromKernel(e, (X-1)*(X+1)*X);
F; Degree(F); Kernel(F);
TorsionSubgroupScheme(Kernel(F), 2);
TorsionSubgroupScheme(Kernel(F), 4);
TorsionSubgroupScheme(Kernel(F), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:44:25 on modular  [Seed = 847174070]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4
Elliptic curve isogeny from: CrvEll: e to CrvEll: e2
taking (x : y : 1) to ((x^4 + 2*x^2 + 1) / (x^3 - x) : (x^6*y - 5*x^4*y - 
    5*x^2*y + y) / (x^6 - 2*x^4 + x^2) : 1)
4
Subgroup scheme of e defined by x^3 - x
Subgroup scheme of e defined by x^3 - x
Subgroup scheme of e defined by x^3 - x
Subgroup scheme of e defined by 1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 22:45:01 2004

Input: E:=EllipticCurve([96, (-16)]);
_<X>:=PolynomialRing(RationalField());



E2, f:=IsogenyFromKernel(E, (X-4)*(X^3-72*X^2+816*X-448));E2;
f;
Kernel(f);
Degree(f);
TorsionSubgroupScheme(Kernel(f), 3);TorsionSubgroupScheme(Kernel(f), 9);

e:=EllipticCurve([-1,0]);
e2, F:=IsogenyFromKernel(e, (X-1)*(X+1)*X);
F; Degree(F); Kernel(F);
TorsionSubgroupScheme(Kernel(F), 2);
TorsionSubgroupScheme(Kernel(F), 4);
TorsionSubgroupScheme(Kernel(F), 9);

Output: Magma V2.11-2     Sun Aug  1 2004 22:45:01 on modular  [Seed = 1241948650]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 110784*x - 14192656 over Rational Field
Elliptic curve isogeny from: CrvEll: E to CrvEll: E2
taking (x : y : 1) to ((x^9 - 152*x^8 + 30160*x^7 - 1518464*x^6 + 33872128*x^5 -
    341396480*x^4 + 1641963520*x^3 - 3324870656*x^2 + 2889809920*x + 160432128) 
/ (x^8 - 152*x^7 + 7984*x^6 - 175232*x^5 + 1786624*x^4 - 8468480*x^3 + 
    17735680*x^2 - 13303808*x + 3211264) : (x^12*y - 228*x^11*y - 1536*x^10*y + 
    47552*x^9*y + 1675008*x^8*y + 25150464*x^7*y + 217227264*x^6*y + 
    790364160*x^5*y - 5695340544*x^4*y - 103939833856*x^3*y - 670697521152*x^2*y
    - 1897830285312*x*y + 6369587494912*y) / (x^12 - 228*x^11 + 20640*x^10 - 
    953536*x^9 + 24484608*x^8 - 367617024*x^7 + 3298541568*x^6 - 17656381440*x^5
    + 55231119360*x^4 - 95941820416*x^3 + 84711309312*x^2 - 35760635904*x + 
    5754585088) : 1)
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
9
Subgroup scheme of E defined by x - 4
Subgroup scheme of E defined by x^4 - 76*x^3 + 1104*x^2 - 3712*x + 1792
Elliptic curve isogeny from: CrvEll: e to CrvEll: e2
taking (x : y : 1) to ((x^4 + 2*x^2 + 1) / (x^3 - x) : (x^6*y - 5*x^4*y - 
    5*x^2*y + y) / (x^6 - 2*x^4 + x^2) : 1)
4
Subgroup scheme of e defined by x^3 - x
Subgroup scheme of e defined by x^3 - x
Subgroup scheme of e defined by x^3 - x
Subgroup scheme of e defined by 1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:05:49 2004

Input: P2<x,j> := PolynomialRing(Integers(),2);

P2!CanonicalModularPolynomial(11);

Output: Magma V2.11-2     Sun Aug  1 2004 23:05:49 on modular  [Seed = 2067240443]
   -------------------------------------

x^12 - 5940*x^11 + 14701434*x^10 - 139755*x^9*j - 19264518900*x^9 + 
    723797800*x^8*j + 13849401061815*x^8 + 67496*x^7*j^2 - 1327909897380*x^7*j -
    4875351166521000*x^7 + 2291468355*x^6*j^2 + 1036871615940600*x^6*j + 
    400050977713074380*x^6 - 5346*x^5*j^3 + 4231762569540*x^5*j^2 - 
    310557763459301490*x^5*j + 122471154456433615800*x^5 + 161201040*x^4*j^3 + 
    755793774757450*x^4*j^2 + 17309546645642506200*x^4*j + 
    6513391734069824031615*x^4 + 132*x^3*j^4 - 49836805205*x^3*j^3 + 
    6941543075967060*x^3*j^2 - 64815179429761398660*x^3*j + 
    104264884483130180036700*x^3 + 468754*x^2*j^4 + 51801406800*x^2*j^3 + 
    214437541826475*x^2*j^2 + 77380735840203400*x^2*j + 804140494949359194*x^2 -
    x*j^5 + 3732*x*j^4 - 4586706*x*j^3 + 2059075976*x*j^2 - 253478654715*x*j + 
    2067305393340*x + 1771561

Total time: 0.569 seconds, Total memory usage: 3.51MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:07:18 2004

Input: P2<x,j> := PolynomialRing(Integers(),2);

P2!CanonicalModularPolynomial(3);

Output: Magma V2.11-2     Sun Aug  1 2004 23:07:18 on modular  [Seed = 2395103333]
   -------------------------------------

x^4 + 36*x^3 + 270*x^2 - x*j + 756*x + 729

Total time: 0.549 seconds, Total memory usage: 3.51MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:10:19 2004

Input: A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
X;

Output: Magma V2.11-2     Sun Aug  1 2004 23:10:19 on modular  [Seed = 2194567956]
   -------------------------------------

Modular Curve over Rational Field defined by
$.1^12 - $.1^11*$.2^11 + 8184*$.1^11*$.2^10 - 28278756*$.1^11*$.2^9 + 
    53686822816*$.1^11*$.2^8 - 61058988656490*$.1^11*$.2^7 + 
    42570393135641712*$.1^11*$.2^6 - 17899526272883039048*$.1^11*$.2^5 + 
    4297837238774928467520*$.1^11*$.2^4 - 529134841844639613861795*$.1^11*$.2^3 
    + 27209811658056645815522600*$.1^11*$.2^2 - 
    374642006356701393515817612*$.1^11*$.2 + 296470902355240575283200000*$.1^11 
    + 8184*$.1^10*$.2^11 + 1608331026427734378*$.1^10*$.2^10 + 
    30134971854812981978547264*$.1^10*$.2^9 + 
    12407796387712093514736413264496*$.1^10*$.2^8 + 
    645470833566425875717489618904152240*$.1^10*$.2^7 + 
    7848482999227584325448694633580010490867*$.1^10*$.2^6 + 
    28890545335855949285086003898461917345026160*$.1^10*$.2^5 + 
    35372414460361796790312007060191890803134127320*$.1^10*$.2^4 + 
    14131378888778142661582693947549844785863493325800*$.1^10*$.2^3 + 
    1587728122949690904187089204116332301200302760915266*$.1^10*$.2^2 + 
    33446467926379842030532687838341039552110187929600000*$.1^10*$.2 + 
    29298331981110197366602526090413106879319244800000000*$.1^10 - 
    28278756*$.1^9*$.2^11 + 30134971854812981978547264*$.1^9*$.2^10 - 
    573388748843683532691009051194955437*$.1^9*$.2^9 + 
    24228593349948582884094197811518266845689352*$.1^9*$.2^8 - 
    51135193038502008150804190472844550800569441050500*$.1^9*$.2^7 + 
    14690460927260804690751501000083244161647396386205851440*$.1^9*$.2^6 - 
    994774826102691960922410649494629085486856242714439003812180*$.1^9*$.2^5 + 
    22148485195925584385790489089697473918894904664093860668378292000*$.1^9*$.2\
    ^4 - 199188452917764242987050083089364860927274115441197382331866126825820*\
    $.1^9*$.2^3 + 8044364183079957387401325981668933650994688420897059005250506\
    27891200000*$.1^9*$.2^2 - 1458178254597295207839980786768623018650234306932\
    331393013634952069120000000*$.1^9*$.2 + 
    965122546660349298406724063940884252743873633176129290337528305418240000000\
    000*$.1^9 + 53686822816*$.1^8*$.2^11 + 
    12407796387712093514736413264496*$.1^8*$.2^10 + 
    24228593349948582884094197811518266845689352*$.1^8*$.2^9 + 
    29211180544704743418963619709378403797452606969172658*$.1^8*$.2^8 + 
    636861023141767565580039581191818069063579259290464688398880*$.1^8*$.2^7 + 
    987807801334019988631500819088661487281712947788833523552559299560*$.1^8*$.\
    2^6 + 208334210762751500564946204497082337222910461284651050215872586641463\
    200*$.1^8*$.2^5 + 849850070872519389071832965523057496281678413944363659108\
    6906768989729050095*$.1^8*$.2^4 + 79513247125057906492841989395207442300133\
    781750924860449090230806481243648000000*$.1^8*$.2^3 + 
    171790435018380416903247878610824648919543398246401012395341432490921925017\
    600000000*$.1^8*$.2^2 + 668063044679983105817933911947911151848051275284130\
    91235284315294143736709120000000000*$.1^8*$.2 + 
    133858640091235707342039979563564340059983691898629798292817933514992045260\
    8000000000000*$.1^8 - 61058988656490*$.1^7*$.2^11 + 
    645470833566425875717489618904152240*$.1^7*$.2^10 - 
    51135193038502008150804190472844550800569441050500*$.1^7*$.2^9 + 
    636861023141767565580039581191818069063579259290464688398880*$.1^7*$.2^8 - 
    64999046469909490143435875140651300541119093852394968074094803537810*$.1^7*\
    $.2^7 + 2479002335619392943886127998574764243648562517690948802880865379042\
    79396400*$.1^7*$.2^6 - 7594858520126797340362753363113899508988264728430748\
    4579413691458563029509971992*$.1^7*$.2^5 + 
    297311967271621221945647188111288856983557557853406512717585681964873268285\
    4604800000*$.1^7*$.2^4 - 22093249696627933419655226823604057638897222562682\
    635800269909178325710985117040640000000*$.1^7*$.2^3 + 
    446812314894189974405030698186550526358063845323811527777553816490156896629\
    76491520000000000*$.1^7*$.2^2 - 2415595725376441897530774282312958618706124\
    3620756339515602571075061236992294518784000000000000*$.1^7*$.2 + 
    618840723107761889896363016885251574078635388443306832549992828319945330157\
    158400000000000000000*$.1^7 + 42570393135641712*$.1^6*$.2^11 + 
    7848482999227584325448694633580010490867*$.1^6*$.2^10 + 
    14690460927260804690751501000083244161647396386205851440*$.1^6*$.2^9 + 
    987807801334019988631500819088661487281712947788833523552559299560*$.1^6*$.\
    2^8 + 247900233561939294388612799857476424364856251769094880288086537904279\
    396400*$.1^6*$.2^7 + 116815016752657583785776151035964777394325808926999260\
    5255478096499695783789300124*$.1^6*$.2^6 + 
    224080399886627495149771654692369177094059649940825305182078225594292057242\
    702643200000*$.1^6*$.2^5 + 193873837382174012147044636866579741283308287387\
    5468530371642913339302678999680942080000000*$.1^6*$.2^4 - 
    721191229974600751053515948619991969748296038927844663255298526387518309189\
    7870581760000000000*$.1^6*$.2^3 + 30494044246550310117871895628421273379173\
    050630568397072391110688366558535804457582592000000000000*$.1^6*$.2^2 - 
    953334473564432872104044973740504041324917632745065486193371896919198110469\
    70438451200000000000000000*$.1^6*$.2 + 
    953562665947317950794933099657566747110587348311644892128115531290587730803\
    52804044800000000000000000000*$.1^6 - 17899526272883039048*$.1^5*$.2^11 + 
    28890545335855949285086003898461917345026160*$.1^5*$.2^10 - 
    994774826102691960922410649494629085486856242714439003812180*$.1^5*$.2^9 + 
    208334210762751500564946204497082337222910461284651050215872586641463200*$.\
    1^5*$.2^8 - 759485852012679734036275336311389950898826472843074845794136914\
    58563029509971992*$.1^5*$.2^7 + 2240803998866274951497716546923691770940596\
    49940825305182078225594292057242702643200000*$.1^5*$.2^6 - 
    150572973117089225265805144105638484783346937586249997741086009686674872608\
    27388477440000000*$.1^5*$.2^5 - 1779946418670752626951849809204626086040603\
    57466681128822395417442867019643767352197120000000000*$.1^5*$.2^4 - 
    132899390746510815213576388699982507144408409988109860756557471614019142636\
    9978927939584000000000000*$.1^5*$.2^3 + 
    971814871813934664738444920164383351748884802969739657428927851591332936052\
    4510494720000000000000000000*$.1^5*$.2^2 - 
    784037924821419672964306279649326942508185993010014130404793290934602248317\
    1510017064960000000000000000000*$.1^5*$.2 - 
    311135714890286591241798839183635025168280538591757187756842266421807890101\
    0004935966720000000000000000000000*$.1^5 + 
    4297837238774928467520*$.1^4*$.2^11 + 3537241446036179679031200706019189080\
    3134127320*$.1^4*$.2^10 + 2214848519592558438579048908969747391889490466409\
    3860668378292000*$.1^4*$.2^9 + 84985007087251938907183296552305749628167841\
    39443636591086906768989729050095*$.1^4*$.2^8 + 
    297311967271621221945647188111288856983557557853406512717585681964873268285\
    4604800000*$.1^4*$.2^7 + 19387383738217401214704463686657974128330828738754\
    68530371642913339302678999680942080000000*$.1^4*$.2^6 - 
    177994641867075262695184980920462608604060357466681128822395417442867019643\
    767352197120000000000*$.1^4*$.2^5 + 150434231655639666456182846097303601760\
    05265392518745580151910727157028699006028388237312000000000000*$.1^4*$.2^4 -
    510387788704673753171746274142812030167891533922654498803534638710043488164\
    11677478092800000000000000000*$.1^4*$.2^3 + 
    378494977797549959360178068152933818044335078157093771639955480261351930169\
    113765048483840000000000000000000*$.1^4*$.2^2 + 
    596596095770309616375411102891120210780911047671877878225490788693942054393\
    02452893450240000000000000000000000*$.1^4*$.2 + 
    437146826371712360213676049668333053099237469748508946653253316043623031097\
    15777067941888000000000000000000000000*$.1^4 - 
    529134841844639613861795*$.1^3*$.2^11 + 
    14131378888778142661582693947549844785863493325800*$.1^3*$.2^10 - 
    199188452917764242987050083089364860927274115441197382331866126825820*$.1^3\
    *$.2^9 + 795132471250579064928419893952074423001337817509248604490902308064\
    81243648000000*$.1^3*$.2^8 - 2209324969662793341965522682360405763889722256\
    2682635800269909178325710985117040640000000*$.1^3*$.2^7 - 
    721191229974600751053515948619991969748296038927844663255298526387518309189\
    7870581760000000000*$.1^3*$.2^6 - 13289939074651081521357638869998250714440\
    84099881098607565574716140191426369978927939584000000000000*$.1^3*$.2^5 - 
    510387788704673753171746274142812030167891533922654498803534638710043488164\
    11677478092800000000000000000*$.1^3*$.2^4 - 
    925461466455522523607980072366478440235575959511945288268604770825451300845\
    059605937520640000000000000000000*$.1^3*$.2^3 + 
    103867720178991499136209046596137730276914706598548722228567268915891817571\
    6097236444119040000000000000000000000*$.1^3*$.2^2 + 
    493751729222149651035457063068642305508233453469401395944974296438196687728\
    770695603159040000000000000000000000000*$.1^3*$.2 - 
    337500037290942764495395868386562971754016116785390841072048221617443316658\
    082155384012800000000000000000000000000000*$.1^3 + 
    27209811658056645815522600*$.1^2*$.2^11 + 
    1587728122949690904187089204116332301200302760915266*$.1^2*$.2^10 + 
    804436418307995738740132598166893365099468842089705900525050627891200000*$.\
    1^2*$.2^9 + 171790435018380416903247878610824648919543398246401012395341432\
    490921925017600000000*$.1^2*$.2^8 + 446812314894189974405030698186550526358\
    06384532381152777755381649015689662976491520000000000*$.1^2*$.2^7 + 
    304940442465503101178718956284212733791730506305683970723911106883665585358\
    04457582592000000000000*$.1^2*$.2^6 + 9718148718139346647384449201643833517\
    488848029697396574289278515913329360524510494720000000000000000000*$.1^2*$.\
    2^5 + 37849
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:11:18 2004

Input: A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
Genus(X);

Output: Magma V2.11-2     Sun Aug  1 2004 23:10:58 on modular  [Seed = 2597743445]
   -------------------------------------



************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:13:26 2004

Input: A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
Genus(X);

Output: Magma V2.11-2     Sun Aug  1 2004 23:13:06 on modular  [Seed = 2464047837]
   -------------------------------------



************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:14:15 2004

Input: A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
Genus(X);Level(X);

Output: Magma V2.11-2     Sun Aug  1 2004 23:13:55 on modular  [Seed = 2867223252]
   -------------------------------------



************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:17:29 2004

Input: A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
Genus(X);Level(X);Points(X);

Output: Magma V2.11-2     Sun Aug  1 2004 23:17:08 on modular  [Seed = 3220393094]
   -------------------------------------



************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:18:48 2004

Input: E:=EllipticCurveFromjInvariant(16384/5);
TorsionSubgroup(E);

A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
 

Output: Magma V2.11-2     Sun Aug  1 2004 23:18:48 on modular  [Seed = 3019849766]
   -------------------------------------

Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0

Total time: 0.590 seconds, Total memory usage: 5.68MB


************** MAGMA *****************
Host x-137-82-99-236.library.ubc.ca. (137.82.99.236)
Time: Sun Aug  1 23:19:04 2004

Input: E:=EllipticCurveFromjInvariant(16384/5);
TorsionSubgroup(E);E;


A:=AffineSpace(RationalField(), 2);

X:=ModularCurve(A, "Classical", 11);
 

Output: Magma V2.11-2     Sun Aug  1 2004 23:19:03 on modular  [Seed = 3414636641]
   -------------------------------------

Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0
Elliptic Curve defined by y^2 + x*y = x^3 - 45/1936*x - 5/7744 over Rational 
Field

Total time: 0.580 seconds, Total memory usage: 5.68MB


************** MAGMA *****************
Host CWPP-p-144-134-225-91.prem.tmns.net.au. (144.134.225.91)
Time: Mon Aug  2 05:13:46 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Mon Aug  2 2004 05:13:45 on modular  [Seed = 4172790817]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host CWPP-p-144-134-225-91.prem.tmns.net.au. (144.134.225.91)
Time: Mon Aug  2 05:14:20 2004

Input: x+x

Output: Magma V2.11-2     Mon Aug  2 2004 05:14:19 on modular  [Seed = 3769607195]
   -------------------------------------


>> x+x;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:31:07 2004

Input: AllIrreduciblePolynomials(F_5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:31:06 on modular  [Seed = 2934005037]
   -------------------------------------


>> AllIrreduciblePolynomials(F_5, 1);
                             ^
User error: Identifier 'F_5' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:31:20 2004

Input: AllIrreduciblePolynomials(Z/5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:31:19 on modular  [Seed = 2800309528]
   -------------------------------------


>> AllIrreduciblePolynomials(Z/5, 1);
                             ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:31:25 2004

Input: AllIrreduciblePolynomials(Z/5Z, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:31:25 on modular  [Seed = 3230610292]
   -------------------------------------


>> AllIrreduciblePolynomials(Z/5Z, 1);
                                ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:38:36 2004

Input: AllIrreduciblePolynomials(Z/5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:38:36 on modular  [Seed = 525396571]
   -------------------------------------


>> AllIrreduciblePolynomials(Z/5, 1);
                             ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:45:37 2004

Input: AllIrreduciblePolynomials(R, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:45:37 on modular  [Seed = 913948975]
   -------------------------------------


>> AllIrreduciblePolynomials(R, 1);
                             ^
User error: Identifier 'R' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:54:03 2004

Input: 
AllIrreduciblePolynomials(z/5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:54:02 on modular  [Seed = 577623233]
   -------------------------------------


>> AllIrreduciblePolynomials(z/5, 1);
                             ^
User error: Identifier 'z' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:54:09 2004

Input: AllIrreduciblePolynomials(Z/5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:54:08 on modular  [Seed = 1511367490]
   -------------------------------------


>> AllIrreduciblePolynomials(Z/5, 1);
                             ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:54:14 2004

Input: AllIrreduciblePolynomials(Z/5Z, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:54:13 on modular  [Seed = 1377676111]
   -------------------------------------


>> AllIrreduciblePolynomials(Z/5Z, 1);
                                ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:58:27 2004

Input: AllIrreduciblePolynomials(Integers(), 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:58:26 on modular  [Seed = 1074772058]
   -------------------------------------


>> AllIrreduciblePolynomials(Integers(), 1);
                            ^
Runtime error in 'AllIrreduciblePolynomials': Bad argument types
Argument types given: RngInt, RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 17:58:50 2004

Input: AllIrreduciblePolynomials(RngInt, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 17:58:50 on modular  [Seed = 2016903290]
   -------------------------------------


>> AllIrreduciblePolynomials(RngInt, 1);
                            ^
Runtime error in 'AllIrreduciblePolynomials': Bad argument types
Argument types given: Cat[RngInt], RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:05:10 2004

Input: AllIrreduciblePolynomials(FieldOfDefinition(5), 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:05:10 on modular  [Seed = 1697292011]
   -------------------------------------


>> AllIrreduciblePolynomials(FieldOfDefinition(5), 1);
                                              ^
Runtime error in 'FieldOfDefinition': Bad argument types
Argument types given: RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:07:44 2004

Input: F:= FiniteField(5,1)
AllIrreduciblePolynomials(F, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:07:43 on modular  [Seed = 2681234856]
   -------------------------------------


>> AllIrreduciblePolynomials(F, 1);
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:07:55 2004

Input: F:= FiniteField(5,1)


Output: Magma V2.11-2     Mon Aug  2 2004 18:07:55 on modular  [Seed = 2547543476]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:08:08 2004

Input: F:= FiniteField(5,2)


Output: Magma V2.11-2     Mon Aug  2 2004 18:08:07 on modular  [Seed = 2177792990]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:08:16 2004

Input: F:= FiniteField(5,1)


Output: Magma V2.11-2     Mon Aug  2 2004 18:08:15 on modular  [Seed = 3119924206]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:08:28 2004

Input: F:= FiniteField(5,1)
AllIrreduciblePolynomials(F, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:08:27 on modular  [Seed = 2986232818]
   -------------------------------------


>> AllIrreduciblePolynomials(F, 1);
   ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:10:30 2004

Input: F5:= FiniteField(5)
AllIrreduciblePolynomials(F5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:10:29 on modular  [Seed = 2917291872]
   -------------------------------------


>> AllIrreduciblePolynomials(F5, 1);
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:10:36 2004

Input: F5:= FiniteField(5)
AllIrreduciblePolynomials(F5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:10:35 on modular  [Seed = 2783600486]
   -------------------------------------


>> AllIrreduciblePolynomials(F5, 1);
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:10:47 2004

Input: F5:= FiniteField(5)


Output: Magma V2.11-2     Mon Aug  2 2004 18:10:47 on modular  [Seed = 3717343010]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:10:55 2004

Input: F5:= FiniteField(5)
AllIrreduciblePolynomials(F5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:10:54 on modular  [Seed = 3583651619]
   -------------------------------------


>> AllIrreduciblePolynomials(F5, 1);
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (138.110.111.116)
Time: Mon Aug  2 18:13:08 2004

Input: F5:= FiniteField(5)
AllIrreduciblePolynomials(F5, 1)

Output: Magma V2.11-2     Mon Aug  2 2004 18:13:07 on modular  [Seed = 3464573861]
   -------------------------------------


>> AllIrreduciblePolynomials(F5, 1);
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host Toronto-HSE-ppp3742357.sympatico.ca. (67.68.72.212)
Time: Mon Aug  2 21:58:02 2004

Input: crm = CremonaDatabase();
E := EllipticCurve(crm,"11A");


Output: Magma V2.11-2     Mon Aug  2 2004 21:58:01 on modular  [Seed = 324838183]
   -------------------------------------


>> crm = CremonaDatabase();
   ^
User error: Identifier 'crm' has not been declared or assigned

>> E := EllipticCurve(crm,"11A");
                      ^
User error: Identifier 'crm' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host Toronto-HSE-ppp3742357.sympatico.ca. (67.68.72.212)
Time: Mon Aug  2 21:58:13 2004

Input: crm := CremonaDatabase();
E := EllipticCurve(crm,"11A");


Output: Magma V2.11-2     Mon Aug  2 2004 21:58:12 on modular  [Seed = 189053730]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 3.57MB


************** MAGMA *****************
Host Toronto-HSE-ppp3742357.sympatico.ca. (67.68.72.212)
Time: Mon Aug  2 21:58:27 2004

Input: crm := CremonaDatabase();
E := EllipticCurve(crm,"11A");
E;

Output: Magma V2.11-2     Mon Aug  2 2004 21:58:26 on modular  [Seed = 627742074]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field

Total time: 0.559 seconds, Total memory usage: 3.57MB


************** MAGMA *****************
Host Toronto-HSE-ppp3742357.sympatico.ca. (67.68.72.212)
Time: Mon Aug  2 21:58:51 2004

Input: crm := CremonaDatabase();
E := EllipticCurve(crm,"11A");
E;
Heegner(E,101);

Output: Magma V2.11-2     Mon Aug  2 2004 21:58:50 on modular  [Seed = 1477961759]
   -------------------------------------

Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field

>> Heegner(E,101);;
   ^
User error: Identifier 'Heegner' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 3.57MB


************** MAGMA *****************
Host www.math.tifr.res.in. (158.144.67.10)
Time: Tue Aug  3 05:48:21 2004

Input: E := EllipticCurve([-12096*25, 276480*125]);
E ;

Output: Magma V2.11-2     Tue Aug  3 2004 05:48:20 on modular  [Seed = 3650602908]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 302400*x + 34560000 over Rational Field

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 05:53:55 2004

Input: Y<t> := PolynomialRing(Integers());
R<x> := FunctionField(GF(9));
P<y> := PolynomialRing(R);
f := y^3 + y + x^5 + x + 1;
F<alpha> := FunctionField(f);
ClassGroup(F)



Output: Magma V2.11-2     Tue Aug  3 2004 05:53:52 on modular  [Seed = 711199674]
   -------------------------------------

Abelian Group isomorphic to Z/13 + Z/13 + Z/13 + Z/13 + Z
Defined on 5 generators
Relations:
    13*$.1 = 0
    13*$.2 = 0
    13*$.3 = 0
    13*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/13 + Z/13 + Z/13 + Z/13 + Z
Defined on 5 generators
Relations:
    13*$.1 = 0
    13*$.2 = 0
    13*$.3 = 0
    13*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/13 + Z/13 + 
Z/13 + Z/13 + Z
Defined on 5 generators
Relations:
    13*$.1 = 0
    13*$.2 = 0
    13*$.3 = 0
    13*$.4 = 0 given by a rule

Total time: 2.190 seconds, Total memory usage: 9.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 05:55:47 2004

Input: 
R<x> := FunctionField(GF(9));
P<y> := PolynomialRing(R);
f := y^3 + y + x^5 + x + 1;
F<alpha> := FunctionField(f);
ClassGroup(F)



Output: Magma V2.11-2     Tue Aug  3 2004 05:55:44 on modular  [Seed = 880415796]
   -------------------------------------

Abelian Group isomorphic to Z/13 + Z/13 + Z/13 + Z/13 + Z
Defined on 5 generators
Relations:
    13*$.1 = 0
    13*$.2 = 0
    13*$.3 = 0
    13*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/13 + Z/13 + Z/13 + Z/13 + Z
Defined on 5 generators
Relations:
    13*$.1 = 0
    13*$.2 = 0
    13*$.3 = 0
    13*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/13 + Z/13 + 
Z/13 + Z/13 + Z
Defined on 5 generators
Relations:
    13*$.1 = 0
    13*$.2 = 0
    13*$.3 = 0
    13*$.4 = 0 given by a rule

Total time: 2.309 seconds, Total memory usage: 9.88MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:00:44 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^5 + x + 1;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:00:43 on modular  [Seed = 358299262]
   -------------------------------------

false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:01:09 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + x + 1;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:01:08 on modular  [Seed = 491994713]
   -------------------------------------

true

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:01:37 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 2*x + 1;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:01:36 on modular  [Seed = 1697334981]
   -------------------------------------

true

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:01:50 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 2*x + 2;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:01:49 on modular  [Seed = 1847610819]
   -------------------------------------

false

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:01:56 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 2*x + 3;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:01:56 on modular  [Seed = 1983403458]
   -------------------------------------

false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:02:03 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 2*x + 4;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:02:02 on modular  [Seed = 2117098948]
   -------------------------------------

false

Total time: 0.639 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:02:09 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 2*x + 5;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:02:08 on modular  [Seed = 1208380360]
   -------------------------------------

false

Total time: 0.570 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:02:20 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 5;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:02:20 on modular  [Seed = 1344173020]
   -------------------------------------

false

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:02:27 2004

Input: R<x> :=PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
IsIrreducible(f)


Output: Magma V2.11-2     Tue Aug  3 2004 06:02:26 on modular  [Seed = 1477868490]
   -------------------------------------

true

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:07:15 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> :=PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := f;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:07:12 on modular  [Seed = 2750251347]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0 given by a rule

Total time: 1.079 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:07:51 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := g;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:07:49 on modular  [Seed = 2883946878]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0 given by a rule

Total time: 1.639 seconds, Total memory usage: 13.17MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:08:15 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := h;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:08:13 on modular  [Seed = 3053162648]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/6 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    6*$.2 = 0 given by a rule

Total time: 1.639 seconds, Total memory usage: 13.17MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:08:30 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := g*h;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:08:27 on modular  [Seed = 3186858118]
   -------------------------------------

Abelian Group isomorphic to Z/15 + Z/195 + Z
Defined on 3 generators
Relations:
    15*$.1 = 0
    195*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/15 + Z/195 + Z
Defined on 3 generators
Relations:
    15*$.1 = 0
    195*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/15 + Z/195 + Z
Defined on 3 generators
Relations:
    15*$.1 = 0
    195*$.2 = 0 given by a rule

Total time: 2.600 seconds, Total memory usage: 13.48MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:08:56 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := g*h^2;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:08:45 on modular  [Seed = 2244714632]
   -------------------------------------

Abelian Group isomorphic to Z/3 + Z/849 + Z
Defined on 3 generators
Relations:
    3*$.1 = 0
    849*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/849 + Z
Defined on 3 generators
Relations:
    3*$.1 = 0
    849*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/849 + Z
Defined on 3 generators
Relations:
    3*$.1 = 0
    849*$.2 = 0 given by a rule

Total time: 10.459 seconds, Total memory usage: 15.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:09:18 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := f*h^2;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:09:13 on modular  [Seed = 2378410212]
   -------------------------------------

Abelian Group isomorphic to Z/39 + Z/39 + Z
Defined on 3 generators
Relations:
    39*$.1 = 0
    39*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/39 + Z/39 + Z
Defined on 3 generators
Relations:
    39*$.1 = 0
    39*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/39 + Z/39 + Z
Defined on 3 generators
Relations:
    39*$.1 = 0
    39*$.2 = 0 given by a rule

Total time: 4.639 seconds, Total memory usage: 14.84MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:09:40 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := f*h^2*g^2;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:09:28 on modular  [Seed = 2514202861]
   -------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/149673 + Z
Defined on 4 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    149673*$.3 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/149673 + Z
Defined on 4 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    149673*$.3 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + 
Z/149673 + Z
Defined on 4 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    149673*$.3 = 0 given by a rule

Total time: 11.649 seconds, Total memory usage: 15.68MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 06:10:07 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := f*h*g;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 06:09:58 on modular  [Seed = 2647898315]
   -------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/9 + Z/10377 + Z
Defined on 5 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    9*$.3 = 0
    10377*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/9 + Z/10377 + Z
Defined on 5 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    9*$.3 = 0
    10377*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/9 
+ Z/10377 + Z
Defined on 5 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    9*$.3 = 0
    10377*$.4 = 0 given by a rule

Total time: 9.110 seconds, Total memory usage: 15.03MB


************** MAGMA *****************
Host host-99-208-cn.riscom.md. (195.138.99.208)
Time: Tue Aug  3 06:15:09 2004

Input: 50!

Output: Magma V2.11-2     Tue Aug  3 2004 06:15:08 on modular  [Seed = 4223000439]
   -------------------------------------


>> 50!;
      ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host host-99-208-cn.riscom.md. (195.138.99.208)
Time: Tue Aug  3 06:18:01 2004

Input: sin(0.3271946967961522441733440852)


Output: Magma V2.11-2     Tue Aug  3 2004 06:17:59 on modular  [Seed = 544081748]
   -------------------------------------


>> sin(0.3271946967961522441733440852)
   ^
User error: Identifier 'sin' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 07:46:00 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := f*h^2*g^2;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 07:45:46 on modular  [Seed = 2447354456]
   -------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/149673 + Z
Defined on 4 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    149673*$.3 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/149673 + Z
Defined on 4 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    149673*$.3 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + 
Z/149673 + Z
Defined on 4 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    149673*$.3 = 0 given by a rule

Total time: 11.699 seconds, Total memory usage: 15.57MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 07:57:39 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^3 + 3*x^2 + 4;
g := x^3 + x + 1;
h := x^3 + 2*x + 1;
D := f*h*g;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Tue Aug  3 2004 07:57:30 on modular  [Seed = 3819822955]
   -------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/9 + Z/10377 + Z
Defined on 5 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    9*$.3 = 0
    10377*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/9 + Z/10377 + Z
Defined on 5 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    9*$.3 = 0
    10377*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/9 
+ Z/10377 + Z
Defined on 5 generators
Relations:
    3*$.1 = 0
    3*$.2 = 0
    9*$.3 = 0
    10377*$.4 = 0 given by a rule

Total time: 8.920 seconds, Total memory usage: 15.13MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:25:20 2004

Input: A=[1,2,2]

Output: Magma V2.11-2     Tue Aug  3 2004 08:25:19 on modular  [Seed = 1047591732]
   -------------------------------------


>> A=[1,2,2];
   ^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:25:40 2004

Input: A:=matrix([1,2,2])


Output: Magma V2.11-2     Tue Aug  3 2004 08:25:40 on modular  [Seed = 105431911]
   -------------------------------------


>> A:=matrix([1,2,2])
      ^
User error: Identifier 'matrix' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:25:49 2004

Input: A:=Matrix([1,2,2])


Output: Magma V2.11-2     Tue Aug  3 2004 08:25:48 on modular  [Seed = 239127399]
   -------------------------------------


>> A:=Matrix([1,2,2])
            ^
Runtime error in 'Matrix': Bad argument types
Argument types given: SeqEnum[RngIntElt]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:29:53 2004

Input: A:=Matrix(GF(2),3,3,[1,0,0,0,1,0,0,0,1])


Output: Magma V2.11-2     Tue Aug  3 2004 08:29:52 on modular  [Seed = 475191417]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:30:04 2004

Input: A:=Matrix(GF(2),3,3,[1,0,0,0,1,0,0,0,1]);
Rank(A)


Output: Magma V2.11-2     Tue Aug  3 2004 08:30:04 on modular  [Seed = 1680515085]
   -------------------------------------

3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:30:19 2004

Input: A:=Matrix(GF(2),3,3,[1,1,0,0,1,1,1,0,1]);
Rank(A)


Output: Magma V2.11-2     Tue Aug  3 2004 08:30:18 on modular  [Seed = 1864477456]
   -------------------------------------

2

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:34:04 2004

Input: A:=Matrix(GF(3),7,7,
[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, 
-1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);
7-Rank(A-ScalarMatrix(7,1))


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:34:51 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);
Rank(A)

Output: Magma V2.11-2     Tue Aug  3 2004 08:34:50 on modular  [Seed = 2050276661]
   -------------------------------------

7

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:35:09 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);
Rank(A-ScalarMatrix(7,1))

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:35:52 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);
ScalarMatrix(7,1)

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:36:48 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

IdenityMatrix(7,1)

Output: Magma V2.11-2     Tue Aug  3 2004 08:36:47 on modular  [Seed = 1494720156]
   -------------------------------------


>> IdenityMatrix(7,1);
   ^
User error: Identifier 'IdenityMatrix' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:36:59 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

UnitMatrix(7,1)

Output: Magma V2.11-2     Tue Aug  3 2004 08:36:58 on modular  [Seed = 2716821102]
   -------------------------------------


>> UnitMatrix(7,1);
   ^
User error: Identifier 'UnitMatrix' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:37:14 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

ZeroMatrix(7,1)

Output: Magma V2.11-2     Tue Aug  3 2004 08:37:14 on modular  [Seed = 2833674103]
   -------------------------------------


>> ZeroMatrix(7,1);
             ^
Runtime error in 'ZeroMatrix': Bad argument types
Argument types given: RngIntElt, RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:37:31 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

ZeroMatrix(GF(3),7,7)

Output: Magma V2.11-2     Tue Aug  3 2004 08:37:30 on modular  [Seed = 3019732380]
   -------------------------------------

[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:37:46 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

ScalarMatrix(GF(3),7,7,1)

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:38:06 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

ScalarMatrix(GF(3),7,1)

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:38:09 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

ScalarMatrix(GF(3),7,1)

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:38:33 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

DiagonalMatrix(GF(3),7,[1,1,1,1,1,1,1])

Output: Magma V2.11-2     Tue Aug  3 2004 08:38:33 on modular  [Seed = 2430490364]
   -------------------------------------

[1 0 0 0 0 0 0]
[0 1 0 0 0 0 0]
[0 0 1 0 0 0 0]
[0 0 0 1 0 0 0]
[0 0 0 0 1 0 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:38:49 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-2,-2,-2,-1,-1]);

E := DiagonalMatrix(GF(3),7,[1,1,1,1,1,1,1]);

Rank(A-E)

Output: Magma V2.11-2     Tue Aug  3 2004 08:38:48 on modular  [Seed = 2564185829]
   -------------------------------------

4

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:39:18 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-2,-2,-2,-2,-2,-1,-1]);

E := DiagonalMatrix(GF(3),7,[1,1,1,1,1,1,1]);

Rank(A-E)

Output: Magma V2.11-2     Tue Aug  3 2004 08:39:17 on modular  [Seed = 4020316607]
   -------------------------------------

4

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:39:36 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-2,-2,-1,-1,-1,-1,-1]);
E := DiagonalMatrix(GF(3),7,[1,1,1,1,1,1,1]);

Rank(A-E)

Output: Magma V2.11-2     Tue Aug  3 2004 08:39:36 on modular  [Seed = 4156109146]
   -------------------------------------

4

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Tue Aug  3 08:39:59 2004

Input: A:=Matrix(GF(3),7,7,[-1,1,0,0,0,0,0, -1,0,0,0,0,0,0, -1,0,0,1,0,0,0, -1,0,0,0,1,0,0, -1,0,1,0,0,0,0, -1,0,0,0,0,0,1, -1-1,-1,-1,-1,-1,-1,-1]);
E := DiagonalMatrix(GF(3),7,[1,1,1,1,1,1,1]);

Rank(A-E)

Output: Magma V2.11-2     Tue Aug  3 2004 08:39:58 on modular  [Seed = 4289804612]
   -------------------------------------

4

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:45:24 2004

Input: 10+40+38+33+36*(1.0925)+10;

Output: Magma V2.11-2     Tue Aug  3 2004 10:45:23 on modular  [Seed = 847042070]
   -------------------------------------

170.329999999999999999999999999256829918409

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:46:57 2004

Input: 10+40+38+33+36*(1.0925)+10;

3+11+7.63+19*(1.0925);


Output: Magma V2.11-2     Tue Aug  3 2004 10:46:56 on modular  [Seed = 964156798]
   -------------------------------------

170.329999999999999999999999999256829918409
42.387499999999999999999999999353

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:47:45 2004

Input: e:=10+40+38+33+36*(1.0925)+10;
e;
z:=3+11+7.63+19*(1.0925);
z;
e-z;


Output: Magma V2.11-2     Tue Aug  3 2004 10:47:45 on modular  [Seed = 22013367]
   -------------------------------------

170.329999999999999999999999999256829918409
42.387499999999999999999999999353
127.942499999999999999999999999903064771966

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:48:07 2004

Input: e:=10+40+38+33+36*(1.0925)+10;
e;
z:=3+11+7.63+19*(1.0925);
z;
e-z;
(e-z)/2;



Output: Magma V2.11-2     Tue Aug  3 2004 10:48:06 on modular  [Seed = 155708808]
   -------------------------------------

170.329999999999999999999999999256829918409
42.387499999999999999999999999353
127.942499999999999999999999999903064771966
63.971249999999999999999999999951532385983

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:51:55 2004

Input: e:=10+40+38+33+36*(1.0925)+10;
e;
z:=3+11+7.63+19*(1.0925)+36*(1.08);
z;
e-z;
(e-z)/2;



Output: Magma V2.11-2     Tue Aug  3 2004 10:51:54 on modular  [Seed = 274659261]
   -------------------------------------

170.329999999999999999999999999256829918409
81.267499999999999999999999998449
89.0625000000000000000000000008077935669463
44.531250000000000000000000000403896783473

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:56:56 2004

Input: 3.68/2+3.45/2+11.40/2+37*(1.0925)+54/2+20*(1.0925)+13.62/2+21.85+25.07+12+10.15/2+5.89/2+(15.90+12.48+9.98)*(1.08)+7/2;



Output: Magma V2.11-2     Tue Aug  3 2004 10:56:55 on modular  [Seed = 1814203132]
   -------------------------------------

217.216299999999999999999999988972

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:57:26 2004

Input: z:=3.68/2+3.45/2+11.40/2+37*(1.0925)+54/2+20*(1.0925)+13.62/2+21.85+25.07+12+10.15/2+5.89/2+(15.90+12.48+9.98)*(1.08)+7/2;
z;
z-45;


Output: Magma V2.11-2     Tue Aug  3 2004 10:57:25 on modular  [Seed = 1949995654]
   -------------------------------------

217.216299999999999999999999988972
172.216299999999999999999999988972

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:58:46 2004

Input: z:=3.68/2+3.45/2+11.40/2+37*(1.0925)+54/2+20*(1.0925)+13.62/2+21.85+25.07+12+10.15/2+5.89/2+(15.90+12.48+9.98)*(1.08)+7/2;
z;
z-45;


Output: Magma V2.11-2     Tue Aug  3 2004 10:58:45 on modular  [Seed = 2083689854]
   -------------------------------------

217.216299999999999999999999988972
172.216299999999999999999999988972

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host user-0cdfmtd.cable.mindspring.com. (24.215.219.173)
Time: Tue Aug  3 10:59:09 2004

Input: z:=3.68/2+3.45/2+11.40/2+37*(1.0925)+54/2+20*(1.0925)+13.62/2+21.85+25.07+12+10.15/2+5.89/2+(15.90+12.48+9.98)*(1.08)+7/2;
z;
z-45;

744/2;

Output: Magma V2.11-2     Tue Aug  3 2004 10:59:09 on modular  [Seed = 1074702682]
   -------------------------------------

217.216299999999999999999999988972
172.216299999999999999999999988972
372

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 11:49:20 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);

Output: Magma V2.11-2     Tue Aug  3 2004 11:49:19 on modular  [Seed = 3280810267]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 11:51:05 2004

Input: X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]);
CharacteristicPolynomial(X);


Output: Magma V2.11-2     Tue Aug  3 2004 11:51:04 on modular  [Seed = 3381083270]
   -------------------------------------

$.1^2 - 5*$.1 - 2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 11:53:55 2004

Input: X := Matrix(IntegerRing(), 5, 5, [0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9]);
CharacteristicPolynomial(X);


Output: Magma V2.11-2     Tue Aug  3 2004 11:53:54 on modular  [Seed = 3750833130]
   -------------------------------------

$.1^5 - 21*$.1^4 - 83*$.1^3 + 507*$.1^2 + 1762*$.1 - 649

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:09:45 2004

Input: A:=Matrix(IntegerRing(),[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3,2,1,3,5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,2,9,5,1,1,5,0,3,0,9,0,6,7,9,7,7,9,4,6,7,7,6,7,3,6,6,5,1,1,8,3,6,3,4,9,0,5,3,0,7,5,9,8,9,8,7,1,8,3,8,6,9,1,0,8,0,2,7,5,4,0,7,7,9,7,8,6,8,0,9,8,8,9,4,8,2,1,6,1,8,6,9,8,6,1,8,5,2,4,9,8,5,4,6,6,9,1,2,5,9,2,7,8,6,9,6,1,4,0,6,3,4,8,7,7,4,9,5,0,6,1,0,7,7,5,9,0,2,9,6,5,8,0,5,6,3,6,3,5,7,7,5,8,4,9,0,9,3,6,7,9,2,5,7,4,1,3,4,9,4,4,1,9,3,8,9,6,3,3,8,1,0,2,2,5,9,3,6,0,3,3,3,3,6,1,9,4,8,2,2,3,6,0,9,5,3,2,2,0,0,5,0,9,9,3,5,6,5,9,1,9,4,6,5,2,6,2,0,8,9,7,2,9,0,7,9,2,0,6,1,8,2,6,8,2,1,6,1,9,0,5,3,6,7,7,5,0,8,5,6,7,5,8,2,4,3,3,6,7,3,0,9,8,5,3,4,3,8,4,7,8,2,0,7,3,5,7,8,7,7,1,2,4,0,1,6,1,1,4,6,2,8,9,9,3,2,7,4,3,3,1,6,1,0,9,9,8,3,6,1,0,3,2,7,1,7,0,9,0,0,4,6,6,2,5,1,0,8,5,3,9,1,5,1,3,2,3,4,1,6,6,2,8,3,1,3,6,8,5,5,7,7,2,6,1,8,4,7,0,5,6,6,1,1,9,7,8,7,1,7,4,5,7,1,8,5,9,7,0,0,0,8,6,8,3,2,0,1,8,6,4,0,8,1,2,0,6,5,0,4,1,6,7,0,3,1,2,1,9,2,2,7,3,0,1,4,5,3,7,8,1,6,7,8,6,8,6,1,4,2,8,3,6,9,6,2,6,8,2,2,4,4,9,8,5,7,1,0,8,0,2,0,6,3,6,9,1,5,2,9,4,1,8,7,7,5,1,2,3,9,0,2,6,9,4,9,0,1,5,4,1,2,5,0,3,0,4,0,5,4,7,5,0,5,0,9,8,1,6,1,8,3,1,8,8,2,9,1,6,8,0,6,0,3,7,6,8,5,8,1,7,7,9,8,2,6,5,1,8,3,5,5,9,3,8,5,7,8,1,4,0,1,8,4,0,9,7,9,9,8,6,0,5,5,6,6,7,6,3,1,9,4,4,6,6,9,4,9,2,1,9,7,5,3,9,8,8,4,6,9,4,9,2,9,8,5,0,1,3,2,8,7,4,1,8,3,5,5,1,1,8,8,5,3,3,5,3,2,6,2,0,7,4,2,9,2,4,3,7,0,1,0,7,5,7,0,8,8,7,3,3,4,5,0,4,1,3,2,5,6,5,7,7,0,1,3,9,5,2,1,6,3,4,4,2,4,4,5,8,1,2,7,8,2,2,5,9,0,1,9,2,9,9,8,0,5,7,4,1,0,3,3,6,6,3,7,1,5,4,9,5,6,0,2,2,3,4,3,4,5,3,8,7,6,0,7,3,8,8,2,5,9,5,7,2,3,7,7,7,6,9,3,1,7,9,8,2,7,8,5,2,1,2,5,0,7,2,7,8,8,8,6,7,4,1,5,8,1,6,8,0,8,8,5,3,5,1,0,6,8,5,4,4,7,6,5,1,5,7,7,9,8,1,9,3,1,6,4,9,2,3,7,4,6,5,6,2,6,3,6,8,5,5,0,4,8,9,7,0,9,6,1,0,1,7,0,5,6,1,3,2,6,0,1,0,0,5,1,7,6,1,0,3,5,1,2,7,0,1,1,0,5,1,2,9,6,9,8,4,9,9,2,9,6,3,0,4,3,3,4,7,6,3,1,3,2,4,3,2,8,8,5,5,8,9,4,8,6,1,1,7,8,8,7,5,5,4,6,4,7,5,3,6,1,3,2,5,1,5,7,3,0,4,8,9,6,7,5,1,8,5,2,2,6,1,1,5,6,0,6,0,6,2,7,2,9,1,3,3,9,1,8,3,9,5,2,5,1,8,3,8,5,4,3,1,5,4,7,2,0,5,1,5,4,3,7,4,7,2,8,5,4,7,9,5,1,6,3,5,9,1,6,5,0,6,6,0,0,5,4,2,8,6,7,7,8,9,7,5,1,5,0,4,1,8,9,1,3,5,4,7,4,8,0,0,8,9,6,1,1,4,6,9,7,4,8,8,0,3,4,8,7,0,3,6,6,8,6,6,3,8,0,9,9,0,2,1,8,1,3,1,9,9,1,9,8,2,5,9,5,5,3,4,4,6,3,1,3,6,6,7,7,8,1,8,6,6,5,8,9,8,6,8,8,1,8,3,4,3,0,0,3,6,4,9,9,8,3,5,0,5,4,3,8,1,3,1,1,5,6,1,4,6,4,9,2,6,4,3,9,1,7,1,4,4,3,3,5,6,4,4,1,3,1,2,9,2,3,5,0,4,1,3,7,9,6,4,1,5,3,7,6,3,1,7,0,3,1,3,5,3,2,7,8,1,4,9,1,2,7,6,8,3,4,8,7,0,3,1,9,1,3,6,1,5,7,0,8,7,9,3,8,4,3,3,9,3,7,3,5,1,0,0,7,5,1,2,0,9,8,1,8,1,3,3,9,7,1,8,0,8,9,9,9,9,7,6,2,5,4,6,8,7,0,7,7,5,1,4,3,2,1,4,2,5,2,9,2,6,1,6,9,3,1,7,3,4,3,8,1,1,4,9,5,5,1,6,6,4,9,7,4,5,2,0,9,6,5,4,5,2,6,2,3,0,4,1,3,4,6,9,4,5,6,0,8,9,2,2,4,7,4,7,6,6,9,1,7,0,4,3,5,4,6,6,2,8,5,1,4,0,4,9,5,8,4,8,9,7,8,6,6,0,8,5,4,6,2,0,4,7,7,7,3,1,1,3,7,0,6,1,3,2,1,7,2,2,9,5,5,1,9,4,6,2,9,4,7,1,9,1,6,1,3,0,2,7,2,1,6,5,6,0,6,3,4,5,5,6,6,9,1,1,3,4,1,6,1,3,4,3,6,0,4,1,1,5,5,6,6,8,4,4,8,5,4,3,6,1,8,9,2,4,2,5,5,6,2,3,6,5,4,0,0,4,7,5,7,9,9,7,3,9,6,7,2,5,5,8,9,4,4,8,0,1,6,7,1,2,5,8,0,4,6,6,9,1,3,1,3,9,3,4,5,4,6,3,1,7,0,5,9,6,3,8,9,3,6,8,7,1,3,9,8,2,7,0,1,1,7,6,7,3,6,7,7,3,5,9,5,9,1,6,2,2,4,9,2,1,5,8,0,1,3,3,1,2,2,6,1,4,3,5,9,3,9,0,3,4,6,5,0,1,9,7,3,6,7,4,4,5,4,9,1,8,1,4,7,0,6,1,1,7,3,6,3,4,3,1,2,1,3,6,4,3,6,2,5,2,3,8,7,3,3,8,2,1,3,4,6,6,4,0,7,5,3,5,8,8,5,6,3,3,0,2,9,7,2,1,0,0,4,6,7,2,9,4,7,5,3,3,5,0,0,6,9,5,6,7,5,9,4,6,7,1,9,6,7,9,0,5,6,8,0,7,2,6,8,3,3,0,9,1,7,3,4,7,5,5,4,8,2,5,6,5,7,5,4,2,7,1,1,7,0,3,1,3,3,5,9,4,4,1,1,7,7,8,5,4,5,9,0,2,7,6,4,7,2,5,8,0,6,6,6,9,1,6,7,5,3,9,5,9,2,7,9,9,7,2,1,5,0,5,4,4,4,6,2,0,5,9,2,5,8,2,8,2,9,1,8,6,1,8,6,5,4,7,2,2,3,1,9,0,0,2,2,2,5,9,9,8,9,9,8,9,1,5,6,4,6,9,8,3,0,2,2,4,1,3,9,9,0,6,2,5,3,1,2,3,0,4,1,6,7,8,9,9,9,0,5,6,6,5,3,3,5,1,8,9,3,5,4,6,7,6,6,9,3,5,1,1,2,0,3,8,3,4,0,9,2,0,1,6,2,8,3,9,7,5,6,3,4,3,2,2,4,1,4,4,7,2,7,5,6,4,4,0,2,5,1,8,4,4,2,1,7,6,3,0,1,4,6,4,9,0,5,5,1,6,6,1,2,8,7,2,4,3,7,2,4,2,7,9,8,8,1,8,3,1,0,4,7,2,3,6,1,2,8,4,9,6,7,2,0,7,1,4,8,5,1,2,5,1,0,2,5,5,8,5,4,9,6,3,4,7,7,2,0,3,1,7,5,7,0,5,4,9,9,4,3,2,1,6,8,9,6,6,7,2,2,2,9,5,2,5,9,7,5,7,0,8,9,8,1,0,8,1,2,3,2,3,8,4,4,7,0,4,2,0,0,1,9,6,0,4,9,9,8,3,5,9,6,7,4,8,4,0,8,7,0,0,4,6,2,1,1,3,3,8,8,5,3,3,2,3,7,7,3,7,3,4,8,9,2,0,6,9,5,3,2,7,1,3,2,4,7,0,9,4,3,2,9,8,9,7,5,1,7,2,5,4,9,6,2,7,0,9,1,1,6,8,2,8,5,4,6,8,1,2,7,0,3,0,9,1,7,4,7,8,3,8,7,7,1,8,0,4,7,1,5,1,2,6,3,7,7,3,5,3,5,5,4,7,3,4,2,7,1,2,7,0,3,4,3,5,6,2,3,6,1,3,0,8,1,9,5,0,4,2,3,3,8,0,0,4,1,4,4,2,1,5,6,7,9,8,5,3,6,9,8,8,4,2,0,0,7,4,8,6,6,0,6,7,0,5,0,1,2,8,5,6,2,8,1,8,0,2,7,6,3,8,0,9,0,6,5,9,4,0,1,1,1,8,0,4,1,9,8,4,5,3,6,7,7,3,1,5,7,2,5,0,0,4,4,9,9,8,5,9,8,3,2,6,1,9,7,2,8,5,3,5,0,8,1,1,6,8,7,2,2,0,9,8,4,9,5,2,7,3,0,7,5,2,4,3,5,7,9,4,6,8,5,4,1,4,7,7,4,5,8,7,7,7,9,3,7,4,2,9,7,3,1,4,4,4,5,4,3,4,0,8,2,7,1,8,3,8,6,3,5,7,9,8,9,0,5,7,9,8,6,8,5,2,6,2,2,6,1,8,8,4,2,4,8,8,4,7,0,7,0,0,1,1,7,2,6,9,3,7,3,7,8,5,9,9,0,5,5,7,9,7,3,6,1,9,4,1,3,4,6,2,8,1,0,6,3,3,0,3,7,1,8,4,9,2,5,8,9,0,3,5,9,7,3,0,6,2,5,9,8,0,8,6,0,1,8,2,7,9,6,7,9,3,6,6,3,3,6,9,2,3,5,6,5,8,3,6,0,1,2,9,1,8,5,7,7,5,5,4,2,0,6,4,2,0,8,6,7,8,1,0,1,6,4,9,4,6,4,3,5,3,1,0,3,8,5,1,8,1,0,9,6,4,0,2,8,9,1,4,1,5,4,5,1,7,7,7,7,1,4,1,2,3,4,3,9,9,4,7,9,2,2,5,8,3,6,3,6,0,1,0,8,7,8,1,9,5,0,9,0,9,3,8,3,2,9,2,2,9,1,7,3]);
CharacteristicPolynomial(A);


Output: Magma V2.11-2     Tue Aug  3 2004 12:09:44 on modular  [Seed = 105447400]
   -------------------------------------


>> A:=Matrix(IntegerRing(),[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,
            ^
Runtime error in 'Matrix': Bad argument types
Argument types given: RngInt, SeqEnum[RngIntElt]

>> CharacteristicPolynomial(A);
                            ^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.819 seconds, Total memory usage: 3.90MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:13:09 2004

Input: A:=Matrix(IntegerRing(),[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3,2,1,3,5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,6,2,7,9,8,4,7,8,9,3,4,3,3,3,1,2,9,5,2,2,5,3,5,0,7,2,0,9,1,8,2,2,5,9,8,1,4,1,3,2,8,7,4,0,8,6,4,5,1,6,7,4,5,5,5,0,6,6,1,7,4,0,1,4,1,9,4,1,7,1,3,4,3,7,2,5,8,2,2,9,2,9,7,1,6,6,9,6,8,5,4,7,8,6,2,2,9,8,1,2,5,8,1,3,1,8,2,7,5,9,4,8,3,0,7,3,4,8,6,7,7,1,6,0,3,5,1,1,2,1,8,5,2,0,2,7,7,3,4,2,5,7,9,8,4,4,0,3,1,9,6,3,4,2,6,4,3,9,7,3,7,1,2,7,6,6,7,5,9,4,5,7,2,8,0,3,4,0,0,5,7,8,6,7,2,1,6,3,1,6,0,0,1,7,1,7,5,0,2,2,8,1,0,2,3,4,2,7,4,1,8,4,0,6,8,1,7,3,3,8,1,7,8,6,7,3,8,7,7,8,4,2,0,1,7,2,2,1,4,2,9,9,4,3,3,9,4,3,6,4,6,2,6,4,6,1,9,1,0,4,7,3,4,3,1,3,9,9,9,3,9,2,0,8,1,7,8,3,4,1,9,1,0,2,7,8,0,4,4,8,0,2,5,2,1,1,5,4,3,4,8,6,9,3,0,5,6,1,3,3,0,5,8,3,8,7,1,5,9,7,1,8,0,0,3,9,5,4,7,2,2,7,9,6,2,9,8,9,1,0,8,9,1,7,6,8,2,4,0,7,1,9,5,7,8,6,1,0,8,0,2,1,7,3,3,3,9,8,8,1,0,9,9,9,3,5,0,7,2,0,1,1,8,6,3,7,6,9,3,8,2,1,5,6,4,8,4,3,5,3,3,1,3,8,5,4,3,7,0,8,1,9,4,6,0,2,4,9,1,6,2,9,0,7,3,5,9,3,4,7,2,4,2,7,0,0,8,5,3,8,2,1,6,0,5,8,1,2,2,1,5,8,0,0,6,0,9,3,9,7,9,3,5,4,4,0,6,3,0,4,3,2,0,4,8,3,8,5,6,8,2,9,8,6,1,4,8,1,0,7,5,7,7,3,9,8,5,1,4,8,9,3,4,2,0,5,0,9,1,8,6,5,3,7,5,7,9,2,5,8,2,1,0,2,5,6,5,6,8,4,5,6,3,9,6,4,4,0,2,2,9,5,5,8,5,0,7,4,2,1,5,6,6,4,7,7,1,7,1,3,7,1,0,1,2,6,1,2,3,2,0,7,0,4,5,9,2,3,1,2,7,4,4,3,3,2,4,3,4,4,3,8,2,9,3,8,1,1,9,9,5,6,5,8,2,0,6,4,5,1,6,8,4,0,2,8,6,8,0,5,3,9,3,9,3,1,2,1,6,8,5,9,1,0,5,4,3,8,4,1,4,2,6,5,8,2,8,3,0,3,8,6,9,2,6,8,3,7,1,6,5,3,3,9,6,6,6,9,5,0,0,6,8,4,0,8,4,3,3,6,3,3,4,4,3,6,2,7,2,2,2,8,2,9,7,4,5,6,4,0,7,6,0,5,6,7,3,4,3,3,4,9,0,4,9,9,9,2,9,6,9,1,5,8,3,5,8,6,3,0,6,8,5,7,7,2,8,9,9,0,7,3,3,1,4,1,0,8,0,8,8,3,4,2,4,3,3,9,4,5,3,8,5,2,7,5,7,1,1,8,8,0,1,3,2,4,0,9,3,7,4,4,1,8,3,3,8,8,2,1,3,9,9,5,8,3,5,4,6,6,7,1,3,7,1,5,7,5,9,6,4,2,5,7,2,8,7,1,5,0,4,2,0,2,2,2,7,0,3,9,5,9,6,2,6,6,8,6,1,0,2,9,8,7,4,8,8,8,0,9,9,0,9,4,9,2,1,7,5,4,5,5,8,6,8,6,7,0,5,9,3,0,5,2,5,9,2,1,5,6,3,9,3,7,9,6,2,3,6,2,9,6,3,2,5,8,1,2,8,9,4,4,4,1,9,8,9,4,9,8,7,1,0,2,2,2,2,8,2,3,3,3,7,9,6,2,2,5,6,0,4,2,8,3,0,6,9,8,8,4,8,3,9,2,7,7,1,1,9,0,7,6,9,2,8,3,2,8,3,4,1,0,2,7,6,3,7,5,5,2,8,2,7,1,7,3,2,8,6,1,8,1,1,3,4,3,1,9,3,1,5,1,9,7,7,5,2,2,7,8,7,3,2,7,9,5,3,7,8,9,6,8,7,7,0,7,9,5,3,9,8,1,1,9,1,6,3,1,4,2,6,1,0,1,6,6,2,5,7,6,5,7,8,9,1,7,1,8,1,8,8,6,9,0,9,0,6,8,9,0,3,2,3,9,6,6,8,2,3,5,2,2,0,7,0,4,9,4,8,1,6,1,0,4,2,9,9,2,7,7,0,3,0,5,1,2,2,9,3,0,5,2,6,9,6,5,3,4,5,2,9,2,7,9,5,8,9,0,5,3,6,1,5,2,5,7,8,1,5,9,6,9,4,4,1,3,4,4,0,3,6,1,5,7,3,6,7,3,4,5,1,3,0,5,6,3,3,6,6,9,7,9,5,3,4,1,0,6,0,6,8,2,8,5,6,2,9,3,1,8,9,7,8,0,0,4,7,7,8,5,1,4,9,5,5,2,0,0,1,4,1,9,7,9,9,9,0,0,0,1,8,3,0,0,6,8,5,4,2,2,1,0,9,9,9,3,7,1,0,4,8,7,5,9,9,9,0,3,0,3,7,6,4,0,0,4,5,9,4,3,9,8,8,7,7,9,1,2,0,2,0,3,8,9,4,7,1,9,3,4,4,0,1,2,2,8,1,1,0,5,3,3,5,0,0,3,1,8,1,3,4,5,2,9,1,2,6,0,9,2,1,5,6,3,2,6,4,6,9,7,3,6,3,8,1,4,6,1,5,2,3,9,6,3,2,7,5,0,9,5,7,3,1,3,1,2,3,2,7,9,8,2,9,4,1,4,7,9,6,5,8,5,2,6,7,8,2,0,9,9,4,7,9,3,2,1,7,7,5,7,2,8,8,5,0,1,8,4,2,1,0,9,6,3,0,4,9,5,4,0,1,3,9,2,8,7,9,8,4,2,4,4,0,9,2,6,0,2,5,5,6,6,3,0,3,6,2,0,7,9,9,7,7,7,5,7,9,3,4,8,4,6,3,9,0,6,4,9,1,1,4,1,6,5,5,2,6,0,1,2,6,3,9,0,3,7,9,4,1,0,6,7,8,5,6,5,4,8,4,2,7,3,8,0,3,0,4,4,3,4,4,9,2,4,4,7,8,4,2,8,4,4,5,2,1,8,8,0,2,6,0,6,1,0,0,2,0,9,8,1,2,1,4,2,4,5,0,8,5,0,0,4,1,8,1,0,6,9,7,9,1,7,8,8,0,1,3,5,0,1,9,5,2,9,9,1,7,5,5,2,7,8,2,6,3,6,8,1,9,6,5,9,9,9,3,6,4,2,2,5,9,1,9,8,5,9,2,9,3,1,2,0,4,8,4,4,8,9,7,1,2,4,1,2,6,7,1,3,7,9,3,3,3,2,4,4,9,5,6,4,1,0,1,2,3,4,4,7,7,9,4,6,9,7,7,2,6,0,2,1,1,0,5,1,9,5,3,6,3,1,2,9,6,9,0,4,7,0,0,0,1,7,2,5,1,4,2,6,0,5,4,4,6,0,6,4,8,2,2,2,3,8,9,5,9,5,1,0,4,8,5,8,9,3,2,3,5,6,0,1,1,6,3,3,7,0,2,5,1,0,9,6,1,8,7,4,8,1,7,5,4,0,9,1,5,8,5,2,8,5,5,5,8,6,8,3,2,7,7,6,9,9,1,5,8,2,5,2,8,2,6,2,8,0,5,9,9,5,4,4,4,2,4,7,5,5,9,8,6,8,7,8,8,0,5,8,0,2,2,6,8,6,1,5,1,0,7,1,1,9,9,0,7,2,3,2,9,4,0,0,3,7,5,2,7,1,7,0,9,4,1,5,0,8,9,0,1,2,7,6,8,7,9,3,3,5,7,8,7,0,9,0,5,0,9,4,9,5,2,6,5,6,9,5,7,4,2,6,6,2,8,2,8,0,0,3,6,7,0,3,3,1,2,2,7,1,0,0,4,8,6,4,1,2,6,5,2,5,6,1,2,0,4,1,9,7,2,0,3,6,1,8,4,1,1,0,7,7,9,5,9,1,1,0,1,8,9,5,7,1,8,7,1,9,4,9,4,9,7,0,2,0,3,4,3,1,6,1,7,1,4,0,9,8,8,8,9,6,9,4,1,7,0,0,1,3,0,2,4,1,8,8,7,4,6,5,6,7,8,2,1,1,4,3,6,0,7,4,4,0,3,1,3,0,6,6,0,3,7,6,8,7,3,3,7,5,3,2,0,9,7,1,5,6,5,2,1,2,2,3,4,3,4,2,5,9,6,7,7,1,2,4,2,6,2,7,7,9,7,5,8,2,9,2,0,8,1,2,7,3,3,9,1,3,9,6,4,3,6,0,8,6,9,8,1,8,7,4,9,7,3,7,0,0,1,7,5,9,3,8,0,6,6,5,4,7,5,9,1,5,5,1,4,4,3,9,0,6,8,8,4,0,6,5,3,6,3,7,4,0,2,2,7,6,7,5,3,7,4,3,2,0,7,2,5,1,1,6,9,2,2,2,7,4,0,5,8,0,5,3,7,5,0,1,3,4,0,3,2,2,1,3,0,7,5,1,5,1,4,3,7,5,7,3,9,6,2,8,9,9,9,5,8,7,1,6,4,1,2,2,2,8,5,8,0,7,4,1,0,2,7,3,1,3,5,9,0,4,8,6,9,7,5,1,5,8,7,3,9,4,7,6,7,2,4,3,6,3,9,7,0,2,2,5,2,1,2,9,2,8,6,9,7,5,9,4,3,6,5,4,5,4,9,6,7,3,9,4,5,4,3,5,7,1,4,9,8,7,4,9,1,0,1,6,4,6,5,3,8,1,8,8,0,8,0,9,6,3,9,7,2,0,8,8,3,1,5,7,7,2,3,9,3,6,8,0,8,5,6,8,8,9,0,2,3,4,1,6,5,7,7,7,0,8,7,0,1,2,9,2,6,5,7,6,9,9,1,5,2,9,4,9,2,8,7,6,3,3,0,2,2,4,8,7,2,4,4,7,6,2,6,3,0,1,1,2,2,3,1,6,3,7,7,6,6,9,5,7,4,7,3,6,3,4,1,8,4,9,5,2,2,9,6,0,6,5,7,4,2,3,7,2,7,2,1,4,5,8,1,2,9,3,0,8,1,1,1,0,8,1,5,9,3,9,2,5,1,2,7,9,1,4,8,5,7,3,2,2,1,2,0,3,5,7,7,2,2,4,8,9,9,3,0,5,2,0,0,3,3,5,4,8,1,4,1,2,6,9,3,2,4,9,4,0,1,2,3,2,9,6,3,6,6,4,5,5,6,9,7,1,9,2,7,6,8,6,7,5,4,5,4,2,2,3,3,4,2,9,6,2,2,3,3,3,6,5,1,5,7,4,4,8,8,6,0,8,5,2,2,8,2,8,1,5,5,1,8,0,8,3,3,8,7,3,5,1,8,0,4,7,0,8]);
CharacteristicPolynomial(A);


Output: Magma V2.11-2     Tue Aug  3 2004 12:13:08 on modular  [Seed = 358346151]
   -------------------------------------


>> A:=Matrix(IntegerRing(),[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,
            ^
Runtime error in 'Matrix': Bad argument types
Argument types given: RngInt, SeqEnum[RngIntElt]

>> CharacteristicPolynomial(A);
                            ^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:14:01 2004

Input: A:=Matrix(IntegerRing(),100,100,[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3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,3,9,7,2,6,2,7,9,8,4,7,8,9,3,4,3,3,3,1,2,9,5,2,2,5,3,5,0,7,2,0,9,1,8,2,2,5,9,8,1,4,1,3,2,8,7,4,0,8,6,4,5,1,6,7,4,5,5,5,0,6,6,1,7,4,0,1,4,1,9,4,1,7,1,3,4,3,7,2,5,8,2,2,9,2,9,7,1,6,6,9,6,8,5,4,7,8,6,2,2,9,8,1,2,5,8,1,3,1,8,2,7,5,9,4,8,3,0,7,3,4,8,6,7,7,1,6,0,3,5,1,1,2,1,8,5,2,0,2,7,7,3,4,2,5,7,9,8,4,4,0,3,1,9,6,3,4,2,6,4,3,9,7,3,7,1,2,7,6,6,7,5,9,4,5,7,2,8,0,3,4,0,0,5,7,8,6,7,2,1,6,3,1,6,0,0,1,7,1,7,5,0,2,2,8,1,0,2,3,4,2,7,4,1,8,4,0,6,8,1,7,3,3,8,1,7,8,6,7,3,8,7,7,8,4,2,0,1,7,2,2,1,4,2,9,9,4,3,3,9,4,3,6,4,6,2,6,4,6,1,9,1,0,4,7,3,4,3,1,3,9,9,9,3,9,2,0,8,1,7,8,3,4,1,9,1,0,2,7,8,0,4,4,8,0,2,5,2,1,1,5,4,3,4,8,6,9,3,0,5,6,1,3,3,0,5,8,3,8,7,1,5,9,7,1,8,0,0,3,9,5,4,7,2,2,7,9,6,2,9,8,9,1,0,8,9,1,7,6,8,2,4,0,7,1,9,5,7,8,6,1,0,8,0,2,1,7,3,3,3,9,8,8,1,0,9,9,9,3,5,0,7,2,0,1,1,8,6,3,7,6,9,3,8,2,1,5,6,4,8,4,3,5,3,3,1,3,8,5,4,3,7,0,8,1,9,4,6,0,2,4,9,1,6,2,9,0,7,3,5,9,3,4,7,2,4,2,7,0,0,8,5,3,8,2,1,6,0,5,8,1,2,2,1,5,8,0,0,6,0,9,3,9,7,9,3,5,4,4,0,6,3,0,4,3,2,0,4,8,3,8,5,6,8,2,9,8,6,1,4,8,1,0,7,5,7,7,3,9,8,5,1,4,8,9,3,4,2,0,5,0,9,1,8,6,5,3,7,5,7,9,2,5,8,2,1,0,2,5,6,5,6,8,4,5,6,3,9,6,4,4,0,2,2,9,5,5,8,5,0,7,4,2,1,5,6,6,4,7,7,1,7,1,3,7,1,0,1,2,6,1,2,3,2,0,7,0,4,5,9,2,3,1,2,7,4,4,3,3,2,4,3,4,4,3,8,2,9,3,8,1,1,9,9,5,6,5,8,2,0,6,4,5,1,6,8,4,0,2,8,6,8,0,5,3,9,3,9,3,1,2,1,6,8,5,9,1,0,5,4,3,8,4,1,4,2,6,5,8,2,8,3,0,3,8,6,9,2,6,8,3,7,1,6,5,3,3,9,6,6,6,9,5,0,0,6,8,4,0,8,4,3,3,6,3,3,4,4,3,6,2,7,2,2,2,8,2,9,7,4,5,6,4,0,7,6,0,5,6,7,3,4,3,3,4,9,0,4,9,9,9,2,9,6,9,1,5,8,3,5,8,6,3,0,6,8,5,7,7,2,8,9,9,0,7,3,3,1,4,1,0,8,0,8,8,3,4,2,4,3,3,9,4,5,3,8,5,2,7,5,7,1,1,8,8,0,1,3,2,4,0,9,3,7,4,4,1,8,3,3,8,8,2,1,3,9,9,5,8,3,5,4,6,6,7,1,3,7,1,5,7,5,9,6,4,2,5,7,2,8,7,1,5,0,4,2,0,2,2,2,7,0,3,9,5,9,6,2,6,6,8,6,1,0,2,9,8,7,4,8,8,8,0,9,9,0,9,4,9,2,1,7,5,4,5,5,8,6,8,6,7,0,5,9,3,0,5,2,5,9,2,1,5,6,3,9,3,7,9,6,2,3,6,2,9,6,3,2,5,8,1,2,8,9,4,4,4,1,9,8,9,4,9,8,7,1,0,2,2,2,2,8,2,3,3,3,7,9,6,2,2,5,6,0,4,2,8,3,0,6,9,8,8,4,8,3,9,2,7,7,1,1,9,0,7,6,9,2,8,3,2,8,3,4,1,0,2,7,6,3,7,5,5,2,8,2,7,1,7,3,2,8,6,1,8,1,1,3,4,3,1,9,3,1,5,1,9,7,7,5,2,2,7,8,7,3,2,7,9,5,3,7,8,9,6,8,7,7,0,7,9,5,3,9,8,1,1,9,1,6,3,1,4,2,6,1,0,1,6,6,2,5,7,6,5,7,8,9,1,7,1,8,1,8,8,6,9,0,9,0,6,8,9,0,3,2,3,9,6,6,8,2,3,5,2,2,0,7,0,4,9,4,8,1,6,1,0,4,2,9,9,2,7,7,0,3,0,5,1,2,2,9,3,0,5,2,6,9,6,5,3,4,5,2,9,2,7,9,5,8,9,0,5,3,6,1,5,2,5,7,8,1,5,9,6,9,4,4,1,3,4,4,0,3,6,1,5,7,3,6,7,3,4,5,1,3,0,5,6,3,3,6,6,9,7,9,5,3,4,1,0,6,0,6,8,2,8,5,6,2,9,3,1,8,9,7,8,0,0,4,7,7,8,5,1,4,9,5,5,2,0,0,1,4,1,9,7,9,9,9,0,0,0,1,8,3,0,0,6,8,5,4,2,2,1,0,9,9,9,3,7,1,0,4,8,7,5,9,9,9,0,3,0,3,7,6,4,0,0,4,5,9,4,3,9,8,8,7,7,9,1,2,0,2,0,3,8,9,4,7,1,9,3,4,4,0,1,2,2,8,1,1,0,5,3,3,5,0,0,3,1,8,1,3,4,5,2,9,1,2,6,0,9,2,1,5,6,3,2,6,4,6,9,7,3,6,3,8,1,4,6,1,5,2,3,9,6,3,2,7,5,0,9,5,7,3,1,3,1,2,3,2,7,9,8,2,9,4,1,4,7,9,6,5,8,5,2,6,7,8,2,0,9,9,4,7,9,3,2,1,7,7,5,7,2,8,8,5,0,1,8,4,2,1,0,9,6,3,0,4,9,5,4,0,1,3,9,2,8,7,9,8,4,2,4,4,0,9,2,6,0,2,5,5,6,6,3,0,3,6,2,0,7,9,9,7,7,7,5,7,9,3,4,8,4,6,3,9,0,6,4,9,1,1,4,1,6,5,5,2,6,0,1,2,6,3,9,0,3,7,9,4,1,0,6,7,8,5,6,5,4,8,4,2,7,3,8,0,3,0,4,4,3,4,4,9,2,4,4,7,8,4,2,8,4,4,5,2,1,8,8,0,2,6,0,6,1,0,0,2,0,9,8,1,2,1,4,2,4,5,0,8,5,0,0,4,1,8,1,0,6,9,7,9,1,7,8,8,0,1,3,5,0,1,9,5,2,9,9,1,7,5,5,2,7,8,2,6,3,6,8,1,9,6,5,9,9,9,3,6,4,2,2,5,9,1,9,8,5,9,2,9,3,1,2,0,4,8,4,4,8,9,7,1,2,4,1,2,6,7,1,3,7,9,3,3,3,2,4,4,9,5,6,4,1,0,1,2,3,4,4,7,7,9,4,6,9,7,7,2,6,0,2,1,1,0,5,1,9,5,3,6,3,1,2,9,6,9,0,4,7,0,0,0,1,7,2,5,1,4,2,6,0,5,4,4,6,0,6,4,8,2,2,2,3,8,9,5,9,5,1,0,4,8,5,8,9,3,2,3,5,6,0,1,1,6,3,3,7,0,2,5,1,0,9,6,1,8,7,4,8,1,7,5,4,0,9,1,5,8,5,2,8,5,5,5,8,6,8,3,2,7,7,6,9,9,1,5,8,2,5,2,8,2,6,2,8,0,5,9,9,5,4,4,4,2,4,7,5,5,9,8,6,8,7,8,8,0,5,8,0,2,2,6,8,6,1,5,1,0,7,1,1,9,9,0,7,2,3,2,9,4,0,0,3,7,5,2,7,1,7,0,9,4,1,5,0,8,9,0,1,2,7,6,8,7,9,3,3,5,7,8,7,0,9,0,5,0,9,4,9,5,2,6,5,6,9,5,7,4,2,6,6,2,8,2,8,0,0,3,6,7,0,3,3,1,2,2,7,1,0,0,4,8,6,4,1,2,6,5,2,5,6,1,2,0,4,1,9,7,2,0,3,6,1,8,4,1,1,0,7,7,9,5,9,1,1,0,1,8,9,5,7,1,8,7,1,9,4,9,4,9,7,0,2,0,3,4,3,1,6,1,7,1,4,0,9,8,8,8,9,6,9,4,1,7,0,0,1,3,0,2,4,1,8,8,7,4,6,5,6,7,8,2,1,1,4,3,6,0,7,4,4,0,3,1,3,0,6,6,0,3,7,6,8,7,3,3,7,5,3,2,0,9,7,1,5,6,5,2,1,2,2,3,4,3,4,2,5,9,6,7,7,1,2,4,2,6,2,7,7,9,7,5,8,2,9,2,0,8,1,2,7,3,3,9,1,3,9,6,4,3,6,0,8,6,9,8,1,8,7,4,9,7,3,7,0,0,1,7,5,9,3,8,0,6,6,5,4,7,5,9,1,5,5,1,4,4,3,9,0,6,8,8,4,0,6,5,3,6,3,7,4,0,2,2,7,6,7,5,3,7,4,3,2,0,7,2,5,1,1,6,9,2,2,2,7,4,0,5,8,0,5,3,7,5,0,1,3,4,0,3,2,2,1,3,0,7,5,1,5,1,4,3,7,5,7,3,9,6,2,8,9,9,9,5,8,7,1,6,4,1,2,2,2,8,5,8,0,7,4,1,0,2,7,3,1,3,5,9,0,4,8,6,9,7,5,1,5,8,7,3,9,4,7,6,7,2,4,3,6,3,9,7,0,2,2,5,2,1,2,9,2,8,6,9,7,5,9,4,3,6,5,4,5,4,9,6,7,3,9,4,5,4,3,5,7,1,4,9,8,7,4,9,1,0,1,6,4,6,5,3,8,1,8,8,0,8,0,9,6,3,9,7,2,0,8,8,3,1,5,7,7,2,3,9,3,6,8,0,8,5,6,8,8,9,0,2,3,4,1,6,5,7,7,7,0,8,7,0,1,2,9,2,6,5,7,6,9,9,1,5,2,9,4,9,2,8,7,6,3,3,0,2,2,4,8,7,2,4,4,7,6,2,6,3,0,1,1,2,2,3,1,6,3,7,7,6,6,9,5,7,4,7,3,6,3,4,1,8,4,9,5,2,2,9,6,0,6,5,7,4,2,3,7,2,7,2,1,4,5,8,1,2,9,3,0,8,1,1,1,0,8,1,5,9,3,9,2,5,1,2,7,9,1,4,8,5,7,3,2,2,1,2,0,3,5,7,7,2,2,4,8,9,9,3,0,5,2,0,0,3,3,5,4,8,1,4,1,2,6,9,3,2,4,9,4,0,1,2,3,2,9,6,3,6,6,4,5,5,6,9,7,1,9,2,7,6,8,6,7,5,4,5,4,2,2,3,3,4,2,9,6,2,2,3,3,3,6,5,1,5,7,4,4,8,8,6,0,8,5,2,2,8,2,8,1,5,5,1,8,0,8,3,3,8,7,3,5,1,8,0,4,7,0,8]);
CharacteristicPolynomial(A);


Output: Magma V2.11-2     Tue Aug  3 2004 12:13:59 on modular  [Seed = 492037628]
   -------------------------------------

$.1^100 - 454*$.1^99 + 3485*$.1^98 + 238375*$.1^97 - 2167475*$.1^96 + 
    145928996*$.1^95 + 766059193*$.1^94 - 102493527178*$.1^93 + 
    410820297044*$.1^92 - 58618484962458*$.1^91 - 148794484256925*$.1^90 + 
    17946628045208882*$.1^89 - 971162741103923403*$.1^88 + 
    122279583007010534625*$.1^87 - 905218001877861096763*$.1^86 - 
    79472037207019667435162*$.1^85 + 1828539975774454149973763*$.1^84 - 
    1005282005136826230701526*$.1^83 - 1273291237552263760044461492*$.1^82 - 
    12221712689012373716369136869*$.1^81 + 
    1002149960751552714477136363691*$.1^80 + 
    10801090462551542195153973118993*$.1^79 - 
    431519013167316973842076126186894*$.1^78 + 
    6599991752980262268123826176021985*$.1^77 + 
    11299482718388699456152994331853325*$.1^76 - 
    10719273675695332199728300429436518426*$.1^75 + 
    193382574457974159246403551227455298161*$.1^74 + 
    3684002560962938444034285554496222993822*$.1^73 - 
    162582554350476861696891840995889841192767*$.1^72 + 
    2670713444735509197925079451238529649395574*$.1^71 + 
    44633024193546938991263494294047143217870414*$.1^70 - 
    1532858490923522026304694235510325259587632752*$.1^69 - 
    2806057320490987966060548155354486029720182269*$.1^68 + 
    562683689458300033727267488597918357685032493126*$.1^67 - 
    23617633477501476534266658170687361055221056107138*$.1^66 - 
    212018394647171682881273088514726067555099874508551*$.1^65 + 
    14767426092095758316823169011979879276748699667737589*$.1^64 - 
    355093933438375350779860777463187674089520106071809829*$.1^63 + 
    1213111456897067212789869136827349031980525672240430275*$.1^62 + 
    226395483982117924166921203316140291018485653187029629891*$.1^61 - 
    3410976730989948156569458904812182896272741738516167226391*$.1^60 - 
    25936553957611170274637564074178807315962907103277953613829*$.1^59 + 
    1635419261391546680126537349005403156200725147404423274685158*$.1^58 - 
    24529590482331318612147743422559152661090852537854321811166654*$.1^57 + 
    179250656761621307004679769550162574600571482506187839294179596*$.1^56 - 
    559912785046392028010063375940009143973378583076309861502474521*$.1^55 - 
    356416233016309687805124058259706188825450812714127953210086087748*$.1^54 + 
    15900913644064428059717334771856369219865182094843653925415361847443*$.1^53 
    - 189907542936384375290190274430393605119527171182661360575611854272987*$.1\
    ^52 - 204647354983405466145549843482249589900678892199558664925629030031081\
    0*$.1^51 + 1575529885021517955188726839001777793713015029557549998119985692\
    00585603*$.1^50 - 231975850360975219002199989253197232403437456281695694327\
    8268668732110002*$.1^49 - 1941677214733337091478249511133912279354388146611\
    9117410276908869601536686*$.1^48 + 1041746499544042126833905057542968873522\
    712264131722991623603371531934895472*$.1^47 - 
    194742971770204379765798650733890250207592627013357142063178826225888093212\
    84*$.1^46 + 367511424478522665210454923517633387044602421606539833687131224\
    29174069618169*$.1^45 + 701371326219931863831407146940647680035460544634676\
    6516348871480056256094559885*$.1^44 - 1330374275490206573169305751706978153\
    21665044438880413416136970240144315323844326*$.1^43 + 
    155063333078062823623157588657010836165246066648360337930689268087699480801\
    2364835*$.1^42 - 1945019152462121597821681310016813908815588513932355870061\
    882567471368562415670374*$.1^41 - 82100417642282461041889003961002731341841\
    3561443173867954948874277108457157539413529*$.1^40 + 
    935809808281043562175632122716528238558314959038084356892842079424474132375\
    1129828469*$.1^39 + 1297877645896464943447171286087957073413313653388762233\
    5576528810196358878596922622682*$.1^38 - 
    716330680824963338885734673596371541421951633002583280279539861320236926904\
    5574597293238*$.1^37 + 1160949378290562276829142896299072375028639328886785\
    11225902149608516971408631510527131865*$.1^36 - 
    158368999998768396197910416850970723744766521004945422155910099983484667844\
    977363371420811*$.1^35 - 23307981447978648616734334714702547784826090507256\
    336779054357376259859167381438025329263424*$.1^34 + 
    399789471454797608827067182712282605578923036821013105463734779427707126109\
    680057219089867725*$.1^33 - 18120429886541256201288791892990703905720564690\
    77706042459917932487477167835445812967506630334*$.1^32 - 
    839177532742689981469323936600322906007619418197924565713128708822656818836\
    56817172063360557304*$.1^31 + 119771117210347065534813195103651315990656202\
    6941123763909039319450605497806870273531151218936243*$.1^30 - 
    324527112283963266572262973408481722216744672476213110153558136107765310396\
    03388651329561187799887*$.1^29 - 789978145769015698170371089355506991668401\
    44099182675602512789251379286164682722383944597352711943*$.1^28 + 
    171645415234495734123120234241100436911163855736559975566517562329500671949\
    4127017581364738585643314*$.1^27 - 1358670334624316894357624018980946706704\
    55431877661270409558568504087548794144662861088317208579499169*$.1^26 + 
    537285983545065320476380664779116272662839000040557613668604921656982384720\
    736288976953278739811523355*$.1^25 - 56551048449197672469329722901550566095\
    94392989672127460008459959845369838268867395097505200999318507730*$.1^24 - 
    182414566674863835323388302148430547947826575032098089103606558927783960267\
    674386262268373592494062990389*$.1^23 + 
    257660316676405051996084784172425412113194111642472602972334717217437162519\
    1908536327498340332350658141478*$.1^22 - 
    538085845292841338142216496441598260928702038593078053761612606793174475580\
    27842573086459447509194211846135*$.1^21 - 
    171442216175565213390489613502751331679094272873819648729957174998953889849\
    124646644462643514884539576509763*$.1^20 + 
    288819994815413794071576439368065514557458420943601227301830269241957521839\
    4630731069783416861546368861100243*$.1^19 - 
    120266937210079788198901734866799654374440959980469293021083249594173685390\
    127916641456300769301420160829573591*$.1^18 - 
    241331481534446869819444615470906311868049228148204015680328445481476037080\
    708466582534087563739116499625591265*$.1^17 + 
    303159142249986801709280918333610044456430942546374323500535807458113943076\
    3779455850558958652193545661104460534*$.1^16 - 
    156989831957622525895732470004653210904463174103565277755424841713423015854\
    061626625425609459304527417913812049391*$.1^15 + 
    183413630845409535796100473184309040760411568108441463700058009443259545741\
    0612706160039951094696199435435886232257*$.1^14 - 
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    71807255878434379231143790512967004946946*$.1^13 + 
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    888245224987572268622579059899817697349993*$.1^11 + 
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    118489650901528822582727342744407206407982766285655425911066854913343118025\
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    14392753682957592011026687093272596919905185862*$.1^5 - 
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    0155454578047811308135544133450724284811505448877*$.1^4 - 
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    4740797922320858045901081836073884470670410217426*$.1^3 + 
    265916393174843619133941412689983664767795385085100580680463877361047439517\
    48230645861065743681359697011029803881532230634011*$.1^2 + 
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    42149482612109713538769047843822089132910024106796*$.1 + 
    533944436219731571965183214310773292674151426710795318076393685522424245006\
    80472810185080287152950201175585831820745130181164

Total time: 1.379 seconds, Total memory usage: 4.07MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:16:58 2004

Input: A:=Matrix(IntegerRing(),300,300,[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3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,3,3,7,8,2,9,5,1,1,5,0,3,0,9,0,6,7,9,7,7,9,4,6,7,7,6,7,3,6,6,5,1,1,8,3,6,3,4,9,0,5,3,0,7,5,9,8,9,8,7,1,8,3,8,6,9,1,0,8,0,2,7,5,4,0,7,7,9,7,8,6,8,0,9,8,8,9,4,8,2,1,6,1,8,6,9,8,6,1,8,5,2,4,9,8,5,4,6,6,9,1,2,5,9,2,7,8,6,9,6,1,4,0,6,3,4,8,7,7,4,9,5,0,6,1,0,7,7,5,9,0,2,9,6,5,8,0,5,6,3,6,3,5,7,7,5,8,4,9,0,9,3,6,7,9,2,5,7,4,1,3,4,9,4,4,1,9,3,8,9,6,3,3,8,1,0,2,2,5,9,3,6,0,3,3,3,3,6,1,9,4,8,2,2,3,6,0,9,5,3,2,2,0,0,5,0,9,9,3,5,6,5,9,1,9,4,6,5,2,6,2,0,8,9,7,2,9,0,7,9,2,0,6,1,8,2,6,8,2,1,6,1,9,0,5,3,6,7,7,5,0,8,5,6,7,5,8,2,4,3,3,6,7,3,0,9,8,5,3,4,3,8,4,7,8,2,0,7,3,5,7,8,7,7,1,2,4,0,1,6,1,1,4,6,2,8,9,9,3,2,7,4,3,3,1,6,1,0,9,9,8,3,6,1,0,3,2,7,1,7,0,9,0,0,4,6,6,2,5,1,0,8,5,3,9,1,5,1,3,2,3,4,1,6,6,2,8,3,1,3,6,8,5,5,7,7,2,6,1,8,4,7,0,5,6,6,1,1,9,7,8,7,1,7,4,5,7,1,8,5,9,7,0,0,0,8,6,8,3,2,0,1,8,6,4,0,8,1,2,0,6,5,0,4,1,6,7,0,3,1,2,1,9,2,2,7,3,0,1,4,5,3,7,8,1,6,7,8,6,8,6,1,4,2,8,3,6,9,6,2,6,8,2,2,4,4,9,8,5,7,1,0,8,0,2,0,6,3,6,9,1,5,2,9,4,1,8,7,7,5,1,2,3,9,0,2,6,9,4,9,0,1,5,4,1,2,5,0,3,0,4,0,5,4,7,5,0,5,0,9,8,1,6,1,8,3,1,8,8,2,9,1,6,8,0,6,0,3,7,6,8,5,8,1,7,7,9,8,2,6,5,1,8,3,5,5,9,3,8,5,7,8,1,4,0,1,8,4,0,9,7,9,9,8,6,0,5,5,6,6,7,6,3,1,9,4,4,6,6,9,4,9,2,1,9,7,5,3,9,8,8,4,6,9,4,9,2,9,8,5,0,1,3,2,8,7,4,1,8,3,5,5,1,1,8,8,5,3,3,5,3,2,6,2,0,7,4,2,9,2,4,3,7,0,1,0,7,5,7,0,8,8,7,3,3,4,5,0,4,1,3,2,5,6,5,7,7,0,1,3,9,5,2,1,6,3,4,4,2,4,4,5,8,1,2,7,8,2,2,5,9,0,1,9,2,9,9,8,0,5,7,4,1,0,3,3,6,6,3,7,1,5,4,9,5,6,0,2,2,3,4,3,4,5,3,8,7,6,0,7,3,8,8,2,5,9,5,7,2,3,7,7,7,6,9,3,1,7,9,8,2,7,8,5,2,1,2,5,0,7,2,7,8,8,8,6,7,4,1,5,8,1,6,8,0,8,8,5,3,5,1,0,6,8,5,4,4,7,6,5,1,5,7,7,9,8,1,9,3,1,6,4,9,2,3,7,4,6,5,6,2,6,3,6,8,5,5,0,4,8,9,7,0,9,6,1,0,1,7,0,5,6,1,3,2,6,0,1,0,0,5,1,7,6,1,0,3,5,1,2,7,0,1,1,0,5,1,2,9,6,9,8,4,9,9,2,9,6,3,0,4,3,3,4,7,6,3,1,3,2,4,3,2,8,8,5,5,8,9,4,8,6,1,1,7,8,8,7,5,5,4,6,4,7,5,3,6,1,3,2,5,1,5,7,3,0,4,8,9,6,7,5,1,8,5,2,2,6,1,1,5,6,0,6,0,6,2,7,2,9,1,3,3,9,1,8,3,9,5,2,5,1,8,3,8,5,4,3,1,5,4,7,2,0,5,1,5,4,3,7,4,7,2,8,5,4,7,9,5,1,6,3,5,9,1,6,5,0,6,6,0,0,5,4,2,8,6,7,7,8,9,7,5,1,5,0,4,1,8,9,1,3,5,4,7,4,8,0,0,8,9,6,1,1,4,6,9,7,4,8,8,0,3,4,8,7,0,3,6,6,8,6,6,3,8,0,9,9,0,2,1,8,1,3,1,9,9,1,9,8,2,5,9,5,5,3,4,4,6,3,1,3,6,6,7,7,8,1,8,6,6,5,8,9,8,6,8,8,1,8,3,4,3,0,0,3,6,4,9,9,8,3,5,0,5,4,3,8,1,3,1,1,5,6,1,4,6,4,9,2,6,4,3,9,1,7,1,4,4,3,3,5,6,4,4,1,3,1,2,9,2,3,5,0,4,1,3,7,9,6,4,1,5,3,7,6,3,1,7,0,3,1,3,5,3,2,7,8,1,4,9,1,2,7,6,8,3,4,8,7,0,3,1,9,1,3,6,1,5,7,0,8,7,9,3,8,4,3,3,9,3,7,3,5,1,0,0,7,5,1,2,0,9,8,1,8,1,3,3,9,7,1,8,0,8,9,9,9,9,7,6,2,5,4,6,8,7,0,7,7,5,1,4,3,2,1,4,2,5,2,9,2,6,1,6,9,3,1,7,3,4,3,8,1,1,4,9,5,5,1,6,6,4,9,7,4,5,2,0,9,6,5,4,5,2,6,2,3,0,4,1,3,4,6,9,4,5,6,0,8,9,2,2,4,7,4,7,6,6,9,1,7,0,4,3,5,4,6,6,2,8,5,1,4,0,4,9,5,8,4,8,9,7,8,6,6,0,8,5,4,6,2,0,4,7,7,7,3,1,1,3,7,0,6,1,3,2,1,7,2,2,9,5,5,1,9,4,6,2,9,4,7,1,9,1,6,1,3,0,2,7,2,1,6,5,6,0,6,3,4,5,5,6,6,9,1,1,3,4,1,6,1,3,4,3,6,0,4,1,1,5,5,6,6,8,4,4,8,5,4,3,6,1,8,9,2,4,2,5,5,6,2,3,6,5,4,0,0,4,7,5,7,9,9,7,3,9,6,7,2,5,5,8,9,4,4,8,0,1,6,7,1,2,5,8,0,4,6,6,9,1,3,1,3,9,3,4,5,4,6,3,1,7,0,5,9,6,3,8,9,3,6,8,7,1,3,9,8,2,7,0,1,1,7,6,7,3,6,7,7,3,5,9,5,9,1,6,2,2,4,9,2,1,5,8,0,1,3,3,1,2,2,6,1,4,3,5,9,3,9,0,3,4,6,5,0,1,9,7,3,6,7,4,4,5,4,9,1,8,1,4,7,0,6,1,1,7,3,6,3,4,3,1,2,1,3,6,4,3,6,2,5,2,3,8,7,3,3,8,2,1,3,4,6,6,4,0,7,5,3,5,8,8,5,6,3,3,0,2,9,7,2,1,0,0,4,6,7,2,9,4,7,5,3,3,5,0,0,6,9,5,6,7,5,9,4,6,7,1,9,6,7,9,0,5,6,8,0,7,2,6,8,3,3,0,9,1,7,3,4,7,5,5,4,8,2,5,6,5,7,5,4,2,7,1,1,7,0,3,1,3,3,5,9,4,4,1,1,7,7,8,5,4,5,9,0,2,7,6,4,7,2,5,8,0,6,6,6,9,1,6,7,5,3,9,5,9,2,7,9,9,7,2,1,5,0,5,4,4,4,6,2,0,5,9,2,5,8,2,8,2,9,1,8,6,1,8,6,5,4,7,2,2,3,1,9,0,0,2,2,2,5,9,9,8,9,9,8,9,1,5,6,4,6,9,8,3,0,2,2,4,1,3,9,9,0,6,2,5,3,1,2,3,0,4,1,6,7,8,9,9,9,0,5,6,6,5,3,3,5,1,8,9,3,5,4,6,7,6,6,9,3,5,1,1,2,0,3,8,3,4,0,9,2,0,1,6,2,8,3,9,7,5,6,3,4,3,2,2,4,1,4,4,7,2,7,5,6,4,4,0,2,5,1,8,4,4,2,1,7,6,3,0,1,4,6,4,9,0,5,5,1,6,6,1,2,8,7,2,4,3,7,2,4,2,7,9,8,8,1,8,3,1,0,4,7,2,3,6,1,2,8,4,9,6,7,2,0,7,1,4,8,5,1,2,5,1,0,2,5,5,8,5,4,9,6,3,4,7,7,2,0,3,1,7,5,7,0,5,4,9,9,4,3,2,1,6,8,9,6,6,7,2,2,2,9,5,2,5,9,7,5,7,0,8,9,8,1,0,8,1,2,3,2,3,8,4,4,7,0,4,2,0,0,1,9,6,0,4,9,9,8,3,5,9,6,7,4,8,4,0,8,7,0,0,4,6,2,1,1,3,3,8,8,5,3,3,2,3,7,7,3,7,3,4,8,9,2,0,6,9,5,3,2,7,1,3,2,4,7,0,9,4,3,2,9,8,9,7,5,1,7,2,5,4,9,6,2,7,0,9,1,1,6,8,2,8,5,4,6,8,1,2,7,0,3,0,9,1,7,4,7,8,3,8,7,7,1,8,0,4,7,1,5,1,2,6,3,7,7,3,5,3,5,5,4,7,3,4,2,7,1,2,7,0,3,4,3,5,6,2,3,6,1,3,0,8,1,9,5,0,4,2,3,3,8,0,0,4,1,4,4,2,1,5,6,7,9,8,5,3,6,9,8,8,4,2,0,0,7,4,8,6,6,0,6,7,0,5,0,1,2,8,5,6,2,8,1,8,0,2,7,6,3,8,0,9,0,6,5,9,4,0,1,1,1,8,0,4,1,9,8,4,5,3,6,7,7,3,1,5,7,2,5,0,0,4,4,9,9,8,5,9,8,3,2,6,1,9,7,2,8,5,3,5,0,8,1,1,6,8,7,2,2,0,9,8,4,9,5,2,7,3,0,7,5,2,4,3,5,7,9,4,6,8,5,4,1,4,7,7,4,5,8,7,7,7,9,3,7,4,2,9,7,3,1,4,4,4,5,4,3,4,0,8,2,7,1,8,3,8,6,3,5,7,9,8,9,0,5,7,9,8,6,8,5,2,6,2,2,6,1,8,8,4,2,4,8,8,4,7,0,7,0,0,1,1,7,2,6,9,3,7,3,7,8,5,9,9,0,5,5,7,9,7,3,6,1,9,4,1,3,4,6,2,8,1,0,6,3,3,0,3,7,1,8,4,9,2,5,8,9,0,3,5,9,7,3,0,6,2,5,9,8,0,8,6,0,1,8,2,7,9,6,7,9,3,6,6,3,3,6,9,2,3,5,6,5,8,3,6,0,1,2,9,1,8,5,7,7,5,5,4,2,0,6,4,2,0,8,6,7,8,1,0,1,6,4,9,4,6,4,3,5,3,1,0,3,8,5,1,8,1,0,9,6,4,0,2,8,9,1,4,1,5,4,5,1,7,7,7,7,1,4,1,2,3,4,3,9,9,4,7,9,2,2,5,8,3,6,3,6,0,1,0,8,7,8,1,9,5,0,9,0,9,3,8,3,2,9,2,2,9,1,7,3]);
CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 12:16:38 on modular  [Seed = 1663932451]
   -------------------------------------



************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:19:03 2004

Input: A:=Matrix(IntegerRing(),150,150[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3,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3,2,0,1,1,5,0,1,0,7,7,2,8,7,9,3,3,6,8,4,5,1,2,0,1,5,0,3,3,0,3,7,9,2,6,4,2,3,4,1,3,9,6,6,7,8,4,2,8,7,4,7,0,2,2,0,6,5,5,7,8,3,5,3,5,6,0,0,0,8,4,4,3,5,0,1,8,6,7,1,3,6,6,4,4,3,3,6,5,0,5,3,4,1,9,6,4,7,2,8,5,7,0,3,9,0,0,8,4,7,8,8,8,6,0,8,0,7,5,0,5,3,2,2,7,9,1,4,9,3,1,9,7,4,7,6,4,9,8,8,7,0,7,3,3,9,0,4,1,0,5,1,5,4,4,7,3,5,2,2,4,2,9,2,6,7,7,2,3,5,2,4,5,3,1,0,3,8,5,5,3,0,0,5,4,4,6,1,0,1,5,1,6,7,8,3,3,1,8,0,4,8,8,4,4,0,2,5,5,0,4,1,7,5,8,5,7,1,7,3,0,8,0,5,1,1,6,4,2,1,3,0,0,6,8,1,5,5,4,3,9,9,0,3,0,1,0,5,5,8,2,8,1,7,3,5,7,4,2,1,3,5,6,5,2,3,1,4,8,2,7,2,0,1,2,3,2,8,7,3,9,6,4,7,4,6,2,7,0,1,7,8,4,5,0,8,1,4,3,4,4,5,2,9,5,3,4,1,9,6,8,9,3,9,1,5,1,5,3,9,1,1,4,8,7,9,7,5,4,9,8,1,4,3,3,5,1,6,1,0,7,1,7,7,3,8,9,3,4,9,2,0,8,4,9,6,4,0,7,4,9,7,9,5,9,6,2,2,5,4,0,6,6,7,6,9,9,9,7,0,0,0,9,6,8,0,9,9,7,9,4,1,3,7,9,7,6,2,2,4,2,2,7,3,5,4,2,9,8,8,9,3,4,5,5,4,3,8,3,5,1,6,0,8,9,9,6,3,9,2,3,7,7,3,5,6,2,6,7,1,0,8,9,4,2,8,6,6,8,3,1,3,6,7,6,6,6,3,5,9,7,6,9,9,8,5,5,6,1,8,5,3,6,2,9,0,7,1,9,8,8,5,9,3,0,1,5,8,1,8,3,3,2,6,7,6,4,4,7,6,8,2,4,8,7,3,6,8,1,3,8,6,7,3,2,8,0,5,9,4,0,1,6,5,4,1,1,0,0,7,4,5,2,8,2,5,2,1,3,1,2,5,9,8,0,4,2,0,4,7,1,9,4,0,1,4,9,0,7,1,2,9,9,1,9,7,1,0,2,8,3,5,7,5,2,7,4,8,7,6,5,7,0,6,2,2,7,8,4,3,2,1,0,2,8,9,2,0,7,4,2,1,2,3,8,9,7,7,8,3,6,3,7,3,3,9,1,1,7,9,3,8,8,0,1,1,8,3,2,1,3,3,0,1,5,3,7,0,5,9,5,4,4,0,8,6,0,5,8,2,2,0,0,2,7,8,7,3,8,4,0,6,8,8,1,1,7,0,8,8,1,3,5,4,9,6,4,7,3,8,3,6,2,9,5,4,5,4,5,4,8,9,3,2,7,5,2,1,2,5,9,9,7,3,5,7,2,0,8,8,0,8,3,5,3,7,4,0,3,4,0,4,1,3,1,1,7,3,3,1,3,3,6,6,9,7,9,9,5,5,0,9,0,4,1,6,0,0,8,4,9,9,2,4,6,0,3,3,2,8,9,7,7,5,3,6,3,4,5,7,3,0,7,3,4,8,4,9,0,7,5,9,3,3,8,9,5,5,9,3,2,4,4,8,4,7,5,1,3,4,7,6,7,4,9,8,5,5,7,6,2,4,7,7,8,7,3,1,5,1,3,8,5,1,1,6,1,9,6,9,0,2,3,9,3,2,8,6,5,7,9,0,3,6,2,6,0,1,8,4,5,9,7,0,9,1,2,5,9,8,6,7,6,3,8,4,0,9,3,1,7,0,5,4,9,6,0,1,9,3,0,1,0,8,6,7,2,6,5,1,9,8,2,7,2,5,8,3,3,1,8,3,6,2,1,3,1,7,3,1,0,1,8,3,0,3,8,0,2,4,1,5,3,3,2,1,4,2,2,5,7,1,5,9,2,7,8,9,6,6,1,6,3,7,3,0,9,9,7,9,0,5,0,5,5,8,1,0,0,8,5,3,2,5,6,6,9,1,1,8,4,8,3,6,2,1,3,1,5,3,7,3,8,1,9,4,5,1,0,1,1,7,8,0,1,8,9,1,1,7,0,1,1,4,9,8,8,7,5,7,3,2,6,0,4,4,0,8,4,5,5,0,3,1,5,0,9,8,6,1,2,7,2,7,0,3,9,0,5,9,6,4,5,7,9,8,5,7,5,0,8,8,8,3,0,4,1,7,0,8,7,6,7,6,0,9,9,0,0,4,9,9,7,7,7,7,6,2,8,4,9,9,1,4,6,7,0,0,2,0,9,6,7,8,8,2,3,9,4,0,1,5,3,1,6,4,6,3,6,2,4,8,0,3,2,2,9,8,3,7,8,8,5,2,4,4,6,1,4,5,7,4,4,2,9,1,4,5,9,6,4,9,7,7,7,3,8,6,2,7,4,0,5,1,6,3,6,2,9,8,0,6,0,6,8,7,1,3,3,0,9,8,7,4,6,0,0,1,6,4,6,8,0,0,2,7,5,2,6,8,9,7,8,7,3,5,7,2,2,9,9,1,3,2,6,5,8,3,8,5,4,9,6,3,3,5,3,1,9,0,1,9,1,7,6,2,4,1,0,0,4,8,4,2,7,8,9,4,5,3,0,0,5,2,5,5,3,8,2,0,2,4,3,0,9,9,1,9,7,5,3,1,1,2,3,0,2,5,7,7,0,3,4,3,2,8,1,7,4,1,4,0,7,5,5,9,3,9,6,3,2,5,9,8,7,0,2,4,9,5,2,9,6,9,1,7,5,8,7,5,0,7,6,4,1,4,7,6,7,1,8,1,7,8,9,1,6,9,4,3,4,1,2,3,6,9,4,6,5,0,3,7,2,2,4,9,1,5,9,5,8,5,8,9,6,0,7,2,3,5,5,9,1,8,8,7,8,7,8,8,9,7,3,2,0,5,0,9,3,2,6,9,2,5,6,0,0,5,5,8,1,3,1,8,7,7,9,3,0,5,2,9,8,9,9,2,8,4,0,6,4,4,0,5,3,3,9,7,9,0,8,6,2,2,9,6,2,4,3,0,1,5,7,7,4,1,3,2,9,5,9,5,7,3,0,7,0,3,2,6,7,0,4,4,2,0,3,4,4,3,9,0,3,5,6,4,6,2,6,4,5,2,0,7,2,2,9,5,9,7,0,9,3,0,2,8,5,9,8,1,9,5,5,3,8,9,3,5,4,6,8,6,3,7,3,8,6,5,0,0,8,5,6,7,8,7,4,5,7,1,6,8,9,7,9,6,6,3,5,8,1,4,1,9,5,0,6,1,6,7,0,7,3,4,4,1,2,4,6,3,9,0,8,9,4,1,6,6,3,8,7,6,0,4,7,2,1,1,8,7,4,2,3,0,9,1,7,7,0,2,2,2,0,0,9,2,4,5,2,7,9,7,1,6,9,8,9,5,2,4,1,6,9,9,0,3,7,4,0,8,7,1,5,7,3,1,9,5,5,2,3,7,8,4,0,8,8,1,5,0,6,5,6,2,6,1,5,6,0,8,8,5,0,9,8,1,0,0,3,2,7,3,9,1,5,0,2,5,7,8,8,8,3,2,8,6,1,3,8,0,2,3,0,8,0,7,5,2,7,2,2,9,6,7,2,5,5,7,5,9,4,6,7,5,1,8,7,3,5,9,5,6,3,5,2,5,1,1,4,8,4,9,9,1,2,6,0,4,3,9,1,8,3,0,5,5,4,9,4,3,7,9,9,8,9,1,3,3,1,6,1,6,6,8,9,4,9,5,5,3,2,0,6,8,6,9,1,5,1,2,8,6,7,7,8,8,5,7,0,3,9,6,2,1,2,7,5,9,1,2,2,9,4,7,9,7,7,8,7,2,5,3,0,1,4,9,7,1,8,4,2,7,6,4,8,4,5,9,9,7,6,4,3,7,3,0,8,1,2,8,8,4,1,1,3,5,1,8,1,7,5,8,8,2,3,0,9,0,3,4,6,2,7,5,8,8,3,4,6,5,9,8,6,9,3,8,6,1,0,5,9,4,8,1,7,8,1,5,9,4,0,5,9,1,2,6,8,2,6,3,8,0,4,1,3,8,9,0,6,3,8,1,2,9,5,3,4,8,2,0,4,2,0,6,7,1,9,4,7,3,2,9,7,2,5,2,3,9,3,1,5,3,2,3,4,5,8,4,1,5,5,4,0,8,0,7,3,8,5,8,6,9,9,4,0,5,9,9,1,2,0,0,8,0,1,2,6,6,9,8,3,9,7,4,6,8,6,2,3,2,9,9,2,3,8,3,3,7,6,9,7,2,5,2,2,7,6,2,2,8,1,1,7,1,2,5,0,4,4,1,6,8,0,6,9,4,3,2,1,0,6,0,3,4,3,5,9,5,3,8,8,8,7,0,9,1,4,0,6,6,9,6,3,7,0,4,5,3,2,4,5,4,6,3,3,8,4,9,4,6,0,3,5,8,7,3,2,3,6,0,6,2,1,7,1,7,8,8,3,9,0,5,8,2,1,2,7,8,2,2,1,4,2,0,3,7,7,7,9,0,0,8,4,1,0,0,5,4,9,3,3,3,2,7,7,3,2,6,6,1,1,6,2,2,8,3,3,4,5,0,5,9,8,1,5,1,4,7,6,3,7,1,1,2,7,8,2,7,1,6,1,1,6,6,0,1,1,7,0,9,7,6,7,4,8,0,3,6,0,0,4,3,3,0,9,1,5,3,8,8,0,9,2,5,3,7,8,5,0,6,8,6,2,8,4,4,2,9,8,1,2,3,6,2,8,5,5,1,9,4,7,6,1,4,4,2,2,3,2,4,3,5,7,1,4,2,7,4,6,7,6,5,2,5,5,7,9,0,9,3,8,6,3,5,5,0,5,7,0,7,3,9,8,7,6,3,5,5,8,4,2,8,9,2,1,6,6,9,8,7,5,7,0,0,4,3,2,6,0,5,1,7,6,5,8,9,7,2,8,8,8,3,2,5,1,0,1,5,8,2,7,4,0,2,0,0,8,9,5,9,3,3,5,2,4,8,0,0,4,0,7,5,2,1,4,8,9,3,3,4,7,0,7,0,4,6,7,4,6,9,2,6,9,6,6,4,4,1,5,2,9,3,9,4,3,4,8,4,7,6,1,8,8,2,7,3,1,1,4,8,4,8,8,8,9,1,9,8,3,3,6,9,6,9,4,5,6,0,4,6,9,8,7,3,8,9,0,5,2,2,1,8,5,9,2,6,6,1,3,2,9,8,5,4,7,8,8,6,9,5,2,5,9,3,9,7,6,7,1,9,2,9,2,2,8,0,0,2,7,8,0,2,5,0,5,7,7,5,3,9,7,3,9,3,5,7,9,4,9,7,2,2,9,7,0,6,3,6,3,7,4,5,8,2,1,6,5,6,6,4,3,4,5,1,8,8,2,7,8,5,7,2,8,9,6,9,9,0,3,8,4,1,8,4,5,2,5,1,9,2,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7,6,6,1,0,1,3,7,5,5,9,4,3,5,8,4,2,4,1,5,1,2,5,6,7,3,9,6,3,9,8,7,4,6,5,8,3,8,2,1,4,3,8,8,3,1,0,5,0,4,1,6,7,7,5,7,8,1,5,8,4,0,2,7,5,5,7,8,4,7,1,5,4,9,4,4,0,2,8,5,1,5,8,3,3,5,6,9,7,0,3,3,9,5,5,8,0,8,1,4,7,8,7,9,4,5,5,5,4,8,6,6,4,5,1,5,3,5,8,0,9,2,8,3,2,8,0,3,0,0,2,5,8,9,0,4,7,8,4,2,3,8,9,2,4,3,3,5,5,0,3,1,0,3,8,3,0,6,3,4,3,4,8,4,9,1,0,0,0,1,0,0,2,4,1,2,4,4,1,8,3,2,1,3,1,0,0,4,1,9,0,6,1,0,4,8,1,0,9,8,8,6,9,9,1,6,4,2,0,8,0,0,8,1,6,6,5,0,7,7,7,3,8,3,0,6,3,2,6,4,6,2,9,3,6,5,6,8,7,1,7,6,6,7,0,7,9,2,8,7,9,5,4,1,1,0,8,3,3,0,8,6,2,6,0,0,0,5,3,9,8,3,2,8,9,0,7,7,7,1,7,3,1,7,2,0,7,9,6,6,7,5,1,8,2,0,6,9,5,7,2,6,9,1,0,6,2,8,1,8,2,4,8,7,0,0,8,4,7,7,8,1,6,9,1,2,8,6,2,2,0,1,0,5,7,9,4,1,0,6,6,4,6,5,2,6,1,7,8,5,5,5,5,2,6,7,0,0,6,9,7,4,2,8,3,9,2,8,0,8,4,3,9,5,7,7,9,4,8,1,2,6,7,7,2,4,0,7,5,2,0,3,1,8,7,0,1,2,8,1,7,4,1,3,2,4,3,6,1,6,0,1,4,9,5,9,0,2,5,8,2,6,1,1,1,1,2,8,4,6,8,0,4,3,5,2,4,8,9,5,1,5,5,6,8,7,9,3,0,0,1,7,3,1,8,2,0,9,6,1,2,8,8,5,8,3,6,9,0,3,1,4,1,5,0,1,6,2,4,5,0,1,5,9,2,9,8,4,3,4,8,2,0,9,8,0,0,2,5,1,1,1,7,7,4,4,0,9,2,6,1,9,7,0,2,7,9,4,9,7,1,0,4,0,2,7,0,7,1,4,8,7,9,2,4,8,2,9,3,8,7,8,2,5,2,5,5,4,3,7,9,3,4,8,3,6,6,8,1,3,8,9,3,1,1,7,8,3,0,9,7,9,7,9,7,5,6,2,6,7,4,8,8,8,5,5,0,3,4,7,8,9,5,0,8,8,9,7,4,6,1,8,0,2,2,1,2,3,8,6,6,9,0,9,6,6,9,6,9,2,6,8,2,1,5,7,8,4,5,8,6,9,5,1,0,8,5,0,7,0,4,8,6,5,5,0,2,5,5,3,3,2,0,5,3,0,7,5,4,4,7,0,0,2,9,1,7,1,5,1,3,7,1,8,0,2,3,7,6,1,2,4,3,8,8,5,8,5,9,1,7,2,2,2,3,7,0,4,7,4,4,2,9,2,2,9,7,9,0,6,2,4,6,7,9,7,7,5,2,4,0,9,9,5,6,8,2,6,7,4,8,2,7,0,6,6,2,6,9,1,5,5,1,4,8,6,8,3,7,1,5,6,6,2,3,2,2,8,8,9,9,8,0,8,8,1,8,7,2,5,3,7,4,2,7,5,5,1,5,9,6,3,7,1,3,8,8,6,4,9,6,6,8,9,5,1,2,5,9,0,2,4,8,3,9,5,9,8,8,5,4,3,5,1,4,4,0,9,8,4,4,6,7,2,9,3,7,4,7,7,1,9,9,8,1,0,9,2,5,9,4,3,8,2,8,4,8,9,6,3,4,9,5,7,4,9,5,0,4,4,4,7,3,3,5,6,7,0,1,5,7,9,8,7,0,6,7,7,4,7,7,2,5,8,2,4,3,6,5,1,7,4,8,2,6,2,0,0,2,7,9,1,2,0,1,5,9,6,2,2,9,6,0,0,3,8,5,2,4,0,0,5,6,5,1,3,5,4,0,7,7,8,2,2,6,7,7,6,9,8,3,5,1,8,8,8,1,4,9,4,6,9,1,3,9,2,1,8,6,5,1,0,6,7,4,0,5,2,7,9,0,2,2,9,7,5,4,9,6,0,0,4,5,0,9,3,3,8,1,5,7,3,0,9,8,8,5,8,7,5,8,3,6,7,3,9,4,5,5,1,0,1,1,0,8,8,4,1,5,3,7,6,8,4,9,6,0,0,4,1,8,6,0,4,2,5,7,1,1,2,2,2,2,3,2,5,5,5,9,8,7,6,5,2,7,6,9,6,8,2,3,3,7,9,6,6,4,6,8,3,8,6,1,8,5,5,0,5,4,7,5,3,2,3,7,2,5,1,5,8,9,3,5,6,5,4,4,4,8,7,0,9,7,1,5,9,8,1,4,0,4,0,4,5,3,1,1,4,1,3,7,8,6,8,5,9,4,3,4,9,5,3,3,0,6,6,5,5,2,4,4,7,3,6,3,8,5,2,9,8,5,9,4,4,6,2,4,8,8,8,0,1,2,2,7,7,8,5,6,9,9,0,4,7,9,9,2,4,9,7,3,2,3,1,8,3,3,2,5,7,3,5,6,4,2,2,5,4,3,5,7,0,5,2,7,8,0,3,2,4,9,9,2,5,7,8,5,2,8,4,6,5,3,4,3,3,6,4,1,3,3,6,5,6,7,8,9,8,5,6,9,7,7,3,0,2,7,0,9,1,8,0,2,3,3,1,3,7,4,8,9,3,1,6,6,3,6,5,8,7,2,8,1,1,8,7,1,9,6,2,2,1,9,7,7,5,1,0,3,6,6,0,1,3,3,0,3,3,1,4,0,0,5,6,3,0,9,1,1,3,2,2,9,9,6,3,1,5,9,5,2,9,5,7,5,5,7,4,5,8,2,4,7,8,7,4,7,7,9,8,8,2,1,9,2,5,0,4,6,4,8,1,3,3,8,3,2,3,4,6,2,4,2,0,3,3,0,1,1,5,9,9,7,8,2,4,2,4,1,3,3,8,2,6,7,2,6,1,2,5,4,0,8,0,0,7,8,9,6,3,2,2,7,2,4,0,5,1,6,2,6,0,8,6,6,5,4,8,4,1,7,6,3,3,2,7,6,6,5,9,3,5,7,7,2,7,1,8,6,5,1,1,2,4,0,8,4,9,9,6,2,5,3,9,4,0,0,1,7,9,0,8,4,5,4,5,1,7,2,9,8,3,6,3,9,2,0,6,2,8,9,5,7,2,8,4,3,9,7,0,2,0,1,0,4,1,1,4,2,7,4,9,9,1,5,2,8,3,5,9,8,9,9,3,0,6,1,9,8,2,4,9,4,8,3,7,2,9,0,0,7,0,1,8,9,7,9,6,0,2,0,4,0,9,6,3,5,7,2,6,5,9,1,7,7,5,3,7,0,0,2,2,5,4,2,9,9,2,5,8,6,0,1,7,3,2,2,2,9,6,7,8,1,4,3,9,2,3,9,7,0,8,6,9,6,8,0,9,3,9,8,7,6,2,5,2,0,6,0,8,7,2,4,8,1,4,4,7,3,5,6,8,6,0,4,5,4,4,2,0,1,0,9,5,4,5,8,0,1,7,9,7,7,0,3,8,2,0,6,1,5,1,2,6,1,7,4,3,1,5,5,4,0,1,4,4,8,4,2,1,4,9,4,4,9,9,0,7,4,6,1,2,9,6,4,3,2,1,7,4,3,7,7,6,6,6,2,8,7,0,4,4,7,4,6,8,6,3,8,9,2,1,7,3,7,5,8,2,4,5,5,6,2,1,3,2,3,0,6,5,3,0,4,3,2,2,0,7,0,6,3,8,9,0,3,6,3,1,7,1,9,3,9,3,4,2,5,2,4,7,1,9,0,1,5,0,0,4,2,6,0,1,9,9,3,9,5,3,3,1,0,8,5,5,8,4,9,7,3,7,5,6,2,7,3,0,2,4,3,1,7,0,6,6,2,6,8,9,0,9,9,6,1,3,0,3,6,4,9,1,7,8,6,5,3,0,7,9,1,1,0,7,4,3,0,7,8,4,4,2,5,1,5,8,4,0,8,5,6,9,9,7,8,9,9,3,7,2,7,9,6,0,9,1,3,9,1,5,4,3,3,6,1,5,7,9,7,7,8,6,5,9,8,0,6,6,7,0,2,7,8,6,8,2,8,1,0,5,0,0,0,7,2,9,1,8,3,7,6,0,3,8,4,3,2,7,8,0,6,6,2,4,8,0,9,7,9,2,4,4,3,1,8,5,8,1,7,9,5,4,2,9,9,2,4,4,2,5,7,4,6,9,7,4,1,2,3,9,6,4,1,8,1,1,2,0,7,6,8,6,5,9,3,6,0,5,8,1,6,7,6,4,8,1,5,0,8,4,4,2,6,0,4,7,7,9,0,2,2,4,9,4,7,1,1,1,2,1,7,6,9,2,8,8,8,0,3,0,1,6,8,1,8,0,6,4,7,2,4,5,8,7,5,3,1,5,3,8,5,5,3,5,6,4,1,8,0,8,5,6,2,3,1,5,0,2,2,6,4,1,7,8,0,7,5,7,0,9,7,0,6,0,5,9,8,4,2,3,1,5,0,1,3,6,7,8,8,2,0,2,3,4,9,5,2,2,7,6,4,0,8,1,3,6,8,9,5,8,9,0,7,5,3,0,1,2,9,2,8,0,3,4,3,1,0,7,8,8,4,0,3,2,1,9,2,3,8,8,1,5,0,1,8,6,4,9,5,8,7,9,0,8,3,4,1,4,2,6,4,7,9,1,4,4,6,7,8,7,0,0,2,1,2,4,7,6,2,8,2,5,5,4,1,8,8,5,1,9,9,4,1,1,5,0,0,0,5,6,3,0,8,9,3,9,7,5,2,8,3,0,2,6,8,2,6,6,4,2,5,7,0,4,7,4,1,4,0,7,7,0,5,7,2,2,0,9,6,3,9,8,3,0,4,3,9,5,1,0,2,5,8,1,5,1,8,9,3,1,6,0,0,1,9,9,6,8,7,1,4,5,9,3,3,9,7,7,6,3,1,0,6,7,1,6,8,9,7,2,4,1,4,4,1,1,7,8,4,9,9,8,7,3,6,1,2,7,3,0,0,5,5,8,4,3,3,4,7,2,2,8,3,7,8,0,9,9,9,7,9,3,6,0,9,1,2,3,4,8,5,3,1,8,2,5,5,2,5,8,4,5,5,0,7,2,5,9,3,2,8,3,5,5,4,5,1,6,6,9,8,9,0,9,2,4,8,1,0,7,5,4,8,6,3,6,5,1,5,6,8,0,4,6,9,0,7,1,1,7,2,9,9,3,2,4,1,7,9,9,1,9,6,1,7,4,8,1,7,0,7,6,2,3,7,9,4,6,8,8,3,8,6,5,8,9,4,7,7,7,1,7,2,3,0,9,9,1,8,8,2,9,5,6,0,8,4,0,7,2,0,7,5,7,0,8,8,7,1,4,5,1,3,0,3,4,6,3,2,7,8,7,2,7,8,7,8,2,7,2,7,7,0,2,3,2,8,7,8,9,1,7,3,2,9,6,9,0,9,9,8,7,0,6,9,1,3,8]);
CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 12:19:02 on modular  [Seed = 1764201145]
   -------------------------------------


>> A:=Matrix(IntegerRing(),150,150[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4
                                  ^
Runtime error in '[]': Bad argument types

>> CharacteristicPolynomial(A);;
                            ^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.750 seconds, Total memory usage: 6.87MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:19:17 2004

Input: A:=Matrix(IntegerRing(),150,150,[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3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,7,6,6,1,0,1,3,7,5,5,9,4,3,5,8,4,2,4,1,5,1,2,5,6,7,3,9,6,3,9,8,7,4,6,5,8,3,8,2,1,4,3,8,8,3,1,0,5,0,4,1,6,7,7,5,7,8,1,5,8,4,0,2,7,5,5,7,8,4,7,1,5,4,9,4,4,0,2,8,5,1,5,8,3,3,5,6,9,7,0,3,3,9,5,5,8,0,8,1,4,7,8,7,9,4,5,5,5,4,8,6,6,4,5,1,5,3,5,8,0,9,2,8,3,2,8,0,3,0,0,2,5,8,9,0,4,7,8,4,2,3,8,9,2,4,3,3,5,5,0,3,1,0,3,8,3,0,6,3,4,3,4,8,4,9,1,0,0,0,1,0,0,2,4,1,2,4,4,1,8,3,2,1,3,1,0,0,4,1,9,0,6,1,0,4,8,1,0,9,8,8,6,9,9,1,6,4,2,0,8,0,0,8,1,6,6,5,0,7,7,7,3,8,3,0,6,3,2,6,4,6,2,9,3,6,5,6,8,7,1,7,6,6,7,0,7,9,2,8,7,9,5,4,1,1,0,8,3,3,0,8,6,2,6,0,0,0,5,3,9,8,3,2,8,9,0,7,7,7,1,7,3,1,7,2,0,7,9,6,6,7,5,1,8,2,0,6,9,5,7,2,6,9,1,0,6,2,8,1,8,2,4,8,7,0,0,8,4,7,7,8,1,6,9,1,2,8,6,2,2,0,1,0,5,7,9,4,1,0,6,6,4,6,5,2,6,1,7,8,5,5,5,5,2,6,7,0,0,6,9,7,4,2,8,3,9,2,8,0,8,4,3,9,5,7,7,9,4,8,1,2,6,7,7,2,4,0,7,5,2,0,3,1,8,7,0,1,2,8,1,7,4,1,3,2,4,3,6,1,6,0,1,4,9,5,9,0,2,5,8,2,6,1,1,1,1,2,8,4,6,8,0,4,3,5,2,4,8,9,5,1,5,5,6,8,7,9,3,0,0,1,7,3,1,8,2,0,9,6,1,2,8,8,5,8,3,6,9,0,3,1,4,1,5,0,1,6,2,4,5,0,1,5,9,2,9,8,4,3,4,8,2,0,9,8,0,0,2,5,1,1,1,7,7,4,4,0,9,2,6,1,9,7,0,2,7,9,4,9,7,1,0,4,0,2,7,0,7,1,4,8,7,9,2,4,8,2,9,3,8,7,8,2,5,2,5,5,4,3,7,9,3,4,8,3,6,6,8,1,3,8,9,3,1,1,7,8,3,0,9,7,9,7,9,7,5,6,2,6,7,4,8,8,8,5,5,0,3,4,7,8,9,5,0,8,8,9,7,4,6,1,8,0,2,2,1,2,3,8,6,6,9,0,9,6,6,9,6,9,2,6,8,2,1,5,7,8,4,5,8,6,9,5,1,0,8,5,0,7,0,4,8,6,5,5,0,2,5,5,3,3,2,0,5,3,0,7,5,4,4,7,0,0,2,9,1,7,1,5,1,3,7,1,8,0,2,3,7,6,1,2,4,3,8,8,5,8,5,9,1,7,2,2,2,3,7,0,4,7,4,4,2,9,2,2,9,7,9,0,6,2,4,6,7,9,7,7,5,2,4,0,9,9,5,6,8,2,6,7,4,8,2,7,0,6,6,2,6,9,1,5,5,1,4,8,6,8,3,7,1,5,6,6,2,3,2,2,8,8,9,9,8,0,8,8,1,8,7,2,5,3,7,4,2,7,5,5,1,5,9,6,3,7,1,3,8,8,6,4,9,6,6,8,9,5,1,2,5,9,0,2,4,8,3,9,5,9,8,8,5,4,3,5,1,4,4,0,9,8,4,4,6,7,2,9,3,7,4,7,7,1,9,9,8,1,0,9,2,5,9,4,3,8,2,8,4,8,9,6,3,4,9,5,7,4,9,5,0,4,4,4,7,3,3,5,6,7,0,1,5,7,9,8,7,0,6,7,7,4,7,7,2,5,8,2,4,3,6,5,1,7,4,8,2,6,2,0,0,2,7,9,1,2,0,1,5,9,6,2,2,9,6,0,0,3,8,5,2,4,0,0,5,6,5,1,3,5,4,0,7,7,8,2,2,6,7,7,6,9,8,3,5,1,8,8,8,1,4,9,4,6,9,1,3,9,2,1,8,6,5,1,0,6,7,4,0,5,2,7,9,0,2,2,9,7,5,4,9,6,0,0,4,5,0,9,3,3,8,1,5,7,3,0,9,8,8,5,8,7,5,8,3,6,7,3,9,4,5,5,1,0,1,1,0,8,8,4,1,5,3,7,6,8,4,9,6,0,0,4,1,8,6,0,4,2,5,7,1,1,2,2,2,2,3,2,5,5,5,9,8,7,6,5,2,7,6,9,6,8,2,3,3,7,9,6,6,4,6,8,3,8,6,1,8,5,5,0,5,4,7,5,3,2,3,7,2,5,1,5,8,9,3,5,6,5,4,4,4,8,7,0,9,7,1,5,9,8,1,4,0,4,0,4,5,3,1,1,4,1,3,7,8,6,8,5,9,4,3,4,9,5,3,3,0,6,6,5,5,2,4,4,7,3,6,3,8,5,2,9,8,5,9,4,4,6,2,4,8,8,8,0,1,2,2,7,7,8,5,6,9,9,0,4,7,9,9,2,4,9,7,3,2,3,1,8,3,3,2,5,7,3,5,6,4,2,2,5,4,3,5,7,0,5,2,7,8,0,3,2,4,9,9,2,5,7,8,5,2,8,4,6,5,3,4,3,3,6,4,1,3,3,6,5,6,7,8,9,8,5,6,9,7,7,3,0,2,7,0,9,1,8,0,2,3,3,1,3,7,4,8,9,3,1,6,6,3,6,5,8,7,2,8,1,1,8,7,1,9,6,2,2,1,9,7,7,5,1,0,3,6,6,0,1,3,3,0,3,3,1,4,0,0,5,6,3,0,9,1,1,3,2,2,9,9,6,3,1,5,9,5,2,9,5,7,5,5,7,4,5,8,2,4,7,8,7,4,7,7,9,8,8,2,1,9,2,5,0,4,6,4,8,1,3,3,8,3,2,3,4,6,2,4,2,0,3,3,0,1,1,5,9,9,7,8,2,4,2,4,1,3,3,8,2,6,7,2,6,1,2,5,4,0,8,0,0,7,8,9,6,3,2,2,7,2,4,0,5,1,6,2,6,0,8,6,6,5,4,8,4,1,7,6,3,3,2,7,6,6,5,9,3,5,7,7,2,7,1,8,6,5,1,1,2,4,0,8,4,9,9,6,2,5,3,9,4,0,0,1,7,9,0,8,4,5,4,5,1,7,2,9,8,3,6,3,9,2,0,6,2,8,9,5,7,2,8,4,3,9,7,0,2,0,1,0,4,1,1,4,2,7,4,9,9,1,5,2,8,3,5,9,8,9,9,3,0,6,1,9,8,2,4,9,4,8,3,7,2,9,0,0,7,0,1,8,9,7,9,6,0,2,0,4,0,9,6,3,5,7,2,6,5,9,1,7,7,5,3,7,0,0,2,2,5,4,2,9,9,2,5,8,6,0,1,7,3,2,2,2,9,6,7,8,1,4,3,9,2,3,9,7,0,8,6,9,6,8,0,9,3,9,8,7,6,2,5,2,0,6,0,8,7,2,4,8,1,4,4,7,3,5,6,8,6,0,4,5,4,4,2,0,1,0,9,5,4,5,8,0,1,7,9,7,7,0,3,8,2,0,6,1,5,1,2,6,1,7,4,3,1,5,5,4,0,1,4,4,8,4,2,1,4,9,4,4,9,9,0,7,4,6,1,2,9,6,4,3,2,1,7,4,3,7,7,6,6,6,2,8,7,0,4,4,7,4,6,8,6,3,8,9,2,1,7,3,7,5,8,2,4,5,5,6,2,1,3,2,3,0,6,5,3,0,4,3,2,2,0,7,0,6,3,8,9,0,3,6,3,1,7,1,9,3,9,3,4,2,5,2,4,7,1,9,0,1,5,0,0,4,2,6,0,1,9,9,3,9,5,3,3,1,0,8,5,5,8,4,9,7,3,7,5,6,2,7,3,0,2,4,3,1,7,0,6,6,2,6,8,9,0,9,9,6,1,3,0,3,6,4,9,1,7,8,6,5,3,0,7,9,1,1,0,7,4,3,0,7,8,4,4,2,5,1,5,8,4,0,8,5,6,9,9,7,8,9,9,3,7,2,7,9,6,0,9,1,3,9,1,5,4,3,3,6,1,5,7,9,7,7,8,6,5,9,8,0,6,6,7,0,2,7,8,6,8,2,8,1,0,5,0,0,0,7,2,9,1,8,3,7,6,0,3,8,4,3,2,7,8,0,6,6,2,4,8,0,9,7,9,2,4,4,3,1,8,5,8,1,7,9,5,4,2,9,9,2,4,4,2,5,7,4,6,9,7,4,1,2,3,9,6,4,1,8,1,1,2,0,7,6,8,6,5,9,3,6,0,5,8,1,6,7,6,4,8,1,5,0,8,4,4,2,6,0,4,7,7,9,0,2,2,4,9,4,7,1,1,1,2,1,7,6,9,2,8,8,8,0,3,0,1,6,8,1,8,0,6,4,7,2,4,5,8,7,5,3,1,5,3,8,5,5,3,5,6,4,1,8,0,8,5,6,2,3,1,5,0,2,2,6,4,1,7,8,0,7,5,7,0,9,7,0,6,0,5,9,8,4,2,3,1,5,0,1,3,6,7,8,8,2,0,2,3,4,9,5,2,2,7,6,4,0,8,1,3,6,8,9,5,8,9,0,7,5,3,0,1,2,9,2,8,0,3,4,3,1,0,7,8,8,4,0,3,2,1,9,2,3,8,8,1,5,0,1,8,6,4,9,5,8,7,9,0,8,3,4,1,4,2,6,4,7,9,1,4,4,6,7,8,7,0,0,2,1,2,4,7,6,2,8,2,5,5,4,1,8,8,5,1,9,9,4,1,1,5,0,0,0,5,6,3,0,8,9,3,9,7,5,2,8,3,0,2,6,8,2,6,6,4,2,5,7,0,4,7,4,1,4,0,7,7,0,5,7,2,2,0,9,6,3,9,8,3,0,4,3,9,5,1,0,2,5,8,1,5,1,8,9,3,1,6,0,0,1,9,9,6,8,7,1,4,5,9,3,3,9,7,7,6,3,1,0,6,7,1,6,8,9,7,2,4,1,4,4,1,1,7,8,4,9,9,8,7,3,6,1,2,7,3,0,0,5,5,8,4,3,3,4,7,2,2,8,3,7,8,0,9,9,9,7,9,3,6,0,9,1,2,3,4,8,5,3,1,8,2,5,5,2,5,8,4,5,5,0,7,2,5,9,3,2,8,3,5,5,4,5,1,6,6,9,8,9,0,9,2,4,8,1,0,7,5,4,8,6,3,6,5,1,5,6,8,0,4,6,9,0,7,1,1,7,2,9,9,3,2,4,1,7,9,9,1,9,6,1,7,4,8,1,7,0,7,6,2,3,7,9,4,6,8,8,3,8,6,5,8,9,4,7,7,7,1,7,2,3,0,9,9,1,8,8,2,9,5,6,0,8,4,0,7,2,0,7,5,7,0,8,8,7,1,4,5,1,3,0,3,4,6,3,2,7,8,7,2,7,8,7,8,2,7,2,7,7,0,2,3,2,8,7,8,9,1,7,3,2,9,6,9,0,9,9,8,7,0,6,9,1,3,8]);
CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 12:19:13 on modular  [Seed = 1899989846]
   -------------------------------------

$.1^150 - 643*$.1^149 - 20515*$.1^148 + 217108*$.1^147 + 17963099*$.1^146 + 
    716939943*$.1^145 + 3680795936*$.1^144 - 541288319912*$.1^143 - 
    20502642294337*$.1^142 - 1209079635632564*$.1^141 - 
    20823068520476910*$.1^140 + 434451871988236818*$.1^139 - 
    4596509010374661077*$.1^138 + 424758193351146625408*$.1^137 + 
    21105976109307845245489*$.1^136 + 1161058765395236623712199*$.1^135 + 
    55119856255160772593936561*$.1^134 - 165104602306038739558805916*$.1^133 - 
    70039009418423228697725085947*$.1^132 - 
    2465256442034056202473436371761*$.1^131 - 
    48840653170737411663934177278299*$.1^130 + 
    885616063876118364090583032670883*$.1^129 + 
    102751748423809355130443849896376194*$.1^128 + 
    3734756526327407655334278176330520950*$.1^127 + 
    84969621747151332633902394506068617390*$.1^126 - 
    1097872890439890132968854768203635238630*$.1^125 - 
    144500752494500139370826932209484742883744*$.1^124 - 
    4364287670178316735877349879124033683377493*$.1^123 - 
    157743781975310894766948811586969351582395876*$.1^122 - 
    4751998817917713175171692285168981075503354867*$.1^121 - 
    3469487304744147025395183659345318728863463174*$.1^120 - 
    537167001342279318854142943975956415748142580729*$.1^119 + 
    31119544885701302021730786623780579375233660371360*$.1^118 + 
    69377933648085307890983644242001630054083358096917*$.1^117 - 
    24697445888079147081770164774894231862351789075512641*$.1^116 + 
    3263699897948093926980674309858746849226736545116707128*$.1^115 + 
    77800437487188345190933710342327718622880765275567441877*$.1^114 + 
    1341576684937072223244635079072283804091120787381604340081*$.1^113 - 
    18759592581984493534464219107753954311558272199009607664135*$.1^112 - 
    1125086081865655123337704655543408077599642324541489393391697*$.1^111 + 
    23399566882175114096445498063134665094091967925498638809020602*$.1^110 + 
    1865524758536718519860595475183418077030131732945506646903834781*$.1^109 + 
    36995543792034766431513660658646360259855152600199927398783985914*$.1^108 + 
    1855305655285641718467518121990977119460185920772790529720708478497*$.1^107 
    - 7120699532342568465168534601808131962873289992629085461496706036835*$.1^1\
    06 - 2475363958373985332260107555467941572022233222206381605982955445666785\
    *$.1^105 - 9039476387419291190003688551930213057064062295603357420010113770\
    3902029*$.1^104 - 222469631682354080145607164700453328957041935979496580427\
    0215299508559827*$.1^103 + 392836396799887011398704966162086590604454391521\
    5062157694164045613403422*$.1^102 + 139819559897966359035758075942060007334\
    2414205600299534566438480316505776444*$.1^101 + 
    199081303709788317203661500917932500063329167358861837659547266885742948913\
    04*$.1^100 + 67350404898848903457769171800255256851491909448438967386669308\
    8163531234931885*$.1^99 + 1239215800631217878820968220014689559980753719949\
    7367844952837109780592724322889*$.1^98 - 
    312687992640616882735306560502584477869669702702694383586336029740872350807\
    555077*$.1^97 - 15290997073276709292762295109535232668239983995724847735306\
    181532197521568825957518*$.1^96 - 77502391066540185281499982473813468888914\
    6118983288411350402622324296815331036617193*$.1^95 - 
    467495458128058835907874521698238571046481238959244079620909684915419738354\
    4300804997*$.1^94 + 5471496894052099956822221917052433362905119843263314330\
    41997869555739538832405590780194*$.1^93 + 
    122130098754931976735422160656422070683100219650438208782019600474289634858\
    15224503084804*$.1^92 + 173699662750795336956743574575390245721268722964725\
    117131815655759850900296507213906854862*$.1^91 - 
    107042427347377872385936830322591207578051590292561853815965161978131596511\
    4670643292763425*$.1^90 + 1055804088999404828529592750112687011914598990880\
    17630808171174382804729287861594895980902262*$.1^89 + 
    108789700073710078966414674879682808051297685289154870317026824764950190444\
    75817275553524856312*$.1^88 + 254250037358510905667124087972431542814520403\
    875143810547138430954853344123899833137793643047955*$.1^87 - 
    138585596449355155731010229787706624636184479153356915193825931540791059291\
    8418389125921684184462*$.1^86 - 1566455613719935942338960460272975534539837\
    15029236642048002875993378341538006952538226739287229200*$.1^85 - 
    506655195348497722589011983500721836814815410048062159036379990428029022418\
    5581412375056919047506984*$.1^84 + 3975018540248862796888261252404185155530\
    9901109069880920728089322620095914392703646096223758811907483*$.1^83 + 
    233775477559390501298627446016262291419629652445416266610552240593344283157\
    1620432610817671709096717470*$.1^82 + 1811586175283044150123349707644826752\
    6666127032902326859602100663004559101226417854368801008695887944216*$.1^81 -
    100771055401965659608018328993999171943791904246821763579550730579004610188\
    8888363705841388350062105981573*$.1^80 - 
    374137709415298467591461013640079611475346071343919130771723427708092615483\
    25881769968333461400387347688388*$.1^79 - 
    329140936654607928836882770225172112469160333588316316452791848501870052108\
    451104281753587279860873139967550*$.1^78 - 
    271213181028904636631304667644843811814023023929575889743230479415173286265\
    78697505026052914579320460099947965*$.1^77 - 
    130594860410579502110443812761906137167433296210718242737401889769237436508\
    9450629170734685677410993233600037751*$.1^76 - 
    226337507624123498820096711969386218672125470207718749992551817936431600038\
    78351919599007396467441515153833766042*$.1^75 - 
    134694300134231617279505498417570069614918634052272448206966404479522680305\
    746342138471380941126590438790157756649*$.1^74 + 
    996651365046580559504512630472382983643598629450240300180541381014061248975\
    1734012185687709059042129984032576025749*$.1^73 + 
    668392034235301065384808266086392321087903666677273964693319119925429219300\
    832171199099103006251220706519588795478628*$.1^72 + 
    987133816984530524564398591300426219770557178279646641547232854251004050257\
    4741698673045988212074136188618807087409014*$.1^71 - 
    173418292508820343912028262699182266802894587556801908148582476979074737309\
    54947067918797026410392742761104604926881145*$.1^70 - 
    959775464314559847697335177124234666401956455797727992450566054658368590642\
    1913434857575919414009976569511707160827157577*$.1^69 - 
    970633750186521934904191856007590368355699031670237182045137835463542206983\
    09793542946586698178521108524309878668278606004*$.1^68 + 
    161286539987018145116637186366049737368747906297281838041240042665076114302\
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    135541894291976703929236109534534540952928407366711*$.1^65 + 
    332755978342125523640292931747859841406485827511445844956411962809085949145\
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    41490443287524070163533164673120383588483566705686367913*$.1^61 + 
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    5596932488694412732015990031298936318014569306004312529156*$.1^60 + 
    240542670679294645050046318640995902671416529274929249986346721911789675793\
    643270399538303607905650599693575378644280343832162521129194*$.1^59 + 
    418315401237666243642027818171246021064238526278179007411193287568075702640\
    1306953629774594031883700669878023306665539089497050825382884*$.1^58 + 
    190931727023374852745871410636403239831310293917269757692661926873657669621\
    996881890524694375022983674183340423432010772469204109787562160*$.1^57 + 
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    6218785968276736680882726533833961652250408193127018099829648249*$.1^56 + 
    598760519738216792099441006211103130839899062488017586840409826848248197690\
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    926685173189334376172349572893377287791616533468143480217651898317944405205\
    910715955431586243561821048920435337083028675412740966468682718380*$.1^54 + 
    767255648903154525929152606554917762290849223407448058348260391844985575992\
    0888829872642102115986857905330274973997004344471654680205323287525*$.1^53 -
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    783942258035957880869715667422752004636669195769130384322538885574585*$.1^5\
    2 - 65098991423789342718986015678206684959284684401739924742074682416867892\
    73055558887101579605098278068987225318173836397380725210785854645974172981*\
    $.1^51 - 213866647627188697358830178641717321794455690917238474592306843047\
    337928049079147799118118897215912126979726913864264027987076412758796838381\
    430999*$.1^50 - 58850122129406769478603329535343670106957046853829585790967\
    220033501116125053815338871011047461057695076940750557183437825678618077662\
    69205803268364*$.1^49 - 687106117210350382505858030257642408522064810037369\
    897696780912693013045693557079131175648221797775005917124711404634161104449\
    96594803050292216693091*$.1^48 + 536360052790380452478050592445636187602667\
    56695490048429903543516994704057873599472288274307959512826
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 12:20:18 2004

Input: A:=Matrix(IntegerRing(),150,150,[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3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,7,6,6,1,0,1,3,7,5,5,9,4,3,5,8,4,2,4,1,5,1,2,5,6,7,3,9,6,3,9,8,7,4,6,5,8,3,8,2,1,4,3,8,8,3,1,0,5,0,4,1,6,7,7,5,7,8,1,5,8,4,0,2,7,5,5,7,8,4,7,1,5,4,9,4,4,0,2,8,5,1,5,8,3,3,5,6,9,7,0,3,3,9,5,5,8,0,8,1,4,7,8,7,9,4,5,5,5,4,8,6,6,4,5,1,5,3,5,8,0,9,2,8,3,2,8,0,3,0,0,2,5,8,9,0,4,7,8,4,2,3,8,9,2,4,3,3,5,5,0,3,1,0,3,8,3,0,6,3,4,3,4,8,4,9,1,0,0,0,1,0,0,2,4,1,2,4,4,1,8,3,2,1,3,1,0,0,4,1,9,0,6,1,0,4,8,1,0,9,8,8,6,9,9,1,6,4,2,0,8,0,0,8,1,6,6,5,0,7,7,7,3,8,3,0,6,3,2,6,4,6,2,9,3,6,5,6,8,7,1,7,6,6,7,0,7,9,2,8,7,9,5,4,1,1,0,8,3,3,0,8,6,2,6,0,0,0,5,3,9,8,3,2,8,9,0,7,7,7,1,7,3,1,7,2,0,7,9,6,6,7,5,1,8,2,0,6,9,5,7,2,6,9,1,0,6,2,8,1,8,2,4,8,7,0,0,8,4,7,7,8,1,6,9,1,2,8,6,2,2,0,1,0,5,7,9,4,1,0,6,6,4,6,5,2,6,1,7,8,5,5,5,5,2,6,7,0,0,6,9,7,4,2,8,3,9,2,8,0,8,4,3,9,5,7,7,9,4,8,1,2,6,7,7,2,4,0,7,5,2,0,3,1,8,7,0,1,2,8,1,7,4,1,3,2,4,3,6,1,6,0,1,4,9,5,9,0,2,5,8,2,6,1,1,1,1,2,8,4,6,8,0,4,3,5,2,4,8,9,5,1,5,5,6,8,7,9,3,0,0,1,7,3,1,8,2,0,9,6,1,2,8,8,5,8,3,6,9,0,3,1,4,1,5,0,1,6,2,4,5,0,1,5,9,2,9,8,4,3,4,8,2,0,9,8,0,0,2,5,1,1,1,7,7,4,4,0,9,2,6,1,9,7,0,2,7,9,4,9,7,1,0,4,0,2,7,0,7,1,4,8,7,9,2,4,8,2,9,3,8,7,8,2,5,2,5,5,4,3,7,9,3,4,8,3,6,6,8,1,3,8,9,3,1,1,7,8,3,0,9,7,9,7,9,7,5,6,2,6,7,4,8,8,8,5,5,0,3,4,7,8,9,5,0,8,8,9,7,4,6,1,8,0,2,2,1,2,3,8,6,6,9,0,9,6,6,9,6,9,2,6,8,2,1,5,7,8,4,5,8,6,9,5,1,0,8,5,0,7,0,4,8,6,5,5,0,2,5,5,3,3,2,0,5,3,0,7,5,4,4,7,0,0,2,9,1,7,1,5,1,3,7,1,8,0,2,3,7,6,1,2,4,3,8,8,5,8,5,9,1,7,2,2,2,3,7,0,4,7,4,4,2,9,2,2,9,7,9,0,6,2,4,6,7,9,7,7,5,2,4,0,9,9,5,6,8,2,6,7,4,8,2,7,0,6,6,2,6,9,1,5,5,1,4,8,6,8,3,7,1,5,6,6,2,3,2,2,8,8,9,9,8,0,8,8,1,8,7,2,5,3,7,4,2,7,5,5,1,5,9,6,3,7,1,3,8,8,6,4,9,6,6,8,9,5,1,2,5,9,0,2,4,8,3,9,5,9,8,8,5,4,3,5,1,4,4,0,9,8,4,4,6,7,2,9,3,7,4,7,7,1,9,9,8,1,0,9,2,5,9,4,3,8,2,8,4,8,9,6,3,4,9,5,7,4,9,5,0,4,4,4,7,3,3,5,6,7,0,1,5,7,9,8,7,0,6,7,7,4,7,7,2,5,8,2,4,3,6,5,1,7,4,8,2,6,2,0,0,2,7,9,1,2,0,1,5,9,6,2,2,9,6,0,0,3,8,5,2,4,0,0,5,6,5,1,3,5,4,0,7,7,8,2,2,6,7,7,6,9,8,3,5,1,8,8,8,1,4,9,4,6,9,1,3,9,2,1,8,6,5,1,0,6,7,4,0,5,2,7,9,0,2,2,9,7,5,4,9,6,0,0,4,5,0,9,3,3,8,1,5,7,3,0,9,8,8,5,8,7,5,8,3,6,7,3,9,4,5,5,1,0,1,1,0,8,8,4,1,5,3,7,6,8,4,9,6,0,0,4,1,8,6,0,4,2,5,7,1,1,2,2,2,2,3,2,5,5,5,9,8,7,6,5,2,7,6,9,6,8,2,3,3,7,9,6,6,4,6,8,3,8,6,1,8,5,5,0,5,4,7,5,3,2,3,7,2,5,1,5,8,9,3,5,6,5,4,4,4,8,7,0,9,7,1,5,9,8,1,4,0,4,0,4,5,3,1,1,4,1,3,7,8,6,8,5,9,4,3,4,9,5,3,3,0,6,6,5,5,2,4,4,7,3,6,3,8,5,2,9,8,5,9,4,4,6,2,4,8,8,8,0,1,2,2,7,7,8,5,6,9,9,0,4,7,9,9,2,4,9,7,3,2,3,1,8,3,3,2,5,7,3,5,6,4,2,2,5,4,3,5,7,0,5,2,7,8,0,3,2,4,9,9,2,5,7,8,5,2,8,4,6,5,3,4,3,3,6,4,1,3,3,6,5,6,7,8,9,8,5,6,9,7,7,3,0,2,7,0,9,1,8,0,2,3,3,1,3,7,4,8,9,3,1,6,6,3,6,5,8,7,2,8,1,1,8,7,1,9,6,2,2,1,9,7,7,5,1,0,3,6,6,0,1,3,3,0,3,3,1,4,0,0,5,6,3,0,9,1,1,3,2,2,9,9,6,3,1,5,9,5,2,9,5,7,5,5,7,4,5,8,2,4,7,8,7,4,7,7,9,8,8,2,1,9,2,5,0,4,6,4,8,1,3,3,8,3,2,3,4,6,2,4,2,0,3,3,0,1,1,5,9,9,7,8,2,4,2,4,1,3,3,8,2,6,7,2,6,1,2,5,4,0,8,0,0,7,8,9,6,3,2,2,7,2,4,0,5,1,6,2,6,0,8,6,6,5,4,8,4,1,7,6,3,3,2,7,6,6,5,9,3,5,7,7,2,7,1,8,6,5,1,1,2,4,0,8,4,9,9,6,2,5,3,9,4,0,0,1,7,9,0,8,4,5,4,5,1,7,2,9,8,3,6,3,9,2,0,6,2,8,9,5,7,2,8,4,3,9,7,0,2,0,1,0,4,1,1,4,2,7,4,9,9,1,5,2,8,3,5,9,8,9,9,3,0,6,1,9,8,2,4,9,4,8,3,7,2,9,0,0,7,0,1,8,9,7,9,6,0,2,0,4,0,9,6,3,5,7,2,6,5,9,1,7,7,5,3,7,0,0,2,2,5,4,2,9,9,2,5,8,6,0,1,7,3,2,2,2,9,6,7,8,1,4,3,9,2,3,9,7,0,8,6,9,6,8,0,9,3,9,8,7,6,2,5,2,0,6,0,8,7,2,4,8,1,4,4,7,3,5,6,8,6,0,4,5,4,4,2,0,1,0,9,5,4,5,8,0,1,7,9,7,7,0,3,8,2,0,6,1,5,1,2,6,1,7,4,3,1,5,5,4,0,1,4,4,8,4,2,1,4,9,4,4,9,9,0,7,4,6,1,2,9,6,4,3,2,1,7,4,3,7,7,6,6,6,2,8,7,0,4,4,7,4,6,8,6,3,8,9,2,1,7,3,7,5,8,2,4,5,5,6,2,1,3,2,3,0,6,5,3,0,4,3,2,2,0,7,0,6,3,8,9,0,3,6,3,1,7,1,9,3,9,3,4,2,5,2,4,7,1,9,0,1,5,0,0,4,2,6,0,1,9,9,3,9,5,3,3,1,0,8,5,5,8,4,9,7,3,7,5,6,2,7,3,0,2,4,3,1,7,0,6,6,2,6,8,9,0,9,9,6,1,3,0,3,6,4,9,1,7,8,6,5,3,0,7,9,1,1,0,7,4,3,0,7,8,4,4,2,5,1,5,8,4,0,8,5,6,9,9,7,8,9,9,3,7,2,7,9,6,0,9,1,3,9,1,5,4,3,3,6,1,5,7,9,7,7,8,6,5,9,8,0,6,6,7,0,2,7,8,6,8,2,8,1,0,5,0,0,0,7,2,9,1,8,3,7,6,0,3,8,4,3,2,7,8,0,6,6,2,4,8,0,9,7,9,2,4,4,3,1,8,5,8,1,7,9,5,4,2,9,9,2,4,4,2,5,7,4,6,9,7,4,1,2,3,9,6,4,1,8,1,1,2,0,7,6,8,6,5,9,3,6,0,5,8,1,6,7,6,4,8,1,5,0,8,4,4,2,6,0,4,7,7,9,0,2,2,4,9,4,7,1,1,1,2,1,7,6,9,2,8,8,8,0,3,0,1,6,8,1,8,0,6,4,7,2,4,5,8,7,5,3,1,5,3,8,5,5,3,5,6,4,1,8,0,8,5,6,2,3,1,5,0,2,2,6,4,1,7,8,0,7,5,7,0,9,7,0,6,0,5,9,8,4,2,3,1,5,0,1,3,6,7,8,8,2,0,2,3,4,9,5,2,2,7,6,4,0,8,1,3,6,8,9,5,8,9,0,7,5,3,0,1,2,9,2,8,0,3,4,3,1,0,7,8,8,4,0,3,2,1,9,2,3,8,8,1,5,0,1,8,6,4,9,5,8,7,9,0,8,3,4,1,4,2,6,4,7,9,1,4,4,6,7,8,7,0,0,2,1,2,4,7,6,2,8,2,5,5,4,1,8,8,5,1,9,9,4,1,1,5,0,0,0,5,6,3,0,8,9,3,9,7,5,2,8,3,0,2,6,8,2,6,6,4,2,5,7,0,4,7,4,1,4,0,7,7,0,5,7,2,2,0,9,6,3,9,8,3,0,4,3,9,5,1,0,2,5,8,1,5,1,8,9,3,1,6,0,0,1,9,9,6,8,7,1,4,5,9,3,3,9,7,7,6,3,1,0,6,7,1,6,8,9,7,2,4,1,4,4,1,1,7,8,4,9,9,8,7,3,6,1,2,7,3,0,0,5,5,8,4,3,3,4,7,2,2,8,3,7,8,0,9,9,9,7,9,3,6,0,9,1,2,3,4,8,5,3,1,8,2,5,5,2,5,8,4,5,5,0,7,2,5,9,3,2,8,3,5,5,4,5,1,6,6,9,8,9,0,9,2,4,8,1,0,7,5,4,8,6,3,6,5,1,5,6,8,0,4,6,9,0,7,1,1,7,2,9,9,3,2,4,1,7,9,9,1,9,6,1,7,4,8,1,7,0,7,6,2,3,7,9,4,6,8,8,3,8,6,5,8,9,4,7,7,7,1,7,2,3,0,9,9,1,8,8,2,9,5,6,0,8,4,0,7,2,0,7,5,7,0,8,8,7,1,4,5,1,3,0,3,4,6,3,2,7,8,7,2,7,8,7,8,2,7,2,7,7,0,2,3,2,8,7,8,9,1,7,3,2,9,6,9,0,9,9,8,7,0,6,9,1,3,8]);
CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 12:20:14 on modular  [Seed = 1427877709]
   -------------------------------------

$.1^150 - 643*$.1^149 - 20515*$.1^148 + 217108*$.1^147 + 17963099*$.1^146 + 
    716939943*$.1^145 + 3680795936*$.1^144 - 541288319912*$.1^143 - 
    20502642294337*$.1^142 - 1209079635632564*$.1^141 - 
    20823068520476910*$.1^140 + 434451871988236818*$.1^139 - 
    4596509010374661077*$.1^138 + 424758193351146625408*$.1^137 + 
    21105976109307845245489*$.1^136 + 1161058765395236623712199*$.1^135 + 
    55119856255160772593936561*$.1^134 - 165104602306038739558805916*$.1^133 - 
    70039009418423228697725085947*$.1^132 - 
    2465256442034056202473436371761*$.1^131 - 
    48840653170737411663934177278299*$.1^130 + 
    885616063876118364090583032670883*$.1^129 + 
    102751748423809355130443849896376194*$.1^128 + 
    3734756526327407655334278176330520950*$.1^127 + 
    84969621747151332633902394506068617390*$.1^126 - 
    1097872890439890132968854768203635238630*$.1^125 - 
    144500752494500139370826932209484742883744*$.1^124 - 
    4364287670178316735877349879124033683377493*$.1^123 - 
    157743781975310894766948811586969351582395876*$.1^122 - 
    4751998817917713175171692285168981075503354867*$.1^121 - 
    3469487304744147025395183659345318728863463174*$.1^120 - 
    537167001342279318854142943975956415748142580729*$.1^119 + 
    31119544885701302021730786623780579375233660371360*$.1^118 + 
    69377933648085307890983644242001630054083358096917*$.1^117 - 
    24697445888079147081770164774894231862351789075512641*$.1^116 + 
    3263699897948093926980674309858746849226736545116707128*$.1^115 + 
    77800437487188345190933710342327718622880765275567441877*$.1^114 + 
    1341576684937072223244635079072283804091120787381604340081*$.1^113 - 
    18759592581984493534464219107753954311558272199009607664135*$.1^112 - 
    1125086081865655123337704655543408077599642324541489393391697*$.1^111 + 
    23399566882175114096445498063134665094091967925498638809020602*$.1^110 + 
    1865524758536718519860595475183418077030131732945506646903834781*$.1^109 + 
    36995543792034766431513660658646360259855152600199927398783985914*$.1^108 + 
    1855305655285641718467518121990977119460185920772790529720708478497*$.1^107 
    - 7120699532342568465168534601808131962873289992629085461496706036835*$.1^1\
    06 - 2475363958373985332260107555467941572022233222206381605982955445666785\
    *$.1^105 - 9039476387419291190003688551930213057064062295603357420010113770\
    3902029*$.1^104 - 222469631682354080145607164700453328957041935979496580427\
    0215299508559827*$.1^103 + 392836396799887011398704966162086590604454391521\
    5062157694164045613403422*$.1^102 + 139819559897966359035758075942060007334\
    2414205600299534566438480316505776444*$.1^101 + 
    199081303709788317203661500917932500063329167358861837659547266885742948913\
    04*$.1^100 + 67350404898848903457769171800255256851491909448438967386669308\
    8163531234931885*$.1^99 + 1239215800631217878820968220014689559980753719949\
    7367844952837109780592724322889*$.1^98 - 
    312687992640616882735306560502584477869669702702694383586336029740872350807\
    555077*$.1^97 - 15290997073276709292762295109535232668239983995724847735306\
    181532197521568825957518*$.1^96 - 77502391066540185281499982473813468888914\
    6118983288411350402622324296815331036617193*$.1^95 - 
    467495458128058835907874521698238571046481238959244079620909684915419738354\
    4300804997*$.1^94 + 5471496894052099956822221917052433362905119843263314330\
    41997869555739538832405590780194*$.1^93 + 
    122130098754931976735422160656422070683100219650438208782019600474289634858\
    15224503084804*$.1^92 + 173699662750795336956743574575390245721268722964725\
    117131815655759850900296507213906854862*$.1^91 - 
    107042427347377872385936830322591207578051590292561853815965161978131596511\
    4670643292763425*$.1^90 + 1055804088999404828529592750112687011914598990880\
    17630808171174382804729287861594895980902262*$.1^89 + 
    108789700073710078966414674879682808051297685289154870317026824764950190444\
    75817275553524856312*$.1^88 + 254250037358510905667124087972431542814520403\
    875143810547138430954853344123899833137793643047955*$.1^87 - 
    138585596449355155731010229787706624636184479153356915193825931540791059291\
    8418389125921684184462*$.1^86 - 1566455613719935942338960460272975534539837\
    15029236642048002875993378341538006952538226739287229200*$.1^85 - 
    506655195348497722589011983500721836814815410048062159036379990428029022418\
    5581412375056919047506984*$.1^84 + 3975018540248862796888261252404185155530\
    9901109069880920728089322620095914392703646096223758811907483*$.1^83 + 
    233775477559390501298627446016262291419629652445416266610552240593344283157\
    1620432610817671709096717470*$.1^82 + 1811586175283044150123349707644826752\
    6666127032902326859602100663004559101226417854368801008695887944216*$.1^81 -
    100771055401965659608018328993999171943791904246821763579550730579004610188\
    8888363705841388350062105981573*$.1^80 - 
    374137709415298467591461013640079611475346071343919130771723427708092615483\
    25881769968333461400387347688388*$.1^79 - 
    329140936654607928836882770225172112469160333588316316452791848501870052108\
    451104281753587279860873139967550*$.1^78 - 
    271213181028904636631304667644843811814023023929575889743230479415173286265\
    78697505026052914579320460099947965*$.1^77 - 
    130594860410579502110443812761906137167433296210718242737401889769237436508\
    9450629170734685677410993233600037751*$.1^76 - 
    226337507624123498820096711969386218672125470207718749992551817936431600038\
    78351919599007396467441515153833766042*$.1^75 - 
    134694300134231617279505498417570069614918634052272448206966404479522680305\
    746342138471380941126590438790157756649*$.1^74 + 
    996651365046580559504512630472382983643598629450240300180541381014061248975\
    1734012185687709059042129984032576025749*$.1^73 + 
    668392034235301065384808266086392321087903666677273964693319119925429219300\
    832171199099103006251220706519588795478628*$.1^72 + 
    987133816984530524564398591300426219770557178279646641547232854251004050257\
    4741698673045988212074136188618807087409014*$.1^71 - 
    173418292508820343912028262699182266802894587556801908148582476979074737309\
    54947067918797026410392742761104604926881145*$.1^70 - 
    959775464314559847697335177124234666401956455797727992450566054658368590642\
    1913434857575919414009976569511707160827157577*$.1^69 - 
    970633750186521934904191856007590368355699031670237182045137835463542206983\
    09793542946586698178521108524309878668278606004*$.1^68 + 
    161286539987018145116637186366049737368747906297281838041240042665076114302\
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    332755978342125523640292931747859841406485827511445844956411962809085949145\
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    41490443287524070163533164673120383588483566705686367913*$.1^61 + 
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    5596932488694412732015990031298936318014569306004312529156*$.1^60 + 
    240542670679294645050046318640995902671416529274929249986346721911789675793\
    643270399538303607905650599693575378644280343832162521129194*$.1^59 + 
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    1306953629774594031883700669878023306665539089497050825382884*$.1^58 + 
    190931727023374852745871410636403239831310293917269757692661926873657669621\
    996881890524694375022983674183340423432010772469204109787562160*$.1^57 + 
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    6218785968276736680882726533833961652250408193127018099829648249*$.1^56 + 
    598760519738216792099441006211103130839899062488017586840409826848248197690\
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    926685173189334376172349572893377287791616533468143480217651898317944405205\
    910715955431586243561821048920435337083028675412740966468682718380*$.1^54 + 
    767255648903154525929152606554917762290849223407448058348260391844985575992\
    0888829872642102115986857905330274973997004344471654680205323287525*$.1^53 -
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    783942258035957880869715667422752004636669195769130384322538885574585*$.1^5\
    2 - 65098991423789342718986015678206684959284684401739924742074682416867892\
    73055558887101579605098278068987225318173836397380725210785854645974172981*\
    $.1^51 - 213866647627188697358830178641717321794455690917238474592306843047\
    337928049079147799118118897215912126979726913864264027987076412758796838381\
    430999*$.1^50 - 58850122129406769478603329535343670106957046853829585790967\
    220033501116125053815338871011047461057695076940750557183437825678618077662\
    69205803268364*$.1^49 - 687106117210350382505858030257642408522064810037369\
    897696780912693013045693557079131175648221797775005917124711404634161104449\
    96594803050292216693091*$.1^48 + 536360052790380452478050592445636187602667\
    56695490048429903543516994704057873599472288274307959512826
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 13:11:19 2004

Input: A:=Matrix(IntegerRing(),150,150,[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3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,7,6,6,1,0,1,3,7,5,5,9,4,3,5,8,4,2,4,1,5,1,2,5,6,7,3,9,6,3,9,8,7,4,6,5,8,3,8,2,1,4,3,8,8,3,1,0,5,0,4,1,6,7,7,5,7,8,1,5,8,4,0,2,7,5,5,7,8,4,7,1,5,4,9,4,4,0,2,8,5,1,5,8,3,3,5,6,9,7,0,3,3,9,5,5,8,0,8,1,4,7,8,7,9,4,5,5,5,4,8,6,6,4,5,1,5,3,5,8,0,9,2,8,3,2,8,0,3,0,0,2,5,8,9,0,4,7,8,4,2,3,8,9,2,4,3,3,5,5,0,3,1,0,3,8,3,0,6,3,4,3,4,8,4,9,1,0,0,0,1,0,0,2,4,1,2,4,4,1,8,3,2,1,3,1,0,0,4,1,9,0,6,1,0,4,8,1,0,9,8,8,6,9,9,1,6,4,2,0,8,0,0,8,1,6,6,5,0,7,7,7,3,8,3,0,6,3,2,6,4,6,2,9,3,6,5,6,8,7,1,7,6,6,7,0,7,9,2,8,7,9,5,4,1,1,0,8,3,3,0,8,6,2,6,0,0,0,5,3,9,8,3,2,8,9,0,7,7,7,1,7,3,1,7,2,0,7,9,6,6,7,5,1,8,2,0,6,9,5,7,2,6,9,1,0,6,2,8,1,8,2,4,8,7,0,0,8,4,7,7,8,1,6,9,1,2,8,6,2,2,0,1,0,5,7,9,4,1,0,6,6,4,6,5,2,6,1,7,8,5,5,5,5,2,6,7,0,0,6,9,7,4,2,8,3,9,2,8,0,8,4,3,9,5,7,7,9,4,8,1,2,6,7,7,2,4,0,7,5,2,0,3,1,8,7,0,1,2,8,1,7,4,1,3,2,4,3,6,1,6,0,1,4,9,5,9,0,2,5,8,2,6,1,1,1,1,2,8,4,6,8,0,4,3,5,2,4,8,9,5,1,5,5,6,8,7,9,3,0,0,1,7,3,1,8,2,0,9,6,1,2,8,8,5,8,3,6,9,0,3,1,4,1,5,0,1,6,2,4,5,0,1,5,9,2,9,8,4,3,4,8,2,0,9,8,0,0,2,5,1,1,1,7,7,4,4,0,9,2,6,1,9,7,0,2,7,9,4,9,7,1,0,4,0,2,7,0,7,1,4,8,7,9,2,4,8,2,9,3,8,7,8,2,5,2,5,5,4,3,7,9,3,4,8,3,6,6,8,1,3,8,9,3,1,1,7,8,3,0,9,7,9,7,9,7,5,6,2,6,7,4,8,8,8,5,5,0,3,4,7,8,9,5,0,8,8,9,7,4,6,1,8,0,2,2,1,2,3,8,6,6,9,0,9,6,6,9,6,9,2,6,8,2,1,5,7,8,4,5,8,6,9,5,1,0,8,5,0,7,0,4,8,6,5,5,0,2,5,5,3,3,2,0,5,3,0,7,5,4,4,7,0,0,2,9,1,7,1,5,1,3,7,1,8,0,2,3,7,6,1,2,4,3,8,8,5,8,5,9,1,7,2,2,2,3,7,0,4,7,4,4,2,9,2,2,9,7,9,0,6,2,4,6,7,9,7,7,5,2,4,0,9,9,5,6,8,2,6,7,4,8,2,7,0,6,6,2,6,9,1,5,5,1,4,8,6,8,3,7,1,5,6,6,2,3,2,2,8,8,9,9,8,0,8,8,1,8,7,2,5,3,7,4,2,7,5,5,1,5,9,6,3,7,1,3,8,8,6,4,9,6,6,8,9,5,1,2,5,9,0,2,4,8,3,9,5,9,8,8,5,4,3,5,1,4,4,0,9,8,4,4,6,7,2,9,3,7,4,7,7,1,9,9,8,1,0,9,2,5,9,4,3,8,2,8,4,8,9,6,3,4,9,5,7,4,9,5,0,4,4,4,7,3,3,5,6,7,0,1,5,7,9,8,7,0,6,7,7,4,7,7,2,5,8,2,4,3,6,5,1,7,4,8,2,6,2,0,0,2,7,9,1,2,0,1,5,9,6,2,2,9,6,0,0,3,8,5,2,4,0,0,5,6,5,1,3,5,4,0,7,7,8,2,2,6,7,7,6,9,8,3,5,1,8,8,8,1,4,9,4,6,9,1,3,9,2,1,8,6,5,1,0,6,7,4,0,5,2,7,9,0,2,2,9,7,5,4,9,6,0,0,4,5,0,9,3,3,8,1,5,7,3,0,9,8,8,5,8,7,5,8,3,6,7,3,9,4,5,5,1,0,1,1,0,8,8,4,1,5,3,7,6,8,4,9,6,0,0,4,1,8,6,0,4,2,5,7,1,1,2,2,2,2,3,2,5,5,5,9,8,7,6,5,2,7,6,9,6,8,2,3,3,7,9,6,6,4,6,8,3,8,6,1,8,5,5,0,5,4,7,5,3,2,3,7,2,5,1,5,8,9,3,5,6,5,4,4,4,8,7,0,9,7,1,5,9,8,1,4,0,4,0,4,5,3,1,1,4,1,3,7,8,6,8,5,9,4,3,4,9,5,3,3,0,6,6,5,5,2,4,4,7,3,6,3,8,5,2,9,8,5,9,4,4,6,2,4,8,8,8,0,1,2,2,7,7,8,5,6,9,9,0,4,7,9,9,2,4,9,7,3,2,3,1,8,3,3,2,5,7,3,5,6,4,2,2,5,4,3,5,7,0,5,2,7,8,0,3,2,4,9,9,2,5,7,8,5,2,8,4,6,5,3,4,3,3,6,4,1,3,3,6,5,6,7,8,9,8,5,6,9,7,7,3,0,2,7,0,9,1,8,0,2,3,3,1,3,7,4,8,9,3,1,6,6,3,6,5,8,7,2,8,1,1,8,7,1,9,6,2,2,1,9,7,7,5,1,0,3,6,6,0,1,3,3,0,3,3,1,4,0,0,5,6,3,0,9,1,1,3,2,2,9,9,6,3,1,5,9,5,2,9,5,7,5,5,7,4,5,8,2,4,7,8,7,4,7,7,9,8,8,2,1,9,2,5,0,4,6,4,8,1,3,3,8,3,2,3,4,6,2,4,2,0,3,3,0,1,1,5,9,9,7,8,2,4,2,4,1,3,3,8,2,6,7,2,6,1,2,5,4,0,8,0,0,7,8,9,6,3,2,2,7,2,4,0,5,1,6,2,6,0,8,6,6,5,4,8,4,1,7,6,3,3,2,7,6,6,5,9,3,5,7,7,2,7,1,8,6,5,1,1,2,4,0,8,4,9,9,6,2,5,3,9,4,0,0,1,7,9,0,8,4,5,4,5,1,7,2,9,8,3,6,3,9,2,0,6,2,8,9,5,7,2,8,4,3,9,7,0,2,0,1,0,4,1,1,4,2,7,4,9,9,1,5,2,8,3,5,9,8,9,9,3,0,6,1,9,8,2,4,9,4,8,3,7,2,9,0,0,7,0,1,8,9,7,9,6,0,2,0,4,0,9,6,3,5,7,2,6,5,9,1,7,7,5,3,7,0,0,2,2,5,4,2,9,9,2,5,8,6,0,1,7,3,2,2,2,9,6,7,8,1,4,3,9,2,3,9,7,0,8,6,9,6,8,0,9,3,9,8,7,6,2,5,2,0,6,0,8,7,2,4,8,1,4,4,7,3,5,6,8,6,0,4,5,4,4,2,0,1,0,9,5,4,5,8,0,1,7,9,7,7,0,3,8,2,0,6,1,5,1,2,6,1,7,4,3,1,5,5,4,0,1,4,4,8,4,2,1,4,9,4,4,9,9,0,7,4,6,1,2,9,6,4,3,2,1,7,4,3,7,7,6,6,6,2,8,7,0,4,4,7,4,6,8,6,3,8,9,2,1,7,3,7,5,8,2,4,5,5,6,2,1,3,2,3,0,6,5,3,0,4,3,2,2,0,7,0,6,3,8,9,0,3,6,3,1,7,1,9,3,9,3,4,2,5,2,4,7,1,9,0,1,5,0,0,4,2,6,0,1,9,9,3,9,5,3,3,1,0,8,5,5,8,4,9,7,3,7,5,6,2,7,3,0,2,4,3,1,7,0,6,6,2,6,8,9,0,9,9,6,1,3,0,3,6,4,9,1,7,8,6,5,3,0,7,9,1,1,0,7,4,3,0,7,8,4,4,2,5,1,5,8,4,0,8,5,6,9,9,7,8,9,9,3,7,2,7,9,6,0,9,1,3,9,1,5,4,3,3,6,1,5,7,9,7,7,8,6,5,9,8,0,6,6,7,0,2,7,8,6,8,2,8,1,0,5,0,0,0,7,2,9,1,8,3,7,6,0,3,8,4,3,2,7,8,0,6,6,2,4,8,0,9,7,9,2,4,4,3,1,8,5,8,1,7,9,5,4,2,9,9,2,4,4,2,5,7,4,6,9,7,4,1,2,3,9,6,4,1,8,1,1,2,0,7,6,8,6,5,9,3,6,0,5,8,1,6,7,6,4,8,1,5,0,8,4,4,2,6,0,4,7,7,9,0,2,2,4,9,4,7,1,1,1,2,1,7,6,9,2,8,8,8,0,3,0,1,6,8,1,8,0,6,4,7,2,4,5,8,7,5,3,1,5,3,8,5,5,3,5,6,4,1,8,0,8,5,6,2,3,1,5,0,2,2,6,4,1,7,8,0,7,5,7,0,9,7,0,6,0,5,9,8,4,2,3,1,5,0,1,3,6,7,8,8,2,0,2,3,4,9,5,2,2,7,6,4,0,8,1,3,6,8,9,5,8,9,0,7,5,3,0,1,2,9,2,8,0,3,4,3,1,0,7,8,8,4,0,3,2,1,9,2,3,8,8,1,5,0,1,8,6,4,9,5,8,7,9,0,8,3,4,1,4,2,6,4,7,9,1,4,4,6,7,8,7,0,0,2,1,2,4,7,6,2,8,2,5,5,4,1,8,8,5,1,9,9,4,1,1,5,0,0,0,5,6,3,0,8,9,3,9,7,5,2,8,3,0,2,6,8,2,6,6,4,2,5,7,0,4,7,4,1,4,0,7,7,0,5,7,2,2,0,9,6,3,9,8,3,0,4,3,9,5,1,0,2,5,8,1,5,1,8,9,3,1,6,0,0,1,9,9,6,8,7,1,4,5,9,3,3,9,7,7,6,3,1,0,6,7,1,6,8,9,7,2,4,1,4,4,1,1,7,8,4,9,9,8,7,3,6,1,2,7,3,0,0,5,5,8,4,3,3,4,7,2,2,8,3,7,8,0,9,9,9,7,9,3,6,0,9,1,2,3,4,8,5,3,1,8,2,5,5,2,5,8,4,5,5,0,7,2,5,9,3,2,8,3,5,5,4,5,1,6,6,9,8,9,0,9,2,4,8,1,0,7,5,4,8,6,3,6,5,1,5,6,8,0,4,6,9,0,7,1,1,7,2,9,9,3,2,4,1,7,9,9,1,9,6,1,7,4,8,1,7,0,7,6,2,3,7,9,4,6,8,8,3,8,6,5,8,9,4,7,7,7,1,7,2,3,0,9,9,1,8,8,2,9,5,6,0,8,4,0,7,2,0,7,5,7,0,8,8,7,1,4,5,1,3,0,3,4,6,3,2,7,8,7,2,7,8,7,8,2,7,2,7,7,0,2,3,2,8,7,8,9,1,7,3,2,9,6,9,0,9,9,8,7,0,6,9,1,3,8]);
P:=CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 13:11:15 on modular  [Seed = 2647858056]
   -------------------------------------


Total time: 4.030 seconds, Total memory usage: 6.22MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 13:12:38 2004

Input: A:=Matrix(IntegerRing(),200,200[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3,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3,2,0,1,1,5,0,1,0,7,7,2,8,7,9,3,3,6,8,4,5,1,2,0,1,5,0,3,3,0,3,7,9,2,6,4,2,3,4,1,3,9,6,6,7,8,4,2,8,7,4,7,0,2,2,0,6,5,5,7,8,3,5,3,5,6,0,0,0,8,4,4,3,5,0,1,8,6,7,1,3,6,6,4,4,3,3,6,5,0,5,3,4,1,9,6,4,7,2,8,5,7,0,3,9,0,0,8,4,7,8,8,8,6,0,8,0,7,5,0,5,3,2,2,7,9,1,4,9,3,1,9,7,4,7,6,4,9,8,8,7,0,7,3,3,9,0,4,1,0,5,1,5,4,4,7,3,5,2,2,4,2,9,2,6,7,7,2,3,5,2,4,5,3,1,0,3,8,5,5,3,0,0,5,4,4,6,1,0,1,5,1,6,7,8,3,3,1,8,0,4,8,8,4,4,0,2,5,5,0,4,1,7,5,8,5,7,1,7,3,0,8,0,5,1,1,6,4,2,1,3,0,0,6,8,1,5,5,4,3,9,9,0,3,0,1,0,5,5,8,2,8,1,7,3,5,7,4,2,1,3,5,6,5,2,3,1,4,8,2,7,2,0,1,2,3,2,8,7,3,9,6,4,7,4,6,2,7,0,1,7,8,4,5,0,8,1,4,3,4,4,5,2,9,5,3,4,1,9,6,8,9,3,9,1,5,1,5,3,9,1,1,4,8,7,9,7,5,4,9,8,1,4,3,3,5,1,6,1,0,7,1,7,7,3,8,9,3,4,9,2,0,8,4,9,6,4,0,7,4,9,7,9,5,9,6,2,2,5,4,0,6,6,7,6,9,9,9,7,0,0,0,9,6,8,0,9,9,7,9,4,1,3,7,9,7,6,2,2,4,2,2,7,3,5,4,2,9,8,8,9,3,4,5,5,4,3,8,3,5,1,6,0,8,9,9,6,3,9,2,3,7,7,3,5,6,2,6,7,1,0,8,9,4,2,8,6,6,8,3,1,3,6,7,6,6,6,3,5,9,7,6,9,9,8,5,5,6,1,8,5,3,6,2,9,0,7,1,9,8,8,5,9,3,0,1,5,8,1,8,3,3,2,6,7,6,4,4,7,6,8,2,4,8,7,3,6,8,1,3,8,6,7,3,2,8,0,5,9,4,0,1,6,5,4,1,1,0,0,7,4,5,2,8,2,5,2,1,3,1,2,5,9,8,0,4,2,0,4,7,1,9,4,0,1,4,9,0,7,1,2,9,9,1,9,7,1,0,2,8,3,5,7,5,2,7,4,8,7,6,5,7,0,6,2,2,7,8,4,3,2,1,0,2,8,9,2,0,7,4,2,1,2,3,8,9,7,7,8,3,6,3,7,3,3,9,1,1,7,9,3,8,8,0,1,1,8,3,2,1,3,3,0,1,5,3,7,0,5,9,5,4,4,0,8,6,0,5,8,2,2,0,0,2,7,8,7,3,8,4,0,6,8,8,1,1,7,0,8,8,1,3,5,4,9,6,4,7,3,8,3,6,2,9,5,4,5,4,5,4,8,9,3,2,7,5,2,1,2,5,9,9,7,3,5,7,2,0,8,8,0,8,3,5,3,7,4,0,3,4,0,4,1,3,1,1,7,3,3,1,3,3,6,6,9,7,9,9,5,5,0,9,0,4,1,6,0,0,8,4,9,9,2,4,6,0,3,3,2,8,9,7,7,5,3,6,3,4,5,7,3,0,7,3,4,8,4,9,0,7,5,9,3,3,8,9,5,5,9,3,2,4,4,8,4,7,5,1,3,4,7,6,7,4,9,8,5,5,7,6,2,4,7,7,8,7,3,1,5,1,3,8,5,1,1,6,1,9,6,9,0,2,3,9,3,2,8,6,5,7,9,0,3,6,2,6,0,1,8,4,5,9,7,0,9,1,2,5,9,8,6,7,6,3,8,4,0,9,3,1,7,0,5,4,9,6,0,1,9,3,0,1,0,8,6,7,2,6,5,1,9,8,2,7,2,5,8,3,3,1,8,3,6,2,1,3,1,7,3,1,0,1,8,3,0,3,8,0,2,4,1,5,3,3,2,1,4,2,2,5,7,1,5,9,2,7,8,9,6,6,1,6,3,7,3,0,9,9,7,9,0,5,0,5,5,8,1,0,0,8,5,3,2,5,6,6,9,1,1,8,4,8,3,6,2,1,3,1,5,3,7,3,8,1,9,4,5,1,0,1,1,7,8,0,1,8,9,1,1,7,0,1,1,4,9,8,8,7,5,7,3,2,6,0,4,4,0,8,4,5,5,0,3,1,5,0,9,8,6,1,2,7,2,7,0,3,9,0,5,9,6,4,5,7,9,8,5,7,5,0,8,8,8,3,0,4,1,7,0,8,7,6,7,6,0,9,9,0,0,4,9,9,7,7,7,7,6,2,8,4,9,9,1,4,6,7,0,0,2,0,9,6,7,8,8,2,3,9,4,0,1,5,3,1,6,4,6,3,6,2,4,8,0,3,2,2,9,8,3,7,8,8,5,2,4,4,6,1,4,5,7,4,4,2,9,1,4,5,9,6,4,9,7,7,7,3,8,6,2,7,4,0,5,1,6,3,6,2,9,8,0,6,0,6,8,7,1,3,3,0,9,8,7,4,6,0,0,1,6,4,6,8,0,0,2,7,5,2,6,8,9,7,8,7,3,5,7,2,2,9,9,1,3,2,6,5,8,3,8,5,4,9,6,3,3,5,3,1,9,0,1,9,1,7,6,2,4,1,0,0,4,8,4,2,7,8,9,4,5,3,0,0,5,2,5,5,3,8,2,0,2,4,3,0,9,9,1,9,7,5,3,1,1,2,3,0,2,5,7,7,0,3,4,3,2,8,1,7,4,1,4,0,7,5,5,9,3,9,6,3,2,5,9,8,7,0,2,4,9,5,2,9,6,9,1,7,5,8,7,5,0,7,6,4,1,4,7,6,7,1,8,1,7,8,9,1,6,9,4,3,4,1,2,3,6,9,4,6,5,0,3,7,2,2,4,9,1,5,9,5,8,5,8,9,6,0,7,2,3,5,5,9,1,8,8,7,8,7,8,8,9,7,3,2,0,5,0,9,3,2,6,9,2,5,6,0,0,5,5,8,1,3,1,8,7,7,9,3,0,5,2,9,8,9,9,2,8,4,0,6,4,4,0,5,3,3,9,7,9,0,8,6,2,2,9,6,2,4,3,0,1,5,7,7,4,1,3,2,9,5,9,5,7,3,0,7,0,3,2,6,7,0,4,4,2,0,3,4,4,3,9,0,3,5,6,4,6,2,6,4,5,2,0,7,2,2,9,5,9,7,0,9,3,0,2,8,5,9,8,1,9,5,5,3,8,9,3,5,4,6,8,6,3,7,3,8,6,5,0,0,8,5,6,7,8,7,4,5,7,1,6,8,9,7,9,6,6,3,5,8,1,4,1,9,5,0,6,1,6,7,0,7,3,4,4,1,2,4,6,3,9,0,8,9,4,1,6,6,3,8,7,6,0,4,7,2,1,1,8,7,4,2,3,0,9,1,7,7,0,2,2,2,0,0,9,2,4,5,2,7,9,7,1,6,9,8,9,5,2,4,1,6,9,9,0,3,7,4,0,8,7,1,5,7,3,1,9,5,5,2,3,7,8,4,0,8,8,1,5,0,6,5,6,2,6,1,5,6,0,8,8,5,0,9,8,1,0,0,3,2,7,3,9,1,5,0,2,5,7,8,8,8,3,2,8,6,1,3,8,0,2,3,0,8,0,7,5,2,7,2,2,9,6,7,2,5,5,7,5,9,4,6,7,5,1,8,7,3,5,9,5,6,3,5,2,5,1,1,4,8,4,9,9,1,2,6,0,4,3,9,1,8,3,0,5,5,4,9,4,3,7,9,9,8,9,1,3,3,1,6,1,6,6,8,9,4,9,5,5,3,2,0,6,8,6,9,1,5,1,2,8,6,7,7,8,8,5,7,0,3,9,6,2,1,2,7,5,9,1,2,2,9,4,7,9,7,7,8,7,2,5,3,0,1,4,9,7,1,8,4,2,7,6,4,8,4,5,9,9,7,6,4,3,7,3,0,8,1,2,8,8,4,1,1,3,5,1,8,1,7,5,8,8,2,3,0,9,0,3,4,6,2,7,5,8,8,3,4,6,5,9,8,6,9,3,8,6,1,0,5,9,4,8,1,7,8,1,5,9,4,0,5,9,1,2,6,8,2,6,3,8,0,4,1,3,8,9,0,6,3,8,1,2,9,5,3,4,8,2,0,4,2,0,6,7,1,9,4,7,3,2,9,7,2,5,2,3,9,3,1,5,3,2,3,4,5,8,4,1,5,5,4,0,8,0,7,3,8,5,8,6,9,9,4,0,5,9,9,1,2,0,0,8,0,1,2,6,6,9,8,3,9,7,4,6,8,6,2,3,2,9,9,2,3,8,3,3,7,6,9,7,2,5,2,2,7,6,2,2,8,1,1,7,1,2,5,0,4,4,1,6,8,0,6,9,4,3,2,1,0,6,0,3,4,3,5,9,5,3,8,8,8,7,0,9,1,4,0,6,6,9,6,3,7,0,4,5,3,2,4,5,4,6,3,3,8,4,9,4,6,0,3,5,8,7,3,2,3,6,0,6,2,1,7,1,7,8,8,3,9,0,5,8,2,1,2,7,8,2,2,1,4,2,0,3,7,7,7,9,0,0,8,4,1,0,0,5,4,9,3,3,3,2,7,7,3,2,6,6,1,1,6,2,2,8,3,3,4,5,0,5,9,8,1,5,1,4,7,6,3,7,1,1,2,7,8,2,7,1,6,1,1,6,6,0,1,1,7,0,9,7,6,7,4,8,0,3,6,0,0,4,3,3,0,9,1,5,3,8,8,0,9,2,5,3,7,8,5,0,6,8,6,2,8,4,4,2,9,8,1,2,3,6,2,8,5,5,1,9,4,7,6,1,4,4,2,2,3,2,4,3,5,7,1,4,2,7,4,6,7,6,5,2,5,5,7,9,0,9,3,8,6,3,5,5,0,5,7,0,7,3,9,8,7,6,3,5,5,8,4,2,8,9,2,1,6,6,9,8,7,5,7,0,0,4,3,2,6,0,5,1,7,6,5,8,9,7,2,8,8,8,3,2,5,1,0,1,5,8,2,7,4,0,2,0,0,8,9,5,9,3,3,5,2,4,8,0,0,4,0,7,5,2,1,4,8,9,3,3,4,7,0,7,0,4,6,7,4,6,9,2,6,9,6,6,4,4,1,5,2,9,3,9,4,3,4,8,4,7,6,1,8,8,2,7,3,1,1,4,8,4,8,8,8,9,1,9,8,3,3,6,9,6,9,4,5,6,0,4,6,9,8,7,3,8,9,0,5,2,2,1,8,5,9,2,6,6,1,3,2,9,8,5,4,7,8,8,6,9,5,2,5,9,3,9,7,6,7,1,9,2,9,2,2,8,0,0,2,7,8,0,2,5,0,5,7,7,5,3,9,7,3,9,3,5,7,9,4,9,7,2,2,9,7,0,6,3,6,3,7,4,5,8,2,1,6,5,6,6,4,3,4,5,1,8,8,2,7,8,5,7,2,8,9,6,9,9,0,3,8,4,1,8,4,5,2,5,1,9,2,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3,2,9,6,9,0,9,9,8,7,0,6,9,1,3,8,8,5,4,3,2,3,4,7,1,6,5,8,6,1,9,9,1,4,5,5,7,9,7,3,4,5,4,9,7,3,0,4,2,5,0,0,5,8,5,1,8,8,0,1,7,0,2,9,6,1,0,7,9,9,4,2,6,0,4,2,6,8,6,0,8,4,9,5,1,5,2,7,2,0,5,7,0,9,8,0,0,4,4,9,3,3,6,3,8,9,3,7,5,8,2,2,7,9,9,0,9,1,5,0,2,8,8,7,6,7,6,1,6,2,7,8,7,4,5,1,0,5,0,6,4,3,5,5,1,3,8,9,8,4,5,2,5,5,3,3,0,9,5,1,5,1,4,0,8,5,8,9,8,5,2,0,4,7,7,6,2,6,9,4,9,1,5,8,0,2,8,5,2,9,6,9,0,1,1,9,5,3,0,7,2,0,3,2,0,0,7,4,8,6,6,3,4,5,3,9,1,1,8,3,7,5,4,2,4,2,0,0,0,7,8,1,3,4,8,0,2,4,0,9,4,6,3,8,2,4,6,0,2,0,1,0,8,5,9,5,5,3,0,0,5,4,0,8,5,3,0,9,9,3,8,8,2,3,9,2,4,8,7,7,3,3,9,0,6,6,3,0,0,9,3,7,3,3,1,5,0,5,9,3,7,1,0,7,5,1,4,3,2,8,2,8,2,3,9,0,0,5,3,2,5,2,1,6,6,8,2,7,2,0,7,5,0,4,1,9,6,4,8,2,0,5,2,6,1,9,7,6,9,7,4,9,2,4,6,2,5,4,0,2,5,0,0,5,5,9,5,5,4,6,8,5,3,7,2,8,4,9,0,9,1,2,3,8,3,8,5,9,3,0,5,3,0,7,0,2,9,8,9,6,4,4,0,8,1,8,0,9,2,7,6,7,1,4,7,1,8,4,0,6,6,4,3,6,7,6,0,4,4,2,4,7,2,7,4,6,7,3,3,2,9,8,3,6,6,5,2,9,4,8,9,3,5,8,4,8,0,1,5,3,6,6,2,8,5,7,5,5,0,1,8,1,7,4,8,8,0,5,0,2,5,1,9,1,5,7,9,9,3,4,3,9,7,0,0,7,9,6,9,8,0,3,7,6,2,1,7,3,7,4,6,3,1,2,4,0,5,4,8,2,4,8,3,8,4,0,7,7,0,0,0,2,2,9,7,8,2,3,2,1,0,3,3,8,0,3,0,1,2,6,7,4,3,1,0,6,6,5,7,2,6,4,8,3,4,9,3,0,4,0,9,6,7,4,6,4,6,6,4,8,1,1,3,4,3,7,3,7,5,6,3,8,8,7,2,3,0,2,8,7,4,4,6,8,9,2,8,6,4,2,8,5,3,3,5,7,4,4,6,9,5,9,8,6,0,5,6,8,8,3,2,7,6,3,2,3,7,0,7,1,8,1,6,4,2,3,7,0,4,0,9,8,0,1,9,4,8,8,4,4,2,7,8,9,0,7,0,7,9,6,2,0,6,6,5,5,5,8,0,4,0,3,8,8,9,9,8,7,8,5,3,5,1,2,7,9,0,4,4,4,0,3,2,4,8,8,1,2,7,6,1,8,3,0,4,4,3,7,9,5,0,1,9,5,1,8,1,3,0,6,4,5,0,6,3,0,8,6,0,5,3,3,9,9,5,9,5,4,4,1,2,2,9,6,3,8,1,8,5,4,5,7,8,8,9,3,2,6,1,7,9,4,1,6,7,2,3,0,7,7,0,8,2,7,0,2,9,8,2,5,6,8,3,8,4,8,8,8,6,9,7,8,0,7,8,2,1,8,3,4,3,7,2,7,9,8,9,2,3,2,7,7,6,9,0,5,7,3,8,2,9,1,6,9,9,3,8,3,6,1,3,1,5,9,0,6,3,9,7,4,7,7,7,2,4,6,3,0,5,6,1,9,2,7,0,4,7,2,5,2,2,2,0,9,5,7,2,8,7,5,9,2,5,3,8,3,7,6,9,2,6,7,0,2,4,7,3,1,4,1,7,6,6,9,6,7,4,8,7,0,2,7,1,5,4,9,7,3,5,6,2,8,7,7,4,6,5,0,1,4,2,6,7,1,5,1,2,4,6,3,3,0,3,6,6,6,0,8,7,8,3,3,5,4,2,1,0,7,8,0,5,9,5,4,7,7,3,4,9,9,5,2,7,6,5,7,6,3,4,2,5,9,8,7,2,8,5,1,9,8,6,0,1,2,9,5,0,7,1,5,3,3,0,9,1,5,4,2,0,2,2,6,2,5,5,6,5,8,9,7,6,3,9,6,7,0,3,4,2,0,8,5,2,2,9,8,0,8,3,2,9,0,8,6,2,0,8,9,5,1,2,9,7,3,8,1,5,7,2,6,9,4,1,7,7,0,2,9,9,9,2,1,2,1,1,4,2,0,4,2,0,6,4,7,1,3,8,8,9,5,6,7,4,4,6,8,8,7,9,4,4,8,6,4,3,8,5,2,7,4,8,9,8,5,4,1,5,7,3,0,2,4,9,7,3,1,0,9,1,7,9,9,4,0,6,6,7,7,4,6,6,3,0,1,7,4,0,1,4,7,6,6,4,3,7,8,1,9,6,9,0,5,2,3,5,6,0,5,6,8,6,2,4,1,9,2,3,4,8,2,5,6,8,5,9,5,8,4,8,0,6,1,1,9,4,3,9,7,2,4,4,6,0,4,1,7,4,7,2,0,1,5,8,5,6,6,7,4,9,3,5,5,3,4,2,1,4,5,4,7,6,3,7,1,8,2,2,4,7,0,0,4,5,6,4,4,2,8,8,7,3,1,9,9,6,3,0,0,2,2,6,2,0,2,3,0,6,2,8,0,5,9,8,0,8,0,2,6,9,2,2,0,4,2,8,6,5,1,9,5,3,9,8,9,1,4,7,4,3,0,2,3,3,3,2,0,9,5,7,0,4,8,6,5,0,8,9,9,1,2,3,6,5,0,0,3,4,2,1,5,5,4,7,4,7,2,0,3,4,4,0,8,5,1,0,9,7,8,7,5,3,7,4,1,2,8,5,1,4,7,3,5,8,3,2,4,2,2,2,0,9,7,6,8,1,7,6,1,5,5,3,4,9,0,6,2,4,9,4,9,9,6,3,6,9,5,2,7,5,8,7,9,8,1,5,7,9,9,5,9,8,9,2,2,2,0,6,8,9,3,0,1,2,6,1,1,4,7,3,7,6,7,3,2,0,4,6,6,3,5,2,1,1,1,7,4,3,7,6,0,6,4,6,0,0,6,4,3,3,1,2,9,2,3,8,8,1,4,2,3,8,4,9,4,7,7,0,5,0,4,0,4,1,5,2,4,4,3,4,2,9,2,2,8,4,2,8,5,7,3,7,2,1,6,9,0,6,7,2,9,2,7,0,9,9,8,3,2,2,8,3,0,8,2,7,5,2,3,9,7,9,3,7,0,8,2,2,7,8,0,8,6,8,5,4,3,0,0,8,9,6,8,5,5,6,0,2,8,7,0,2,7,9,6,7,6,8,8,2,8,7,8,9,1,3,4,2,8,8,7,6,5,8,4,0,8,2,1,4,9,6,7,2,2,7,0,7,5,0,9,6,2,6,8,0,5,8,1,5,1,0,6,6,7,4,0,8,4,8,9,0,5,6,3,9,2,4,7,2,3,5,8,0,5,7,6,5,9,7,1,5,8,4,7,4,5,5,3,4,9,8,4,7,7,0,8,0,5,4,5,5,6,7,0,7,3,6,4,1,7,0,9,4,6,2,1,1,4,2,9,0,6,0,6,4,6,0,7,1,2,3,4,8,8,3,2,4,1,6,6,7,9,4,6,1,9,2,6,6,8,9,9,0,7,2,9,2,0,4,2,1,2,4,2,6,5,2,7,0,7,3,8,6,6,6,2,9,5,1,2,2,6,7,9,7,2,2,1,1,5,9,8,6,5,1,0,7,3,2,0,6,7,5,2,7,5,3,7,6,5,5,1,0,9,4,2,6,4,6,4,8,0,8,3,9,3,4,8,7,3,2,5,2,6,8,4,9,6,9,8,9,7,4,6,0,3,3,3,3,5,1,3,4,4,0,4,9,3,2,7,7,7,3,3,7,7,5,5,0,2,1,7,0,4,5,7,1,5,3,3,9,0,4,5,6,9,0,0,3,9,9,7,6,2,1,6,3,6,1,3,9,6,0,6,3,3,0,5,4,1,5,9,8,5,6,8,5,5,0,0,8,1,9,3,8,7,9,5,6,3,3,3,7,5,8,4,5,6,7,4,2,9,2,4,2,2,4,3,1,7,4,1,6,0,7,9,8,2,4,2,4,9,9,7,5,4,2,1,6,5,1,5,0,4,0,3,0,8,3,1,9,2,1,8,0,9,8,4,3,9,0,4,8,4,4,6,4,6,9,2,5,2,2,4,4,9,7,5,6,6,2,4,2,2,7,6,2,4,7,7,2,7,0,9,0,5,1,2,6,2,4,7,3,6,4,1,3,9,6,1,5,2,8,5,3,0,0,0,2,9,1,2,8,9,7,6,5,0,6,0,8,5,1,3,8,4,0,8,1,6,8,8,8,6,8,4,5,1,2,1,4,2,9,3,2,5,1,3,2,9,5,5,9,5,7,2,0,2,8,3,4,2,2,3,3,1,8,7,6,1,8,9,6,0,2,8,2,8,3,7,4,7,3,3,4,8,7,9,4,0,2,4,2,1,7,0,4,7,8,4,1,2,3,3,5,6,3,9,1,9,4,1,2,7,5,1,4,4,7,3,6,7,6,7,9,9,3,0,8,5,7,3,5,1,6,7,5,0,2,4,0,0,0,8,2,7,4,0,7,2,7,1,2,5,7,2,8,8,7,3,7,3,5,4,9,7,5,0,8,6,9,5,4,3,6,1,3,5,9,2,2,7,8,8,4,8,7,3,3,1,8,4,3,5,3,9,8,2,1,6,0,7,8,5,8,9,3,7,5,4,1,3,0,8,0,3,6,5,6,5,9,2,2,9,0,8,9,0,2,9,9,2,9,9,7,7,8,9,4,1,2,6,9,9,4,6,5,9,6,5,3,3,3,0,4,3,2,9,7,3,8,7,3,4,8,2,7,7,7,1,1,0,3,5,1,0,1,4,9,6,5,8,2,3,4,2,5,2,7,4,7,6,5,4,4,9,9,0,0,8,8,0,1,7,8,2,5,1,3,9,2,8,3,0,4,6,6,8,7,8,4,9,1,9,6,0,9,3,8,7,8,8,6,9,3,0,2,8,0,7,5,4,2,4,4,4,7,2,0,9,8,6,3,7,4,2,6,4,8,5,7,3,2,8,0,6,9,6,2,1,2,6,1,7,2,8,6,4,7,0,0,9,5,0,0,8,7,3,7,7,2,8,2,5,4,8,9,3,2,9,8,1,2,7,5,7,3,4,5,7,6,2,8,0,4,2,9,8,8,2,6,7,0,7,1,3,1,3,1,3,8,2,6,5,6,3,7,7,9,1,0,6,6,5,6,0,0,1,4,0,5,4,9,2,2,5,3,3,3,9,9,5,6,1,7,5,6,0,9,9,7,7,5,4,2,3,7,1,3,4,0,9,4,3,0,1,9,9,0,9,2,4,4,3,4,1,7,5,7,3,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6,7,6,2,2,9,8,3,2,2,9,3,8,5,2,2,5,5,1,3,8,5,1,0,7,4,5,1,1,3,4,9,1,3,8,5,3,3,5,7,7,0,3,5,0,4,8,8,4,9,0,5,6,2,1,8,6,5,4,4,4,1,0,3,5,8,9,6,7,5,4,6,8,4,1,7,2,9,5,2,7,1,3,3,9,5,1,3,4,8,2,6,7,7,6,4,6,7,8,8,5,8,6,8,9,0,5,5,5,5,1,6,6,2,7,3,0,8,3,2,2,6,0,9,5,8,7,8,8,4,9,4,4,9,6,0,6,8,1,1,3,4,3,8,1,0,8,7,3,4,9,5,5,3,9,9,1,0,6,8,5,5,4,7,3,4,8,3,2,6,6,5,5,8,2,3,8,7,8,5,7,6,8,4,0,1,3,0,8,6,7,1,8,1,3,6,7,7,5,6,2,6,4,5,8,6,4,9,0,8,8,1,1,0,3,4,7,9,2,3,0,3,8,8,3,6,1,9,0,1,8,3,8,8,7,9,1,1,5,3,9,8,8,5,8,2,2,8,5,0,0,9,6,9,6,4,0,2,2,4,5,7,0,5,1,5,9,9,5,3,3,5,5,3,4,7,5,5,6,9,0,2,3,4,7,6,7,8,9,0,8,5,9,6,7,2,7,3,1,7,3,3,0,0,1,3,9,5,7,0,3,2,2,1,0,8,4,3,5,7,5,3,2,9,1,0,8,9,9,6,5,9,5,4,2,2,3,1,1,8,4,9,4,1,0,3,8,0,8,3,8,7,8,3,4,3,2,9,6,4,1,8,7,5,8,0,1,2,2,1,4,0,9,9,2,8,4,5,4,9,7,2,4,2,5,2,3,3,6,8,9,4,4,0,2,1,1,3,9,7,0,4,1,2,7,5,2,2,9,2,6,5,8,3,1,1,5,1,5,0,0,4,2,8,3,9,2,7,8,4,8,4,5,2,6,8,4,7,5,5,8,0,6,4,4,7,9,4,1,6,6,6,7,6,4,5,6,1,1,7,3,6,6,9,5,3,1,5,8,9,9,7,7,7,4,0,8,6,2,9,0,2,4,3,8,2,7,4,3,5,4,6,3,3,5,8,3,4,8,3,4,2,6,9,0,2,5,0,5,2,5,1,8,4,9,6,0,8,2,6,0,9,9,8,4,7,9,5,7,6,4,4,6,5,7,5,6,7,6,4,4,0,0,8,0,8,8,3,8,7,2,6,5,7,6,2,3,5,9,4,6,1,7,8,9,8,7,6,3,0,4,8,4,5,1,3,4,4,9,3,0,1,5,7,5,0,6,6,9,4,9,2,4,1,9,7,6,4,3,3,3,2,3,3,7,5,1,3,2,0,3,6,3,3,2,8,8,4,9,1,4,9,3,4,7,3,5,7,5,3,8,3,4,0,3,3,4,4,1,3,9,7,8,0,6,4,8,5,8,4,9,3,7,8,4,9,6,7,7,4,1,7,2,0,6,4,0,5,4,5,5,1,5,7,2,3,0,8,3,3,2,3,8,4,4,5,5,4,5,9,5,6,1,4,1,2,1,2,5,5,3,9,0,5,7,6,4,9,6,2,6,6,6,9,1,0,3,0,6,2,0,4,2,5,4,8,6,0,3,7,6,7,4,3,5,2,0,0,2,2,0,4,2,7,9,4,5,8,2,1,2,5,9,5,6,1,3,3,7,3,9,9,3,1,5,1,1,7,4,3,8,3,9,9,6,2,8,6,5,9,5,2,8,8,0,8,7,0,9,9,4,6,9,7,9,3,4,9,3,5,3,7,4,8,2,4,6,6,3,6,3,2,1,2,7,2,3,1,8,4,3,6,7,8,7,0,0,5,5,0,7,3,2,2,9,0,4,9,0,1,0,6,4,0,0,3,8,4,8,1,1,7,9,8,8,7,8,2,4,5,4,9,5,1,5,9,7,3,2,4,8,2,8,2,3,5,7,4,9,6,0,8,0,4,4,8,9,9,1,1,1,3,8,5,4,3,6,7,4,3,4,0,1,1,9,2,4,3,9,2,4,9,3,8,7,3,9,4,6,5,2,9,0,9,5,2,9,8,5,3,9,7,3,0,9,3,5,0,1,0,7,5,4,3,7,0,5,3,4,3,2,2,4,1,5,8,4,0,3,1,0,8,0,5,2,2,4,3,2,0,8,7,0,9,4,7,7,5,5,0,8,4,8,5,7,5,6,6,0,9,9,5,1,7,9,0,4,3,1,4,2,3,9,1,2,3,1,2,2,1,4,7,5,7,9,8,0,5,0,8,6,6,9,4,8,8,1,9,0,1,9,5,3,3,1,6,8,0,4,9,6,8,0,0,5,4,0,4,5,3,1,4,5,0,1,9,8,8,8,4,7,0,5,1,1,0,9,1,1,8,5,7,0,1,5,5,9,2,5,2,7,1,8,5,7,8,6,7,9,1,0,6,4,8,8,7,9,3,1,0,8,0,5,0,8,6,1,4,2,4,8,9,9,5,9,5,1,7,8,7,7,5,4,6,5,5,0,1,7,3,1,9,8,1,9,5,8,2,3,1,6,6,3,5,9,4,0,7,6,9,7,9,5,9,2,4,2,5,0,9,3,4,9,8,7,9,7,6,5,3,6,0,0,7,8,1,3,4,9,0,7,6,3,9,4,8,4,2,9,4,8,4,7,8,3,8,2,6,2,4,9,7,5,7,1,6,1,3,6,9,0,0,9,6,3,4,6,0,8,1,3,4,9,0,7,9,8,3,2,9,6,8,7,7,1,2,2,3,0,4,6,0,8,9,6,0,0,7,4,3,1,0,8,1,2,7,0,0,2,8,4,9,2,9,2,0,9,5,2,8,8,5,6,5,2,9,1,3,7,9,6,8,1,1,5,2,5,0,6,4,7,9,9,6,7,1,3,0,0,4,8,0,1,5,5,8,0,4,3,0,6,5,4,5,2,0,7,1,2,7,3,1,6,2,5,5,3,7,3,1,5,1,7,6,3,9,0,0,4,8,9,0,4,6,7,2,3,9,3,7,1,9,5,5,6,9,9,9,0,2,0,4,5,3,5,2,1,9,8,6,2,5,4,3,8,7,3,8,0,5,4,9,2,5,1,9,8,1,4,8,4,3,7,3,8,2,1,1,2,6,3,5,0,7,3,9,0,4,0,8,2,6,1,9,0,0,3,5,0,0,5,4,3,2,6,5,2,1,8,0,3,4,6,8,1,4,8,8,3,1,0,2,1,3,4,2,8,9,6,7,7,9,9,8,7,9,9,0,6,4,4,3,8,0,5,1,9,7,0,5,8,1,3,8,0,8,6,4,3,1,1,6,2,4,1,9,1,5,2,4,4,8,7,4,0,3,6,8,3,5,0,7,7,0,5,8,2,8,6,1,9,4,3,9,1,1,4,1,1,3,2,4,3,1,0,2,8,2,5,5,7,4,8,3,5,5,2,9,6,3,6,5,3,6,5,8,0,3,4,9,1,8,9,8,5,3,9,6,8,7,8,2,1,9,0,1,7,6,5,8,4,5,9,2,8,1,3,5,3,6,8,9,4,1,4,7,2,6,3,6,9,5,8,4,6,2,1,5,8,0,0,5,6,2,3,4,5,5,8,3,8,1,1,5,9,6,0,0,1,8,9,5,8,1,1,7,9,3,9,6,6,7,9,4,1,6,9,4,2,7,0,7,4,0,3,1,4,5,2,5,9,3,7,4,4,4,9,9,5,9,1,3,8,6,1,0,7,1,3,7,5,0,5,5,1,6,7,5,8,3,9,4,3,9,6,7,3,0,0,5,7,0,2,5,3,2,6,6,4,3,5,4,0,1,3,5,2,5,4,5,4,3,9,5,0,0,5,6,3,3,4,2,0,7,3,0,3,8,7,6,1,0,2,9,3,6,1,4,1,1,9,7,3,6,9,1,3,0,9,6,3,4,8,6,5,8,8,6,1,1,1,6,8,0,2,2,7,6,7,0,4,2,3,5,5,4,7,1,7,7,5,0,1,4,8,9,5,1,8,0,7,2,6,6,9,5,6,1,7,9,1,1,4,0,3,9,2,6,3,9,8,1,0,2,7,9,0,0,9,0,9,3,0,0,6,9,4,5,8,5,3,8,1,4,9,7,2,8,4,8,2,5,0,0,1,4,5,7,6,9,7,9,3,5,3,4,2,0,8,2,2,1,2,3,5,8,3,3,6,4,0,1,8,9,8,4,2,5,0,3,8,4,9,0,0,0,7,3,0,5,5,7,5,0,8,1,6,5,8,0,0,8,2,5,2,2,7,2,4,6,3,6,9,4,3,1,1,1,5,6,4,8,3,0,3,1,6,7,9,3,0,4,3,3,7,1,5,5,1,8,6,3,7,1,3,2,1,5,8,1,3,4,6,8,1,0,3,3,5,2,8,6,6,2,0,7,9,6,9,8,3,1,2,1,8,9,0,6,3,6,3,0,1,7,4,0,9,7,7,5,4,3,0,9,1,1,6,4,1,9,6,7,2,7,3,3,7,3,2,6,9,7,1,5,0,2,6,1,5,6,8,2,2,3,0,9,9,5,5,5,8,5,7,3,7,7,5,5,3,5,7,3,2,2,9,5,8,7,8,2,2,3,7,6,9,9,6,2,6,3,2,1,8,9,4,3,6,1,8,8,0,4,1,7,4,8,1,8,3,9,9,2,4,9,4,8,9,0,3,2,2,9,6,0,4,4,9,5,7,7,9,8,7,7,7,7,3,3,3,6,7,8,7,1,7,1,6,9,3,1,9,2,5,8,8,1,5,1,4,5,0,7,1,1,5,5,7,5,0,6,7,2,1,5,2,8,0,7,4,9,8,7,5,5,2,4,1,7,0,1,9,8,4,3,6,1,3,6,9,9,3,2,0,3,6,1,9,3,3,3,5,4,3,5,4,1,9,0,7,6,5,6,0,4,1,3,4,4,3,0,1,0,4,1,7,5,5,5,7,0,4,5,2,5,5,0,7,0,4,6,1,8,5,9,4,1,5,3,5,8,1,6,7,9,8,0,8,1,0,6,6,5,9,9,6,3,2,3,0,2,2,8,6,4,7,4,1,4,9,7,6,8,7,0,4,8,5,4,5,6,8,3,9,5,3,4,0,9,5,6,4,2,1,0,5,1,9,0,5,4,7,1,4,3,0,2,2,5,9,1,6,6,2,1,0,1,6,7,0,1,3,2,5,3,2,8,3,1,6,9,6,9,3,7,7,9,8,0,5,7,1,9,4,1,4,7,6,5,6,0,1,9,6,2,3,9,3,8,4,5,5,2,6,5,2,3,3,8,1,4,3,4,5,0,8,0,7,6,5,2,8,8,8,4,5,7,8,8,8,2,9,0,6,3,6,1,8,0,4,0,8,1,0,0,9,6,0,2,6,3,6,2,6,0,7,9,1,5,2,9,0,2,3,0,2,2,2,3,7,3,9,7,0,9,2,6,8,6,2,1,9,1,6,5,0,4,7,2,6,3,6,8,4,4,7,9,4,0,6,9,4,8,3,9,5,8,2,5,4,5,7,4,1,5,3,6,5,7,6,9,8,9,6,7,1,5,2,4,4,3,2,6,3,4,4,5,0,3,8,1,3,9,1,0,7,2,1,1,9,3,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2,2,2,4,0,4,0,3,0,1,1,4,9,3,5,8,1,2,4,9,4,1,8,5,8,7,8,9,8,2,1,1,6,4,0,0,5,4,4,9,1,4,1,1,3,7,7,7,2,7,7,0,7,9,9,1,7,3,6,8,8,0,1,0,1,0,0,4,2,9,2,3,9,7,0,2,5,2,2,8,8,0,5,6,8,6,0,4,6,4,0,2,4,6,7,2,9,7,2,3,2,6,4,5,4,7,1,1,2,1,4,3,6,3,5,1,7,3,5,5,2,6,6,4,1,7,4,2,2,4,7,1,0,4,0,2,3,1,2,6,4,3,4,3,8,1,3,0,5,2,0,4,5,9,6,9,2,1,5,5,8,9,1,7,3,5,8,2,2,1,7,1,2,8,5,1,8,6,5,3,9,1,5,5,3,0,0,7,8,2,4,6,1,8,0,5,2,7,6,6,1,7,7,5,1,7,4,6,1,4,5,1,6,0,9,7,2,6,2,1,1,7,1,4,6,8,7,8,3,7,8,0,2,4,6,4,7,9,1,2,5,5,3,1,7,8,8,1,2,1,5,2,4,7,3,6,3,2,0,7,9,2,8,9,4,6,6,3,9,0,0,6,3,3,2,3,1,8,5,2,8,7,4,0,2,4,3,7,1,8,7,8,5,2,4,5,9,4,9,4,3,6,2,7,4,6,5,8,0,1,4,1,4,9,3,6,2,9,2,2,5,8,4,9,3,1,6,3,0,2,8,0,6,6,4,8,5,6,0,9,3,3,8,8,4,0,0,8,5,7,5,4,6,2,2,2,6,3,4,1,9,8,9,1,2,9,1,9,3,8,1,4,1,8,4,4,6,0,9,6,1,8,0,0,9,5,1,5,4,0,2,0,6,3,6,4,9,0,6,9,4,3,0,1,4,9,4,1,4,3,2,8,3,0,8,9,2,6,9,2,2,8,5,3,2,8,0,0,5,3,3,4,7,2,3,1,0,9,9,4,7,3,0,4,0,2,0,9,2,3,1,1,8,6,0,9,5,9,5,5,1,2,9,7,0,8,7,7,0,5,8,8,9,3,3,6,3,9,6,9,7,4,5,2,6,9,9,3,7,4,9,5,5,0,9,1,3,0,6,5,8,3,2,5,6,4,4,4,3,3,7,3,5,0,7,5,5,5,9,4,6,4,3,2,6,7,7,0,8,0,0,5,9,5,7,0,2,4,5,6,6,3,4,4,3,4,3,3,9,8,0,1,8,1,5,8,5,2,0,8,2,4,0,5,4,6,2,5,3,5,2,8,9,4,5,8,6,2,4,7,5,2,3,3,7,7,7,6,3,4,5,8,1,5,2,8,4,9,4,2,3,8,9,0,4,4,5,8,2,0,1,1,7,7,7,5,7,1,2,1,8,7,2,4,4,0,6,6,1,0,3,6,8,5,2,4,1,3,1,9,4,6,9,0,2,3,3,3,7,6,2,9,5,8,4,2,4,5,7,2,2,5,2,8,9,2,0,0,6,4,3,0,2,7,6,8,7,9,5,8,9,2,3,4,7,6,6,9,8,8,9,8,5,9,0,9,2,0,8,0,7,0,6,2,7,8,0,6,6,8,6,2,7,1,9,0,1,9,4,9,1,0,6,9,8,7,3,0,1,4,0,3,1,5,5,6,7,3,7,6,8,4,5,2,3,6,7,6,8,7,7,9,1,3,3,3,5,2,4,2,7,8,2,7,2,6,4,1,7,4,8,1,0,3,6,2,9,9,9,4,1,5,2,5,9,9,2,6,1,8,8,6,6,0,8,1,3,3,0,6,6,2,8,7,1,1,6,9,6,0,9,1,0,2,6,4,5,9,9,4,6,5,5,7,6,9,0,9,3,8,6,0,0,9,4,8,0,6,8,3,2,7,2,1,8,8,1,0,9,8,7,3,2,4,2,4,7,6,9,2,0,3,9,6,5,5,8,0,1,8,7,7,1,4,6,1,3,9,3,2,3,4,4,9,4,4,8,6,9,3,3,8,7,0,1,7,6,6,4,7,1,6,7,7,7,9,3,5,1,8,2,7,2,7,4,8,7,5,3,2,2,2,5,9,1,3,8,1,7,6,6,1,2,0,4,8,0,2,8,1,0,0,7,4,4,4,4,4,3,7,0,0,8,0,5,3,5,6,2,5,6,3,1,4,0,5,7,1,3,5,9,7,7,4,2,0,9,9,0,7,6,6,4,5,0,7,1,3,8,5,4,1,1,1,5,2,9,2,8,9,0,6,6,7,9,2,3,2,1,1,4,9,8,8,4,5,6,3,2,4,1,4,2,0,0,2,4,1,9,3,3,7,7,3,6,7,3,2,5,9,0,6,6,8,0,5,2,1,6,7,4,8,3,0,4,4,5,0,1,4,3,7,0,2,8,4,3,9,4,1,7,6,1,6,2,6,5,4,0,7,2,2,5,3,2,9,5,8,8,1,6,7,1,4,1,5,3,6,7,7,5,6,6,6,7,2,1,8,7,2,2,0,6,2,1,4,3,0,0,3,4,1,1,7,4,8,6,2,1,3,9,5,7,6,1,8,2,9,0,2,8,1,7,7,1,7,6,2,1,6,6,4,7,9,6,8,3,3,3,2,6,9,9,1,4,7,2,1,9,9,3,3,5,5,3,1,5,9,5,3,7,3,6,7,7,9,8,3,1,3,9,3,8,3,7,2,1,5,9,3,3,0,6,1,0,4,0,7,8,5,9,4,2,3,6,4,6,1,5,2,7,4,7,6,9,4,0,6,9,1,7,9,8,7,9,5,4,6,3,6,2,6,0,2,0,1,6,8,4,0,9,6,9,1,8,5,5,6,2,2,3,9,5,3,5,8,6,7,2,5,7,3,7,2,4,5,6,4,9,0,6,7,5,8,2,3,4,7,6,9,3,8,6,8,8,4,5,3,6,8,8,6,3,7,4,3,9,8,7,4,1,7,8,4,9,8,9,1,4,6,5,7,7,7,8,5,1,0,0,5,0,9,7,1,0,9,1,2,7,9,4,8,0,2,6,9,0,8,3,5,9,1,8,3,2,7,2,2,8,0,2,3,0,6,2,5,6,2,2,2,1,2,4,7,6,9,8,0,0,0,8,1,4,6,3,0,7,1,3,2,4,7,3,5,8,3,8,3,2,3,5,5,3,6,1,1,4,8,5,2,5,6,1,2,1,8,6,2,1,6,0,5,0,2,1,3,6,0,8,7,8,0,4,3,9,5,4,8,9,8,7,8,7,0,2,4,4,0,7,1,2,8,0,8,6,8,3,0,6,7,0,2,9,6,6,6,0,2,8,1,4,3,7,2,0,0,1,6,7,5,7,0,8,3,9,9,3,0,7,8,3,5,9,5,2,5,3,1,4,9,4,7,5,8,2,8,9,4,0,5,3,4,2,3,1,5,6,9,0,7,1,7,1,5,1,2,5,8,8,9,2,6,3,6,9,9,8,5,3,8,9,5,8,2,0,6,7,6,2,7,3,6,5,6,8,1,2,9,2,3,2,8,2,1,9,9,9,5,1,2,0,9,3,1,4,0,7,5,5,6,6,9,5,6,2,4,5,8,5,7,7,7,6,0,4,4,3,3,7,6,4,9,9,6,2,5,8,5,7,0,8,5,9,8,3,0,4,9,6,1,5,9,0,4,3,0,5,4,8,4,8,7,1,8,5,9,9,0,5,0,9,1,7,3,7,8,5,5,8,7,1,6,8,7,2,8,1,0,1,7,1,6,3,7,6,7,5,7,9,6,6,5,5,1,8,2,5,5,0,0,3,9,3,4,3,3,4,6,5,6,6,8,5,8,2,9,5,1,7,0,9,6,7,5,2,4,3,3,5,2,3,0,6,8,4,3,9,6,9,2,3,4,0,7,3,5,2,2,4,7,7,1,3,1,3,6,1,6,2,7,3,0,0,5,2,0,6,0,3,7,3,4,9,8,5,4,1,3,2,1,4,1,7,4,2,9,1,5,3,3,6,4,3,4,2,2,3,3,2,1,4,8,5,5,8,2,2,3,4,3,2,3,7,1,6,8,7,3,1,4,9,4,2,7,5,2,0,7,4,8,0,7,5,4,2,0,0,8,8,7,9,7,7,7,8,2,1,7,5,9,2,2,9,6,3,8,2,8,0,1,5,7,6,2,6,6,4,5,4,6,8,0,9,1,2,4,2,0,7,3,1,3,3,9,2,3,9,6,8,7,7,4,0,6,2,4,4,2,8,5,4,2,0,3,7,7,4,9,4,9,0,6,6,8,3,7,0,2,4,9,0,0,8,3,3,0,5,3,4,8,1,6,4,0,2,5,3,5,3,5,1,6,1,0,2,9,8,5,6,3,8,0,5,0,1,3,5,7,8,1,3,7,0,9,8,0,6,2,4,7,8,7,1,8,1,1,6,1,0,3,4,4,4,5,5,5,3,5,0,9,1,0,0,0,9,3,9,9,9,6,3,9,8,8,1,9,8,3,7,8,2,7,1,2,4,6,9,9,5,0,2,0,9,0,7,1,7,5,1,3,0,9,7,1,3,6,7,3,0,4,6,2,4,0,4,7,2,1,9,5,2,9,5,4,5,7,1,7,7,7,7,2,6,5,1,7,2,2,3,1,9,2,6,2,4,9,1,6,5,4,5,8,3,1,5,5,2,2,3,3,5,2,1,1,7,6,0,2,3,7,0,8,3,0,1,9,0,0,6,3,9,1,2,4,2,5,3,2,3,1,8,7,8,5,5,7,9,8,4,2,1,2,6,4,3,8,0,0,9,3,1,8,4,6,7,5,3,0,1,5,1,7,3,7,2,1,6,4,2,1,0,0,9,7,2,9,5,9,6,3,4,5,0,4,0,9,6,4,9,8,2,2,7,4,0,6,6,4,8,2,3,9,9,5,8,3,3,4,4,3,4,6,2,4,6,8,8,1,0,6,5,2,7,9,3,5,4,5,1,0,1,7,0,7,5,3,7,4,3,3,4,1,9,8,5,8,5,4,8,0,0,1,0,2,1,9,1,8,6,8,0,8,9,4,1,0,1,6,2,1,6,4,9,7,8,6,4,0,3,4,0,3,5,8,5,1,7,7,9,6,5,2,4,0,2,6,7,2,7,1,8,7,3,2,0,2,7,6,4,0,0,9,9,8,8,8,8,3,1,9,7,8,0,8,1,8,6,9,6,2,8,1,0,9,6,6,1,1,1,4,5,5,5,5,1,9,6,5,2,5,8,8,2,0,6,4,3,4,7,3,2,0,8,4,8,0,9,8,6,6,1,3,0,3,2,1,3,5,5,2,9,9,2,8,9,3,1,2,5,6,2,7,3,3,9,3,6,0,4,0,1,6,6,0,8,3,6,8,3,4,2,7,8,2,1,5,1,4,0,9,4,1,5,0,6,5,6,3,7,4,3,4,0,4,1,3,2,1,2,1,3,7,4,0,0,0,7,8,8,5,2,2,5,9,4,6,4,7,9,4,1,6,0,5,2,2,0,7,4,0,3,0,1,1,0,9,3,0,0,2,6,2,0,9,3,6,8,1,5,1,1,0,2,3,5,2,2,0,0,9,6,5,0,7,3,4,5,6,3,9,1,7,5,7,7,7,0,9,6,9,3,7,8,4,0,6,5,1,2,3,2,7,4,1,9,8,8,2,8,9,8,0,8,5,4,2]);
P:=CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 13:12:37 on modular  [Seed = 3802948673]
   -------------------------------------


>> A:=Matrix(IntegerRing(),200,200[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4
                                  ^
Runtime error in '[]': Bad argument types

>> P:=CharacteristicPolynomial(A);;
                               ^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.919 seconds, Total memory usage: 9.89MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Tue Aug  3 13:13:11 2004

Input: A:=Matrix(IntegerRing(),200,200,[0,8,5,6,6,6,9,1,2,6,3,1,1,9,5,4,2,1,2,3,8,4,4,9,9,6,5,5,2,0,5,0,4,7,6,6,4,8,8,0,6,9,0,9,9,7,6,4,9,2,5,6,4,6,6,7,0,8,0,8,0,8,9,6,9,4,7,5,7,0,0,3,2,7,0,4,6,7,1,0,9,7,6,9,3,0,1,0,1,5,1,6,4,1,0,6,6,3,4,8,3,8,3,8,5,6,5,2,0,0,6,6,1,1,8,5,1,1,8,6,9,2,2,6,8,1,1,4,0,0,6,3,0,9,6,9,3,5,1,0,5,1,8,9,9,1,0,5,0,9,7,3,5,1,4,9,2,8,2,9,6,4,8,7,6,4,9,8,9,6,2,7,2,2,5,0,6,5,0,5,8,7,2,5,8,2,6,2,5,3,5,0,5,4,3,1,1,9,2,9,0,6,0,2,5,1,1,1,4,2,1,8,2,9,6,6,8,3,6,9,3,3,8,1,8,4,5,8,0,8,0,4,7,6,1,9,2,8,3,3,3,5,9,4,4,9,9,3,4,0,7,2,4,5,8,9,7,0,5,5,7,6,5,5,5,8,9,2,1,2,3,0,9,8,3,8,0,2,5,1,2,1,4,0,8,6,7,0,7,9,6,9,2,5,1,1,3,7,4,0,2,0,1,7,0,3,0,3,6,4,6,8,4,1,1,7,1,4,5,4,1,8,2,3,5,4,3,4,7,5,2,0,5,6,5,8,3,5,1,8,6,8,3,7,8,6,1,0,2,7,1,8,3,2,0,2,4,9,9,9,6,6,3,1,3,6,0,4,4,1,3,1,9,9,0,9,8,9,9,7,3,8,1,6,2,1,7,3,6,4,9,2,1,7,0,0,6,5,2,3,7,7,0,1,3,7,3,6,5,1,0,7,8,1,1,5,8,1,1,1,7,6,4,6,5,7,9,1,0,3,5,5,4,6,1,9,8,8,1,9,5,2,2,4,9,0,9,5,9,7,7,1,3,1,0,7,9,5,8,2,7,6,8,6,6,0,8,2,4,6,8,6,3,3,7,7,8,8,2,0,0,6,4,0,8,8,5,0,9,1,4,2,9,9,9,8,5,5,0,5,5,0,0,5,6,4,3,3,1,7,5,0,4,8,1,1,8,5,9,2,0,1,2,6,9,1,6,3,6,5,0,3,1,9,8,8,8,4,7,1,7,1,3,9,7,9,8,0,9,0,1,5,9,0,4,5,9,0,4,9,4,4,8,6,8,9,4,5,4,0,7,2,4,4,0,1,1,1,1,0,0,1,1,7,3,1,5,9,1,6,3,8,6,0,7,0,7,6,8,6,6,1,9,5,0,2,4,6,8,0,2,7,5,4,1,8,1,7,6,3,3,8,5,2,7,1,8,5,2,0,5,1,8,2,6,7,2,9,5,9,5,4,8,2,0,9,6,8,4,8,2,7,9,1,5,4,1,3,8,9,9,0,1,0,5,3,7,7,9,8,8,8,1,4,1,1,5,2,2,7,2,8,8,5,8,3,5,2,9,6,7,1,5,3,6,7,6,6,1,8,1,9,4,4,0,7,5,5,6,3,2,5,8,0,2,6,6,0,5,9,1,1,0,2,7,3,7,0,1,3,5,7,3,8,4,7,8,5,7,1,0,8,8,7,5,0,8,8,0,1,0,9,3,6,4,7,3,4,4,1,1,1,7,7,5,8,4,6,4,4,6,2,9,7,6,6,7,5,1,5,1,8,0,7,7,6,5,9,2,5,5,8,9,0,5,6,3,5,2,7,8,2,3,5,3,2,0,4,5,2,0,2,0,7,1,9,2,6,0,9,6,7,3,4,8,5,4,5,6,5,0,7,9,1,4,1,8,2,8,6,7,3,2,4,5,9,0,0,6,4,2,7,4,4,2,7,3,1,3,2,2,5,0,7,0,9,6,9,2,1,5,1,4,3,6,6,7,9,9,3,9,8,5,2,4,2,4,8,9,4,7,8,8,6,7,3,1,3,4,0,0,5,2,1,2,2,2,9,4,7,8,6,7,1,4,7,5,7,3,5,4,4,9,1,9,8,6,4,3,3,6,7,4,9,5,5,3,9,1,4,1,5,1,5,6,6,4,7,6,2,5,1,5,6,7,0,2,1,0,5,5,4,3,7,4,3,1,3,4,3,8,0,3,5,8,8,9,5,9,8,1,0,9,8,3,9,6,8,2,8,7,6,4,5,6,3,2,9,7,5,7,6,1,5,8,8,8,7,0,5,0,6,2,5,4,7,1,3,3,2,7,0,1,9,5,2,0,0,4,1,6,1,9,4,5,2,1,3,0,0,0,3,0,2,0,5,2,1,4,7,8,9,0,5,0,3,3,0,1,9,1,7,8,3,4,8,2,9,7,4,6,9,0,1,4,7,8,1,7,2,3,8,0,0,5,1,5,5,8,4,4,2,9,9,7,5,9,1,3,9,2,1,2,0,1,4,4,2,2,2,7,0,0,0,2,8,2,5,3,1,9,2,3,0,2,7,1,5,9,3,3,0,8,3,8,7,2,2,2,8,5,0,2,9,6,1,2,4,1,9,5,5,5,0,3,6,0,6,5,3,2,7,8,1,4,1,4,7,9,9,6,8,0,9,1,1,6,8,1,3,0,9,9,1,1,5,1,5,5,7,1,9,3,9,8,4,5,3,1,1,3,0,7,5,9,7,1,0,8,8,6,6,2,2,9,8,4,7,9,5,1,7,5,9,5,0,5,7,9,7,9,7,6,6,9,1,3,9,2,6,8,5,9,4,1,9,1,4,4,1,9,5,2,7,4,9,1,7,1,5,1,1,4,8,6,6,8,2,4,0,8,0,3,6,9,9,9,6,2,0,2,4,3,7,1,6,0,3,0,4,0,4,9,2,7,2,1,6,1,5,5,2,1,3,5,1,9,9,2,5,6,4,5,4,5,6,8,8,5,5,8,6,8,0,8,7,2,4,1,0,7,2,7,5,5,1,3,7,5,5,6,2,5,1,0,2,5,7,3,8,6,5,6,3,2,8,2,4,8,0,3,9,9,4,9,4,8,5,6,9,2,7,4,0,4,3,2,4,3,1,9,8,5,6,4,7,9,3,0,3,7,9,9,4,4,1,3,7,5,5,4,7,5,0,8,6,3,4,4,3,9,1,0,4,0,0,6,9,3,1,5,9,5,9,8,5,0,4,6,2,3,4,2,9,0,7,0,6,8,8,2,2,3,3,5,5,4,2,2,2,3,0,9,4,1,4,1,5,1,5,4,8,4,0,9,2,2,2,8,0,9,1,9,3,3,1,1,3,3,3,2,9,9,3,4,6,1,8,8,7,4,9,3,2,4,2,0,9,8,8,4,5,1,7,0,0,6,2,7,7,1,3,9,2,2,4,5,8,7,1,0,9,3,1,3,6,7,0,0,0,2,5,5,2,9,2,8,4,1,4,6,4,3,5,3,9,7,5,8,7,7,1,8,7,4,8,0,6,2,6,6,6,3,6,9,9,6,6,0,6,8,3,0,2,3,6,9,3,1,3,6,7,1,2,1,8,5,1,7,3,9,8,1,1,4,0,7,6,0,7,2,6,8,8,1,5,5,6,2,3,6,6,9,6,6,6,0,5,7,3,6,7,0,4,7,6,2,4,0,1,4,9,5,5,9,9,4,3,5,1,2,2,2,5,1,5,9,1,4,8,9,5,9,7,6,2,1,6,8,5,3,9,3,2,4,6,2,9,8,3,9,1,4,8,7,0,2,6,2,2,6,1,0,2,4,4,1,8,2,5,0,6,3,9,9,4,8,5,8,6,2,1,9,4,2,9,4,2,7,6,3,3,2,5,0,5,7,2,1,0,8,2,2,0,4,5,6,0,6,4,4,0,8,7,5,5,7,2,3,3,9,8,0,5,5,9,8,9,3,9,6,4,8,3,7,3,3,3,1,0,8,8,8,2,3,3,8,9,5,3,1,6,6,8,5,0,0,0,3,9,4,3,5,4,0,4,2,2,2,6,0,9,1,0,1,4,1,1,3,6,6,5,2,8,0,6,9,5,5,4,3,1,2,3,1,7,3,7,4,5,5,7,7,1,8,2,0,4,8,5,5,9,7,7,3,6,1,8,0,0,1,7,5,0,3,1,5,7,5,8,0,7,5,6,4,3,6,3,9,3,0,4,1,5,0,7,5,1,1,7,0,4,2,4,6,2,5,9,9,1,2,1,4,8,8,5,9,7,4,8,9,2,1,6,8,0,5,6,4,8,9,7,0,0,0,2,6,2,8,3,2,1,1,3,7,3,7,6,5,6,1,7,7,6,1,9,1,9,1,4,9,2,7,4,2,6,8,5,8,0,3,7,7,6,0,3,0,6,7,6,2,5,4,2,1,0,1,8,1,8,1,4,3,2,9,8,0,8,9,9,1,3,2,5,6,2,8,5,5,2,9,0,0,4,3,8,6,8,7,7,3,1,9,7,5,9,7,5,5,0,1,2,5,7,1,0,5,4,7,7,2,5,6,0,0,5,4,4,7,9,1,2,5,5,3,1,9,7,5,9,3,1,9,2,9,4,8,8,1,5,7,9,0,2,8,2,3,0,9,2,8,1,6,1,3,6,1,6,2,7,0,5,0,4,8,1,4,5,7,9,1,3,9,9,3,6,6,8,5,5,7,2,0,7,4,4,2,7,2,3,7,3,2,9,3,6,5,0,6,1,3,0,0,0,9,5,7,0,0,9,5,3,2,5,4,1,4,5,4,6,7,3,2,0,1,9,0,2,5,2,2,1,0,1,1,8,8,6,8,1,2,4,8,9,7,6,9,6,0,3,8,3,2,8,4,6,9,4,9,6,1,3,9,0,4,2,9,5,6,5,4,2,4,9,1,9,5,2,5,2,7,4,8,0,5,7,0,2,8,4,7,5,8,5,8,7,1,8,9,1,4,8,5,2,9,7,4,2,1,9,7,4,6,4,2,9,1,0,8,0,1,1,2,8,2,6,0,1,7,6,7,8,3,7,3,9,7,2,9,1,2,3,2,8,5,5,2,6,6,4,1,5,2,5,2,3,8,8,3,8,0,6,5,8,9,4,6,3,7,8,8,6,9,7,8,9,1,6,4,6,3,6,6,3,5,4,2,7,5,9,9,0,5,0,8,9,7,1,2,7,8,0,8,6,6,2,2,2,7,6,9,5,7,8,1,1,2,2,4,8,3,0,7,8,6,5,0,8,6,8,9,9,3,8,7,5,2,1,3,0,5,3,0,0,2,7,5,2,1,6,2,9,0,8,0,2,1,8,2,8,5,4,5,7,5,1,1,6,6,2,7,8,5,8,3,1,7,9,7,5,4,2,2,6,3,1,3,7,7,1,6,3,5,1,2,8,2,7,9,9,8,3,3,5,0,1,6,8,3,6,7,9,6,4,1,8,4,5,1,7,9,8,4,2,8,6,0,4,9,6,3,5,1,7,8,6,5,4,9,4,3,9,4,7,3,0,9,9,6,0,0,3,1,2,9,3,3,8,1,8,6,3,9,2,7,5,2,4,6,0,2,3,4,3,5,4,1,9,0,7,2,6,4,3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,2,2,2,4,0,4,0,3,0,1,1,4,9,3,5,8,1,2,4,9,4,1,8,5,8,7,8,9,8,2,1,1,6,4,0,0,5,4,4,9,1,4,1,1,3,7,7,7,2,7,7,0,7,9,9,1,7,3,6,8,8,0,1,0,1,0,0,4,2,9,2,3,9,7,0,2,5,2,2,8,8,0,5,6,8,6,0,4,6,4,0,2,4,6,7,2,9,7,2,3,2,6,4,5,4,7,1,1,2,1,4,3,6,3,5,1,7,3,5,5,2,6,6,4,1,7,4,2,2,4,7,1,0,4,0,2,3,1,2,6,4,3,4,3,8,1,3,0,5,2,0,4,5,9,6,9,2,1,5,5,8,9,1,7,3,5,8,2,2,1,7,1,2,8,5,1,8,6,5,3,9,1,5,5,3,0,0,7,8,2,4,6,1,8,0,5,2,7,6,6,1,7,7,5,1,7,4,6,1,4,5,1,6,0,9,7,2,6,2,1,1,7,1,4,6,8,7,8,3,7,8,0,2,4,6,4,7,9,1,2,5,5,3,1,7,8,8,1,2,1,5,2,4,7,3,6,3,2,0,7,9,2,8,9,4,6,6,3,9,0,0,6,3,3,2,3,1,8,5,2,8,7,4,0,2,4,3,7,1,8,7,8,5,2,4,5,9,4,9,4,3,6,2,7,4,6,5,8,0,1,4,1,4,9,3,6,2,9,2,2,5,8,4,9,3,1,6,3,0,2,8,0,6,6,4,8,5,6,0,9,3,3,8,8,4,0,0,8,5,7,5,4,6,2,2,2,6,3,4,1,9,8,9,1,2,9,1,9,3,8,1,4,1,8,4,4,6,0,9,6,1,8,0,0,9,5,1,5,4,0,2,0,6,3,6,4,9,0,6,9,4,3,0,1,4,9,4,1,4,3,2,8,3,0,8,9,2,6,9,2,2,8,5,3,2,8,0,0,5,3,3,4,7,2,3,1,0,9,9,4,7,3,0,4,0,2,0,9,2,3,1,1,8,6,0,9,5,9,5,5,1,2,9,7,0,8,7,7,0,5,8,8,9,3,3,6,3,9,6,9,7,4,5,2,6,9,9,3,7,4,9,5,5,0,9,1,3,0,6,5,8,3,2,5,6,4,4,4,3,3,7,3,5,0,7,5,5,5,9,4,6,4,3,2,6,7,7,0,8,0,0,5,9,5,7,0,2,4,5,6,6,3,4,4,3,4,3,3,9,8,0,1,8,1,5,8,5,2,0,8,2,4,0,5,4,6,2,5,3,5,2,8,9,4,5,8,6,2,4,7,5,2,3,3,7,7,7,6,3,4,5,8,1,5,2,8,4,9,4,2,3,8,9,0,4,4,5,8,2,0,1,1,7,7,7,5,7,1,2,1,8,7,2,4,4,0,6,6,1,0,3,6,8,5,2,4,1,3,1,9,4,6,9,0,2,3,3,3,7,6,2,9,5,8,4,2,4,5,7,2,2,5,2,8,9,2,0,0,6,4,3,0,2,7,6,8,7,9,5,8,9,2,3,4,7,6,6,9,8,8,9,8,5,9,0,9,2,0,8,0,7,0,6,2,7,8,0,6,6,8,6,2,7,1,9,0,1,9,4,9,1,0,6,9,8,7,3,0,1,4,0,3,1,5,5,6,7,3,7,6,8,4,5,2,3,6,7,6,8,7,7,9,1,3,3,3,5,2,4,2,7,8,2,7,2,6,4,1,7,4,8,1,0,3,6,2,9,9,9,4,1,5,2,5,9,9,2,6,1,8,8,6,6,0,8,1,3,3,0,6,6,2,8,7,1,1,6,9,6,0,9,1,0,2,6,4,5,9,9,4,6,5,5,7,6,9,0,9,3,8,6,0,0,9,4,8,0,6,8,3,2,7,2,1,8,8,1,0,9,8,7,3,2,4,2,4,7,6,9,2,0,3,9,6,5,5,8,0,1,8,7,7,1,4,6,1,3,9,3,2,3,4,4,9,4,4,8,6,9,3,3,8,7,0,1,7,6,6,4,7,1,6,7,7,7,9,3,5,1,8,2,7,2,7,4,8,7,5,3,2,2,2,5,9,1,3,8,1,7,6,6,1,2,0,4,8,0,2,8,1,0,0,7,4,4,4,4,4,3,7,0,0,8,0,5,3,5,6,2,5,6,3,1,4,0,5,7,1,3,5,9,7,7,4,2,0,9,9,0,7,6,6,4,5,0,7,1,3,8,5,4,1,1,1,5,2,9,2,8,9,0,6,6,7,9,2,3,2,1,1,4,9,8,8,4,5,6,3,2,4,1,4,2,0,0,2,4,1,9,3,3,7,7,3,6,7,3,2,5,9,0,6,6,8,0,5,2,1,6,7,4,8,3,0,4,4,5,0,1,4,3,7,0,2,8,4,3,9,4,1,7,6,1,6,2,6,5,4,0,7,2,2,5,3,2,9,5,8,8,1,6,7,1,4,1,5,3,6,7,7,5,6,6,6,7,2,1,8,7,2,2,0,6,2,1,4,3,0,0,3,4,1,1,7,4,8,6,2,1,3,9,5,7,6,1,8,2,9,0,2,8,1,7,7,1,7,6,2,1,6,6,4,7,9,6,8,3,3,3,2,6,9,9,1,4,7,2,1,9,9,3,3,5,5,3,1,5,9,5,3,7,3,6,7,7,9,8,3,1,3,9,3,8,3,7,2,1,5,9,3,3,0,6,1,0,4,0,7,8,5,9,4,2,3,6,4,6,1,5,2,7,4,7,6,9,4,0,6,9,1,7,9,8,7,9,5,4,6,3,6,2,6,0,2,0,1,6,8,4,0,9,6,9,1,8,5,5,6,2,2,3,9,5,3,5,8,6,7,2,5,7,3,7,2,4,5,6,4,9,0,6,7,5,8,2,3,4,7,6,9,3,8,6,8,8,4,5,3,6,8,8,6,3,7,4,3,9,8,7,4,1,7,8,4,9,8,9,1,4,6,5,7,7,7,8,5,1,0,0,5,0,9,7,1,0,9,1,2,7,9,4,8,0,2,6,9,0,8,3,5,9,1,8,3,2,7,2,2,8,0,2,3,0,6,2,5,6,2,2,2,1,2,4,7,6,9,8,0,0,0,8,1,4,6,3,0,7,1,3,2,4,7,3,5,8,3,8,3,2,3,5,5,3,6,1,1,4,8,5,2,5,6,1,2,1,8,6,2,1,6,0,5,0,2,1,3,6,0,8,7,8,0,4,3,9,5,4,8,9,8,7,8,7,0,2,4,4,0,7,1,2,8,0,8,6,8,3,0,6,7,0,2,9,6,6,6,0,2,8,1,4,3,7,2,0,0,1,6,7,5,7,0,8,3,9,9,3,0,7,8,3,5,9,5,2,5,3,1,4,9,4,7,5,8,2,8,9,4,0,5,3,4,2,3,1,5,6,9,0,7,1,7,1,5,1,2,5,8,8,9,2,6,3,6,9,9,8,5,3,8,9,5,8,2,0,6,7,6,2,7,3,6,5,6,8,1,2,9,2,3,2,8,2,1,9,9,9,5,1,2,0,9,3,1,4,0,7,5,5,6,6,9,5,6,2,4,5,8,5,7,7,7,6,0,4,4,3,3,7,6,4,9,9,6,2,5,8,5,7,0,8,5,9,8,3,0,4,9,6,1,5,9,0,4,3,0,5,4,8,4,8,7,1,8,5,9,9,0,5,0,9,1,7,3,7,8,5,5,8,7,1,6,8,7,2,8,1,0,1,7,1,6,3,7,6,7,5,7,9,6,6,5,5,1,8,2,5,5,0,0,3,9,3,4,3,3,4,6,5,6,6,8,5,8,2,9,5,1,7,0,9,6,7,5,2,4,3,3,5,2,3,0,6,8,4,3,9,6,9,2,3,4,0,7,3,5,2,2,4,7,7,1,3,1,3,6,1,6,2,7,3,0,0,5,2,0,6,0,3,7,3,4,9,8,5,4,1,3,2,1,4,1,7,4,2,9,1,5,3,3,6,4,3,4,2,2,3,3,2,1,4,8,5,5,8,2,2,3,4,3,2,3,7,1,6,8,7,3,1,4,9,4,2,7,5,2,0,7,4,8,0,7,5,4,2,0,0,8,8,7,9,7,7,7,8,2,1,7,5,9,2,2,9,6,3,8,2,8,0,1,5,7,6,2,6,6,4,5,4,6,8,0,9,1,2,4,2,0,7,3,1,3,3,9,2,3,9,6,8,7,7,4,0,6,2,4,4,2,8,5,4,2,0,3,7,7,4,9,4,9,0,6,6,8,3,7,0,2,4,9,0,0,8,3,3,0,5,3,4,8,1,6,4,0,2,5,3,5,3,5,1,6,1,0,2,9,8,5,6,3,8,0,5,0,1,3,5,7,8,1,3,7,0,9,8,0,6,2,4,7,8,7,1,8,1,1,6,1,0,3,4,4,4,5,5,5,3,5,0,9,1,0,0,0,9,3,9,9,9,6,3,9,8,8,1,9,8,3,7,8,2,7,1,2,4,6,9,9,5,0,2,0,9,0,7,1,7,5,1,3,0,9,7,1,3,6,7,3,0,4,6,2,4,0,4,7,2,1,9,5,2,9,5,4,5,7,1,7,7,7,7,2,6,5,1,7,2,2,3,1,9,2,6,2,4,9,1,6,5,4,5,8,3,1,5,5,2,2,3,3,5,2,1,1,7,6,0,2,3,7,0,8,3,0,1,9,0,0,6,3,9,1,2,4,2,5,3,2,3,1,8,7,8,5,5,7,9,8,4,2,1,2,6,4,3,8,0,0,9,3,1,8,4,6,7,5,3,0,1,5,1,7,3,7,2,1,6,4,2,1,0,0,9,7,2,9,5,9,6,3,4,5,0,4,0,9,6,4,9,8,2,2,7,4,0,6,6,4,8,2,3,9,9,5,8,3,3,4,4,3,4,6,2,4,6,8,8,1,0,6,5,2,7,9,3,5,4,5,1,0,1,7,0,7,5,3,7,4,3,3,4,1,9,8,5,8,5,4,8,0,0,1,0,2,1,9,1,8,6,8,0,8,9,4,1,0,1,6,2,1,6,4,9,7,8,6,4,0,3,4,0,3,5,8,5,1,7,7,9,6,5,2,4,0,2,6,7,2,7,1,8,7,3,2,0,2,7,6,4,0,0,9,9,8,8,8,8,3,1,9,7,8,0,8,1,8,6,9,6,2,8,1,0,9,6,6,1,1,1,4,5,5,5,5,1,9,6,5,2,5,8,8,2,0,6,4,3,4,7,3,2,0,8,4,8,0,9,8,6,6,1,3,0,3,2,1,3,5,5,2,9,9,2,8,9,3,1,2,5,6,2,7,3,3,9,3,6,0,4,0,1,6,6,0,8,3,6,8,3,4,2,7,8,2,1,5,1,4,0,9,4,1,5,0,6,5,6,3,7,4,3,4,0,4,1,3,2,1,2,1,3,7,4,0,0,0,7,8,8,5,2,2,5,9,4,6,4,7,9,4,1,6,0,5,2,2,0,7,4,0,3,0,1,1,0,9,3,0,0,2,6,2,0,9,3,6,8,1,5,1,1,0,2,3,5,2,2,0,0,9,6,5,0,7,3,4,5,6,3,9,1,7,5,7,7,7,0,9,6,9,3,7,8,4,0,6,5,1,2,3,2,7,4,1,9,8,8,2,8,9,8,0,8,5,4,2]);
P:=CharacteristicPolynomial(A);

Output: Magma V2.11-2     Tue Aug  3 2004 13:13:00 on modular  [Seed = 3953487185]
   -------------------------------------


Total time: 10.770 seconds, Total memory usage: 10.36MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 14:40:38 2004

Input: Pi(100);

Output: Magma V2.11-2     Tue Aug  3 2004 14:40:37 on modular  [Seed = 3230555599]
   -------------------------------------


>> Pi(100);;
     ^
Runtime error in 'Pi': Bad argument types
Argument types given: RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:15:40 2004

Input: IsPrime(2^7-1);

Output: Magma V2.11-2     Tue Aug  3 2004 15:15:40 on modular  [Seed = 441761646]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:15:47 2004

Input: IsPrime(2^11-1);

Output: Magma V2.11-2     Tue Aug  3 2004 15:15:46 on modular  [Seed = 308066136]
   -------------------------------------

false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:15:52 2004

Input: IsPrime(2^5-1);

Output: Magma V2.11-2     Tue Aug  3 2004 15:15:52 on modular  [Seed = 1780797226]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:15:57 2004

Input: IsPrime(2^3-1);

Output: Magma V2.11-2     Tue Aug  3 2004 15:15:57 on modular  [Seed = 1647101735]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:16:06 2004

Input: Factorization(2^11-1);

Output: Magma V2.11-2     Tue Aug  3 2004 15:16:05 on modular  [Seed = 2050285351]
   -------------------------------------

[ <23, 1>, <89, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:19:58 2004

Input: (2^16 - 1)/(2^4-1)

Output: Magma V2.11-2     Tue Aug  3 2004 15:19:58 on modular  [Seed = 1258680125]
   -------------------------------------

4369

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 15:25:09 2004

Input: (2^81 - 1)/(2^27-1)

Output: Magma V2.11-2     Tue Aug  3 2004 15:25:08 on modular  [Seed = 2883914775]
   -------------------------------------

18014398643699713

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:02:56 2004

Input: X := Matrix([[4,-1,-1,-1],[-1,4,-1,-1],[-1,-1,4,-1],[-1,-1,-1,4]]);
Y:=X^-1;

Output: Magma V2.11-2     Tue Aug  3 2004 22:02:56 on modular  [Seed = 4222286086]
   -------------------------------------


>> Y:=X^-1;;
       ^
Runtime error in '^': Argument 1 is not invertible

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:05:51 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4]);
X;
Y:=X^-1;

Output: Magma V2.11-2     Tue Aug  3 2004 22:05:50 on modular  [Seed = 4070832033]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:06:04 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4]);
X;
Y:=X^-1;
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:06:03 on modular  [Seed = 3399208812]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[2/5 1/5 1/5 1/5]
[1/5 2/5 1/5 1/5]
[1/5 1/5 2/5 1/5]
[1/5 1/5 1/5 2/5]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:07:02 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,-1]);
X;
Y:=X^-1;
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:07:01 on modular  [Seed = 3716995125]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1 -1]
[ 1/5    0    0 -1/5]
[   0  1/5    0 -1/5]
[   0    0  1/5 -1/5]
[-1/5 -1/5 -1/5 -2/5]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:07:48 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,-1,-1, -1,-1,-1,4]);
X;
Y:=X^-1;
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:07:48 on modular  [Seed = 3582251020]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1 -1 -1]
[-1 -1 -1  4]
[ 1/5    0 -1/5    0]
[   0  1/5 -1/5    0]
[-1/5 -1/5 -2/5 -1/5]
[   0    0 -1/5  1/5]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:08:34 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,-1,-1,-1, -1,-1,-1,4, -1,-1,-1,4]);
X;
Y:=X^-1;
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:08:33 on modular  [Seed = 780085795]
   -------------------------------------

[ 4 -1 -1 -1]
[-1 -1 -1 -1]
[-1 -1 -1  4]
[-1 -1 -1  4]

>> Y:=X^-1;
       ^
Runtime error in '^': Argument 1 is not invertible

>> Y;;
   ^
User error: Identifier 'Y' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:08:50 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,-1,-1,-1, -1,-1,4,-1, -1,-1,-1,4]);
X;
Y:=X^-1;
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:08:49 on modular  [Seed = 645341755]
   -------------------------------------

[ 4 -1 -1 -1]
[-1 -1 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[ 1/5 -1/5    0    0]
[-1/5 -2/5 -1/5 -1/5]
[   0 -1/5  1/5    0]
[   0 -1/5    0  1/5]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ws14.fas.harvard.edu. (140.247.31.114)
Time: Tue Aug  3 22:15:15 2004

Input: E:= EllipticCurve([0,1,1,-12,2]);


Output: Magma V2.11-2     Tue Aug  3 2004 22:15:14 on modular  [Seed = 996818085]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ws14.fas.harvard.edu. (140.247.31.114)
Time: Tue Aug  3 22:24:12 2004

Input: E:= EllipticCurve([0,1,1,-12,2]);
L:= AnalyticRank(E);



Output: Magma V2.11-2     Tue Aug  3 2004 22:24:11 on modular  [Seed = 356785394]
   -------------------------------------


Total time: 0.600 seconds, Total memory usage: 7.19MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:39:57 2004

Input: X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Kernel(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:39:56 on modular  [Seed = 1681221941]
   -------------------------------------


>> X := Matrix(RationalField(),4,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1
              ^
Runtime error in 'Matrix': Sequence should have length 16

>> X;
   ^
User error: Identifier 'X' has not been declared or assigned

>> Y:=Kernel(X);
             ^
User error: Identifier 'X' has not been declared or assigned

>> Y;;
   ^
User error: Identifier 'Y' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:40:18 2004

Input: X := Matrix(RationalField(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Kernel(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:40:17 on modular  [Seed = 1209615861]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
Vector space of degree 5, dimension 1 over Rational Field
Echelonized basis:
(1 1 1 1 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:42:17 2004

Input: X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Kernel(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:42:16 on modular  [Seed = 1493718397]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:43:30 2004

Input: X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Nullspace(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:43:29 on modular  [Seed = 1358978348]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:57:37 2004

Input: F := FreeAbelianGroup(5);
m1 := F![4,-1,-1,-1,-1];
X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Nullspace(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:57:37 on modular  [Seed = 3169692977]
   -------------------------------------

[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 22:57:49 2004

Input: F := FreeAbelianGroup(5);
m1 := F![4,-1,-1,-1,-1];
m1;
X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Nullspace(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 22:57:48 on modular  [Seed = 3034948916]
   -------------------------------------

4*F.1 - F.2 - F.3 - F.4 - F.5
[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 23:00:10 2004

Input: F := FreeAbelianGroup(5);
m1 := F![4,-1,-1,-1,-1];
m2:=F![-1,4,-1,-1,-1];
m3:=F![-1,-1,4,-1,-1];
m4:=F![-1,-1,-1,4,-1];
S:=sub<F|m1,m2,m3,m4>;
Q:=quo<F|S>;
Q;
X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Nullspace(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 23:00:09 on modular  [Seed = 2681114506]
   -------------------------------------

Abelian Group isomorphic to Z/5 + Z/5 + Z/5 + Z
Defined on 4 generators
Relations:
    5*Q.1 = 0
    5*Q.2 = 0
    5*Q.3 = 0
[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 23:00:51 2004

Input: F(x1,x2,x3,x4,x5) := FreeAbelianGroup(5);
m1 := F![4,-1,-1,-1,-1];
m2:=F![-1,4,-1,-1,-1];
m3:=F![-1,-1,4,-1,-1];
m4:=F![-1,-1,-1,4,-1];
S:=sub<F|m1,m2,m3,m4>;
Q:=quo<F|S>;
Q;
X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Nullspace(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 23:00:50 on modular  [Seed = 2428600542]
   -------------------------------------


>> F(x1,x2,x3,x4,x5) := FreeAbelianGroup(5);
                     ^
User error: Illegal left hand side of an assignment statement

>> m1 := F![4,-1,-1,-1,-1];
         ^
User error: Identifier 'F' has not been declared or assigned

>> m2:=F![-1,4,-1,-1,-1];
       ^
User error: Identifier 'F' has not been declared or assigned

>> m3:=F![-1,-1,4,-1,-1];
       ^
User error: Identifier 'F' has not been declared or assigned

>> m4:=F![-1,-1,-1,4,-1];
       ^
User error: Identifier 'F' has not been declared or assigned

>> S:=sub<F|m1,m2,m3,m4>;
          ^
User error: Identifier 'F' has not been declared or assigned

>> Q:=quo<F|S>;
          ^
User error: Identifier 'F' has not been declared or assigned

>> Q;
   ^
User error: Identifier 'Q' has not been declared or assigned
[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host modemcable159.191-202-24.mc.videotron.ca. (24.202.191.159)
Time: Tue Aug  3 23:01:18 2004

Input: F<x1,x2,x3,x4,x5> := FreeAbelianGroup(5);
m1 := F![4,-1,-1,-1,-1];
m2:=F![-1,4,-1,-1,-1];
m3:=F![-1,-1,4,-1,-1];
m4:=F![-1,-1,-1,4,-1];
S:=sub<F|m1,m2,m3,m4>;
Q:=quo<F|S>;
Q;
X := Matrix(IntegerRing(),5,4, [4,-1,-1,-1, -1,4,-1,-1, -1,-1,4,-1, -1,-1,-1,4, -1,-1,-1,-1]);
X;
Y:=Nullspace(X);
Y;

Output: Magma V2.11-2     Tue Aug  3 2004 23:01:17 on modular  [Seed = 3904501945]
   -------------------------------------

Abelian Group isomorphic to Z/5 + Z/5 + Z/5 + Z
Defined on 4 generators
Relations:
    5*Q.1 = 0
    5*Q.2 = 0
    5*Q.3 = 0
[ 4 -1 -1 -1]
[-1  4 -1 -1]
[-1 -1  4 -1]
[-1 -1 -1  4]
[-1 -1 -1 -1]
RSpace of degree 5, dimension 1 over Integer Ring
Echelonized basis:
(1 1 1 1 1)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 23:55:38 2004

Input: factorization(1621);

Output: Magma V2.11-2     Tue Aug  3 2004 23:55:38 on modular  [Seed = 525205514]
   -------------------------------------


>> factorization(1621);;
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-75-184-223.dsl.emhril.ameritech.net. (68.75.184.223)
Time: Tue Aug  3 23:55:42 2004

Input: Factorization(1621);

Output: Magma V2.11-2     Tue Aug  3 2004 23:55:42 on modular  [Seed = 390465542]
   -------------------------------------

[ <1621, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.6.183.6)
Time: Wed Aug  4 03:48:39 2004

Input: 1+1

Output: Magma V2.11-2     Wed Aug  4 2004 03:48:31 on modular  [Seed = 1815984530]
   -------------------------------------

2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.6.183.6)
Time: Wed Aug  4 03:49:01 2004

Input: 1+7*(34+8)/8

Output: Magma V2.11-2     Wed Aug  4 2004 03:49:01 on modular  [Seed = 1175950234]
   -------------------------------------

151/4

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (80.41.76.227)
Time: Wed Aug  4 04:53:54 2004

Input: 123;


Output: Magma V2.11-2     Wed Aug  4 2004 04:53:53 on modular  [Seed = 474872077]
   -------------------------------------

123

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (80.41.76.227)
Time: Wed Aug  4 04:54:00 2004

Input: 123;
2+2;

Output: Magma V2.11-2     Wed Aug  4 2004 04:53:59 on modular  [Seed = 72737043]
   -------------------------------------

123
4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 05:04:51 2004

Input: 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CharacteristicPolynomial(A);

Output: Magma V2.11-2     Wed Aug  4 2004 05:04:45 on modular  [Seed = 1664255230]
   -------------------------------------

$.1^300 - 430*$.1^299 + 79780*$.1^298 - 8318568*$.1^297 + 530631715*$.1^296 - 
    21004902271*$.1^295 + 491853938629*$.1^294 - 5670191285029*$.1^293 + 
    5119297560678*$.1^292 + 408776503258752*$.1^291 - 686586941009605*$.1^290 - 
    13636012832091205*$.1^289 - 43325370251438632*$.1^288 + 
    62362835482280668*$.1^287 + 1228369225202993101*$.1^286 + 
    6884300087031476290*$.1^285 + 26767568072590636202*$.1^284 + 
    84210561453662525907*$.1^283 + 229091948548099990361*$.1^282 + 
    559334753628727626799*$.1^281 + 1254232216185577171650*$.1^280 + 
    2624003848136833242137*$.1^279 + 5181343924547236971857*$.1^278 + 
    9740747196880825173464*$.1^277 + 17552647991467011536710*$.1^276 + 
    30481920848567388576095*$.1^275 + 51241644009135942994194*$.1^274 + 
    83692764551903722365018*$.1^273 + 133223685049178819646688*$.1^272 + 
    207223759314167103979260*$.1^271 + 315665279641255423009129*$.1^270 + 
    471808059594457982131055*$.1^269 + 693047214872364230259983*$.1^268 + 
    1001923611075181347717287*$.1^267 + 1427317497384959810065068*$.1^266 + 
    2005847016325102879081211*$.1^265 + 2783499203508742970110341*$.1^264 + 
    3817518978062070871895563*$.1^263 + 5178584951991916394333186*$.1^262 + 
    6953300448977946674185570*$.1^261 + 9247025924163503170198519*$.1^260 + 
    12187084368764291879769774*$.1^259 + 15926363666026109807937438*$.1^258 + 
    20647348113866267730184570*$.1^257 + 26566602905204387631756476*$.1^256 + 
    33939772595710354163913567*$.1^255 + 43067071598334815431704972*$.1^254 + 
    54299349019943610944761521*$.1^253 + 68044713870670475424892697*$.1^252 + 
    84775754509475210497542432*$.1^251 + 105037301249041883268029207*$.1^250 + 
    129454868273942702392832077*$.1^249 + 158743641446213282410704192*$.1^248 + 
    193718069962917112238685638*$.1^247 + 235302095463450757386239830*$.1^246 + 
    284539894600971693133083306*$.1^245 + 342607209443248485460447663*$.1^244 + 
    410823159494768189968778088*$.1^243 + 490662535399180804263265087*$.1^242 + 
    583768341459043696916132022*$.1^241 + 691964828583128681909178242*$.1^240 + 
    817270505409869075703738205*$.1^239 + 961911367930414967221095398*$.1^238 + 
    1128334165604308143589145012*$.1^237 + 1319219415617809175736940855*$.1^236 
    + 1537494248518031963288083402*$.1^235 + 
    1786344960218332204812450461*$.1^234 + 2069228945136221270142434227*$.1^233 
    + 2389885760285284674788712486*$.1^232 + 
    2752347596561879329018312403*$.1^231 + 3160948400511150452948722780*$.1^230 
    + 3620331827386987121046393152*$.1^229 + 
    4135457984098045336369515939*$.1^228 + 4711608131579799909169611399*$.1^227 
    + 5354387989325172250676405283*$.1^226 + 
    6069728640833004388920971449*$.1^225 + 6863885521291552501786833506*$.1^224 
    + 7743434255259342266817488872*$.1^223 + 
    8715264876935846632941107374*$.1^222 + 9786571753507286458882884420*$.1^221 
    + 10964841702924687555336213365*$.1^220 + 
    12257837957285328638174890796*$.1^219 + 
    13673581318437185336576596327*$.1^218 + 
    15220327035440425263947955153*$.1^217 + 
    16906539181833525877062164669*$.1^216 + 
    18740860164719853790148133412*$.1^215 + 
    20732077299668155695880752456*$.1^214 + 
    22889085044109654062655674594*$.1^213 + 
    25220843689330608960727917283*$.1^212 + 
    27736334316122547295055419344*$.1^211 + 
    30444510435118091070757229269*$.1^210 + 
    33354245851070523765925385725*$.1^209 + 
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    39813157228442083771459143271*$.1^207 + 
    43379170770057715397763749621*$.1^206 + 
    47180294111944351223798960640*$.1^205 + 
    51224117228305999102342197326*$.1^204 + 
    55517778928228012945146196400*$.1^203 + 
    60067896689538890050640187497*$.1^202 + 
    64880497551436756710632222412*$.1^201 + 
    69960945736650415796302098151*$.1^200 + 
    75313872905595130309774342164*$.1^199 + 
    80943106254859313133962752322*$.1^198 + 
    86851599560581335204455902090*$.1^197 + 
    93041364384090571672568360462*$.1^196 + 
    99513404556107411798233069159*$.1^195 + 
    106267651213964149319861680587*$.1^194 + 
    113302904572388025443280550668*$.1^193 + 
    120616776260447186879177222307*$.1^192 + 
    128205638517007317346324102007*$.1^191 + 
    136064578246792011415789243846*$.1^190 + 
    144187356932132252189145689499*$.1^189 + 
    152566375805564961536864363386*$.1^188 + 
    161192651274982939386978477242*$.1^187 + 
    170055793160738268679862820885*$.1^186 + 
    179143996290145594194242006000*$.1^185 + 
    188444033896046116760453736519*$.1^184 + 
    197941269075689151091901334292*$.1^183 + 
    207619660550167229671245218179*$.1^182 + 
    217461798961493469515181787006*$.1^181 + 
    227448925662902422530725973555*$.1^180 + 
    237560989633073209280380920526*$.1^179 + 
    247776685369842791081967687077*$.1^178 + 
    258073527815059879060982985232*$.1^177 + 
    268427907040428832504842343012*$.1^176 + 
    278815182920474594174567445493*$.1^175 + 
    289209758215751617054650917996*$.1^174 + 
    299585185452460949567277294528*$.1^173 + 
    309914262484153154769743692416*$.1^172 + 
    320169150241495173655370795693*$.1^171 + 
    330321484776904615950428646519*$.1^170 + 
    340342506515675641617616232040*$.1^169 + 
    350203188409902937951923124322*$.1^168 + 
    359874367767125122567078487270*$.1^167 + 
    369326892178175072292638938353*$.1^166 + 
    378531749749570265635366394993*$.1^165 + 
    387460226581088104366340575494*$.1^164 + 
    396084035459785650295063913712*$.1^163 + 
    404375481181442075699059109359*$.1^162 + 
    412307580082293274172877676710*$.1^161 + 
    419854229864207375364096865526*$.1^160 + 
    426990319722726321783350601342*$.1^159 + 
    433691892478495215718179749918*$.1^158 + 
    439936246843379300547243658766*$.1^157 + 
    445702089006767597129816267815*$.1^156 + 
    450969618152025834593006650420*$.1^155 + 
    455720667744887317012130135961*$.1^154 + 
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 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 09:47:44 2004

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CharacteristicPolynomial(A);

Output: Magma V2.11-2     Wed Aug  4 2004 09:47:34 on modular  [Seed = 306428880]
   -------------------------------------

$.1^300 - 430*$.1^299 + 79780*$.1^298 - 8318568*$.1^297 + 530631715*$.1^296 - 
    21004902271*$.1^295 + 491853938629*$.1^294 - 5670191285029*$.1^293 + 
    5119297560678*$.1^292 + 408776503258752*$.1^291 - 686586941009605*$.1^290 - 
    13636012832091205*$.1^289 - 43325370251438632*$.1^288 + 
    62362835482280668*$.1^287 + 1228369225202993101*$.1^286 + 
    6884300087031476290*$.1^285 + 26767568072590636202*$.1^284 + 
    84210561453662525907*$.1^283 + 229091948548099990361*$.1^282 + 
    559334753628727626799*$.1^281 + 1254232216185577171650*$.1^280 + 
    2624003848136833242137*$.1^279 + 5181343924547236971857*$.1^278 + 
    9740747196880825173464*$.1^277 + 17552647991467011536710*$.1^276 + 
    30481920848567388576095*$.1^275 + 51241644009135942994194*$.1^274 + 
    83692764551903722365018*$.1^273 + 133223685049178819646688*$.1^272 + 
    207223759314167103979260*$.1^271 + 315665279641255423009129*$.1^270 + 
    471808059594457982131055*$.1^269 + 693047214872364230259983*$.1^268 + 
    1001923611075181347717287*$.1^267 + 1427317497384959810065068*$.1^266 + 
    2005847016325102879081211*$.1^265 + 2783499203508742970110341*$.1^264 + 
    3817518978062070871895563*$.1^263 + 5178584951991916394333186*$.1^262 + 
    6953300448977946674185570*$.1^261 + 9247025924163503170198519*$.1^260 + 
    12187084368764291879769774*$.1^259 + 15926363666026109807937438*$.1^258 + 
    20647348113866267730184570*$.1^257 + 26566602905204387631756476*$.1^256 + 
    33939772595710354163913567*$.1^255 + 43067071598334815431704972*$.1^254 + 
    54299349019943610944761521*$.1^253 + 68044713870670475424892697*$.1^252 + 
    84775754509475210497542432*$.1^251 + 105037301249041883268029207*$.1^250 + 
    129454868273942702392832077*$.1^249 + 158743641446213282410704192*$.1^248 + 
    193718069962917112238685638*$.1^247 + 235302095463450757386239830*$.1^246 + 
    284539894600971693133083306*$.1^245 + 342607209443248485460447663*$.1^244 + 
    410823159494768189968778088*$.1^243 + 490662535399180804263265087*$.1^242 + 
    583768341459043696916132022*$.1^241 + 691964828583128681909178242*$.1^240 + 
    817270505409869075703738205*$.1^239 + 961911367930414967221095398*$.1^238 + 
    1128334165604308143589145012*$.1^237 + 1319219415617809175736940855*$.1^236 
    + 1537494248518031963288083402*$.1^235 + 
    1786344960218332204812450461*$.1^234 + 2069228945136221270142434227*$.1^233 
    + 2389885760285284674788712486*$.1^232 + 
    2752347596561879329018312403*$.1^231 + 3160948400511150452948722780*$.1^230 
    + 3620331827386987121046393152*$.1^229 + 
    4135457984098045336369515939*$.1^228 + 4711608131579799909169611399*$.1^227 
    + 5354387989325172250676405283*$.1^226 + 
    6069728640833004388920971449*$.1^225 + 6863885521291552501786833506*$.1^224 
    + 7743434255259342266817488872*$.1^223 + 
    8715264876935846632941107374*$.1^222 + 9786571753507286458882884420*$.1^221 
    + 10964841702924687555336213365*$.1^220 + 
    12257837957285328638174890796*$.1^219 + 
    13673581318437185336576596327*$.1^218 + 
    15220327035440425263947955153*$.1^217 + 
    16906539181833525877062164669*$.1^216 + 
    18740860164719853790148133412*$.1^215 + 
    20732077299668155695880752456*$.1^214 + 
    22889085044109654062655674594*$.1^213 + 
    25220843689330608960727917283*$.1^212 + 
    27736334316122547295055419344*$.1^211 + 
    30444510435118091070757229269*$.1^210 + 
    33354245851070523765925385725*$.1^209 + 
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    39813157228442083771459143271*$.1^207 + 
    43379170770057715397763749621*$.1^206 + 
    47180294111944351223798960640*$.1^205 + 
    51224117228305999102342197326*$.1^204 + 
    55517778928228012945146196400*$.1^203 + 
    60067896689538890050640187497*$.1^202 + 
    64880497551436756710632222412*$.1^201 + 
    69960945736650415796302098151*$.1^200 + 
    75313872905595130309774342164*$.1^199 + 
    80943106254859313133962752322*$.1^198 + 
    86851599560581335204455902090*$.1^197 + 
    93041364384090571672568360462*$.1^196 + 
    99513404556107411798233069159*$.1^195 + 
    106267651213964149319861680587*$.1^194 + 
    113302904572388025443280550668*$.1^193 + 
    120616776260447186879177222307*$.1^192 + 
    128205638517007317346324102007*$.1^191 + 
    136064578246792011415789243846*$.1^190 + 
    144187356932132252189145689499*$.1^189 + 
    152566375805564961536864363386*$.1^188 + 
    161192651274982939386978477242*$.1^187 + 
    170055793160738268679862820885*$.1^186 + 
    179143996290145594194242006000*$.1^185 + 
    188444033896046116760453736519*$.1^184 + 
    197941269075689151091901334292*$.1^183 + 
    207619660550167229671245218179*$.1^182 + 
    217461798961493469515181787006*$.1^181 + 
    227448925662902422530725973555*$.1^180 + 
    237560989633073209280380920526*$.1^179 + 
    247776685369842791081967687077*$.1^178 + 
    258073527815059879060982985232*$.1^177 + 
    268427907040428832504842343012*$.1^176 + 
    278815182920474594174567445493*$.1^175 + 
    289209758215751617054650917996*$.1^174 + 
    299585185452460949567277294528*$.1^173 + 
    309914262484153154769743692416*$.1^172 + 
    320169150241495173655370795693*$.1^171 + 
    330321484776904615950428646519*$.1^170 + 
    340342506515675641617616232040*$.1^169 + 
    350203188409902937951923124322*$.1^168 + 
    359874367767125122567078487270*$.1^167 + 
    369326892178175072292638938353*$.1^166 + 
    378531749749570265635366394993*$.1^165 + 
    387460226581088104366340575494*$.1^164 + 
    396084035459785650295063913712*$.1^163 + 
    404375481181442075699059109359*$.1^162 + 
    412307580082293274172877676710*$.1^161 + 
    419854229864207375364096865526*$.1^160 + 
    426990319722726321783350601342*$.1^159 + 
    433691892478495215718179749918*$.1^158 + 
    439936246843379300547243658766*$.1^157 + 
    445702089006767597129816267815*$.1^156 + 
    450969618152025834593006650420*$.1^155 + 
    455720667744887317012130135961*$.1^154 + 
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 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 09:48:04 2004

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P:=CharacteristicPolynomial(A):

Output: Magma V2.11-2     Wed Aug  4 2004 09:48:03 on modular  [Seed = 441168444]
   -------------------------------------


>> P:=CharacteristicPolynomial(A):;
                                 ^
User error: bad syntax

Total time: 0.840 seconds, Total memory usage: 4.23MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 09:48:29 2004

Input: 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P:=CharacteristicPolynomial(A);


Output: Magma V2.11-2     Wed Aug  4 2004 09:48:23 on modular  [Seed = 39037456]
   -------------------------------------


Total time: 5.180 seconds, Total memory usage: 6.14MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 10:00:16 2004

Input: A:=Matrix(IntegerRing(),300,300,[75,37,56,42,4,81,62,64,73,83,14,59,45,30,5,40,2,35,45,1,59,73,23,47,73,26,68,31,64,47,64,75,77,14,45,99,18,6,70,2,66,57,44,66,1,58,6,3,88,6,0,80,90,20,21,76,71,79,77,55,1,96,4,37,85,9,65,54,18,64,10,43,96,70,65,30,77,44,64,88,52,27,27,72,82,50,66,37,80,25,16,85,53,66,31,82,9,53,77,72,90,81,83,54,68,15,68,27,95,60,16,16,37,62,2,91,80,43,98,4,4,13,0,52,25,2,0,56,86,9,97,80,14,67,67,62,43,31,21,66,96,97,53,54,0,52,47,48,8,8,40,97,69,47,80,12,4,63,69,88,59,16,4,43,36,9,85,51,69,87,1,52,16,65,9,38,41,92,79,8,75,53,84,95,12,21,93,69,32,95,43,98,17,99,75,79,71,15,61,45,66,86,44,86,12,97,84,36,13,61,72,4,61,0,6,3,88,11,80,71,7,48,59,41,38,16,90,56,42,81,56,100,87,64,31,17,92,56,71,40,42,93,58,67,37,47,55,88,20,18,86,8,0,48,51,92,73,67,68,12,70,8,81,37,84,67,89,38,87,11,46,32,18,77,24,25,19,42,42,38,24,46,76,47,44,13,8,41,77,2,69,81,59,95,65,89,19,29,95,88,19,98,67,91,92,80,42,55,43,30,56,96,90,82,70,0,9,51,54,77,54,53,13,76,67,25,82,17,56,29,76,88,82,42,95,56,65,85,77,4,4,28,12,76,90,52,38,39,20,13,42,34,75,56,22,21,53,21,22,77,98,22,36,52,50,30,43,24,28,43,61,29,24,56,67,75,100,51,85,23,62,27,14,91,17,6,7,30,52,32,67,53,18,84,86,26,78,32,43,95,12,36,26,26,15,35,29,2,98,16,35,45,75,92,10,70,73,97,7,48,57,84,52,8,20,54,48,22,81,56,33,47,16,83,79,24,85,93,64,76,29,72,89,11,47,36,33,96,14,11,39,26,83,41,50,47,74,32,45,7,94,55,42,13,90,28,36,88,94,60,29,17,18,63,53,27,94,35,83,82,83,63,23,37,32,87,78,10,62,36,8,8,42,40,95,52,26,59,47,2,70,21,35,5,2,28,49,36,69,60,12,3,78,75,97,38,79,85,58,38,24,8,65,96,3,59,25,58,34,8,98,59,13,56,82,58,61,76,12,100,97,48,82,91,12,81,29,22,37,37,71,78,89,7,37,76,46,69,91,1,64,97,52,71,62,13,67,14,89,40,1,28,89,91,54,36,53,34,8,82,32,75,19,42,24,96,58,82,83,66,63,31,16,30,39,24,57,17,6,5,91,76,45,35,98,86,94,59,80,60,77,39,57,89,43,59,92,40,93,0,66,11,16,7,57,64,77,82,63,56,54,21,55,79,62,15,88,57,55,85,22,56,86,95,12,49,24,55,59,65,97,81,23,13,92,4,66,51,48,98,17,13,26,57,38,97,76,84,22,86,1,34,17,69,30,40,63,62,63,50,13,18,65,35,46,72,55,100,25,79,81,64,58,10,63,41,40,10,30,71,37,52,29,58,36,32,8,89,68,35,14,37,40,62,11,53,43,76,81,44,4,28,26,75,88,45,54,69,49,25,48,22,7,55,43,76,95,26,100,44,32,16,3,10,72,98,23,55,94,60,76,17,3,3,79,100,31,89,40,43,0,2,67,10,63,84,10,81,82,19,66,24,52,34,35,24,66,83,78,26,88,88,47,50,18,41,21,46,61,41,60,3,92,5,17,69,97,72,26,88,81,41,90,49,59,25,9,75,93,64,43,74,35,1,21,3,53,98,35,71,42,14,0,9,49,34,69,99,6,19,48,8,3,65,56,2,55,9,33,36,54,92,12,91,46,100,39,87,36,8,79,63,20,93,5,86,8,89,41,11,83,65,56,52,25,92,6,22,63,48,5,5,76,99,96,12,100,58,77,54,54,27,38,95,43,16,31,63,54,60,90,1,37,100,96,7,12,22,44,48,43,57,59,76,56,57,22,72,3,39,15,95,42,33,28,45,9,8,16,45,66,18,81,10,12,99,22,72,16,99,100,13,26,2,56,48,64,4,58,16,69,40,19,41,50,88,53,46,24,100,1,62,47,23,64,82,12,46,75,43,79,52,57,64,39,70,31,58,61,77,73,90,8,10,3,13,6,50,24,57,2,41,41,10,92,6,98,84,83,47,7,100,4,55,73,58,20,2,36,22,65,99,92,24,45,50,36,18,63,40,37,52,8,76,63,21,68,60,71,76,0,53,20,0,73,42,86,23,22,54,29,46,89,7,93,70,44,58,100,83,33,75,52,65,90,60,20,76,100,64,11,92,10,47,55,99,73,33,75,15,19,50,66,60,44,6,51,84,59,34,65,46,22,55,10,0,89,76,1,12,17,17,46,80,79,71,85,20,18,64,77,83,95,7,79,34,19,71,24,18,44,27,62,52,85,82,56,6,79,21,77,99,82,38,3,39,30,20,35,72,72,25,33,32,92,79,14,40,79,87,64,3,73,60,29,61,39,92,20,76,48,89,53,66,28,73,90,49,55,74,4,21,25,6,13,20,80,45,15,29,35,55,66,30,80,65,26,18,86,97,62,85,62,57,25,6,98,17,97,5,69,33,12,54,32,5,31,76,36,48,60,42,18,92,51,45,84,50,8,62,77,41,7,21,75,73,2,22,61,82,19,17,58,11,90,70,71,12,0,64,11,36,19,76,8,71,97,37,32,92,37,46,94,39,76,3,16,24,98,20,47,8,43,98,36,54,84,83,11,40,81,56,60,21,49,72,38,0,53,52,13,34,74,13,4,92,81,37,17,63,53,84,26,54,70,35,69,61,82,88,39,11,15,14,53,88,30,95,35,2,22,8,100,81,94,78,86,14,6,90,70,88,24,28,2,97,42,23,54,45,73,14,48,75,8,45,93,43,22,48,60,65,88,24,63,67,63,38,82,55,98,58,72,58,55,54,91,88,28,94,60,91,13,49,90,47,34,86,56,79,46,77,40,21,35,71,88,84,55,36,83,54,13,56,94,45,32,41,5,90,75,82,39,9,19,98,78,40,13,2,27,62,51,80,0,80,87,98,69,37,77,95,93,59,87,30,88,25,87,31,43,76,58,39,81,93,21,10,46,34,34,50,74,38,100,63,76,96,25,26,99,74,40,68,40,16,79,16,85,99,1,35,16,87,81,79,90,31,7,67,77,93,95,32,82,30,78,81,41,77,48,84,16,60,1,33,26,78,29,79,66,31,48,34,24,51,14,51,51,8,97,27,8,48,81,99,48,71,91,39,29,46,2,92,11,23,50,95,49,36,22,42,3,6,100,47,77,35,67,14,90,23,100,98,47,33,32,39,94,64,95,24,91,8,27,48,9,91,68,59,60,70,69,100,74,42,67,61,84,46,8,98,3,1,40,7,63,51,62,35,100,68,33,65,45,5,96,81,50,17,56,1,33,57,87,49,61,16,68,0,38,4,53,0,82,59,96,70,12,0,10,43,45,46,39,84,29,10,62,44,42,52,50,7,4,24,10,92,48,93,78,64,14,84,4,3,16,64,5,84,55,53,2,98,18,8,95,32,25,55,72,96,44,31,10,63,21,1,9,87,40,26,91,32,40,67,48,3,40,42,23,16,60,14,74,88,40,64,99,72,22,33,73,72,17,36,29,92,46,37,92,98,35,98,64,33,41,32,93,65,13,99,93,36,35,76,23,6,62,18,93,37,78,54,6,45,28,37,39,33,12,48,9,25,43,30,30,49,48,29,96,29,75,96,96,84,37,61,78,45,98,24,35,54,11,18,22,40,27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48,99,31,31,93,67,50,37,17,81,26,35,19,30,71,77,27,8,63,0,66,18,95,53,46,71,87,77,76,54,32,63,82,23,62]);
P:=CharacteristicPolynomial(A):

Output: Magma V2.11-2     Wed Aug  4 2004 10:00:15 on modular  [Seed = 1359018891]
   -------------------------------------


>> P:=CharacteristicPolynomial(A):;
                                 ^
User error: bad syntax

Total time: 0.870 seconds, Total memory usage: 4.36MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 10:01:01 2004

Input: A:=Matrix(IntegerRing(),300,300,[75,37,56,42,4,81,62,64,73,83,14,59,45,30,5,40,2,35,45,1,59,73,23,47,73,26,68,31,64,47,64,75,77,14,45,99,18,6,70,2,66,57,44,66,1,58,6,3,88,6,0,80,90,20,21,76,71,79,77,55,1,96,4,37,85,9,65,54,18,64,10,43,96,70,65,30,77,44,64,88,52,27,27,72,82,50,66,37,80,25,16,85,53,66,31,82,9,53,77,72,90,81,83,54,68,15,68,27,95,60,16,16,37,62,2,91,80,43,98,4,4,13,0,52,25,2,0,56,86,9,97,80,14,67,67,62,43,31,21,66,96,97,53,54,0,52,47,48,8,8,40,97,69,47,80,12,4,63,69,88,59,16,4,43,36,9,85,51,69,87,1,52,16,65,9,38,41,92,79,8,75,53,84,95,12,21,93,69,32,95,43,98,17,99,75,79,71,15,61,45,66,86,44,86,12,97,84,36,13,61,72,4,61,0,6,3,88,11,80,71,7,48,59,41,38,16,90,56,42,81,56,100,87,64,31,17,92,56,71,40,42,93,58,67,37,47,55,88,20,18,86,8,0,48,51,92,73,67,68,12,70,8,81,37,84,67,89,38,87,11,46,32,18,77,24,25,19,42,42,38,24,46,76,47,44,13,8,41,77,2,69,81,59,95,65,89,19,29,95,88,19,98,67,91,92,80,42,55,43,30,56,96,90,82,70,0,9,51,54,77,54,53,13,76,67,25,82,17,56,29,76,88,82,42,95,56,65,85,77,4,4,28,12,76,90,52,38,39,20,13,42,34,75,56,22,21,53,21,22,77,98,22,36,52,50,30,43,24,28,43,61,29,24,56,67,75,100,51,85,23,62,27,14,91,17,6,7,30,52,32,67,53,18,84,86,26,78,32,43,95,12,36,26,26,15,35,29,2,98,16,35,45,75,92,10,70,73,97,7,48,57,84,52,8,20,54,48,22,81,56,33,47,16,83,79,24,85,93,64,76,29,72,89,11,47,36,33,96,14,11,39,26,83,41,50,47,74,32,45,7,94,55,42,13,90,28,36,88,94,60,29,17,18,63,53,27,94,35,83,82,83,63,23,37,32,87,78,10,62,36,8,8,42,40,95,52,26,59,47,2,70,21,35,5,2,28,49,36,69,60,12,3,78,75,97,38,79,85,58,38,24,8,65,96,3,59,25,58,34,8,98,59,13,56,82,58,61,76,12,100,97,48,82,91,12,81,29,22,37,37,71,78,89,7,37,76,46,69,91,1,64,97,52,71,62,13,67,14,89,40,1,28,89,91,54,36,53,34,8,82,32,75,19,42,24,96,58,82,83,66,63,31,16,30,39,24,57,17,6,5,91,76,45,35,98,86,94,59,80,60,77,39,57,89,43,59,92,40,93,0,66,11,16,7,57,64,77,82,63,56,54,21,55,79,62,15,88,57,55,85,22,56,86,95,12,49,24,55,59,65,97,81,23,13,92,4,66,51,48,98,17,13,26,57,38,97,76,84,22,86,1,34,17,69,30,40,63,62,63,50,13,18,65,35,46,72,55,100,25,79,81,64,58,10,63,41,40,10,30,71,37,52,29,58,36,32,8,89,68,35,14,37,40,62,11,53,43,76,81,44,4,28,26,75,88,45,54,69,49,25,48,22,7,55,43,76,95,26,100,44,32,16,3,10,72,98,23,55,94,60,76,17,3,3,79,100,31,89,40,43,0,2,67,10,63,84,10,81,82,19,66,24,52,34,35,24,66,83,78,26,88,88,47,50,18,41,21,46,61,41,60,3,92,5,17,69,97,72,26,88,81,41,90,49,59,25,9,75,93,64,43,74,35,1,21,3,53,98,35,71,42,14,0,9,49,34,69,99,6,19,48,8,3,65,56,2,55,9,33,36,54,92,12,91,46,100,39,87,36,8,79,63,20,93,5,86,8,89,41,11,83,65,56,52,25,92,6,22,63,48,5,5,76,99,96,12,100,58,77,54,54,27,38,95,43,16,31,63,54,60,90,1,37,100,96,7,12,22,44,48,43,57,59,76,56,57,22,72,3,39,15,95,42,33,28,45,9,8,16,45,66,18,81,10,12,99,22,72,16,99,100,13,26,2,56,48,64,4,58,16,69,40,19,41,50,88,53,46,24,100,1,62,47,23,64,82,12,46,75,43,79,52,57,64,39,70,31,58,61,77,73,90,8,10,3,13,6,50,24,57,2,41,41,10,92,6,98,84,83,47,7,100,4,55,73,58,20,2,36,22,65,99,92,24,45,50,36,18,63,40,37,52,8,76,63,21,68,60,71,76,0,53,20,0,73,42,86,23,22,54,29,46,89,7,93,70,44,58,100,83,33,75,52,65,90,60,20,76,100,64,11,92,10,47,55,99,73,33,75,15,19,50,66,60,44,6,51,84,59,34,65,46,22,55,10,0,89,76,1,12,17,17,46,80,79,71,85,20,18,64,77,83,95,7,79,34,19,71,24,18,44,27,62,52,85,82,56,6,79,21,77,99,82,38,3,39,30,20,35,72,72,25,33,32,92,79,14,40,79,87,64,3,73,60,29,61,39,92,20,76,48,89,53,66,28,73,90,49,55,74,4,21,25,6,13,20,80,45,15,29,35,55,66,30,80,65,26,18,86,97,62,85,62,57,25,6,98,17,97,5,69,33,12,54,32,5,31,76,36,48,60,42,18,92,51,45,84,50,8,62,77,41,7,21,75,73,2,22,61,82,19,17,58,11,90,70,71,12,0,64,11,36,19,76,8,71,97,37,32,92,37,46,94,39,76,3,16,24,98,20,47,8,43,98,36,54,84,83,11,40,81,56,60,21,49,72,38,0,53,52,13,34,74,13,4,92,81,37,17,63,53,84,26,54,70,35,69,61,82,88,39,11,15,14,53,88,30,95,35,2,22,8,100,81,94,78,86,14,6,90,70,88,24,28,2,97,42,23,54,45,73,14,48,75,8,45,93,43,22,48,60,65,88,24,63,67,63,38,82,55,98,58,72,58,55,54,91,88,28,94,60,91,13,49,90,47,34,86,56,79,46,77,40,21,35,71,88,84,55,36,83,54,13,56,94,45,32,41,5,90,75,82,39,9,19,98,78,40,13,2,27,62,51,80,0,80,87,98,69,37,77,95,93,59,87,30,88,25,87,31,43,76,58,39,81,93,21,10,46,34,34,50,74,38,100,63,76,96,25,26,99,74,40,68,40,16,79,16,85,99,1,35,16,87,81,79,90,31,7,67,77,93,95,32,82,30,78,81,41,77,48,84,16,60,1,33,26,78,29,79,66,31,48,34,24,51,14,51,51,8,97,27,8,48,81,99,48,71,91,39,29,46,2,92,11,23,50,95,49,36,22,42,3,6,100,47,77,35,67,14,90,23,100,98,47,33,32,39,94,64,95,24,91,8,27,48,9,91,68,59,60,70,69,100,74,42,67,61,84,46,8,98,3,1,40,7,63,51,62,35,100,68,33,65,45,5,96,81,50,17,56,1,33,57,87,49,61,16,68,0,38,4,53,0,82,59,96,70,12,0,10,43,45,46,39,84,29,10,62,44,42,52,50,7,4,24,10,92,48,93,78,64,14,84,4,3,16,64,5,84,55,53,2,98,18,8,95,32,25,55,72,96,44,31,10,63,21,1,9,87,40,26,91,32,40,67,48,3,40,42,23,16,60,14,74,88,40,64,99,72,22,33,73,72,17,36,29,92,46,37,92,98,35,98,64,33,41,32,93,65,13,99,93,36,35,76,23,6,62,18,93,37,78,54,6,45,28,37,39,33,12,48,9,25,43,30,30,49,48,29,96,29,75,96,96,84,37,61,78,45,98,24,35,54,11,18,22,40,27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48,99,31,31,93,67,50,37,17,81,26,35,19,30,71,77,27,8,63,0,66,18,95,53,46,71,87,77,76,54,32,63,82,23,62]);
P:=CharacteristicPolynomial(A);

Output: Magma V2.11-2     Wed Aug  4 2004 10:00:40 on modular  [Seed = 1493759076]
   -------------------------------------



************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 11:05:52 2004

Input: A:=Matrix(IntegerRing(),100,100,[0,67,28,73,15,5,37,4,35,86,84,17,47,24,89,5,16,61,35,21,96,99,39,62,75,75,68,58,25,2,92,41,86,38,43,82,67,96,1,59,36,98,41,38,23,96,62,21,53,80,25,60,33,8,7,7,79,95,26,4,33,74,74,84,23,20,60,43,10,76,72,49,42,39,38,40,1,43,40,48,34,14,74,40,5,27,96,38,37,69,31,1,29,90,42,27,4,62,10,35,75,36,62,23,70,97,53,70,44,90,35,76,40,30,75,39,62,35,2,99,41,71,97,43,10,18,76,48,4,94,73,77,75,58,33,93,39,22,20,85,96,82,41,73,98,5,69,52,83,88,82,23,46,63,40,76,35,14,50,42,62,93,27,25,45,61,46,71,85,4,52,14,69,26,66,95,72,96,76,7,32,62,21,11,26,87,36,87,19,88,2,0,49,48,53,33,7,95,55,44,83,6,15,90,14,9,33,2,4,93,72,38,3,30,64,5,71,15,45,59,88,81,16,51,71,29,64,75,92,66,63,58,46,93,80,30,42,44,44,0,42,35,60,85,45,33,42,64,73,80,49,29,24,70,73,12,93,91,48,73,91,80,21,34,31,97,2,71,41,95,8,60,20,92,66,51,0,88,97,0,19,79,77,65,89,25,46,59,99,73,21,24,26,54,0,4,48,46,54,65,9,99,13,33,29,58,12,87,9,28,64,95,8,8,90,85,92,72,11,68,68,42,7,62,63,1,59,71,13,85,62,80,83,99,50,49,64,91,40,31,12,75,88,50,47,49,23,49,71,4,88,67,61,98,38,82,89,100,88,23,46,99,11,54,8,35,49,61,3,23,10,14,20,78,97,5,93,45,0,94,96,73,24,8,20,12,82,71,12,14,59,81,27,63,0,54,88,88,38,46,100,21,25,11,93,83,44,99,44,30,56,59,33,24,34,68,40,11,19,69,70,24,8,18,83,94,69,91,20,43,51,100,94,20,18,70,1,71,8,61,22,89,5,67,83,6,59,71,58,48,18,64,32,61,92,88,22,94,57,96,28,39,45,32,40,60,47,9,49,94,21,14,92,60,56,23,100,37,87,87,20,16,91,55,100,40,10,61,1,95,8,76,41,77,8,4,72,49,37,68,100,77,99,37,66,38,94,42,58,67,31,73,20,65,76,48,97,62,75,33,12,35,70,71,64,2,18,30,58,50,8,52,32,21,23,49,29,97,56,88,67,99,0,90,93,48,81,54,16,14,74,71,89,29,92,72,78,97,77,47,40,58,16,33,7,72,65,77,46,57,99,40,97,43,31,68,75,75,71,47,66,58,73,2,47,69,30,38,75,93,99,27,0,82,33,54,55,15,95,2,38,95,56,83,17,4,67,79,14,55,57,71,0,20,33,10,38,91,94,38,43,39,87,17,67,69,92,99,11,17,91,58,59,92,98,8,19,79,73,22,69,31,71,96,83,82,82,35,37,4,75,63,43,64,17,91,55,37,26,56,4,83,10,73,11,10,43,83,84,36,6,83,89,54,91,88,70,61,100,13,7,57,70,60,67,7,45,87,50,28,80,45,30,61,26,95,8,94,38,26,88,14,13,10,45,47,30,2,58,47,9,63,42,54,82,32,31,57,27,39,82,51,2,54,75,4,51,35,95,54,89,87,41,51,73,65,7,56,10,92,89,66,64,68,3,81,8,5,6,57,58,56,11,56,95,20,83,71,31,56,4,50,60,31,20,35,50,15,81,52,31,26,81,1,46,38,15,26,17,52,54,20,57,13,22,36,65,20,25,47,2,42,78,15,62,95,93,68,26,3,17,47,83,6,83,32,99,86,19,59,5,43,38,39,44,75,39,47,64,0,69,52,37,52,53,53,69,9,12,66,97,38,42,95,67,18,27,75,29,89,9,14,10,75,69,72,55,27,23,99,12,85,3,93,22,52,10,71,63,69,42,47,51,13,48,87,17,44,34,72,52,45,3,0,40,41,24,31,81,4,99,95,27,52,57,97,71,33,33,21,37,0,72,61,91,15,13,17,37,54,16,11,98,27,30,7,22,86,0,76,57,22,25,44,41,1,53,68,87,77,78,50,94,100,99,95,55,38,91,46,63,49,5,32,29,75,45,50,35,1,17,3,31,82,27,50,65,10,56,17,36,29,71,80,69,78,11,25,89,79,40,38,11,89,69,29,31,28,65,29,33,43,9,18,19,3,1,77,31,49,10,88,38,66,38,34,13,12,64,88,24,66,44,92,62,33,26,68,0,73,98,73,78,84,75,63,74,72,58,27,86,61,43,12,57,65,70,0,79,33,11,82,59,19,31,82,77,6,83,74,1,50,57,28,98,84,74,98,4,40,67,91,97,53,39,5,19,35,46,35,49,48,52,64,84,97,11,63,32,38,97,35,72,14,77,61,64,80,21,34,47,80,1,9,70,2,87,53,34,47,32,66,42,4,24,77,20,3,90,7,82,95,36,31,87,59,39,6,47,43,71,22,20,57,28,82,60,60,78,4,66,30,70,9,70,60,67,31,30,72,93,48,37,53,58,22,37,86,0,33,69,60,5,25,24,87,86,42,41,7,95,28,77,99,38,55,91,51,85,31,60,15,34,89,3,38,87,92,70,42,0,24,26,14,4,48,64,49,49,23,16,46,12,31,96,11,37,25,87,39,99,73,74,1,2,79,81,25,12,55,2,41,41,27,11,64,81,20,49,10,51,19,89,5,87,18,14,94,85,32,42,57,70,61,17,60,78,94,73,12,88,82,12,77,71,74,83,85,15,60,14,53,14,67,25,81,55,73,83,63,33,89,39,29,50,37,95,7,77,17,32,62,9,46,90,89,79,15,42,29,46,33,90,60,44,29,28,58,27,52,100,12,20,77,20,96,57,49,84,16,63,18,92,0,34,10,63,26,97,41,51,73,11,26,18,51,75,95,25,76,25,33,27,63,94,97,9,35,91,100,28,93,7,72,40,29,50,85,2,61,70,44,49,99,11,45,91,9,63,18,39,94,74,2,44,53,91,54,28,77,67,12,75,30,61,8,76,62,36,88,16,61,12,60,62,25,68,94,69,56,35,37,72,39,43,36,16,44,91,80,65,56,94,100,76,10,0,66,31,65,23,64,24,19,53,35,1,63,23,46,79,42,29,62,37,97,1,25,42,43,27,0,85,1,1,89,42,83,92,47,93,32,9,88,69,72,37,90,73,29,45,99,41,65,45,47,7,5,1,82,12,41,7,35,18,74,41,13,69,48,91,2,12,93,65,62,62,41,97,12,10,92,7,54,62,2,22,40,5,96,66,66,15,31,50,75,54,22,44,26,32,62,33,28,45,14,33,9,33,37,25,20,27,22,31,74,24,29,100,98,15,72,4,60,91,8,40,24,19,71,80,50,68,41,53,51,93,89,98,47,23,40,26,13,48,21,13,38,87,23,66,22,38,1,6,91,88,83,97,94,60,80,9,16,13,87,30,94,97,94,60,64,40,21,77,31,70,99,45,41,3,21,23,2,0,14,57,33,14,82,57,87,36,6,38,37,40,80,67,97,59,46,20,43,20,5,88,0,26,66,81,24,56,99,79,67,64,9,65,71,84,55,44,31,30,83,95,33,49,26,20,88,44,74,52,53,35,98,78,85,57,33,33,41,76,93,80,5,68,3,17,63,58,42,47,86,59,12,38,32,43,5,41,41,51,60,26,20,22,35,52,61,71,97,22,33,37,90,79,83,70,57,3,65,18,74,56,8,34,25,43,18,12,40,23,79,53,49,9,0,0,89,92,30,20,63,50,39,17,89,74,11,15,74,76,70,30,34,68,77,0,86,26,91,20,31,0,35,22,66,38,73,79,28,75,26,9,64,16,70,22,8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62,28,45,75,70,56,10,22,6,69,6,17,61,17,83,69,59,24,6,63,17,81,12,16,32,93,89,28,31,44,25,69,3,83,16,56,83,27,29,49,51,83,70,4,9,0,72,60,59,94,62,58,5,68,10,76,15,27,81,22,52,55,19,48,72,34,77,85,2,34,78,2,5,3,42,71,99,3,94,60,30,76,38,95,60,83,32,69,92,87,70,74,67,75,82,8,33,12,86,26,44,1,7,84,5,70,96,16,99,60,44,66,31,84,60,57,1,24,20,94,92,81,89,72,32,83,67,77,85,85,1,64,13,76,85,72,9,96,46,14,40,14,74,70,34,51,10,79,55,71,94,92,46,30,7,32,39,64,9,55,51,56,19,71,80,12,95,59,26,83,4,6,49,86,2,82,96,81,44,97,11,0,2,14,26,82,62,23,52,95,57,64,38,40,39,34,80,62,96,97,62,32,53,38,65,6,4,18,40,4,6,87,31,77,18,28,15,22,8,32,77,30,87,52,6,92,38,31,64,0,60,0,80,44,28,4,77,87,47,27,1,73,26,54,34,48,13,0,66,41,25,59,28,72,10,17,0,35,84,71,44,92,62,2,16,39,17,72,16,9,94,1,98,34,63,79,98,63,91,26,65,42,80,53,38,67,97,26,43,62,3,94,18,20,79,27,23,52,77,39,59,38,75,36,4,61,16,51,36,96,54,39,12,74,81,42,79,93,55,85,80,86,34,80,25,28,86,49,53,6,58,80,80,38,47,39,67,77,62,19,67,80,50,86,9,10,15,30,26,42,32,36,15,63,35,36,85,23,19,4,35,55,19,49,31,48,21,80,64,63,47,79,42,95,58,32,95,58,23,33,30,83,66,81,77,84,5,33,90,91,74,91,39,82,49,47,66,37,45,71,84,24,12,52,77,86,12,93,50,0,41,79,33,65,97,14,28,82,97,82,60,70,97,51,55,55,34,79,12,74,56,10,25,47,78,91,11,46,8,19,32,2,54,0,56,93,59,4,49,52,39,97,44,78,48,7,66,18,21,97,36,48,27,91,69,2,50,100,28,93,43,22,64,39,23,82,37,79,99,1,0,28,93,68,82,93,73,84,97,99,75,78,15,5,75,41,74,53,32,43,79,32,3,15,55,24,46,12,37,68,45,26,10,88,37,80,87,49,50,14,57,82,32,88,8,1,89,28,14,1,11,85,22,3,24,89,20,77,97,0,60,4,66,1,60,29,0,78,47,96,100,3,4,37,64,9,24,100,9,35,5,7,94,65,50,27,59,11,85,93,33,32,15,7,12,14,81,1,84,79,55,30,68,72,56,50,52,53,61,96,81,24,75,44,80,49,83,40,53,61,24,39,84,78,52,16,54,33,55,43,26,63,49,66,100,20,21,63,83,35,16,78,10,4,85,62,19,20,55,37,63,7,33,65,65,27,41,50,62,9,64,42,66,45,92,6,57,16,19,65,50,79,24,47,20,67,33,61,7,97,8,62,53,1,83,3,47,95,99,70,49,42,98,1,46,58,14,53,20,96,57,50,45,73,97,46,67,49,8,92,89,100,98,3,21,52,74,44,49,17,44,51,35,67,20,24,44,80,41,85,50,86,49,90,95,56,100,47,46,90,85,75,15,53,15,45,54,95,26,8,21,63,51,31,23,94,95,76,13,82,51,37,78,80,2,14,4,61,100,76,38,68,11,48,68,92,23,22,64,61,86,94,16,31,56,90,74,10,59,66,87,13,34,66,33,100,75,6,29,16,69,64,41,83,7,98,97,29,37,88,60,37,31,82,48,96,22,51,54,69,71,0,53,41,4,21,47,40,62,67,45,7,37,41,67,22,77,12,37,55,17,63,40,48,7,86,47,36,37,85,93,33,26,64,29,57,99,89,66,1,69,22,85,29,63,84,6,42,69,27,35,69,48,31,40,48,91,28,28,49,31,45,99,80,54,59,13,82,29,79,27,10,35,21,1,66,58,77,49,25,29,61,12,85,24,75,78,85,39,95,57,83,54,25,23,27,82,88,23,29,30,61,40,89,6,88,36,23,89,58,35,0,85,63,53,86,52,57,84,79,15,10,0,45,82,85,59,79,12,20,50,36,52,36,56,9,4,35,73,99,5,8,2,23,95,1,18,61,98,20,96,82,0,63,71,78,46,75,73,69,36,66,76,53,17,10,57,39,38,47,39,29,46,35,65,25,0,51,53,37,52,56,5,71,27,18,51,94,59,92,78,88,54,75,59,31,29,71,83,2,41,36,56,9,30,90,19,66,41,60,58,61,35,96,72,68,23,80,57,86,25,9,46,36,10,33,53,74,99,69,95,24,95,80,30,24,71,17,7,2,2,51,81,40,90,2,82,17,72,36,39,34,20,85,52,97,88,61,4,16,97,35,65,68,34,37,73,86,98,43,19,42,25,28,41,100,10,86,46,26,98,59,88,15,92,8,59,39,25,34,2,69,32,6,74,16,45,98,15,53,73,14,49,78,53,28,46,96,33,15,12,36,30,57,52,75,82,52,41,39,32,77,45,21,42,44,67,48,46,86,94,48,50,92,18,99,79,70,33,87,58,31,6,81,38,73,89,37,85,42,75,56,46,14,34,82,76,0,78,56,86,66,90,92,92,17,93,94,14,79,7,55,96,11,34,80,51,38,56,50,54,85,4,4,98,91,6,2,35,50,64,62,64,65,79,10,63,42,97,55,72,52,69,84,55,2,2,18,51,10,81,56,81,51,70,48,16,82,33,47,70,22,58,74,9,93,3,86,83,62,85,49,0,64,41,57,45,50,69,31,77,99,97,40,13,61,21,74,78,8,23,79,55,78,29,73,36,88,80,44,92,1,86,47,59,34,17,13,26,15,85,31,50,30,17,39,60,10,51,76,88,78,58,13,65,15,78,74,87,93,34,59,97,91,30,23,55,16,41,86,37,0,54,89,92,18,96,18,23,2,80,5,77,26,99,69,67,50,92,85,37,83,39,92,79,12,85,19,81,80,77,99,39,86,67,47,7,31,38,47,56,61,37,33,4,19,27,81,31,68,39,7,46,27,76,10,10,71,6,7,16,68,75,51,6,43,70,52,31,61,76,49,50,5,48,19,60,54,57,40,34,73,61,29,26,40,71,45,53,14,68,49,96,65,61,22,94,34,84,28,24,94,93,74,39,23,62,80,86,59,76,3,22,14,30,69]);
P:=CharacteristicPolynomial(A);

Output: Magma V2.11-2     Wed Aug  4 2004 11:05:50 on modular  [Seed = 3649594274]
   -------------------------------------


Total time: 1.810 seconds, Total memory usage: 4.25MB


************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 11:07:16 2004

Input: A:=Matrix(IntegerRing(),100,100,[0,67,28,73,15,5,37,4,35,86,84,17,47,24,89,5,16,61,35,21,96,99,39,62,75,75,68,58,25,2,92,41,86,38,43,82,67,96,1,59,36,98,41,38,23,96,62,21,53,80,25,60,33,8,7,7,79,95,26,4,33,74,74,84,23,20,60,43,10,76,72,49,42,39,38,40,1,43,40,48,34,14,74,40,5,27,96,38,37,69,31,1,29,90,42,27,4,62,10,35,75,36,62,23,70,97,53,70,44,90,35,76,40,30,75,39,62,35,2,99,41,71,97,43,10,18,76,48,4,94,73,77,75,58,33,93,39,22,20,85,96,82,41,73,98,5,69,52,83,88,82,23,46,63,40,76,35,14,50,42,62,93,27,25,45,61,46,71,85,4,52,14,69,26,66,95,72,96,76,7,32,62,21,11,26,87,36,87,19,88,2,0,49,48,53,33,7,95,55,44,83,6,15,90,14,9,33,2,4,93,72,38,3,30,64,5,71,15,45,59,88,81,16,51,71,29,64,75,92,66,63,58,46,93,80,30,42,44,44,0,42,35,60,85,45,33,42,64,73,80,49,29,24,70,73,12,93,91,48,73,91,80,21,34,31,97,2,71,41,95,8,60,20,92,66,51,0,88,97,0,19,79,77,65,89,25,46,59,99,73,21,24,26,54,0,4,48,46,54,65,9,99,13,33,29,58,12,87,9,28,64,95,8,8,90,85,92,72,11,68,68,42,7,62,63,1,59,71,13,85,62,80,83,99,50,49,64,91,40,31,12,75,88,50,47,49,23,49,71,4,88,67,61,98,38,82,89,100,88,23,46,99,11,54,8,35,49,61,3,23,10,14,20,78,97,5,93,45,0,94,96,73,24,8,20,12,82,71,12,14,59,81,27,63,0,54,88,88,38,46,100,21,25,11,93,83,44,99,44,30,56,59,33,24,34,68,40,11,19,69,70,24,8,18,83,94,69,91,20,43,51,100,94,20,18,70,1,71,8,61,22,89,5,67,83,6,59,71,58,48,18,64,32,61,92,88,22,94,57,96,28,39,45,32,40,60,47,9,49,94,21,14,92,60,56,23,100,37,87,87,20,16,91,55,100,40,10,61,1,95,8,76,41,77,8,4,72,49,37,68,100,77,99,37,66,38,94,42,58,67,31,73,20,65,76,48,97,62,75,33,12,35,70,71,64,2,18,30,58,50,8,52,32,21,23,49,29,97,56,88,67,99,0,90,93,48,81,54,16,14,74,71,89,29,92,72,78,97,77,47,40,58,16,33,7,72,65,77,46,57,99,40,97,43,31,68,75,75,71,47,66,58,73,2,47,69,30,38,75,93,99,27,0,82,33,54,55,15,95,2,38,95,56,83,17,4,67,79,14,55,57,71,0,20,33,10,38,91,94,38,43,39,87,17,67,69,92,99,11,17,91,58,59,92,98,8,19,79,73,22,69,31,71,96,83,82,82,35,37,4,75,63,43,64,17,91,55,37,26,56,4,83,10,73,11,10,43,83,84,36,6,83,89,54,91,88,70,61,100,13,7,57,70,60,67,7,45,87,50,28,80,45,30,61,26,95,8,94,38,26,88,14,13,10,45,47,30,2,58,47,9,63,42,54,82,32,31,57,27,39,82,51,2,54,75,4,51,35,95,54,89,87,41,51,73,65,7,56,10,92,89,66,64,68,3,81,8,5,6,57,58,56,11,56,95,20,83,71,31,56,4,50,60,31,20,35,50,15,81,52,31,26,81,1,46,38,15,26,17,52,54,20,57,13,22,36,65,20,25,47,2,42,78,15,62,95,93,68,26,3,17,47,83,6,83,32,99,86,19,59,5,43,38,39,44,75,39,47,64,0,69,52,37,52,53,53,69,9,12,66,97,38,42,95,67,18,27,75,29,89,9,14,10,75,69,72,55,27,23,99,12,85,3,93,22,52,10,71,63,69,42,47,51,13,48,87,17,44,34,72,52,45,3,0,40,41,24,31,81,4,99,95,27,52,57,97,71,33,33,21,37,0,72,61,91,15,13,17,37,54,16,11,98,27,30,7,22,86,0,76,57,22,25,44,41,1,53,68,87,77,78,50,94,100,99,95,55,38,91,46,63,49,5,32,29,75,45,50,35,1,17,3,31,82,27,50,65,10,56,17,36,29,71,80,69,78,11,25,89,79,40,38,11,89,69,29,31,28,65,29,33,43,9,18,19,3,1,77,31,49,10,88,38,66,38,34,13,12,64,88,24,66,44,92,62,33,26,68,0,73,98,73,78,84,75,63,74,72,58,27,86,61,43,12,57,65,70,0,79,33,11,82,59,19,31,82,77,6,83,74,1,50,57,28,98,84,74,98,4,40,67,91,97,53,39,5,19,35,46,35,49,48,52,64,84,97,11,63,32,38,97,35,72,14,77,61,64,80,21,34,47,80,1,9,70,2,87,53,34,47,32,66,42,4,24,77,20,3,90,7,82,95,36,31,87,59,39,6,47,43,71,22,20,57,28,82,60,60,78,4,66,30,70,9,70,60,67,31,30,72,93,48,37,53,58,22,37,86,0,33,69,60,5,25,24,87,86,42,41,7,95,28,77,99,38,55,91,51,85,31,60,15,34,89,3,38,87,92,70,42,0,24,26,14,4,48,64,49,49,23,16,46,12,31,96,11,37,25,87,39,99,73,74,1,2,79,81,25,12,55,2,41,41,27,11,64,81,20,49,10,51,19,89,5,87,18,14,94,85,32,42,57,70,61,17,60,78,94,73,12,88,82,12,77,71,74,83,85,15,60,14,53,14,67,25,81,55,73,83,63,33,89,39,29,50,37,95,7,77,17,32,62,9,46,90,89,79,15,42,29,46,33,90,60,44,29,28,58,27,52,100,12,20,77,20,96,57,49,84,16,63,18,92,0,34,10,63,26,97,41,51,73,11,26,18,51,75,95,25,76,25,33,27,63,94,97,9,35,91,100,28,93,7,72,40,29,50,85,2,61,70,44,49,99,11,45,91,9,63,18,39,94,74,2,44,53,91,54,28,77,67,12,75,30,61,8,76,62,36,88,16,61,12,60,62,25,68,94,69,56,35,37,72,39,43,36,16,44,91,80,65,56,94,100,76,10,0,66,31,65,23,64,24,19,53,35,1,63,23,46,79,42,29,62,37,97,1,25,42,43,27,0,85,1,1,89,42,83,92,47,93,32,9,88,69,72,37,90,73,29,45,99,41,65,45,47,7,5,1,82,12,41,7,35,18,74,41,13,69,48,91,2,12,93,65,62,62,41,97,12,10,92,7,54,62,2,22,40,5,96,66,66,15,31,50,75,54,22,44,26,32,62,33,28,45,14,33,9,33,37,25,20,27,22,31,74,24,29,100,98,15,72,4,60,91,8,40,24,19,71,80,50,68,41,53,51,93,89,98,47,23,40,26,13,48,21,13,38,87,23,66,22,38,1,6,91,88,83,97,94,60,80,9,16,13,87,30,94,97,94,60,64,40,21,77,31,70,99,45,41,3,21,23,2,0,14,57,33,14,82,57,87,36,6,38,37,40,80,67,97,59,46,20,43,20,5,88,0,26,66,81,24,56,99,79,67,64,9,65,71,84,55,44,31,30,83,95,33,49,26,20,88,44,74,52,53,35,98,78,85,57,33,33,41,76,93,80,5,68,3,17,63,58,42,47,86,59,12,38,32,43,5,41,41,51,60,26,20,22,35,52,61,71,97,22,33,37,90,79,83,70,57,3,65,18,74,56,8,34,25,43,18,12,40,23,79,53,49,9,0,0,89,92,30,20,63,50,39,17,89,74,11,15,74,76,70,30,34,68,77,0,86,26,91,20,31,0,35,22,66,38,73,79,28,75,26,9,64,16,70,22,8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62,28,45,75,70,56,10,22,6,69,6,17,61,17,83,69,59,24,6,63,17,81,12,16,32,93,89,28,31,44,25,69,3,83,16,56,83,27,29,49,51,83,70,4,9,0,72,60,59,94,62,58,5,68,10,76,15,27,81,22,52,55,19,48,72,34,77,85,2,34,78,2,5,3,42,71,99,3,94,60,30,76,38,95,60,83,32,69,92,87,70,74,67,75,82,8,33,12,86,26,44,1,7,84,5,70,96,16,99,60,44,66,31,84,60,57,1,24,20,94,92,81,89,72,32,83,67,77,85,85,1,64,13,76,85,72,9,96,46,14,40,14,74,70,34,51,10,79,55,71,94,92,46,30,7,32,39,64,9,55,51,56,19,71,80,12,95,59,26,83,4,6,49,86,2,82,96,81,44,97,11,0,2,14,26,82,62,23,52,95,57,64,38,40,39,34,80,62,96,97,62,32,53,38,65,6,4,18,40,4,6,87,31,77,18,28,15,22,8,32,77,30,87,52,6,92,38,31,64,0,60,0,80,44,28,4,77,87,47,27,1,73,26,54,34,48,13,0,66,41,25,59,28,72,10,17,0,35,84,71,44,92,62,2,16,39,17,72,16,9,94,1,98,34,63,79,98,63,91,26,65,42,80,53,38,67,97,26,43,62,3,94,18,20,79,27,23,52,77,39,59,38,75,36,4,61,16,51,36,96,54,39,12,74,81,42,79,93,55,85,80,86,34,80,25,28,86,49,53,6,58,80,80,38,47,39,67,77,62,19,67,80,50,86,9,10,15,30,26,42,32,36,15,63,35,36,85,23,19,4,35,55,19,49,31,48,21,80,64,63,47,79,42,95,58,32,95,58,23,33,30,83,66,81,77,84,5,33,90,91,74,91,39,82,49,47,66,37,45,71,84,24,12,52,77,86,12,93,50,0,41,79,33,65,97,14,28,82,97,82,60,70,97,51,55,55,34,79,12,74,56,10,25,47,78,91,11,46,8,19,32,2,54,0,56,93,59,4,49,52,39,97,44,78,48,7,66,18,21,97,36,48,27,91,69,2,50,100,28,93,43,22,64,39,23,82,37,79,99,1,0,28,93,68,82,93,73,84,97,99,75,78,15,5,75,41,74,53,32,43,79,32,3,15,55,24,46,12,37,68,45,26,10,88,37,80,87,49,50,14,57,82,32,88,8,1,89,28,14,1,11,85,22,3,24,89,20,77,97,0,60,4,66,1,60,29,0,78,47,96,100,3,4,37,64,9,24,100,9,35,5,7,94,65,50,27,59,11,85,93,33,32,15,7,12,14,81,1,84,79,55,30,68,72,56,50,52,53,61,96,81,24,75,44,80,49,83,40,53,61,24,39,84,78,52,16,54,33,55,43,26,63,49,66,100,20,21,63,83,35,16,78,10,4,85,62,19,20,55,37,63,7,33,65,65,27,41,50,62,9,64,42,66,45,92,6,57,16,19,65,50,79,24,47,20,67,33,61,7,97,8,62,53,1,83,3,47,95,99,70,49,42,98,1,46,58,14,53,20,96,57,50,45,73,97,46,67,49,8,92,89,100,98,3,21,52,74,44,49,17,44,51,35,67,20,24,44,80,41,85,50,86,49,90,95,56,100,47,46,90,85,75,15,53,15,45,54,95,26,8,21,63,51,31,23,94,95,76,13,82,51,37,78,80,2,14,4,61,100,76,38,68,11,48,68,92,23,22,64,61,86,94,16,31,56,90,74,10,59,66,87,13,34,66,33,100,75,6,29,16,69,64,41,83,7,98,97,29,37,88,60,37,31,82,48,96,22,51,54,69,71,0,53,41,4,21,47,40,62,67,45,7,37,41,67,22,77,12,37,55,17,63,40,48,7,86,47,36,37,85,93,33,26,64,29,57,99,89,66,1,69,22,85,29,63,84,6,42,69,27,35,69,48,31,40,48,91,28,28,49,31,45,99,80,54,59,13,82,29,79,27,10,35,21,1,66,58,77,49,25,29,61,12,85,24,75,78,85,39,95,57,83,54,25,23,27,82,88,23,29,30,61,40,89,6,88,36,23,89,58,35,0,85,63,53,86,52,57,84,79,15,10,0,45,82,85,59,79,12,20,50,36,52,36,56,9,4,35,73,99,5,8,2,23,95,1,18,61,98,20,96,82,0,63,71,78,46,75,73,69,36,66,76,53,17,10,57,39,38,47,39,29,46,35,65,25,0,51,53,37,52,56,5,71,27,18,51,94,59,92,78,88,54,75,59,31,29,71,83,2,41,36,56,9,30,90,19,66,41,60,58,61,35,96,72,68,23,80,57,86,25,9,46,36,10,33,53,74,99,69,95,24,95,80,30,24,71,17,7,2,2,51,81,40,90,2,82,17,72,36,39,34,20,85,52,97,88,61,4,16,97,35,65,68,34,37,73,86,98,43,19,42,25,28,41,100,10,86,46,26,98,59,88,15,92,8,59,39,25,34,2,69,32,6,74,16,45,98,15,53,73,14,49,78,53,28,46,96,33,15,12,36,30,57,52,75,82,52,41,39,32,77,45,21,42,44,67,48,46,86,94,48,50,92,18,99,79,70,33,87,58,31,6,81,38,73,89,37,85,42,75,56,46,14,34,82,76,0,78,56,86,66,90,92,92,17,93,94,14,79,7,55,96,11,34,80,51,38,56,50,54,85,4,4,98,91,6,2,35,50,64,62,64,65,79,10,63,42,97,55,72,52,69,84,55,2,2,18,51,10,81,56,81,51,70,48,16,82,33,47,70,22,58,74,9,93,3,86,83,62,85,49,0,64,41,57,45,50,69,31,77,99,97,40,13,61,21,74,78,8,23,79,55,78,29,73,36,88,80,44,92,1,86,47,59,34,17,13,26,15,85,31,50,30,17,39,60,10,51,76,88,78,58,13,65,15,78,74,87,93,34,59,97,91,30,23,55,16,41,86,37,0,54,89,92,18,96,18,23,2,80,5,77,26,99,69,67,50,92,85,37,83,39,92,79,12,85,19,81,80,77,99,39,86,67,47,7,31,38,47,56,61,37,33,4,19,27,81,31,68,39,7,46,27,76,10,10,71,6,7,16,68,75,51,6,43,70,52,31,61,76,49,50,5,48,19,60,54,57,40,34,73,61,29,26,40,71,45,53,14,68,49,96,65,61,22,94,34,84,28,24,94,93,74,39,23,62,80,86,59,76,3,22,14,30,69]);
CharacteristicPolynomial(A);

Output: Magma V2.11-2     Wed Aug  4 2004 11:07:14 on modular  [Seed = 3230759511]
   -------------------------------------

$.1^100 - 4900*$.1^99 - 530133*$.1^98 + 628082305*$.1^97 + 41800335052*$.1^96 - 
    35002462696760*$.1^95 - 3663375905155882*$.1^94 - 873639926288234540*$.1^93 
    - 600186988167748055686*$.1^92 + 180669543151825828666437*$.1^91 + 
    71351991500639873683457473*$.1^90 - 1739194168390617138615204502*$.1^89 - 
    3028497521723594501827366017313*$.1^88 - 
    913085951547120174148296696466611*$.1^87 - 
    18082322141453419053267715714999228*$.1^86 - 
    11147282840488396298604418793153121903*$.1^85 + 
    6088617320578599383739236754904311364854*$.1^84 + 
    7682887319093250554554922214379911885252001*$.1^83 + 
    417218398307207997768632982719312293279368737*$.1^82 - 
    364781296129837856291395311436468671467406091158*$.1^81 - 
    63654932060603184760071381781834587634649430086581*$.1^80 - 
    9342742770458717461589569885607855318231843896579307*$.1^79 - 
    2605399728168541733145564504863559824669093184473932382*$.1^78 + 
    601091707997465511376512490524136556861604547775068124253*$.1^77 + 
    454390270009541509290181576645663238998222143088133333774719*$.1^76 + 
    113942565927844451952789137606239696720869831047372475081229385*$.1^75 - 
    27897451542396506927753214917054850814056794749780515082291062663*$.1^74 - 
    2439945425072800771310384484768784157920199686790480502107256122223*$.1^73 +
    2076167547833430964027595661644258475945389446031104253711650396503928*$.1^\
    72 - 2673043346393663385147005956788271042854949469277488643652173029837410\
    79*$.1^71 - 191163931940060117568517852410509042427237324922947639163588735\
    127581485556*$.1^70 + 20548513269568787891895382146961779770560289552883875\
    839252505676309481557245*$.1^69 + 11546161139313851155053427343948286605260\
    916109671522423501888798720408360231324*$.1^68 - 
    920383045322529908148487678253138464133314821746666002859174874453314279948\
    050399*$.1^67 - 11840173160210762743406074875342056639699573254989488140455\
    2389287304239838648955524*$.1^66 + 1101883410294897871090114957038281794667\
    91282052093986140007396459039221507779766478335*$.1^65 - 
    846138832565090680561280517809109286877319766838398635876589453825340700242\
    2175684214607*$.1^64 - 1170766005098608361677159001673111220323112078158161\
    0646985712878640655834966284069999856169*$.1^63 - 
    115030861615502542268345194091701811579765730317610049434042715294278787997\
    3035892461607872005*$.1^62 + 2804638496474086367143428915826006599194929781\
    16681253042648920602965889345392973217583429506744*$.1^61 + 
    816563118182424913627441692316733531536675655473497764696117568689131393675\
    71302279002878506155738*$.1^60 - 158636034333654099068578449334217313915297\
    7015533496616481436818224394191708973692022191839339439101*$.1^59 - 
    134939542230213130688060173670677264777622026400230709162877677625294683569\
    7777170340275837774891859862*$.1^58 - 2660905985500322043805649054573705367\
    22755980634147273802557993471302853179443774351706686401726939817162*$.1^57 
    - 1227542498315024954373044631320198850283062840627579425354572041626010495\
    57124473709660743687910957134594116*$.1^56 + 
    130941703687508060282919050264445254565326061042284234356513156087072635342\
    27083901151413629677886183728606043*$.1^55 + 
    185146984817225997305237749685392122289755040954416889530596277022613529612\
    23098106768964150173103920546419358484*$.1^54 + 
    365400628147106266886241438112242257268434713269561055640754011151153846801\
    8252506710975520653870634357046171983459*$.1^53 + 
    371952101843264355338463344547135487947587647945102263283543184472356455507\
    024203285396508315873936380193633335333181*$.1^52 - 
    230088842259266824188257612038052758563796019970205019299593884683629733112\
    7751602977388299281829077055224228306957718*$.1^51 - 
    256771625934658651478498780536808631326086238607313640134048122865682618291\
    69676596545069918491359461074678118200119358345*$.1^50 - 
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 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host portos.matesco.unican.es. (193.144.183.203)
Time: Wed Aug  4 11:12:43 2004

Input: A:=Matrix(IntegerRing(),200,200,[0,118,95,186,166,196,89,21,12,146,73,121,121,129,85,104,22,31,62,153,188,74,124,169,199,6,175,75,122,130,155,160,104,197,46,26,44,38,138,90,46,49,10,9,99,37,26,124,159,42,175,136,74,176,136,117,100,98,80,8,150,18,129,96,39,174,47,25,167,40,30,183,12,147,80,74,166,177,111,40,9,97,156,49,23,190,41,100,71,35,121,86,174,51,170,66,136,53,84,108,3,188,193,128,25,196,25,112,120,0,136,26,111,81,158,95,191,1,108,136,139,142,142,196,78,41,121,4,160,150,146,103,60,199,136,49,153,185,71,30,35,151,58,109,189,141,140,175,110,149,187,103,5,101,154,19,122,178,122,169,66,94,28,197,86,84,189,38,169,36,22,97,172,122,55,60,176,185,80,45,88,37,132,115,8,102,186,2,85,193,65,140,155,144,183,51,61,9,22,59,140,196,60,12,15,61,61,61,4,2,151,68,112,159,66,146,48,173,186,99,173,113,138,11,118,104,55,108,180,168,150,124,127,186,11,59,152,148,143,163,83,195,29,104,124,29,129,183,114,180,37,82,44,175,18,169,47,90,95,45,57,166,105,45,5,28,199,92,11,122,153,170,99,128,173,78,150,52,125,61,2,1,64,60,8,126,107,130,107,59,76,89,62,95,91,171,43,157,94,40,12,100,71,157,120,93,180,193,196,144,106,18,114,71,111,37,91,44,75,114,21,78,42,13,65,174,73,184,107,65,42,110,175,166,125,178,93,95,61,118,16,28,53,57,128,146,61,0,122,27,181,68,153,112,20,92,84,9,69,49,76,36,63,151,23,116,160,44,54,41,53,121,79,109,120,109,8,199,79,17,153,128,61,86,172,91,167,3,36,34,109,162,31,107,10,10,66,25,162,103,167,7,80,141,13,47,113,36,125,121,40,77,108,191,191,115,58,21,151,181,77,126,84,96,195,177,199,161,10,123,145,175,134,166,81,79,198,78,11,129,35,12,182,144,159,180,119,175,69,97,7,111,3,121,190,157,9,75,18,72,157,76,8,56,116,80,158,2,94,166,18,136,103,133,187,197,118,18,122,150,140,116,164,180,58,38,55,190,159,51,134,92,189,89,179,118,95,115,0,155,105,10,170,125,36,134,163,73,141,167,75,100,64,8,161,121,118,155,179,32,40,111,32,176,119,181,86,173,106,115,150,133,131,199,168,108,78,54,27,31,167,21,53,149,47,99,148,10,59,50,111,165,49,170,124,185,39,190,174,49,74,34,98,116,168,49,14,25,34,190,47,92,114,184,150,181,181,1,31,10,100,191,101,187,93,161,165,19,1,126,93,158,146,110,17,70,27,36,18,96,36,91,139,75,40,62,114,16,108,180,142,157,15,184,131,108,121,7,96,73,113,18,185,152,87,131,158,45,122,180,175,141,118,82,66,177,102,89,155,59,115,154,118,112,70,79,116,78,104,48,152,87,139,181,85,44,91,163,118,149,159,20,41,140,95,183,57,97,49,78,38,8,171,14,131,191,55,82,52,187,102,88,138,115,18,133,125,132,29,76,197,131,95,33,196,57,96,36,51,48,51,89,24,44,90,37,145,5,116,123,112,145,88,180,82,166,116,100,5,149,111,1,110,162,167,143,157,120,191,183,45,17,113,78,4,187,188,105,27,151,130,78,98,187,185,150,28,198,20,151,170,139,173,166,94,47,73,74,54,61,151,11,187,57,175,128,134,66,124,24,166,192,149,57,56,156,77,5,91,175,141,178,190,27,187,56,65,29,122,5,85,188,69,140,185,36,113,45,162,27,118,62,173,45,73,182,60,114,185,162,140,52,140,57,151,159,142,26,130,169,46,117,173,154,28,15,74,165,186,175,60,187,119,61,14,161,98,42,108,16,57,83,122,154,85,159,120,140,106,184,142,127,184,174,42,97,193,71,123,32,32,115,40,87,90,139,26,9,92,81,195,41,24,83,146,116,37,129,189,103,89,198,105,162,14,52,64,198,119,184,167,58,38,76,27,33,51,3,144,0,90,15,62,171,122,22,192,79,134,27,58,186,17,1,134,87,155,27,163,45,114,134,179,71,79,48,16,94,183,113,26,27,74,39,135,105,43,129,71,134,181,25,51,35,86,36,154,137,146,182,135,171,55,86,107,50,152,161,90,35,185,154,53,77,174,103,171,103,184,23,28,70,53,135,68,148,19,35,169,148,161,130,89,138,153,99,66,128,22,188,127,146,14,145,36,123,92,129,7,65,77,156,91,195,148,128,18,187,180,155,190,6,162,115,44,167,181,113,133,172,107,180,51,129,145,82,140,80,14,1,6,11,69,44,55,32,61,73,80,90,30,183,70,32,10,165,52,151,94,197,88,19,20,55,80,163,143,90,161,49,81,157,68,73,44,188,22,49,187,54,66,199,20,51,84,17,78,91,77,92,73,18,190,0,85,31,75,75,138,84,14,122,49,119,77,175,39,71,113,179,172,171,92,140,51,84,94,122,32,122,187,20,40,100,172,48,82,25,33,111,129,172,153,110,122,117,61,25,129,193,103,90,178,83,58,167,22,132,142,138,45,190,82,89,26,31,22,14,31,129,125,185,165,70,123,106,160,176,105,163,102,47,18,121,194,91,144,107,169,9,56,58,40,59,151,81,136,8,191,63,40,59,179,191,21,175,51,65,55,47,11,89,163,19,198,124,25,143,51,11,73,110,57,105,79,37,181,190,168,58,196,166,32,42,159,108,114,17,179,55,51,117,65,119,35,180,145,97,49,107,109,37,186,16,149,41,93,159,152,86,198,105,129,184,21,99,101,84,34,51,119,185,72,197,54,129,171,107,61,185,191,51,4,148,86,106,168,142,134,30,68,140,53,146,169,49,89,146,82,90,192,14,173,107,41,196,190,3,110,94,30,34,39,122,187,12,51,96,141,5,45,182,141,163,105,111,169,179,42,75,136,4,65,24,55,136,108,118,125,25,88,96,58,40,68,77,22,24,61,70,177,82,87,75,95,161,103,87,5,45,186,42,125,141,160,92,25,157,123,158,136,95,126,53,122,118,92,24,18,70,63,9,119,104,129,184,78,105,66,19,192,17,14,170,4,33,42,174,153,141,19,58,145,66,124,57,109,113,90,23,137,169,69,4,84,51,53,187,55,55,134,17,95,20,178,176,73,4,114,3,169,141,80,4,110,60,76,49,53,21,65,69,105,189,28,115,20,144,176,142,93,14,72,19,190,17,10,16,88,13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,45,123,190,100,27,18,102,14,46,11,138,20,145,172,87,106,76,121,7,127,125,151,197,14,176,91,114,155,151,46,180,79,197,192,126,32,141,141,27,121,184,56,148,17,18,163,17,58,70,152,4,176,64,127,89,51,72,5,25,163,111,77,118,168,121,102,1,75,42,144,47,13,46,123,162,10,137,119,52,88,149,154,46,26,193,9,110,100,166,183,183,162,13,131,178,25,132,48,27,34,80,142,134,103,117,121,168,147,128,35,122,154,165,99,24,9,84,153,96,52,127,4,46,155,118,130,141,64,11,44,199,23,146,92,189,42,32,75,178,104,149,43,121,26,3,110,112,18,70,146,196,104,38,185,196,50,79,193,33,118,58,44,90,80,188,165,127,155,4,16,12,102,162,196,173,4,131,9,88,159,41,72,189,11,119,3,98,131,34,41,68,194,44,46,0,199,106,101,48,110,100,139,65,31,165,154,80,62,160,86,133,46,114,79,0,66,39,44,63,50,21,104,49,94,61,124,13,42,128,73,100,78,189,112,166,129,192,112,168,65,183,82,98,170,190,125,23,73,74,137,62,43,171,50,69,39,114,27,13,180,154,20,112,0,179,162,103,111,1,178,56,100,99,185,29,175,15,131,72,179,147,30,138,107,7,50,115,128,78,119,3,113,76,43,79,176,9,87,24,85,42,196,149,9,73,87,24,169,115,95,150,109,31,63,120,156,175,28,183,22,135,76,84,14,194,73,13,17,163,105,180,87,65,75,185,109,44,16,104,173,132,156,197,67,170,88,140,100,85,109,85,37,70,22,84,45,176,106,103,24,14,133,104,113,193,59,98,20,41,8,1,5,88,15,2,120,158,172,194,190,95,184,66,192,65,193,55,172,178,99,24,25,198,56,32,184,157,95,12,193,123,67,167,167,146,3,144,25,58,121,5,142,128,74,129,84,92,113,8,29,20,184,124,95,118,12,0,31,91,147,177,137,15,77,101,62,61,108,147,162,64,114,90,16,196,21,190,13,146,58,85,182,194,51,103,71,179,134,196,129,110,172,143,183,73,177,96,102,119,15,168,174,92,114,125,137,22,72,85,62,88,199,192,10,0,146,14,13,0,42,127,116,138,117,89,25,188,149,12,163,154,127,146,26,139,198,58,179,148,85,59,20,89,102,190,158,10,97,20,156,162,147,158,180,106,146,68,176,172,27,141,169,180,121,29,34,9,51,20,156,49,88,187,123,50,81,194,140,53,171,45,105,76,127,93,187,36,88,114,155,142,113,86,77,176,168,77,97,49,91,153,63,73,165,82,94,102,197,178,42,187,52,126,24,91,17,144,158,51,50,33,196,22,49,109,89,154,161,175,92,15,99,59,112,56,121,98,178,26,166,80,18,81,33,113,20,26,116,82,58,187,61,181,136,199,176,140,179,21,30,182,6,144,135,79,99,154,96,65,35,97,56,169,170,99,13,148,66,30,150,89,74,168,140,136,18,53,82,127,22,71,38,38,101,0,59,48,157,43,92,194,12,104,47,176,29,182,180,43,69,186,65,135,138,70,131,168,127,77,171,124,46,131,3,59,3,82,83,124,144,199,124,114,58,186,39,163,143,28,147,0,131,67,186,96,174,177,111,136,147,187,7,29,63,125,41,138,132,107,82,37,194,178,57,35,113,52,52,12,85,139,61,193,158,61,157,66,26,61,132,180,194,58,50,112,38,161,60,30,197,54,134,24,14,144,73,147,100,170,138,120,65,53,15,186,2,75,166,143,131,94,60,65,167,111,183,135,189,107,57,4,42,80,129,129,0,197,96,86,144,175,140,147,161,183,108,85,4,81,1,21,115,192,29,2,38,69,20,126,106,167,19,62,103,92,41,131,44,29,8,78,184,55,56,113,32,14,81,184,32,180,90,102,184,111,19,163,53,17,107,43,176,137,23,2,55,159,120,156,46,148,160,185,162,71,136,77,154,148,153,30,154,144,125,110,181,144,193,97,150,182,18,64,123,149,104,11,47,116,171,46,2,126,105,194,160,27,162,132,195,143,152,139,5,8,158,131,46,77,91,14,181,105,123,106,167,167,115,86,146,56,127,22,61,168,177,62,62,30,96,2,191,114,83,180,110,153,144,151,151,67,54,48,136,62,11,53,49,155,187,166,141,118,102,159,10,92,148,71,177,77,151,107,186,32,181,116,136,174,57,119,116,158,13,163,33,192,46,149,19,101,164,47,52,171,29,199,173,143,125,75,13,51,155,59,65,183,27,143,136,67,187,119,18,123,61,33,109,43,8,133,187,162,171,165,179,83,143,120,186,21,80,174,70,157,168,45,199,154,72,113,106,54,76,51,115,92,177,64,167,36,69,154,140,116,139,141,37,89,98,47,189,75,114,146,143,166,42,46,120,52,40,191,106,128,134,70,189,166,109,131,148,15,25,56,82,192,153,169,15,193,105,88,146,27,62,45,197,43,197,122,184,155,96,44,99,0,126,117,75,118,142,183,144,87,96,19,73,98,176,8,68,24,175,183,126,58,128,186,83,47,84,93,59,18,67,164,121,87,168,164,169,158,119,71,54,56,125,87,197,127,148,155,41,130,10,135,20,69,157,141,190,199,61,42,117,189,94,28,50,132,16,119,140,108,53,175,99,71,118,103,42,57,82,32,18,50,172,173,160,166,192,195,186,182,2,62,51,112,44,47,56,49,138,10,190,130,98,171,34,96,13,120,37,101,13,162,154,157,123,125,78,3,118,183,42,113,185,165,63,46,1,41,64,138,105,152,45,126,21,192,161,118,96,22,121,176,50,85,150,62,81,83,26,110,138,117,148,180,44,43,79,85,194,198,189,68,187,118,67,170,192,64,34,190,97,21,2,28,140,198,186,138,43,130,16,37,40,122,9,106,16,36,110,112,178,131,84,83,107,72,30,180,111,106,17,75,37,120,108,143,79,199,153,20,197,48,93,155,189,65,192,55,193,171,104,179,54,107,65,138,92,18,49,14,110,55,3,194,152,53,131,35,176,79,160,97,11,47,11,155,21,62,35,128,68,29,122,66,73,106,39,29,108,15,153,158,59,85,108,102,110,126,107,46,122,7,163,156,105,36,48,91,2,149,22,113,42,198,142,121,39,189,19,145,61,92,0,199,63,71,144,60,67,95,185,106,26,109,45,66,122,34,135,158,195,107,127,37,66,10,194,164,53,63,137,186,4,189,19,156,72,185,58,175,107,110,88,165,179,68,3,190,84,199,196,31,185,179,40,64,63,100,65,24,198,124,148,187,101,158,135,139,169,0,55,100,129,61,67,33,97,128,185,165,58,197,131,196,18,57,102,88,61,10,31,167,111,96,33,97,196,67,175,87,79,6,146,95,115,121,88,92,105,45,90,50,103,169,153,64,153,113,4,126,15,6,136,118,155,128,172,159,45,31,167,100,149,106,57,195,92,174,123,153,135,32,123,130,176,158,104,143,19,176,39,72,3,4,120,97,23,15,152,2,44,47,67,181,103,61,173,156,71,56,102,107,53,60,0,65,162,170,86,60,83,137,83,74,139,138,195,4,141,113,122,181,84,191,167,144,122,109,61,135,193,163,46,64,33,94,12,162,23,63,22,61,174,168,155,135,28,162,142,43,164,123,182,173,187,131,96,128,137,53,51,104,199,74,152,67,95,32,100,17,164,98,180,117,135,194,92,100,130,18,28,27,149,127,127,77,28,102,41,97,65,9,12,162,139,66,143,128,162,48,20,131,85,127,76,32,66,66,74,45,114,156,168,190,199,51,122,34,82,150,117,143,141,173,83,169,82,103,199,106,78,17,87,164,70,106,42,34,84,132,168,5,174,172,0,153,107,107,34,119,114,69,10,46,146,198,93,27,0,52,124,79,80,0,98,103,83,70,115,63,144,28,131,176,34,80,192,145,183,25,93,25,41,176,11,90,42,199,198,185,96,63,58,50,195,120,41,153,55,57,58,171,123,7,30,179,28,170,26,112,94,27,108,27,81,178,21,191,196,61,90,153,24,154,134,95,195,85,23,125,160,29,131,90,160,120,119,113,39,39,59,196,13,69,118,58,191,169,58,73,57,18,92,167,91,2,114,146,149,59,145,120,192,190,9,120,107,11,127,15,191,163,120,199,47,81,93,146,167,23,40,124,176,52,64,30,4,107,172,71,69,135,42,109,85,74,155,97,41,117,117,57,87,42,116,15,161,37,62,142,53,161,89,132,26,102,44,99,1,56,15,194,45,148,63,41,25,195,162,122,93,153,35,162,61,31,187,46,150,12,173,67,100,178,43,150,21,189,50,50,116,103,199,31,132,134,132,55,113,142,83,61,68,67,158,95,155,7,169,138,194,162,181,12,106,184,33,108,140,60,79,133,51,98,24,106,147,145,133,140,121,95,11,167,153,47,162,171,126,54,2,101,10,60,59,77,122,149,95,139,76,143,54,115,160,14,30,119,16,154,29,68,182,42,197,84,160,26,186,194,138,192,3,149,89,45,178,43,103,174,34,63,64,26,12,54,96,118,78,171,30,156,65,82,137,59,133,145,94,135,131,170,51,137,70,117,35,73,87,114,103,63,44,21,29,98,165,58,175,24,18,80,50,171,100,82,81,189,151,168,126,178,0,188,29,124,121,120,181,36,142,101,116,124,139,127,198,146,84,100,153,14,160,123,15,148,115,41,137,157,159,6,85,192,14,30,132,46,47,12,67,131,18,177,43,152,90,122,7,86,94,80,10,69,19,88,18,98,58,123,181,199,177,128,190,68,81,148,116,139,196,92,88,1,80,169,56,16,181,91,101,194,175,65,5,185,151,139,6,145,12,75,128,38,162,0,166,74,133,74,177,23,52,180,48,74,68,170,119,168,56,76,91,163,50,83,152,141,153,145,175,62,159,149,32,8,149,123,151,182,165,146,62,157,163,23,199,123,66,40,164,100,191,66,46,20,28,83,126,198,163,84,82,107,148,22,111,175,101,54,40,149,14,11,65,90,126,75,26,63,77,134,43,184,70,34,41,113,152,141,82,161,43,137,34,110,130,90,147,168,8,115,42,2,195,199,84,186,64,147,69,194,161,56,0,95,162,22,160,7,84,100,193,160,11,181,20,99,83,140,190,102,26,32,60,169,73,26,68,81,125,51,91,120,12,3,95,142,22,60,80,9,146,5,80,7,153,154,155,76,3,169,101,7,5,167,167,127,20,9,126,19,113,7,128,94,80,26,195,1,182,63,12,187,14,51,89,108,88,182,68,199,8,140,148,45,94,102]);
P:=CharacteristicPolynomial(A);

Output: Magma V2.11-2     Wed Aug  4 2004 11:12:26 on modular  [Seed = 1914949532]
   -------------------------------------


Total time: 17.620 seconds, Total memory usage: 12.82MB


************** MAGMA *****************
Host spc1-chel1-3-0-cust126.lond.broadband.ntl.com. (80.2.51.126)
Time: Wed Aug  4 17:30:17 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Wed Aug  4 2004 17:30:16 on modular  [Seed = 2767499509]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d213.math.mtholyoke.edu. (138.110.3.213)
Time: Wed Aug  4 17:56:01 2004

Input: AllIrreduciblePolynomials(F_5, 3) 

Output: Magma V2.11-2     Wed Aug  4 2004 17:56:00 on modular  [Seed = 3820222890]
   -------------------------------------


>> AllIrreduciblePolynomials(F_5, 3) ;
                             ^
User error: Identifier 'F_5' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-53.mtholyoke.edu. (138.110.72.53)
Time: Wed Aug  4 18:03:55 2004

Input: AllIrreduciblePolynomials(GF(5), 3) 

Output: Magma V2.11-2     Wed Aug  4 2004 18:03:54 on modular  [Seed = 3466515133]
   -------------------------------------

{
    $.1^3 + 2*$.1 + 4,
    $.1^3 + $.1 + 4,
    $.1^3 + $.1^2 + 3*$.1 + 4,
    $.1^3 + 3*$.1^2 + 2*$.1 + 2,
    $.1^3 + 2*$.1 + 1,
    $.1^3 + 4*$.1^2 + 4*$.1 + 2,
    $.1^3 + $.1^2 + 4*$.1 + 1,
    $.1^3 + 3*$.1^2 + $.1 + 2,
    $.1^3 + $.1 + 1,
    $.1^3 + $.1^2 + 3*$.1 + 1,
    $.1^3 + 2*$.1^2 + 4*$.1 + 4,
    $.1^3 + $.1^2 + $.1 + 4,
    $.1^3 + 3*$.1^2 + 2,
    $.1^3 + 4*$.1^2 + $.1 + 2,
    $.1^3 + 4*$.1 + 3,
    $.1^3 + $.1^2 + 1,
    $.1^3 + 2*$.1^2 + $.1 + 4,
    $.1^3 + 3*$.1 + 3,
    $.1^3 + 3*$.1^2 + 4*$.1 + 1,
    $.1^3 + $.1^2 + 4*$.1 + 3,
    $.1^3 + 4*$.1^2 + 4*$.1 + 4,
    $.1^3 + 2*$.1^2 + 1,
    $.1^3 + 4*$.1^2 + 3*$.1 + 4,
    $.1^3 + 3*$.1^2 + 4,
    $.1^3 + 3*$.1^2 + $.1 + 1,
    $.1^3 + 4*$.1^2 + 3*$.1 + 1,
    $.1^3 + $.1^2 + $.1 + 3,
    $.1^3 + 4*$.1^2 + 4,
    $.1^3 + 2*$.1^2 + 2*$.1 + 3,
    $.1^3 + 4*$.1^2 + $.1 + 1,
    $.1^3 + 4*$.1 + 2,
    $.1^3 + 3*$.1^2 + 4*$.1 + 3,
    $.1^3 + 2*$.1^2 + $.1 + 3,
    $.1^3 + 3*$.1 + 2,
    $.1^3 + 2*$.1^2 + 3,
    $.1^3 + 3*$.1^2 + 2*$.1 + 3,
    $.1^3 + 2*$.1^2 + 4*$.1 + 2,
    $.1^3 + 4*$.1^2 + 3,
    $.1^3 + $.1^2 + 2,
    $.1^3 + 2*$.1^2 + 2*$.1 + 2
}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-53.mtholyoke.edu. (138.110.72.53)
Time: Wed Aug  4 18:04:21 2004

Input: AllIrreduciblePolynomials(GF(5), 1) 

Output: Magma V2.11-2     Wed Aug  4 2004 18:04:21 on modular  [Seed = 3331775130]
   -------------------------------------

{
    $.1 + 2,
    $.1 + 1,
    $.1 + 4,
    $.1,
    $.1 + 3
}

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-53.mtholyoke.edu. (138.110.72.53)
Time: Wed Aug  4 18:04:39 2004

Input: AllIrreduciblePolynomials(GF(5), 3) 

Output: Magma V2.11-2     Wed Aug  4 2004 18:04:38 on modular  [Seed = 1064248177]
   -------------------------------------

{
    $.1^3 + 2*$.1 + 4,
    $.1^3 + $.1 + 4,
    $.1^3 + $.1^2 + 3*$.1 + 4,
    $.1^3 + 3*$.1^2 + 2*$.1 + 2,
    $.1^3 + 2*$.1 + 1,
    $.1^3 + 4*$.1^2 + 4*$.1 + 2,
    $.1^3 + $.1^2 + 4*$.1 + 1,
    $.1^3 + 3*$.1^2 + $.1 + 2,
    $.1^3 + $.1 + 1,
    $.1^3 + $.1^2 + 3*$.1 + 1,
    $.1^3 + 2*$.1^2 + 4*$.1 + 4,
    $.1^3 + $.1^2 + $.1 + 4,
    $.1^3 + 3*$.1^2 + 2,
    $.1^3 + 4*$.1^2 + $.1 + 2,
    $.1^3 + 4*$.1 + 3,
    $.1^3 + $.1^2 + 1,
    $.1^3 + 2*$.1^2 + $.1 + 4,
    $.1^3 + 3*$.1 + 3,
    $.1^3 + 3*$.1^2 + 4*$.1 + 1,
    $.1^3 + $.1^2 + 4*$.1 + 3,
    $.1^3 + 4*$.1^2 + 4*$.1 + 4,
    $.1^3 + 2*$.1^2 + 1,
    $.1^3 + 4*$.1^2 + 3*$.1 + 4,
    $.1^3 + 3*$.1^2 + 4,
    $.1^3 + 3*$.1^2 + $.1 + 1,
    $.1^3 + 4*$.1^2 + 3*$.1 + 1,
    $.1^3 + $.1^2 + $.1 + 3,
    $.1^3 + 4*$.1^2 + 4,
    $.1^3 + 2*$.1^2 + 2*$.1 + 3,
    $.1^3 + 4*$.1^2 + $.1 + 1,
    $.1^3 + 4*$.1 + 2,
    $.1^3 + 3*$.1^2 + 4*$.1 + 3,
    $.1^3 + 2*$.1^2 + $.1 + 3,
    $.1^3 + 3*$.1 + 2,
    $.1^3 + 2*$.1^2 + 3,
    $.1^3 + 3*$.1^2 + 2*$.1 + 3,
    $.1^3 + 2*$.1^2 + 4*$.1 + 2,
    $.1^3 + 4*$.1^2 + 3,
    $.1^3 + $.1^2 + 2,
    $.1^3 + 2*$.1^2 + 2*$.1 + 2
}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-53.mtholyoke.edu. (138.110.72.53)
Time: Wed Aug  4 18:04:49 2004

Input: AllIrreduciblePolynomials(GF(9), 3) 

Output: Magma V2.11-2     Wed Aug  4 2004 18:04:49 on modular  [Seed = 929508238]
   -------------------------------------

{
    $.1^3 + $.1^5*$.1^2 + $.1^7*$.1 + 1,
    $.1^3 + $.1*$.1^2 + $.1*$.1 + $.1^3,
    $.1^3 + $.1^5*$.1^2 + $.1^2*$.1 + $.1^5,
    $.1^3 + $.1*$.1^2 + 2*$.1 + $.1^7,
    $.1^3 + $.1^2 + $.1^7*$.1 + $.1^3,
    $.1^3 + $.1^6*$.1 + $.1^3,
    $.1^3 + 2*$.1^2 + $.1 + $.1^6,
    $.1^3 + $.1^3*$.1^2 + $.1^3*$.1 + $.1^2,
    $.1^3 + $.1^5*$.1^2 + $.1^5*$.1 + $.1,
    $.1^3 + $.1*$.1^2 + $.1^7*$.1 + $.1^3,
    $.1^3 + 2*$.1 + 2,
    $.1^3 + $.1^3*$.1^2 + $.1*$.1 + $.1^3,
    $.1^3 + $.1^7*$.1^2 + $.1^2*$.1 + $.1^5,
    $.1^3 + $.1^6*$.1^2 + $.1^5*$.1 + $.1,
    $.1^3 + $.1^2*$.1^2 + $.1^7*$.1 + $.1^3,
    $.1^3 + 2*$.1^2 + $.1*$.1 + $.1^3,
    $.1^3 + $.1^2 + $.1^3*$.1 + $.1^5,
    $.1^3 + $.1^2*$.1 + $.1^5,
    $.1^3 + 2*$.1^2 + 2*$.1 + $.1^7,
    $.1^3 + $.1^7*$.1^2 + $.1^7,
    $.1^3 + $.1^6*$.1^2 + $.1^3*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1^2 + $.1^5*$.1 + 2,
    $.1^3 + $.1^6*$.1^2 + $.1^6*$.1 + $.1^6,
    $.1^3 + $.1^2 + $.1^6*$.1 + $.1,
    $.1^3 + $.1 + $.1^6,
    $.1^3 + $.1^2 + $.1*$.1 + $.1^6,
    $.1^3 + $.1^3*$.1^2 + $.1^5*$.1 + 2,
    $.1^3 + $.1^2*$.1^2 + $.1 + $.1,
    $.1^3 + $.1^2*$.1^2 + 1,
    $.1^3 + $.1^6*$.1^2 + $.1*$.1 + $.1^3,
    $.1^3 + 2*$.1^2 + $.1^2*$.1 + 1,
    $.1^3 + $.1*$.1^2 + $.1*$.1 + $.1^6,
    $.1^3 + 2*$.1^2 + $.1^5*$.1 + 2,
    $.1^3 + $.1^6*$.1 + $.1^6,
    $.1^3 + $.1^2*$.1^2 + $.1^6*$.1 + $.1,
    $.1^3 + $.1^2*$.1^2 + $.1*$.1 + $.1^6,
    $.1^3 + $.1*$.1^2 + 2*$.1 + $.1^2,
    $.1^3 + $.1^5*$.1^2 + $.1^5*$.1 + 2,
    $.1^3 + $.1*$.1^2 + $.1^7*$.1 + $.1^6,
    $.1^3 + 2*$.1^2 + 1,
    $.1^3 + $.1^2 + $.1^2*$.1 + $.1^3,
    $.1^3 + 2*$.1 + $.1^7,
    $.1^3 + $.1^7*$.1^2 + $.1^7*$.1 + $.1^3,
    $.1^3 + $.1^3*$.1^2 + $.1*$.1 + $.1^6,
    $.1^3 + $.1^2*$.1^2 + 2*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1^2 + $.1^7*$.1 + $.1^6,
    $.1^3 + $.1^5*$.1^2 + $.1^3*$.1 + $.1^5,
    $.1^3 + 2*$.1^2 + $.1^6*$.1 + $.1,
    $.1^3 + $.1^2 + $.1 + 2,
    $.1^3 + $.1^7*$.1^2 + $.1^2*$.1 + 1,
    $.1^3 + $.1^3*$.1^2 + 2*$.1 + $.1^2,
    $.1^3 + $.1^6*$.1^2 + 1,
    $.1^3 + $.1^2*$.1^2 + $.1^2*$.1 + $.1^3,
    $.1^3 + $.1^6*$.1^2 + $.1^3*$.1 + $.1^5,
    $.1^3 + $.1*$.1^2 + $.1^5,
    $.1^3 + $.1*$.1^2 + $.1 + 2,
    $.1^3 + $.1^2 + $.1^3*$.1 + 1,
    $.1^3 + $.1^2*$.1 + 1,
    $.1^3 + $.1^2 + $.1^6*$.1 + 2,
    $.1^3 + $.1^7*$.1^2 + $.1 + $.1,
    $.1^3 + $.1^7*$.1^2 + $.1^3*$.1 + $.1^5,
    $.1^3 + $.1^6*$.1^2 + $.1^6*$.1 + $.1,
    $.1^3 + $.1^5*$.1^2 + 2*$.1 + $.1^2,
    $.1^3 + $.1*$.1^2 + $.1^6*$.1 + 2,
    $.1^3 + $.1 + $.1,
    $.1^3 + 2*$.1^2 + $.1^2*$.1 + $.1^3,
    $.1^3 + $.1^7*$.1^2 + $.1^6*$.1 + $.1,
    $.1^3 + 2*$.1^2 + $.1^5*$.1 + $.1^7,
    $.1^3 + $.1^3*$.1^2 + $.1^5,
    $.1^3 + $.1^3*$.1^2 + $.1 + 2,
    $.1^3 + $.1^5*$.1^2 + $.1^2*$.1 + $.1^3,
    $.1^3 + $.1^2 + $.1^7*$.1 + $.1,
    $.1^3 + $.1^5*$.1^2 + $.1^5*$.1 + $.1^7,
    $.1^3 + $.1^7*$.1^2 + 2*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1^2 + $.1*$.1 + $.1,
    $.1^3 + $.1^6*$.1^2 + $.1^2*$.1 + $.1^3,
    $.1^3 + $.1^5*$.1^2 + $.1^5,
    $.1^3 + $.1^5*$.1^2 + $.1 + 2,
    $.1^3 + $.1^3*$.1^2 + $.1*$.1 + $.1,
    $.1^3 + $.1^2 + $.1^6,
    $.1^3 + $.1^3*$.1^2 + 2*$.1 + $.1^5,
    $.1^3 + $.1*$.1^2 + $.1 + $.1^7,
    $.1^3 + 2*$.1^2 + 2*$.1 + $.1^5,
    $.1^3 + $.1^3*$.1^2 + $.1^7*$.1 + $.1,
    $.1^3 + $.1^7*$.1^2 + $.1 + 2,
    $.1^3 + $.1^2*$.1^2 + $.1 + $.1^7,
    $.1^3 + $.1*$.1^2 + $.1^3*$.1 + $.1^3,
    $.1^3 + $.1^7*$.1^2 + $.1^3*$.1 + 1,
    $.1^3 + $.1^3*$.1^2 + $.1^5*$.1 + $.1^2,
    $.1^3 + $.1*$.1^2 + $.1*$.1 + 2,
    $.1^3 + $.1^2 + 2*$.1 + 1,
    $.1^3 + $.1^6*$.1 + 2,
    $.1^3 + 2*$.1^2 + $.1^6,
    $.1^3 + $.1^3*$.1^2 + $.1^6*$.1 + $.1^7,
    $.1^3 + $.1^6*$.1^2 + $.1^2*$.1 + $.1^6,
    $.1^3 + $.1*$.1^2 + $.1^7*$.1 + 2,
    $.1^3 + 2*$.1 + $.1^5,
    $.1^3 + $.1^2*$.1^2 + 2*$.1 + 1,
    $.1^3 + $.1^7*$.1^2 + $.1^2*$.1 + $.1^6,
    $.1^3 + $.1^6*$.1^2 + $.1^5*$.1 + $.1^2,
    $.1^3 + $.1^6*$.1^2 + $.1^6,
    $.1^3 + $.1*$.1^2 + $.1^2*$.1 + $.1,
    $.1^3 + $.1*$.1^2 + $.1^5*$.1 + $.1^5,
    $.1^3 + $.1^2 + $.1 + $.1^2,
    $.1^3 + $.1^5*$.1^2 + $.1^6*$.1 + $.1^7,
    $.1^3 + 2*$.1^2 + $.1*$.1 + 2,
    $.1^3 + $.1^2*$.1 + $.1^6,
    $.1^3 + $.1^6*$.1^2 + $.1^3*$.1 + $.1^3,
    $.1^3 + $.1^2*$.1^2 + $.1^5*$.1 + $.1^5,
    $.1^3 + 2*$.1^2 + $.1^7*$.1 + 2,
    $.1^3 + $.1^2 + $.1*$.1 + $.1^7,
    $.1^3 + $.1 + $.1^7,
    $.1^3 + $.1^3*$.1^2 + $.1^2*$.1 + $.1,
    $.1^3 + $.1^7*$.1^2 + $.1^6*$.1 + $.1^7,
    $.1^3 + $.1^2*$.1^2 + $.1^3*$.1 + $.1^6,
    $.1^3 + $.1^2 + 2*$.1 + $.1^3,
    $.1^3 + 2*$.1^2 + $.1^5*$.1 + $.1^5,
    $.1^3 + $.1^3*$.1^2 + $.1^3,
    $.1^3 + $.1^6*$.1 + $.1^7,
    $.1^3 + $.1^6*$.1^2 + 2*$.1 + 1,
    $.1^3 + $.1^2*$.1^2 + $.1^6*$.1 + $.1^2,
    $.1^3 + $.1^6*$.1^2 + $.1^7*$.1 + 2,
    $.1^3 + $.1^2*$.1^2 + $.1*$.1 + $.1^7,
    $.1^3 + $.1^5*$.1^2 + $.1^2*$.1 + $.1,
    $.1^3 + 2*$.1^2 + $.1 + $.1^2,
    $.1^3 + $.1^2 + $.1^2*$.1 + 2,
    $.1^3 + 2*$.1^2 + $.1^3*$.1 + $.1^6,
    $.1^3 + $.1^7*$.1^2 + $.1^7*$.1 + 2,
    $.1^3 + $.1^5*$.1^2 + $.1^3,
    $.1^3 + 2*$.1 + 1,
    $.1^3 + $.1^5*$.1^2 + $.1^3*$.1 + $.1^6,
    $.1^3 + $.1^2 + $.1^5*$.1 + 1,
    $.1^3 + $.1^2 + 2,
    $.1^3 + $.1^7*$.1^2 + $.1^5*$.1 + $.1^5,
    $.1^3 + $.1^6*$.1^2 + $.1 + $.1^2,
    $.1^3 + $.1^3*$.1^2 + $.1^7*$.1 + $.1^7,
    $.1^3 + $.1*$.1^2 + $.1^5*$.1 + 1,
    $.1^3 + $.1^5*$.1^2 + $.1^6*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1 + $.1,
    $.1^3 + $.1^5*$.1^2 + $.1*$.1 + $.1^7,
    $.1^3 + $.1^2 + $.1^6*$.1 + $.1^5,
    $.1^3 + 2*$.1^2 + $.1^7*$.1 + $.1^7,
    $.1^3 + $.1^7*$.1^2 + $.1^3,
    $.1^3 + $.1^3*$.1^2 + $.1^2*$.1 + 2,
    $.1^3 + $.1^7*$.1^2 + $.1^3*$.1 + $.1^6,
    $.1^3 + $.1^2*$.1^2 + 2,
    $.1^3 + $.1*$.1^2 + $.1^3*$.1 + $.1,
    $.1^3 + $.1^5*$.1^2 + 2*$.1 + $.1^3,
    $.1^3 + $.1 + $.1^2,
    $.1^3 + $.1^5*$.1^2 + $.1^7*$.1 + $.1^7,
    $.1^3 + $.1^3*$.1^2 + $.1 + $.1^5,
    $.1^3 + $.1^2*$.1^2 + $.1^3*$.1 + $.1,
    $.1^3 + $.1^7*$.1^2 + $.1*$.1 + $.1^7,
    $.1^3 + $.1^2*$.1^2 + $.1^6*$.1 + $.1^5,
    $.1^3 + $.1^6*$.1^2 + $.1^7*$.1 + $.1^7,
    $.1^3 + $.1*$.1^2 + 2*$.1 + $.1^6,
    $.1^3 + $.1^6*$.1 + $.1^2,
    $.1^3 + $.1^3*$.1^2 + $.1^3*$.1 + $.1,
    $.1^3 + $.1^2 + $.1^2*$.1 + $.1^7,
    $.1^3 + $.1^3*$.1^2 + $.1^6*$.1 + $.1^5,
    $.1^3 + $.1*$.1^2 + $.1^2*$.1 + $.1^7,
    $.1^3 + 2*$.1^2 + $.1^3*$.1 + $.1,
    $.1^3 + $.1^2 + $.1^5*$.1 + $.1^3,
    $.1^3 + 2*$.1 + $.1^3,
    $.1^3 + 2*$.1^2 + $.1^6*$.1 + $.1^5,
    $.1^3 + $.1^3*$.1^2 + 2*$.1 + $.1^6,
    $.1^3 + $.1^6*$.1^2 + $.1^5*$.1 + 1,
    $.1^3 + $.1^6*$.1^2 + 2,
    $.1^3 + $.1^6*$.1^2 + $.1 + $.1^5,
    $.1^3 + $.1^2*$.1^2 + $.1^2*$.1 + $.1^7,
    $.1^3 + $.1*$.1^2 + $.1^5*$.1 + $.1^3,
    $.1^3 + 2*$.1^2 + $.1*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1 + 2,
    $.1^3 + $.1^7*$.1^2 + $.1^5*$.1 + 1,
    $.1^3 + $.1*$.1^2 + $.1 + 1,
    $.1^3 + $.1^6*$.1^2 + $.1^6*$.1 + $.1^5,
    $.1^3 + $.1*$.1^2 + $.1,
    $.1^3 + $.1^5*$.1^2 + $.1*$.1 + $.1^2,
    $.1^3 + $.1^5*$.1^2 + 2*$.1 + $.1^6,
    $.1^3 + $.1 + $.1^5,
    $.1^3 + 2*$.1^2 + $.1^2*$.1 + $.1^7,
    $.1^3 + $.1^6*$.1^2 + $.1*$.1 + $.1^2,
    $.1^3 + $.1^6*$.1^2 + 2*$.1 + $.1^6,
    $.1^3 + $.1^5*$.1^2 + $.1^7*$.1 + $.1^2,
    $.1^3 + $.1^2 + 2*$.1 + $.1,
    $.1^3 + $.1^3*$.1^2 + $.1 + 1,
    $.1^3 + $.1^7*$.1^2 + $.1*$.1 + $.1^2,
    $.1^3 + $.1^3*$.1^2 + $.1^3*$.1 + 2,
    $.1^3 + $.1^7*$.1^2 + 2*$.1 + $.1^6,
    $.1^3 + $.1^6*$.1^2 + $.1^7*$.1 + $.1^2,
    $.1^3 + $.1^6*$.1^2 + $.1^2*$.1 + $.1^7,
    $.1^3 + 2*$.1^2 + $.1 + 1,
    $.1^3 + 2*$.1^2 + $.1^3*$.1 + 2,
    $.1^3 + $.1^5*$.1^2 + $.1 + 1,
    $.1^3 + $.1^5*$.1^2 + $.1,
    $.1^3 + 2*$.1^2 + $.1^6*$.1 + 1,
    $.1^3 + $.1^2 + $.1^2,
    $.1^3 + $.1^2*$.1^2 + $.1^2*$.1 + $.1^2,
    $.1^3 + $.1^5*$.1^2 + $.1^6*$.1 + 1,
    $.1^3 + $.1^2*$.1^2 + $.1^5*$.1 + $.1^6,
    $.1^3 + $.1^7*$.1^2 + $.1,
    $.1^3 + $.1^7*$.1^2 + $.1 + 1,
    $.1^3 + 2*$.1^2 + $.1^7*$.1 + $.1^5,
    $.1^3 + $.1^3*$.1^2 + $.1^2*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1^2 + $.1^2,
    $.1^3 + $.1^6*$.1^2 + $.1*$.1 + $.1^5,
    $.1^3 + $.1^2*$.1^2 + $.1^3*$.1 + $.1^7,
    $.1^3 + $.1*$.1^2 + $.1^6*$.1 + $.1^3,
    $.1^3 + $.1^2 + $.1*$.1 + 1,
    $.1^3 + $.1^7*$.1^2 + $.1*$.1 + $.1^5,
    $.1^3 + $.1^2 + $.1^7*$.1 + 1,
    $.1^3 + $.1^6*$.1 + 1,
    $.1^3 + 2*$.1^2 + $.1^2,
    $.1^3 + $.1^7*$.1^2 + 2*$.1 + $.1,
    $.1^3 + $.1^3*$.1^2 + $.1^6*$.1 + $.1^3,
    $.1^3 + $.1^7*$.1^2 + $.1^7*$.1 + $.1^5,
    $.1^3 + $.1^2*$.1^2 + 2*$.1 + 2,
    $.1^3 + $.1^5*$.1^2 + $.1 + $.1^3,
    $.1^3 + $.1*$.1^2 + $.1^2*$.1 + $.1^5,
    $.1^3 + $.1^2 + $.1^5*$.1 + $.1,
    $.1^3 + 2*$.1 + $.1,
    $.1^3 + $.1^5*$.1^2 + $.1^3*$.1 + $.1^7,
    $.1^3 + $.1^2 + $.1 + $.1^6,
    $.1^3 + $.1^2*$.1^2 + $.1^7*$.1 + 1,
    $.1^3 + $.1^7*$.1^2 + $.1^5*$.1 + $.1^6,
    $.1^3 + $.1^6*$.1^2 + $.1 + $.1^3,
    $.1^3 + $.1*$.1^2 + $.1^7,
    $.1^3 + $.1^2 + $.1^3*$.1 + $.1^2,
    $.1^3 + $.1^2*$.1 + $.1^2,
    $.1^3 + 2*$.1^2 + 2*$.1 + 2,
    $.1^3 + $.1^3*$.1^2 + $.1^7*$.1 + 1,
    $.1^3 + $.1^5*$.1^2 + $.1*$.1 + 1,
    $.1^3 + $.1^2*$.1^2 + $.1 + $.1^6,
    $.1^3 + $.1*$.1^2 + $.1^3*$.1 + $.1^2,
    $.1^3 + $.1*$.1^2 + $.1^6*$.1 + $.1^6,
    $.1^3 + $.1 + $.1^3,
    $.1^3 + $.1^3*$.1^2 + $.1^5*$.1 + $.1,
    $.1^3 + $.1^7*$.1^2 + $.1^6*$.1 + $.1^3,
    $.1^3 + $.1^3*$.1^2 + $.1^7,
    $.1^3 + $.1^6*$.1^2 + 2*$.1 + 2
}

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host ma-dual72-53.mtholyoke.edu. (138.110.72.53)
Time: Wed Aug  4 18:05:53 2004

Input: AllIrreduciblePolynomials(GF(9), 1) 

Output: Magma V2.11-2     Wed Aug  4 2004 18:05:52 on modular  [Seed = 544226520]
   -------------------------------------

{
    $.1 + $.1^6,
    $.1 + $.1^2,
    $.1 + $.1^5,
    $.1 + $.1,
    $.1 + 2,
    $.1 + 1,
    $.1 + $.1^7,
    $.1 + $.1^3,
    $.1
}

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Wed Aug  4 23:20:28 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Wed Aug  4 2004 23:20:27 on modular  [Seed = 3314885508]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 03:46:47 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug  5 2004 03:46:47 on modular  [Seed = 828478952]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 03:47:25 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug  5 2004 03:47:25 on modular  [Seed = 508475693]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 03:47:34 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug  5 2004 03:47:34 on modular  [Seed = 373731646]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 03:56:07 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug  5 2004 03:56:06 on modular  [Seed = 173712162]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:11:36 2004

Input: Factorization(10^64+1)


Output: Magma V2.11-2     Thu Aug  5 2004 04:11:35 on modular  [Seed = 1159065548]
   -------------------------------------

[ <1265011073, 1>, <15343168188889137818369, 1>, 
<515217525265213267447869906815873, 1> ]

Total time: 0.659 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:11:49 2004

Input: Factorization(20^64+1)


Output: Magma V2.11-2     Thu Aug  5 2004 04:11:48 on modular  [Seed = 3186431815]
   -------------------------------------

[ <4213987444481, 1>, <19781545588481, 1>, <82832842974154279534081, 1>, 
<26715523979628786958854098728207361, 1> ]

Total time: 0.649 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:11:57 2004

Input: Factorization(48^64+1)


Output: Magma V2.11-2     Thu Aug  5 2004 04:11:57 on modular  [Seed = 3051691846]
   -------------------------------------

[ <417813806500107334422529, 1>, <171384369229251163605657601, 1>, 
<5552456881248637644862314271332224732069465077963326031873, 1> ]

Total time: 0.740 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:12:23 2004

Input: Factorization(74^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:12:16 on modular  [Seed = 2919040883]
   -------------------------------------

[ <4993, 1>, <85598961686630541019703711504465625022979806006329364706055995454\
912745801978400934751164259420206853171729389071489, 1> ]

Total time: 7.009 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:12:33 2004

Input: Factorization(86^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:12:32 on modular  [Seed = 2784300907]
   -------------------------------------

[ <78900878834510645468600608760004949814056831637765367937, 1>, 
<81436488526243427856680489618098138294437750338052584204172809607041, 1> ]

Total time: 1.010 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:13:01 2004

Input: Factorization(132^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:12:40 on modular  [Seed = 2647471963]
   -------------------------------------



************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:13:12 2004

Input: Factorization(140^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:13:11 on modular  [Seed = 2512730300]
   -------------------------------------

[ <12289, 1>, <2574337, 1>, <76098975831041, 1>, 
<934616682192372585604215164559778946714873470800789511722021208604404690841797\
42104482556143365887650587291186177, 1> ]

Total time: 0.659 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:13:46 2004

Input: Factorization(194^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:13:25 on modular  [Seed = 2380079254]
   -------------------------------------



************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:14:15 2004

Input: Factorization(254^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:13:54 on modular  [Seed = 2245339385]
   -------------------------------------



************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:15:01 2004

Input: Factorization(200^64+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:14:41 on modular  [Seed = 4070727613]
   -------------------------------------



************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:15:36 2004

Input: Factorization(12^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:15:17 on modular  [Seed = 3954918976]
   -------------------------------------

[ <257, 1>, <531210157490247155121100985879261370135996785169317634891322426295\
4673066874179441584772343144224572301982521857107589870210046272536321, 1> ]

Total time: 19.149 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:15:54 2004

Input: Factorization(14^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:15:53 on modular  [Seed = 3820179044]
   -------------------------------------

[ <257, 1>, <100497382788383295179961898289105815085380571534081, 1>, 
<196020138507203278697869533834579351411809002450889699299814209319971266212961\
08976373946936321, 1> ]

Total time: 1.409 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:16:21 2004

Input: Factorization(18^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:16:01 on modular  [Seed = 3683350052]
   -------------------------------------

[ <13183521051511297, 1>, <4944182613719870977, 1>, 
<725696006448854888453708776743258949473501279877685909103412548833896377843152\
575870233525080178308106769190133140108902828033, 1> ]

Total time: 19.729 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:16:31 2004

Input: Factorization(20^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:16:30 on modular  [Seed = 3498081584]
   -------------------------------------

[ <257, 1>, <36097, 1>, <12818782843691777, 1>, 
<1824448644331953437805185594358681323803649, 1>, 
<156839980152800728021646204730001269580086006946735576131204987806231126567668\
202731547125644464093953, 1> ]

Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:16:59 2004

Input: Factorization(22^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:16:38 on modular  [Seed = 3365430544]
   -------------------------------------



************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:17:59 2004

Input: Factorization(24^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:17:58 on modular  [Seed = 1815920666]
   -------------------------------------

[ <257, 1>, <81409, 1>, <854017, 1>, <5517313, 1>, <109622687233, 1>, 
<213489965156632342154361892190421761, 1>, 
<201354503369125007945828290128475361741923145825397793187345381614654872256304\
776207726862388216546131502108673, 1> ]

Total time: 0.649 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:18:10 2004

Input: Factorization(60^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:18:09 on modular  [Seed = 1948571765]
   -------------------------------------

[ <9145601, 1>, <15335609291619082678943874049, 1>, 
<286053169027760556908016110422204196791335968376084286926628309053470274372654\
2375803548153576263567043090168320707499670503798905537468098481691741318578951\
188732652670475664823852636777314049, 1> ]

Total time: 1.589 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-169-134.dynamic.hinet.net. (220.136.169.134)
Time: Thu Aug  5 04:18:39 2004

Input: Factorization(56^128+1)



Output: Magma V2.11-2     Thu Aug  5 2004 04:18:18 on modular  [Seed = 2083311734]
   -------------------------------------



************** MAGMA *****************
Host lxbill.macs.hw.ac.uk. (137.195.27.25)
Time: Thu Aug  5 07:21:37 2004

Input: a>=10 and a>=100


Output: Magma V2.11-2     Thu Aug  5 2004 07:21:35 on modular  [Seed = 5462397]
   -------------------------------------


>> a>=10 and a>=100
    ^
User error: bad syntax

Total time: 0.649 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:20:19 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:20:18 on modular  [Seed = 190348892]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 190348892
Time to this point: 0.6
Illegal instruction

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:18 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:17 on modular  [Seed = 322987743]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 322987743
Time to this point: 0.6
Illegal instruction

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:21 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:20 on modular  [Seed = 457731795]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 457731795
Time to this point: 0.6
Illegal instruction

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:23 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:22 on modular  [Seed = 594564840]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 594564840
Time to this point: 0.6
Illegal instruction

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:26 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:25 on modular  [Seed = 729308927]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 729308927
Time to this point: 0.61
Illegal instruction

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:28 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:27 on modular  [Seed = 861947621]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 861947621
Time to this point: 0.6
Illegal instruction

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:30 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:30 on modular  [Seed = 996691688]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 996691688
Time to this point: 0.61
Illegal instruction

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:34 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:33 on modular  [Seed = 3281040927]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 3281040927
Time to this point: 0.6
Illegal instruction

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache4.nottingham.ac.uk. (128.243.220.42)
Time: Thu Aug  5 09:22:38 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


Output: Magma V2.11-2     Thu Aug  5 2004 09:22:37 on modular  [Seed = 3415784979]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 3415784979
Time to this point: 0.61
Illegal instruction

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:37:58 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug  5 2004 09:37:58 on modular  [Seed = 3769866643]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:38:48 2004

Input: cyc:=CyclotomicField(8);


Output: Magma V2.11-2     Thu Aug  5 2004 09:38:48 on modular  [Seed = 3938030535]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:39:37 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);


Output: Magma V2.11-2     Thu Aug  5 2004 09:39:36 on modular  [Seed = 4256072736]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:42:31 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
for e in eqns do
e;
end for;


Output: Magma V2.11-2     Thu Aug  5 2004 09:42:31 on modular  [Seed = 2445470099]
   -------------------------------------

X - z^3*W
Y + z^3*Z
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:42:41 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];


Output: Magma V2.11-2     Thu Aug  5 2004 09:42:41 on modular  [Seed = 2580210061]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:42:55 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;


Output: Magma V2.11-2     Thu Aug  5 2004 09:42:55 on modular  [Seed = 2717047227]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:10 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:10 on modular  [Seed = 2851787138]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:21 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:20 on modular  [Seed = 2984429964]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 2984429964
Time to this point: 0.65
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.600 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:38 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:38 on modular  [Seed = 3119169910]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 3119169910
Time to this point: 0.64
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:42 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:41 on modular  [Seed = 1075001481]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1075001481
Time to this point: 0.64
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:44 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:44 on modular  [Seed = 1209741468]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1209741468
Time to this point: 0.64
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:46 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:46 on modular  [Seed = 1342384262]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1342384262
Time to this point: 0.64
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:48 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:47 on modular  [Seed = 1477124239]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1477124239
Time to this point: 0.63
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:49 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:48 on modular  [Seed = 1613961392]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1613961392
Time to this point: 0.63
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:50 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:50 on modular  [Seed = 1748701370]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1748701370
Time to this point: 0.63
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:43:54 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:43:53 on modular  [Seed = 1881344173]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 1881344173
Time to this point: 0.64
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Thu Aug  5 09:45:13 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
S;
Dimension(S);
Points(S);


Output: Magma V2.11-2     Thu Aug  5 2004 09:45:12 on modular  [Seed = 2016084180]
   -------------------------------------

Scheme over Univariate rational function field over cyc defined by
X - z^3*W,
Y + z^3*Z,
Z^3 + Z*W^2 + (-z*u^3 - z^3*u)*W^3
0


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 2016084180
Time to this point: 0.64
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:10:20 2004

Input: 504^1187 mod 35;


Output: Magma V2.11-2     Thu Aug  5 2004 14:10:19 on modular  [Seed = 173617991]
   -------------------------------------

14

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:11:32 2004

Input: Factorization(2881);

Output: Magma V2.11-2     Thu Aug  5 2004 14:11:31 on modular  [Seed = 322972166]
   -------------------------------------

[ <43, 1>, <67, 1> ]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:14:41 2004

Input: 42*67;

Output: Magma V2.11-2     Thu Aug  5 2004 14:14:40 on modular  [Seed = 457712461]
   -------------------------------------

2814

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:15:08 2004

Input: 42*66;


Output: Magma V2.11-2     Thu Aug  5 2004 14:15:07 on modular  [Seed = 594549582]
   -------------------------------------

2772

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:15:24 2004

Input: 1/5 mod 2772;


Output: Magma V2.11-2     Thu Aug  5 2004 14:15:23 on modular  [Seed = 679153749]
   -------------------------------------


>> 1/5 mod 2772;
       ^
Runtime error in 'mod': Bad argument types
Argument types given: FldRatElt, FldRatElt

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:15:35 2004

Input: 5^(-1) mod 2772;


Output: Magma V2.11-2     Thu Aug  5 2004 14:15:34 on modular  [Seed = 811796528]
   -------------------------------------


>> 5^(-1) mod 2772;
          ^
Runtime error in 'mod': Bad argument types
Argument types given: FldRatElt, FldRatElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:15:46 2004

Input: Integers(2772) ! 1/5;


Output: Magma V2.11-2     Thu Aug  5 2004 14:15:45 on modular  [Seed = 946536495]
   -------------------------------------

1109

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:17:34 2004

Input: (Integers(2881) ! 504)^1109;

Output: Magma V2.11-2     Thu Aug  5 2004 14:17:33 on modular  [Seed = 3483170612]
   -------------------------------------

400

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:21:36 2004

Input: (504 mod 2881)^1109;

Output: Magma V2.11-2     Thu Aug  5 2004 14:21:36 on modular  [Seed = 4022129689]
   -------------------------------------

9896119206912106898089193835194961518414664435645949247511826806281068564221305\
1416113375058416658646025849046604891181521243671085105535917387545054069637401\
2664111052944020902306626157978774158167309892786299168736482979601031494850955\
0922808245213644920056884052130032110854782380306481612667539398947016680749640\
0070949218205491716982740768054378797192210305704040459966812428140802572065084\
2554997514407871674068054519341244634668014923195819676477513382283209275114755\
3388850093955181370503382887743510987763115684012463044628668645653732116561077\
4699206436970769195585913964137392048877333299095962483643145457162529444119493\
8145253444036540801132044758603094476773930593998865134076856670087566767131497\
1770459177887289672135403472341220131744288356151404863273673116628965622910346\
9009314498702700825518331568933321044903727687563893318329397361646363172436171\
5446409852328941256479416538411773078486563298673831346576708479971036206911583\
3458032935315229214069264688183290146861791304403352894901544719659303122327960\
9301041895105531240607051824116915225460265910379660472603687345514456445463550\
3563432024381981057162931806451314586463763182305825274514524486731131493141083\
5508018848073342496430531190563054972649540695176208217561634018758746616625900\
9045649774408982052171449904383498965785048271193903803694678595876100158881085\
5088226235626076762916863316085273582197825721821153035827815513899066077033925\
6038272509005398192094447572409020738767849526452075935540185121890005639069102\
2249279552186009005092049729811377384230816604486285468249710692308981334899471\
8309985967682009154958955775317779944572583220429741398107293640399320636659089\
6403845264176064222122427225225390516099075987599382010245924795182515598511752\
6419138567407470590237601849216591412252182235571357193536609763937335243284632\
0172099622497584796340042290874117320640389022161854489454629130314224852922312\
9117790598086463223213353385032670788674590319037142759360296951181568382875404\
3593501623423858323994388544123062446110280108292873313581001329539294341372679\
4383632590853208648236354965938099478898596493912825330123891676687665562459142\
6071260719256243064544186513294471240154626398984169842674263915770700142783811\
5254350840932653121148501958019423257905711172552239714222546117149036660563344\
2043924335090585140854392043035372209889065365714840713604896365347721772313026\
0796152497947607931109085830526474992684524810532254152381391608311300180845729\
5071694210218502206879651370904026382437579120255040405337635741370030944432239\
8899488971286523380386373790230060345512236521036893672637267932694297309572504\
1254420710214323955241177754087679250605549388141922381930308601771799775728446\
4127493529702972578156558532971929459588846613188052663957387782420247537548335\
1938786630800771165150465452286555277156118952772157425399694739386022400996289\
5433897927573004374019251942211835215820432203687334049939900588205142788729391\
27201776497373530327017063332723867683616360492520804508636302401700102144

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:24:03 2004

Input: 26^2 + 1 mod 1927;

Output: Magma V2.11-2     Thu Aug  5 2004 14:24:02 on modular  [Seed = 4121350129]
   -------------------------------------

677

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:24:17 2004

Input: 677^2 + 1 mod 1927;

Output: Magma V2.11-2     Thu Aug  5 2004 14:24:17 on modular  [Seed = 4256090090]
   -------------------------------------

458330

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:24:26 2004

Input: (677^2 + 1) mod 1927;

Output: Magma V2.11-2     Thu Aug  5 2004 14:24:26 on modular  [Seed = 2245443481]
   -------------------------------------

1631

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host eva-wlan-108.AirBears.Berkeley.EDU. (169.229.253.123)
Time: Thu Aug  5 14:25:41 2004

Input: Gcd(21,1927);

Output: Magma V2.11-2     Thu Aug  5 2004 14:25:40 on modular  [Seed = 2329522280]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host evans-100-14.Lib.Berkeley.EDU. (128.32.158.187)
Time: Thu Aug  5 14:52:48 2004

Input: Integers (2881)! 504^1109;

Output: Magma V2.11-2     Thu Aug  5 2004 14:52:47 on modular  [Seed = 3051779340]
   -------------------------------------

400

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host evans-100-14.Lib.Berkeley.EDU. (128.32.158.187)
Time: Thu Aug  5 14:53:21 2004

Input: Integers (2881)! 504^1109;
Integers (2881)! 1874^1109;

Output: Magma V2.11-2     Thu Aug  5 2004 14:53:20 on modular  [Seed = 3152574685]
   -------------------------------------

400
1902

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host evans-100-14.Lib.Berkeley.EDU. (128.32.158.187)
Time: Thu Aug  5 14:54:36 2004

Input: Integers (2881)! 504^1109;
Integers (2881)! 1874^1109;
Integers (2881)! 0347^1109;
Integers (2881)! 0515^1109;
Integers (2881)! 2088^1109;
Integers (2881)! 2356^1109;


Output: Magma V2.11-2     Thu Aug  5 2004 14:54:36 on modular  [Seed = 1277136745]
   -------------------------------------

400
1902
714
214
1100
1904

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host evans-100-14.Lib.Berkeley.EDU. (128.32.158.187)
Time: Thu Aug  5 14:55:22 2004

Input: Integers (2881)! 504^1109;
Integers (2881)! 1874^1109;
Integers (2881)! 0347^1109;
Integers (2881)! 0515^1109;
Integers (2881)! 2088^1109;
Integers (2881)! 2356^1109;
Integers (2881)! 0736^1109;
Integers (2881)! 0468^1109;

Output: Magma V2.11-2     Thu Aug  5 2004 14:55:22 on modular  [Seed = 1192526996]
   -------------------------------------

400
1902
714
214
1100
1904
200
1004

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 16:41:16 2004

Input: AllIrreduciblePolynomials(GF(5), 1)

Output: Magma V2.11-2     Thu Aug  5 2004 16:41:16 on modular  [Seed = 1091738470]
   -------------------------------------

{
    $.1 + 2,
    $.1 + 1,
    $.1 + 4,
    $.1,
    $.1 + 3
}

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 16:41:31 2004

Input: AllIrreduciblePolynomials(GF(5), 2)

Output: Magma V2.11-2     Thu Aug  5 2004 16:41:31 on modular  [Seed = 1493861225]
   -------------------------------------

{
    $.1^2 + 3*$.1 + 4,
    $.1^2 + 2,
    $.1^2 + 4*$.1 + 1,
    $.1^2 + 3*$.1 + 3,
    $.1^2 + $.1 + 2,
    $.1^2 + 2*$.1 + 4,
    $.1^2 + $.1 + 1,
    $.1^2 + 2*$.1 + 3,
    $.1^2 + 3,
    $.1^2 + 4*$.1 + 2
}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 16:44:30 2004

Input: AllIrreduciblePolynomials(GF(5), 3)

Output: Magma V2.11-2     Thu Aug  5 2004 16:44:30 on modular  [Seed = 1664138758]
   -------------------------------------

{
    $.1^3 + 2*$.1 + 4,
    $.1^3 + $.1 + 4,
    $.1^3 + $.1^2 + 3*$.1 + 4,
    $.1^3 + 3*$.1^2 + 2*$.1 + 2,
    $.1^3 + 2*$.1 + 1,
    $.1^3 + 4*$.1^2 + 4*$.1 + 2,
    $.1^3 + $.1^2 + 4*$.1 + 1,
    $.1^3 + 3*$.1^2 + $.1 + 2,
    $.1^3 + $.1 + 1,
    $.1^3 + $.1^2 + 3*$.1 + 1,
    $.1^3 + 2*$.1^2 + 4*$.1 + 4,
    $.1^3 + $.1^2 + $.1 + 4,
    $.1^3 + 3*$.1^2 + 2,
    $.1^3 + 4*$.1^2 + $.1 + 2,
    $.1^3 + 4*$.1 + 3,
    $.1^3 + $.1^2 + 1,
    $.1^3 + 2*$.1^2 + $.1 + 4,
    $.1^3 + 3*$.1 + 3,
    $.1^3 + 3*$.1^2 + 4*$.1 + 1,
    $.1^3 + $.1^2 + 4*$.1 + 3,
    $.1^3 + 4*$.1^2 + 4*$.1 + 4,
    $.1^3 + 2*$.1^2 + 1,
    $.1^3 + 4*$.1^2 + 3*$.1 + 4,
    $.1^3 + 3*$.1^2 + 4,
    $.1^3 + 3*$.1^2 + $.1 + 1,
    $.1^3 + 4*$.1^2 + 3*$.1 + 1,
    $.1^3 + $.1^2 + $.1 + 3,
    $.1^3 + 4*$.1^2 + 4,
    $.1^3 + 2*$.1^2 + 2*$.1 + 3,
    $.1^3 + 4*$.1^2 + $.1 + 1,
    $.1^3 + 4*$.1 + 2,
    $.1^3 + 3*$.1^2 + 4*$.1 + 3,
    $.1^3 + 2*$.1^2 + $.1 + 3,
    $.1^3 + 3*$.1 + 2,
    $.1^3 + 2*$.1^2 + 3,
    $.1^3 + 3*$.1^2 + 2*$.1 + 3,
    $.1^3 + 2*$.1^2 + 4*$.1 + 2,
    $.1^3 + 4*$.1^2 + 3,
    $.1^3 + $.1^2 + 2,
    $.1^3 + 2*$.1^2 + 2*$.1 + 2
}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:11:38 2004

Input: AllIrreduciblePolynomials(GF(5), 4)


Output: Magma V2.11-2     Thu Aug  5 2004 17:11:37 on modular  [Seed = 306311632]
   -------------------------------------

{
    $.1^4 + 4*$.1^3 + 2*$.1^2 + 4*$.1 + 2,
    $.1^4 + 2*$.1^2 + 3*$.1 + 1,
    $.1^4 + 4*$.1^3 + 3*$.1^2 + 3,
    $.1^4 + $.1^3 + 3*$.1^2 + 4*$.1 + 4,
    $.1^4 + 2*$.1^3 + $.1^2 + 3*$.1 + 4,
    $.1^4 + $.1^3 + 2*$.1^2 + $.1 + 3,
    $.1^4 + 4*$.1^3 + 3*$.1^2 + $.1 + 2,
    $.1^4 + $.1^3 + 2*$.1^2 + 2*$.1 + 2,
    $.1^4 + $.1^3 + 4*$.1^2 + $.1 + 4,
    $.1^4 + 2*$.1^3 + 2*$.1 + 1,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + 4*$.1 + 4,
    $.1^4 + 4*$.1 + 4,
    $.1^4 + $.1^3 + 3*$.1^2 + 1,
    $.1^4 + 2*$.1^3 + 2*$.1^2 + 2*$.1 + 2,
    $.1^4 + 2*$.1^3 + 4*$.1^2 + $.1 + 4,
    $.1^4 + 3*$.1^3 + $.1 + 2,
    $.1^4 + $.1^3 + 4*$.1^2 + 4*$.1 + 1,
    $.1^4 + 4*$.1^3 + $.1^2 + 3*$.1 + 4,
    $.1^4 + $.1^2 + 2*$.1 + 3,
    $.1^4 + 4*$.1^3 + $.1^2 + 4*$.1 + 3,
    $.1^4 + 4*$.1^3 + $.1 + 2,
    $.1^4 + $.1^2 + 3*$.1 + 2,
    $.1^4 + 3*$.1^3 + 4*$.1^2 + 2*$.1 + 3,
    $.1^4 + $.1^3 + $.1^2 + $.1 + 4,
    $.1^4 + $.1^2 + 4*$.1 + 1,
    $.1^4 + 3*$.1^3 + 4*$.1^2 + 3*$.1 + 2,
    $.1^4 + 4*$.1^3 + 2*$.1^2 + 3*$.1 + 1,
    $.1^4 + 4*$.1^2 + $.1 + 2,
    $.1^4 + 3*$.1^3 + 4*$.1 + 4,
    $.1^4 + 2*$.1^3 + $.1^2 + 2*$.1 + 3,
    $.1^4 + $.1^3 + 2*$.1^2 + 2,
    $.1^4 + 4*$.1^3 + 3*$.1^2 + 1,
    $.1^4 + $.1^3 + 3*$.1^2 + 4*$.1 + 2,
    $.1^4 + 4*$.1^2 + 2*$.1 + 1,
    $.1^4 + 4*$.1^3 + 4*$.1^2 + 4*$.1 + 1,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + 2*$.1 + 4,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + 3*$.1 + 3,
    $.1^4 + 2*$.1 + 4,
    $.1^4 + 2*$.1^3 + 2*$.1^2 + $.1 + 1,
    $.1^4 + $.1^3 + 2*$.1 + 4,
    $.1^4 + 4*$.1^3 + $.1^2 + 2*$.1 + 3,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + 4*$.1 + 2,
    $.1^4 + $.1^3 + 4*$.1 + 2,
    $.1^4 + 3*$.1^2 + $.1 + 3,
    $.1^4 + $.1^3 + 2*$.1^2 + 3*$.1 + 4,
    $.1^4 + 4*$.1^3 + 2*$.1^2 + 2,
    $.1^4 + 2*$.1^3 + 3*$.1 + 3,
    $.1^4 + 2*$.1^3 + 4*$.1 + 2,
    $.1^4 + 2*$.1^3 + $.1^2 + 2*$.1 + 1,
    $.1^4 + 3*$.1^3 + 2*$.1^2 + 3*$.1 + 4,
    $.1^4 + 4*$.1^3 + 3*$.1 + 3,
    $.1^4 + 3*$.1^3 + 4*$.1^2 + 4*$.1 + 4,
    $.1^4 + 3*$.1^3 + $.1^2 + 2*$.1 + 1,
    $.1^4 + $.1^3 + 4,
    $.1^4 + 2*$.1^2 + 2*$.1 + 3,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + 2*$.1 + 2,
    $.1^4 + $.1^3 + $.1 + 3,
    $.1^4 + 2*$.1^3 + 4*$.1^2 + 1,
    $.1^4 + 4*$.1^3 + 2*$.1^2 + 4*$.1 + 3,
    $.1^4 + 4*$.1^3 + $.1^2 + $.1 + 2,
    $.1^4 + 4*$.1^3 + 4*$.1^2 + 4*$.1 + 4,
    $.1^4 + 2*$.1^3 + 4,
    $.1^4 + 3*$.1^3 + 4*$.1^2 + 1,
    $.1^4 + 2*$.1^3 + $.1 + 3,
    $.1^4 + 4*$.1^2 + 4*$.1 + 2,
    $.1^4 + 3*$.1^2 + $.1 + 1,
    $.1^4 + 2*$.1^3 + 2*$.1 + 2,
    $.1^4 + 4*$.1^3 + 3*$.1^2 + 3*$.1 + 1,
    $.1^4 + $.1^3 + $.1^2 + 1,
    $.1^4 + 3*$.1^3 + 4,
    $.1^4 + 4*$.1^3 + 4,
    $.1^4 + 3*$.1^3 + 3*$.1 + 1,
    $.1^4 + 2*$.1^3 + 4*$.1^2 + 3*$.1 + 3,
    $.1^4 + 4*$.1^3 + $.1^2 + 4*$.1 + 4,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + 2,
    $.1^4 + $.1^2 + 3*$.1 + 3,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + $.1 + 1,
    $.1^4 + 3*$.1^3 + 2*$.1^2 + 3*$.1 + 2,
    $.1^4 + 2,
    $.1^4 + 3*$.1^3 + 4*$.1^2 + 2*$.1 + 4,
    $.1^4 + 4*$.1^3 + 2*$.1 + 2,
    $.1^4 + 4*$.1^3 + 2*$.1^2 + $.1 + 4,
    $.1^4 + 3*$.1^3 + 2*$.1^2 + 4*$.1 + 1,
    $.1^4 + $.1^3 + $.1^2 + 2*$.1 + 4,
    $.1^4 + 2*$.1^2 + 3,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + 2,
    $.1^4 + 3*$.1^2 + 4*$.1 + 3,
    $.1^4 + $.1^3 + $.1^2 + 3*$.1 + 3,
    $.1^4 + 4*$.1^3 + 2*$.1^2 + 3*$.1 + 2,
    $.1^4 + 4*$.1^3 + $.1^2 + 1,
    $.1^4 + $.1^3 + $.1^2 + 4*$.1 + 2,
    $.1^4 + 2*$.1^2 + 2*$.1 + 1,
    $.1^4 + 4*$.1^2 + $.1 + 3,
    $.1^4 + $.1^3 + 2*$.1^2 + $.1 + 2,
    $.1^4 + 4*$.1^2 + 3*$.1 + 1,
    $.1^4 + $.1^3 + 2*$.1^2 + 2*$.1 + 1,
    $.1^4 + 3*$.1^3 + $.1^2 + 2*$.1 + 4,
    $.1^4 + 2*$.1^3 + 2*$.1^2 + 3,
    $.1^4 + 3*$.1 + 4,
    $.1^4 + 3*$.1^3 + $.1^2 + 3*$.1 + 3,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + 3*$.1 + 4,
    $.1^4 + 3*$.1^3 + 2*$.1^2 + 3,
    $.1^4 + 2*$.1^3 + 4*$.1^2 + 2*$.1 + 2,
    $.1^4 + $.1^2 + 2*$.1 + 2,
    $.1^4 + 4*$.1^3 + $.1 + 1,
    $.1^4 + 3*$.1^3 + 4*$.1^2 + $.1 + 3,
    $.1^4 + $.1^3 + 2*$.1^2 + 4*$.1 + 4,
    $.1^4 + $.1^3 + $.1^2 + $.1 + 3,
    $.1^4 + 4*$.1^3 + 4*$.1^2 + $.1 + 3,
    $.1^4 + 3*$.1^2 + 4*$.1 + 1,
    $.1^4 + 4*$.1^2 + 2,
    $.1^4 + 3*$.1^3 + 4*$.1 + 3,
    $.1^4 + 2*$.1^3 + $.1^2 + 3*$.1 + 1,
    $.1^4 + $.1 + 4,
    $.1^4 + $.1^3 + 4*$.1^2 + 2,
    $.1^4 + 4*$.1^3 + 3*$.1 + 4,
    $.1^4 + $.1^3 + 4*$.1^2 + $.1 + 1,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + 3*$.1 + 2,
    $.1^4 + 2*$.1^3 + 2*$.1^2 + 1,
    $.1^4 + 4*$.1^3 + 4*$.1 + 3,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + $.1 + 4,
    $.1^4 + 3*$.1^3 + $.1^2 + 3*$.1 + 1,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + 2*$.1 + 3,
    $.1^4 + 2*$.1^2 + 3*$.1 + 3,
    $.1^4 + $.1^3 + 2*$.1 + 3,
    $.1^4 + $.1^2 + 2,
    $.1^4 + 3*$.1^3 + 2*$.1^2 + 1,
    $.1^4 + 4*$.1^3 + 3*$.1^2 + $.1 + 4,
    $.1^4 + 3*$.1^3 + 3*$.1^2 + 4*$.1 + 1,
    $.1^4 + $.1^2 + $.1 + 1,
    $.1^4 + $.1^3 + 3*$.1 + 2,
    $.1^4 + 3*$.1^2 + 3,
    $.1^4 + 2*$.1^3 + $.1 + 4,
    $.1^4 + $.1^3 + 4*$.1 + 1,
    $.1^4 + 4*$.1^2 + 4*$.1 + 3,
    $.1^4 + 2*$.1^3 + 2*$.1^2 + 2*$.1 + 4,
    $.1^4 + $.1^3 + 3*$.1^2 + 3,
    $.1^4 + 4*$.1^3 + 4*$.1^2 + 2,
    $.1^4 + $.1^3 + 4*$.1^2 + 4*$.1 + 3,
    $.1^4 + 2*$.1^3 + $.1^2 + 2,
    $.1^4 + 3*$.1^3 + 2*$.1 + 3,
    $.1^4 + 4*$.1^3 + 4*$.1^2 + $.1 + 1,
    $.1^4 + $.1^3 + 3*$.1^2 + 2*$.1 + 1,
    $.1^4 + 2*$.1^3 + 4*$.1^2 + 3*$.1 + 4,
    $.1^4 + 3*$.1^3 + 3*$.1 + 2,
    $.1^4 + 2*$.1^3 + 4*$.1^2 + 4*$.1 + 3,
    $.1^4 + 2*$.1^3 + 3*$.1^2 + $.1 + 2,
    $.1^4 + 3,
    $.1^4 + 3*$.1^3 + $.1^2 + 2,
    $.1^4 + 4*$.1^3 + 2*$.1^2 + 2*$.1 + 4
}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:36:02 2004

Input: AllIrreduciblePolynomials(GF(5), 2
)


Output: Magma V2.11-2     Thu Aug  5 2004 17:36:01 on modular  [Seed = 3399033792]
   -------------------------------------

{
    $.1^2 + 3*$.1 + 4,
    $.1^2 + 2,
    $.1^2 + 4*$.1 + 1,
    $.1^2 + 3*$.1 + 3,
    $.1^2 + $.1 + 2,
    $.1^2 + 2*$.1 + 4,
    $.1^2 + $.1 + 1,
    $.1^2 + 2*$.1 + 3,
    $.1^2 + 3,
    $.1^2 + 4*$.1 + 2
}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:37:13 2004

Input: AllIrreduciblePolynomials(GF(9), 1
)


Output: Magma V2.11-2     Thu Aug  5 2004 17:37:12 on modular  [Seed = 3247581186]
   -------------------------------------

{
    $.1 + $.1^6,
    $.1 + $.1^2,
    $.1 + $.1^5,
    $.1 + $.1,
    $.1 + 2,
    $.1 + 1,
    $.1 + $.1^7,
    $.1 + $.1^3,
    $.1
}

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:47:03 2004

Input: F3: = GF(3)
P<x> := PolynomialRing(F3);
p := x^2 + x + 2;
F<z> := ext< F7 | p >;
F;


Output: Magma V2.11-2     Thu Aug  5 2004 17:47:02 on modular  [Seed = 3853913720]
   -------------------------------------


>> F3: = GF(3)
       ^
User error: bad syntax

>> P<x> := PolynomialRing(F3);
                          ^
User error: Identifier 'F3' has not been declared or assigned

>> p := x^2 + x + 2;
        ^
User error: Identifier 'x' has not been declared or assigned

>> F<z> := ext< F7 | p >;
                ^
User error: Identifier 'F7' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:47:12 2004

Input: F3: = Finitefield(3)
P<x> := PolynomialRing(F3);
p := x^2 + x + 2;
F<z> := ext< F7 | p >;
F;


Output: Magma V2.11-2     Thu Aug  5 2004 17:47:12 on modular  [Seed = 4256044630]
   -------------------------------------


>> F3: = Finitefield(3)
       ^
User error: bad syntax

>> P<x> := PolynomialRing(F3);
                          ^
User error: Identifier 'F3' has not been declared or assigned

>> p := x^2 + x + 2;
        ^
User error: Identifier 'x' has not been declared or assigned

>> F<z> := ext< F7 | p >;
                ^
User error: Identifier 'F7' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:47:29 2004

Input: F3: = FiniteField(3)
P<x> := PolynomialRing(F3);
p := x^2 + x + 2;
F<z> := ext< F7 | p >;
F;


Output: Magma V2.11-2     Thu Aug  5 2004 17:47:28 on modular  [Seed = 4121304654]
   -------------------------------------


>> F3: = FiniteField(3)
       ^
User error: bad syntax

>> P<x> := PolynomialRing(F3);
                          ^
User error: Identifier 'F3' has not been declared or assigned

>> p := x^2 + x + 2;
        ^
User error: Identifier 'x' has not been declared or assigned

>> F<z> := ext< F7 | p >;
                ^
User error: Identifier 'F7' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host d216.math.mtholyoke.edu. (138.110.3.216)
Time: Thu Aug  5 17:47:59 2004

Input: F3: = FiniteField(3)
P<x> := PolynomialRing(F3);
p := x^2 + x + 2;
F<z> := ext< F7 | p >;
F;


Output: Magma V2.11-2     Thu Aug  5 2004 17:47:59 on modular  [Seed = 2380163017]
   -------------------------------------


>> F3: = FiniteField(3)
       ^
User error: bad syntax

>> P<x> := PolynomialRing(F3);
                          ^
User error: Identifier 'F3' has not been declared or assigned

>> p := x^2 + x + 2;
        ^
User error: Identifier 'x' has not been declared or assigned

>> F<z> := ext< F7 | p >;
                ^
User error: Identifier 'F7' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:12:58 2004

Input: Factorize(11111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:12:57 on modular  [Seed = 1310460488]
   -------------------------------------


>> Factorize(11111111111111111);
   ^
User error: Identifier 'Factorize' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:13:06 2004

Input: Factorization(11111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:13:06 on modular  [Seed = 1175716443]
   -------------------------------------

[ <2071723, 1>, <5363222357, 1> ]

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:13:15 2004

Input: Factorization(1111111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:13:15 on modular  [Seed = 1577851466]
   -------------------------------------

[ <1111111111111111111, 1> ]

Total time: 0.590 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:14:17 2004

Input: Factorization(111111111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:14:16 on modular  [Seed = 1443107457]
   -------------------------------------

[ <3, 1>, <37, 1>, <43, 1>, <239, 1>, <1933, 1>, <4649, 1>, <10838689, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:17:47 2004

Input: Factorization(11111111111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:17:46 on modular  [Seed = 1782066511]
   -------------------------------------

[ <11111111111111111111111, 1> ]

Total time: 0.620 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:18:15 2004

Input: Factorization(11111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:18:15 on modular  [Seed = 1647322538]
   -------------------------------------

[ <2071723, 1>, <5363222357, 1> ]

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:18:50 2004

Input: Factorization(1111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:18:49 on modular  [Seed = 2049457564]
   -------------------------------------

[ <53, 1>, <79, 1>, <265371653, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Fri Aug  6 00:20:46 2004

Input: Factorization(1111111111111111);


Output: Magma V2.11-2     Fri Aug  6 2004 00:20:45 on modular  [Seed = 440949832]
   -------------------------------------

[ <11, 1>, <17, 1>, <73, 1>, <101, 1>, <137, 1>, <5882353, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:31:40 2004

Input: Mod (9^5000000, 1000000000)



Output: Magma V2.11-2     Fri Aug  6 2004 03:31:36 on modular  [Seed = 796745126]
   -------------------------------------


>> Mod (9^5000000, 1000000000)
       ^
Runtime error in procedure call: Attempting to call something that is not 
callable

Total time: 3.349 seconds, Total memory usage: 20.65MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:32:01 2004

Input: 9^50000

Output: Magma V2.11-2     Fri Aug  6 2004 03:31:59 on modular  [Seed = 3649809255]
   -------------------------------------

1334971414230401469458914390489782292245248507606277355345627993984127414621589\
6869522305980255798233239149889425419590524332428873537083020782279802984670783\
1741929738848757721062024898109651957506705400177291046532531249067542250887334\
2629571008941299300172233033166129544456836299498452579486504015455214736381320\
7209965356768946943602282911944326154630492113002579642323048858295434770136138\
1807531506158288312619405016500120857253910525756220107559776493580774834595066\
4391476350300829536533954865604481712000952705040802828803086444633043581934923\
3745903249195549325378269055546256255906921806226622155440527634094668066864913\
6623767583909873402089078517647264604516160581720475547210448366081967137447991\
8226442651928529699886492703878073655308269499457937484930238033529298447444330\
5592397659315237841028937215223851003498757650130412927359617600578030416190379\
6298302903624866963435298923914989181690433716204345541925220382491809472656081\
5100985838795186158194775604404398151067087953994291069425659662679592924634171\
4202829694934465304337015784361135937440940664714154737267519782717648220624437\
7297495311363139117182846526847396011100256641964726915840529026133350440572152\
8773250558502655312168986343564871064654334827513005332648722336798578355121274\
6606106199891326833236919894249821574280609481988804468986557501778462928403152\
8807251034659243061300457098151802838555328959349882183372411452749569160369571\
4743361010656708814466807351536259662486169634113312883567962395107127472503411\
6042262749977206507262437895238456653520219653531978179499712629802187572575395\
6687297376185556357271688531139890579653883304482771789483031388421357481008509\
8565935921766781917463457858769230646231584554088864174529684257142410973222364\
9817540134839891873620127918668509134869736194958920383674812649484543522305782\
2100302592646807575727578194260717181543935482870403359180749233077716153034001\
1793589361924475858272465008394729371715225666239011244161943950834583986014699\
7174686693257680063934668354311100491354219636350945161847892966360191444321041\
5814538534529238970509876596798896164377609768509217186822053642712881560512260\
8931134394917645728564527112075649899243588509896189777871982262490841773371456\
3282280705117960125913614359871691670603977668478901681124754489210554082390746\
8944197028644713521165393320189401484955745717592888716939502494769978142085727\
9416589261535802589227216947994510155816971487967110284575709335449414531466148\
7827312807482491775681483079035986821162264588779661180105819077546376651029290\
7711997110626974295341783046136344293634320740538611689722973260771662996279029\
0594693258720290527962515742948541908629615920387702713284405532221912639580505\
7934699127235739861503038989250127304616711372778706981341392639654455238652201\
7597218238761187391586599662062413539213518918645513578338850493396100319844660\
5208670744749144430074910090059537659949842997826728577039649773069544827611866\
7756543639772410681399983929270452748169361509813391108129985672725008227765388\
5213638983701151082116587029152088099597676866999187286174366535315208022160397\
7438626211594841556156961018093472784135886679204847504736973577572701881274901\
6750931462912955125594990141946585753506471581028434134030334253795501120437081\
5544893482812679643003407025461492617584333495534436165867788382504662944539048\
8477556467905980634307147917907324010231216353890005861558147227617286591360275\
7323014454633136379106944743507849778763582887527437449170717108602424789427423\
4355538016716002066957451504280434714564531123845691200969031783298829274131199\
9586824327799175771292478825777377168640034704639941266192370954227236366120326\
5890314172863777680215765908406658926806646326817842515365371167556944030615284\
3418579518627215615782318174869054982177438953670549959292281935795634816307186\
9600441148786972830758543218792320712760035735487848071421875243850801279845349\
1057359195756540776837477244064221930590143121983577298182656237987162764092981\
5289234292533868773599625692945016310457215117554325069427871208178917592341317\
7907055910603419879418725138782466192194904226294595706839605932337431233494629\
4356669650495836863646061179558326934103380974998937492264627350053185617549472\
5182154617056021251141479526577709631435946389382553489002507234840005564419979\
8397611636958589582563067615424314091593835242358762107095442779316504216289376\
5245650686307707212763130705657093765605944832005356656517514369489808699210259\
0778607813704693284658981270561235460448718448868526049020018210678078465447276\
9932811968492232580293770486523408319152137170374071112327031570327514487430519\
4888994126792022738384085792232919851738923726460019795291895781083785682532241\
0660197053207521147962288726832598906690938066795503989684267240497199944162010\
2587002389055667070810316786601458582941570359373708315525780401241430070248873\
0288149452569380882923587421428258970340997214682459415086807761182313990330758\
2322997578299578657363484930382373188199149084726979933695431352177806126415524\
7856275391133217083869277859968305367203603243060441431916049561622118488060739\
9321315072111813308673783744452434556234137273517093201664640449765453517042831\
5069923102237582553762833647922076684706723536313800601426921013889928581905936\
3526419344006775798309414501256889071364557285302146843458961506093670297695754\
9923043459213550580288565197182923237617256358806942894250764873424456953158127\
7528867606210391411313046048850834217937973303617128444971859871599069013231716\
9665961842234909776670587288821661651139948921457487140834846076973801304222950\
4629877367228799354440270720238103482259479407771105100014641359796408059164038\
0734396832157063050392563338171682883502037570557465637738936493706488029344926\
5816539688572542746440669831417201261933866120750641748439942962043642095844763\
4566173233824861969734665981026258879069389796035842980981978195801209204556935\
8296811182977171849461912211870262255015472191879796123333702732308642716895453\
0599802817401657993469292257129487969901266593493068148727684217569536396446003\
3258410333729517266574619913957170757527085914212725614304749731787707661283667\
4996774739526648338595429354974077264904919911066668919787202294856954581271540\
8353034477721529527873023680998824005098060529330768524842394953639010703169832\
5693499275600875271439688411524153169835134206457648001601913757246398917800483\
8908277350637076404601772926009191022512391148104297894927339732899540427820539\
5057818617768084014464787134781602124601084605012871297700574201445739342571183\
5522774914697489379199011407890872461274425621513663890343008568873964862410662\
5340069555129830501302507365972347187438333656996917932935218331379882921921935\
8066632512330505982753224920270949856479726151109895867734980085820139985755461\
4999655938395227808617048459846919382756038570105572337770195651317073145272491\
9022955592599573988787436852840113428859046510655685808443916595581932537909065\
5701524823432110002456567585197050701832617425631703221938485194731029800855574\
2479373663302429056278626149941761647917637508044893881755330791064287334133384\
1030292090426685240328073378172427807890484457090197682380462268873546396988199\
4028929873779841027214400147177492414099043144303487317973521208466651501512232\
3238893216982424280076917234107503861276205927377367185287432851342232757010642\
0607588797091887203138123610646595800981955390232335256130838081965035617068532\
7151570800176776979203356858700893316588686835813326673994567314913372820187372\
6597496708946312560973160356684129728544946372294611958711750729130026958710952\
1749715038257426057993403999933344247318125144822079210452393296177076423951006\
1661516371346206436460008186609934412376199854355562969351803923656353243970817\
0051749857738316313985893707659291972370187279309128741430326523422491151109050\
1150396443016645330052023462851860297816657081191634082984107602122842947520729\
2175481198462819094242041167442560153996413406957900827965574946523786905664663\
7265960300498496780342902924717383508640912312874044250080553012881363962657304\
8466362795234900377128566069109562498971814178550863326894320476419797600293064\
1435248038590880978488813919119161940729099965902931480502232251690243453997185\
6900875372513973604553767654950877489526448350324849795882039529551826068796753\
0964850188123796012343279515006302388264219518380675742552567849332271710119137\
1791385608432555648481983126822468787716619820803216979605115414238696910342784\
1141050361004973761829430350559862396979945988500831480681600776379028931668735\
4716440211402790799648515762956844596236585676101942227183812772209320431517182\
2017816947879312788677431731050377520062182210827218697852645534260696275069914\
4483557267776119064522878746969147634370638975366767436070675208212251922423671\
7973266469860317229699253702035733823853947467763206656630609953068106798763682\
2044778676790571526156752682098054008060114222048648235211088677652001733408972\
3904040212348587337498166956391055169726819502134965644809188811214703082450567\
4661432254495813032622478334872293769452151767150054404576681408107994962406006\
4148141994717787006797204280361180807876033049761456459736601225700682679513329\
3696671352803961223914709109598489933103263702275569203725595982540831266635392\
7839853466911764727507808170177601072547287285970651032607461977529053857354086\
7490363049236404542295177687297794359172552178522669357542909897340384086004138\
4689245507547791562513587227152500782734563124006954754554171637939547310318754\
8731671291477822677719948204266687600763155928248355933413026348454510166847294\
3337107974636189072668256721441101751960657630930579890571217013133779253750178\
8862346007151266814711927321948769679747053463999423708280575959959013839379892\
6
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:32:21 2004

Input: 9^50000 mod 100000000000000000000000000

Output: Magma V2.11-2     Fri Aug  6 2004 03:32:20 on modular  [Seed = 3247682708]
   -------------------------------------

9664574250669865522000001

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:32:35 2004

Input: 9^100000 mod 100000000000000000000000000

Output: Magma V2.11-2     Fri Aug  6 2004 03:32:34 on modular  [Seed = 3382426762]
   -------------------------------------

56146712833823731044000001

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:32:50 2004

Input: 9^1000000 mod 100000000000000000000000000

Output: Magma V2.11-2     Fri Aug  6 2004 03:32:49 on modular  [Seed = 4054025345]
   -------------------------------------

95607428185357310440000001

Total time: 1.000 seconds, Total memory usage: 6.40MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:33:04 2004

Input: 9^10000000 mod 100000000000000000000000000

Output: Magma V2.11-2     Fri Aug  6 2004 03:32:57 on modular  [Seed = 4188769409]
   -------------------------------------

47928266565573104400000001

Total time: 6.860 seconds, Total memory usage: 38.42MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 03:33:37 2004

Input: 9^20000000 mod 100000000000000000000000000

Output: Magma V2.11-2     Fri Aug  6 2004 03:33:23 on modular  [Seed = 3786642675]
   -------------------------------------

16509832491146208800000001

Total time: 13.940 seconds, Total memory usage: 73.11MB


************** MAGMA *****************
Host 220-136-175-6.dynamic.hinet.net. (220.136.175.6)
Time: Fri Aug  6 04:22:13 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug  6 2004 04:22:12 on modular  [Seed = 1832850313]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-175-6.dynamic.hinet.net. (220.136.175.6)
Time: Fri Aug  6 04:22:14 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug  6 2004 04:22:14 on modular  [Seed = 357002227]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.31.235.43)
Time: Fri Aug  6 06:34:12 2004

Input: 123!

Output: Magma V2.11-2     Fri Aug  6 2004 06:34:10 on modular  [Seed = 3220021327]
   -------------------------------------


>> 123!;
       ^
User error: bad syntax

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 08:45:36 2004

Input: 100!


Output: Magma V2.11-2     Fri Aug  6 2004 08:45:35 on modular  [Seed = 2211561406]
   -------------------------------------


>> ;
   ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 62-2-79-21.business.cablecom.ch. (62.2.79.21)
Time: Fri Aug  6 08:46:11 2004

Input: 1000#


Output: Magma V2.11-2     Fri Aug  6 2004 08:46:10 on modular  [Seed = 2851837289]
   -------------------------------------


>> 1000#
       ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host net-84617.fas.harvard.edu. (140.247.28.54)
Time: Fri Aug  6 09:24:26 2004

Input: E:= EllipticCurve([1,1,0,4305,184229]);
Conductor(E);

Output: Magma V2.11-2     Fri Aug  6 2004 09:24:25 on modular  [Seed = 845215213]
   -------------------------------------

13454

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host net-84617.fas.harvard.edu. (140.247.28.54)
Time: Fri Aug  6 09:26:34 2004

Input: E:= EllipticCurve([ 1, 1, 0, -1212, 7011 ]);
Conductor(E);

Output: Magma V2.11-2     Fri Aug  6 2004 09:26:33 on modular  [Seed = 712567926]
   -------------------------------------

1815

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host net-84617.fas.harvard.edu. (140.247.28.54)
Time: Fri Aug  6 09:29:21 2004

Input: E:= EllipticCurve([0, 0, 0, -44, 7120]);
Conductor(E);

Output: Magma V2.11-2     Fri Aug  6 2004 09:29:20 on modular  [Seed = 3432909353]
   -------------------------------------

1088

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host net-84617.fas.harvard.edu. (140.247.28.54)
Time: Fri Aug  6 09:31:06 2004

Input: E:= EllipticCurve([0, 1, 0, -37, 81 ]);
Conductor(E);

Output: Magma V2.11-2     Fri Aug  6 2004 09:31:05 on modular  [Seed = 4087429823]
   -------------------------------------

1216

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:00:43 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^2 - 3;
D := f;
F<alpha> := FunctionField(y^2 - D);
ClassGroup(F)

Output: Magma V2.11-2     Fri Aug  6 2004 10:00:42 on modular  [Seed = 1577881600]
   -------------------------------------

Abelian Group isomorphic to Z
Defined on 1 generator (free)
Mapping from: Abelian Group isomorphic to Z
Defined on 1 generator (free) to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z
Defined on 1 generator (free) given by a rule

Total time: 0.740 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:01:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^2 - 3;
Isirreducible(f)

Output: Magma V2.11-2     Fri Aug  6 2004 10:01:46 on modular  [Seed = 1327333713]
   -------------------------------------


>> Isirreducible(f);
   ^
User error: Identifier 'Isirreducible' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:01:57 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^2 - 3;
IsIrreducible(f)

Output: Magma V2.11-2     Fri Aug  6 2004 10:01:56 on modular  [Seed = 1998961015]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:02:11 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^2 - 2;
IsIrreducible(f)

Output: Magma V2.11-2     Fri Aug  6 2004 10:02:11 on modular  [Seed = 2133700936]
   -------------------------------------

false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:02:27 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 - 3;
IsIrreducible(f)

Output: Magma V2.11-2     Fri Aug  6 2004 10:02:26 on modular  [Seed = 1731569984]
   -------------------------------------

false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:02:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 - 3;
D := f;
F<alpha> := FunctionField(y^2 - D);
ClassGroup(F)


Output: Magma V2.11-2     Fri Aug  6 2004 10:02:46 on modular  [Seed = 1866310077]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/4 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    4*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/4 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    4*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/4 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    4*$.2 = 0 given by a rule

Total time: 0.860 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:07:10 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 - 3;
IsIrreducible(f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:07:09 on modular  [Seed = 508350407]
   -------------------------------------

false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:07:20 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 - 2;
IsIrreducible(f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:07:19 on modular  [Seed = 106223557]
   -------------------------------------

false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:09:54 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
IsIrreducible(f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:09:53 on modular  [Seed = 140171373]
   -------------------------------------

true

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:09:57 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
IsIrreducible(f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:09:56 on modular  [Seed = 811786320]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:10:12 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := f;
F<alpha> := FunctionField(y^2 - D);
ClassGroup(F)


Output: Magma V2.11-2     Fri Aug  6 2004 10:10:11 on modular  [Seed = 996797228]
   -------------------------------------

Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0 given by a rule

Total time: 1.480 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:10:25 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
ClassGroup(F)


Output: Magma V2.11-2     Fri Aug  6 2004 10:10:24 on modular  [Seed = 746519592]
   -------------------------------------

Abelian Group isomorphic to Z/4 + Z
Defined on 2 generators
Relations:
    4*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/4 + Z
Defined on 2 generators
Relations:
    4*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/4 + Z
Defined on 2 generators
Relations:
    4*$.1 = 0 given by a rule

Total time: 1.349 seconds, Total memory usage: 12.97MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:27:17 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
SClassGroup(F,f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:27:16 on modular  [Seed = 3382386137]
   -------------------------------------


>> SClassGroup(F,f)
              ^
Runtime error in 'SClassGroup': Bad argument types
Argument types given: FldFun, RngUPolElt[FldFin]

Total time: 1.189 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:27:40 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
SClassGroup(f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:27:39 on modular  [Seed = 4054001150]
   -------------------------------------


>> SClassGroup(f)
              ^
Runtime error in 'SClassGroup': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 1.210 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:32:38 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Place(f)

Output: Magma V2.11-2     Fri Aug  6 2004 10:32:37 on modular  [Seed = 4205325611]
   -------------------------------------


>> Place(f);
        ^
Runtime error in 'Place': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:33:14 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Places(F)

Output: Magma V2.11-2     Fri Aug  6 2004 10:33:13 on modular  [Seed = 3803198751]
   -------------------------------------

Set of places of F

Total time: 1.189 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:39:17 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Zeros(f)


Output: Magma V2.11-2     Fri Aug  6 2004 10:39:16 on modular  [Seed = 2546290391]
   -------------------------------------


>> Zeros(f)
        ^
Runtime error in 'Zeros': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:40:31 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Places(F,4)



Output: Magma V2.11-2     Fri Aug  6 2004 10:40:29 on modular  [Seed = 2346275458]
   -------------------------------------

[ (x^2 + 6*x + 3), (x^2 + x + 6), (x^2 + 4), (x^2 + 4*x + 1), (x^2 + 1), (x^2 + 
    5*x + 3), (x^2 + 5*x + 5), (x^2 + 3*x + 1), (x^2 + 2), (x^2 + x + 3), (x^2 +
    2*x + 2), (x^2 + 3*x + 6), (x^2 + 2*x + 5), (x^4 + 5*x^2 + 4*x + 3, alpha + 
    2*x^2 + 3), (x^4 + 5*x^2 + 4*x + 3, alpha + 5*x^2 + 4), (x^4 + 3*x^3 + 3*x^2
    + 2, alpha + x^2 + 4*x + 3), (x^4 + 3*x^3 + 3*x^2 + 2, alpha + 6*x^2 + 3*x +
    4), (x^4 + 4*x^3 + 6*x^2 + 5*x + 4, alpha + 3*x^3 + 5), (x^4 + 4*x^3 + 6*x^2
    + 5*x + 4, alpha + 4*x^3 + 2), (x^4 + x + 1, alpha + x^3 + 6*x^2 + 2*x + 6),
(x^4 + x + 1, alpha + 6*x^3 + x^2 + 5*x + 1), (x^4 + 6*x^3 + 2*x^2 + 4*x + 6, 
    alpha + x^2 + x + 1), (x^4 + 6*x^3 + 2*x^2 + 4*x + 6, alpha + 6*x^2 + 6*x + 
    6), (x^4 + 6*x^3 + x^2 + 4*x + 4, alpha + x^3 + 6*x^2 + 3*x), (x^4 + 6*x^3 +
    x^2 + 4*x + 4, alpha + 6*x^3 + x^2 + 4*x), (x^4 + 5*x^2 + 5*x + 5, alpha + 
    2*x^3 + 6*x^2 + 4*x + 2), (x^4 + 5*x^2 + 5*x + 5, alpha + 5*x^3 + x^2 + 3*x 
    + 5), (x^4 + 2*x + 6, alpha + 2*x^3 + x^2 + x + 5), (x^4 + 2*x + 6, alpha + 
    5*x^3 + 6*x^2 + 6*x + 2), (x^4 + 3*x^3 + 3*x^2 + x + 1, alpha + 2*x^3 + 6*x 
    + 3), (x^4 + 3*x^3 + 3*x^2 + x + 1, alpha + 5*x^3 + x + 4), (x^4 + x^3 + 
    2*x^2 + 3*x + 3, alpha + 2*x^3 + 3*x^2 + 2*x), (x^4 + x^3 + 2*x^2 + 3*x + 3,
alpha + 5*x^3 + 4*x^2 + 5*x), (x^4 + x^3 + 3*x^2 + 6*x + 2, alpha + 2*x^3 + 
    2*x^2 + 3*x), (x^4 + x^3 + 3*x^2 + 6*x + 2, alpha + 5*x^3 + 5*x^2 + 4*x), 
(x^4 + 3*x^3 + x^2 + 5*x + 5, alpha + x^3 + x^2 + x + 4), (x^4 + 3*x^3 + x^2 + 
    5*x + 5, alpha + 6*x^3 + 6*x^2 + 6*x + 3), (x^4 + x^3 + x^2 + x + 2, alpha +
    2*x^2 + 2*x + 1), (x^4 + x^3 + x^2 + x + 2, alpha + 5*x^2 + 5*x + 6), (x^4 +
    2*x^3 + 2*x^2 + 5, alpha + 3*x^2 + 2*x + 6), (x^4 + 2*x^3 + 2*x^2 + 5, alpha
    + 4*x^2 + 5*x + 1), (x^4 + 5*x^2 + 3*x + 1, alpha + x^3 + 3*x^2 + 4*x + 1), 
(x^4 + 5*x^2 + 3*x + 1, alpha + 6*x^3 + 4*x^2 + 3*x + 6), (x^4 + 3*x^2 + 3*x + 
    3, alpha + 3*x^3 + 6*x^2 + 3*x + 6), (x^4 + 3*x^2 + 3*x + 3, alpha + 4*x^3 +
    x^2 + 4*x + 1), (x^4 + x^3 + 6*x^2 + 2*x + 6, alpha + 2*x^3 + 3*x^2 + 6*x + 
    1), (x^4 + x^3 + 6*x^2 + 2*x + 6, alpha + 5*x^3 + 4*x^2 + x + 6), (x^4 + 
    2*x^3 + 4*x^2 + 5*x + 4, alpha + 2*x^3 + 3*x^2 + 2*x + 1), (x^4 + 2*x^3 + 
    4*x^2 + 5*x + 4, alpha + 5*x^3 + 4*x^2 + 5*x + 6), (x^4 + 6*x^3 + x + 3, 
    alpha + 3*x^3 + 3*x^2 + 2*x + 6), (x^4 + 6*x^3 + x + 3, alpha + 4*x^3 + 
    4*x^2 + 5*x + 1), (x^4 + 2*x^3 + 6*x^2 + 3*x + 6, alpha + x^2 + 5*x + 6), 
(x^4 + 2*x^3 + 6*x^2 + 3*x + 6, alpha + 6*x^2 + 2*x + 1), (x^4 + 5*x^3 + x^2 + 
    4*x + 4, alpha + 3*x^3 + 5*x^2 + x + 2), (x^4 + 5*x^3 + x^2 + 4*x + 4, alpha
    + 4*x^3 + 2*x^2 + 6*x + 5), (x^4 + 2*x^3 + x^2 + 3*x + 5, alpha + 2*x^3 + 
    5*x + 5), (x^4 + 2*x^3 + x^2 + 3*x + 5, alpha + 5*x^3 + 2*x + 2), (x^4 + 
    5*x^3 + 5*x^2 + 5*x + 2, alpha + 2*x^2 + 3*x + 6), (x^4 + 5*x^3 + 5*x^2 + 
    5*x + 2, alpha + 5*x^2 + 4*x + 1), (x^4 + 2*x^2 + 6*x + 4, alpha + 2*x^3 + 
    3*x^2 + x), (x^4 + 2*x^2 + 6*x + 4, alpha + 5*x^3 + 4*x^2 + 6*x), (x^4 + 
    2*x^3 + 3*x^2 + 6*x + 5, alpha + 2*x^2 + 4*x + 2), (x^4 + 2*x^3 + 3*x^2 + 
    6*x + 5, alpha + 5*x^2 + 3*x + 5), (x^4 + 3*x^3 + 3*x + 1, alpha + x^3 + 
    2*x^2 + 5*x), (x^4 + 3*x^3 + 3*x + 1, alpha + 6*x^3 + 5*x^2 + 2*x), (x^4 + 
    4*x^3 + x^2 + 6, alpha + 3*x^3 + x^2 + 6*x + 1), (x^4 + 4*x^3 + x^2 + 6, 
    alpha + 4*x^3 + 6*x^2 + x + 6), (x^4 + 6*x + 4, alpha + x^3 + 5*x^2 + 5*x + 
    6), (x^4 + 6*x + 4, alpha + 6*x^3 + 2*x^2 + 2*x + 1), (x^4 + x^2 + 4*x + 5, 
alpha + 2*x^2 + 2), (x^4 + x^2 + 4*x + 5, alpha + 5*x^2 + 5), (x^4 + 3*x^3 + 
    6*x^2 + x + 1, alpha + 3*x^3 + 4), (x^4 + 3*x^3 + 6*x^2 + x + 1, alpha + 
    4*x^3 + 3), (x^4 + 2*x^3 + 5*x^2 + 6*x + 3, alpha + x^3 + 6*x^2 + 2*x), (x^4
    + 2*x^3 + 5*x^2 + 6*x + 3, alpha + 6*x^3 + x^2 + 5*x), (x^4 + 6*x^3 + x^2 + 
    2*x + 2, alpha + 3*x^3 + 4*x^2 + 5*x), (x^4 + 6*x^3 + x^2 + 2*x + 2, alpha +
    4*x^3 + 3*x^2 + 2*x), (x^4 + 3*x^3 + 5, alpha + 3*x^3 + 2*x^2 + 3*x + 2), 
(x^4 + 3*x^3 + 5, alpha + 4*x^3 + 5*x^2 + 4*x + 5), (x^4 + 4*x^3 + 2*x^2 + 5*x +
    1, alpha + 3*x^3 + 5*x^2 + 2*x + 2), (x^4 + 4*x^3 + 2*x^2 + 5*x + 1, alpha +
    4*x^3 + 2*x^2 + 5*x + 5), (x^4 + 4*x^3 + 4*x^2 + 2, alpha + 3*x^3 + 2*x^2 + 
    6*x + 5), (x^4 + 4*x^3 + 4*x^2 + 2, alpha + 4*x^3 + 5*x^2 + x + 2), (x^4 + 
    5*x^3 + 4*x^2 + 2*x + 6, alpha + 2*x^3 + 6*x^2 + 4), (x^4 + 5*x^3 + 4*x^2 + 
    2*x + 6, alpha + 5*x^3 + x^2 + 3), (x^4 + 6*x^3 + 3*x^2 + 5*x + 3, alpha + 
    x^2 + x), (x^4 + 6*x^3 + 3*x^2 + 5*x + 3, alpha + 6*x^2 + 6*x), (x^4 + 6*x^3
    + x^2 + 6*x + 2, alpha + 3*x^3 + 4*x^2 + x + 6), (x^4 + 6*x^3 + x^2 + 6*x + 
    2, alpha + 4*x^3 + 3*x^2 + 6*x + 1), (x^4 + x^2 + 6, alpha + 3*x^3 + 2*x^2 +
    2*x + 3), (x^4 + x^2 + 6, alpha + 4*x^3 + 5*x^2 + 5*x + 4), (x^4 + 6*x^3 + 
    2*x^2 + 4, alpha + x^3 + 5*x^2 + 5*x + 4), (x^4 + 6*x^3 + 2*x^2 + 4, alpha +
    6*x^3 + 2*x^2 + 2*x + 3), (x^4 + x^3 + x^2 + 1, alpha + x^2 + 6*x + 2), (x^4
    + x^3 + x^2 + 1, alpha + 6*x^2 + x + 5), (x^4 + 4*x^3 + 2*x + 3, alpha + 
    2*x^3 + 3*x^2 + 3), (x^4 + 4*x^3 + 2*x + 3, alpha + 5*x^3 + 4*x^2 + 4), (x^4
    + 5*x^3 + 4*x^2 + 6*x + 2, alpha + 3*x^3 + 2*x^2 + 3*x + 1), (x^4 + 5*x^3 + 
    4*x^2 + 6*x + 2, alpha + 4*x^3 + 5*x^2 + 4*x + 6), (x^4 + 4*x^3 + 2*x^2 + 6,
alpha + x^3 + 4), (x^4 + 4*x^3 + 2*x^2 + 6, alpha + 6*x^3 + 3), (x^4 + 5*x^3 + 
    6*x^2 + x + 4, alpha + 3*x^2 + 5*x + 3), (x^4 + 5*x^3 + 6*x^2 + x + 4, alpha
    + 4*x^2 + 2*x + 4), (x^4 + 4*x^3 + 2*x^2 + 5*x + 5, alpha + x^3 + 3*x^2), 
(x^4 + 4*x^3 + 2*x^2 + 5*x + 5, alpha + 6*x^3 + 4*x^2), (x^4 + 6*x^3 + 2*x + 4, 
alpha + x^3 + 6*x^2 + 6), (x^4 + 6*x^3 + 2*x + 4, alpha + 6*x^3 + x^2 + 1), (x^4
    + 2*x^3 + 4*x^2 + 3*x + 1, alpha + 3*x^3 + x^2 + 5*x + 6), (x^4 + 2*x^3 + 
    4*x^2 + 3*x + 1, alpha + 4*x^3 + 6*x^2 + 2*x + 1), (x^4 + 5*x^3 + 5*x^2 + 
    5*x + 1, alpha + 3*x^3 + 3*x^2 + 2*x + 3), (x^4 + 5*x^3 + 5*x^2 + 5*x + 1, 
    alpha + 4*x^3 + 4*x^2 + 5*x + 4), (x^4 + 3*x^3 + 4*x^2 + 5*x + 5, alpha + 
    2*x^3 + 6*x^2 + x + 1), (x^4 + 3*x^3 + 4*x^2 + 5*x + 5, alpha + 5*x^3 + x^2 
    + 6*x + 6), (x^4 + 6*x^3 + 6*x + 3, alpha + 2*x^3 + 6*x + 5), (x^4 + 6*x^3 +
    6*x + 3, alpha + 5*x^3 + x + 2), (x^4 + 3*x^3 + 2*x + 3, alpha + 2*x^3 + 3*x
    + 6), (x^4 + 3*x^3 + 2*x + 3, alpha + 5*x^3 + 4*x + 1), (x^4 + 6*x^3 + 6*x^2
    + 2, alpha + x^3 + x + 6), (x^4 + 6*x^3 + 6*x^2 + 2, alpha + 6*x^3 + 6*x + 
    1), (x^4 + 2*x^3 + 5*x^2 + 2*x + 6, alpha + 3*x^3 + 5*x^2 + 4*x + 1), (x^4 +
    2*x^3 + 5*x^2 + 2*x + 6, alpha + 4*x^3 + 2*x^2 + 3*x + 6), (x^4 + 6*x^3 + 
    6*x^2 + x + 5, alpha + 2*x^3 + 2*x^2 + 5*x + 3), (x^4 + 6*x^3 + 6*x^2 + x + 
    5, alpha + 5*x^3 + 5*x^2 + 2*x + 4), (x^4 + 2*x^3 + 4*x^2 + x + 4, alpha + 
    3*x^3 + 6*x^2 + 4*x + 4), (x^4 + 2*x^3 + 4*x^2 + x + 4, alpha + 4*x^3 + x^2 
    + 3*x + 3), (x^4 + 3*x^3 + 4*x^2 + 4*x + 1, alpha + x^2 + 4*x + 2), (x^4 + 
    3*x^3 + 4*x^2 + 4*x + 1, alpha + 6*x^2 + 3*x + 5), (x^4 + 4*x^3 + 5*x^2 + 
    6*x + 3, alpha + 2*x^3 + 5*x^2 + x + 2), (x^4 + 4*x^3 + 5*x^2 + 6*x + 3, 
    alpha + 5*x^3 + 2*x^2 + 6*x + 5), (x^4 + 6*x^3 + x + 2, alpha + 2*x^2 + 5*x 
    + 6), (x^4 + 6*x^3 + x + 2, alpha + 5*x^2 + 2*x + 1), (x^4 + 4*x^3 + 6*x^2 +
    6*x + 6, alpha + 2*x^3 + 5*x^2 + 2*x + 4), (x^4 + 4*x^3 + 6*x^2 + 6*x + 6, 
    alpha + 5*x^3 + 2*x^2 + 5*x + 3), (x^4 + 5*x^3 + 2*x^2 + 2*x + 3, alpha + 
    2*x^3 + 4*x^2 + 5*x + 6), (x^4 + 5*x^3 + 2*x^2 + 2*x + 3, alpha + 5*x^3 + 
    3*x^2 + 2*x + 1), (x^4 + 5*x^3 + 6*x + 6, alpha + 3*x^3 + 6*x), (x^4 + 5*x^3
    + 6*x + 6, alpha + 4*x^3 + x), (x^4 + 4*x^3 + 4*x^2 + 3*x + 5, alpha + x^3 +
    5*x^2 + 6*x + 6), (x^4 + 4*x^3 + 4*x^2 + 3*x + 5, alpha + 6*x^3 + 2*x^2 + x 
    + 1), (x^4 + 3*x^3 + x^2 + 6*x + 6, alpha + x^3 + 4*x^2 + 6*x + 2), (x^4 + 
    3*x^3 + x^2 + 6*x + 6, alpha + 6*x^3 + 3*x^2 + x + 5), (x^4 + 6*x^3 + 6*x^2 
    + 2*x + 4, alpha + 2*x^3 + 3*x^2 + 2*x + 4), (x^4 + 6*x^3 + 6*x^2 + 2*x + 4,
alpha + 5*x^3 + 4*x^2 + 5*x + 3), (x^4 + 6*x^3 + 2*x^2 + 3*x + 5, alpha + x^3 + 
    2*x^2 + 6*x + 4), (x^4 + 6*x^3 + 2*x^2 + 3*x + 5, alpha + 6*x^3 + 5*x^2 + x 
    + 3), (x^4 + 6*x^2 + 2*x + 3, alpha + 3*x^3 + 2*x^2 + 5*x), (x^4 + 6*x^2 + 
    2*x + 3, alpha + 4*x^3 + 5*x^2 + 2*x), (x^4 + 5*x^3 + 4*x^2 + 2, alpha + x^3
    + 2*x^2 + 2*x + 2), (x^4 + 5*x^3 + 4*x^2 + 2, alpha + 6*x^3 + 5*x^2 + 5*x + 
    5), (x^4 + x^3 + 4*x^2 + 6*x + 3, alpha + x^3 + 5*x^2 + 4*x + 6), (x^4 + x^3
    + 4*x^2 + 6*x + 3, alpha + 6*x^3 + 2*x^2 + 3*x + 1), (x^4 + 3*x^3 + 5*x^2 + 
    2*x + 2, alpha + 2*x^2 + 6*x + 1), (x^4 + 3*x^3 + 5*x^2 + 2*x + 2, alpha + 
    5*x^2 + x + 6), (x^4 + 6*x^3 + 5*x + 6, alpha + 2*x^3 + 2*x^2), (x^4 + 6*x^3
    + 5*x + 6, alpha + 5*x^3 + 5*x^2), (x^4 + 4*x^3 + 2*x^2 + 6*x + 5, alpha + 
    2*x^3 + 2*x^2 + x + 2), (x^4 + 4*x^3 + 2*x^2 + 6*x + 5, alpha + 5*x^3 + 
    5*x^2 + 6*x + 5), (x^4 + 4*x^3 + 2*x^2 + x + 4, alpha + 2*x^3 + x^2 + 5), 
(x^4 + 4*x^3 + 2*x^2 + x + 4, alpha + 5*x^3 + 6*x^2 + 2), (x^4 + 2*x^3 + 2*x^2 +
    3*x + 1, alpha + 3*x^3 + 2*x^2 + 4*x + 5), (x^4 + 2*x^3 + 2*x^2 + 3*x + 1, 
    alpha + 4*x^3 + 5*x^2 + 3*x + 2), (x^4 + 2*x^3 + 3*x^2 + 3, alpha + x^3 + 
    5*x^2 + 6*x + 4), (x^4 + 2*x^3 + 3*x^2 + 3, alpha + 6*x^3 + 2*x^2 + x + 3), 
(x^4 + x^3 + 6*x^2 + 5*x + 2, alpha + x^3 + x^2 + 5*x + 1), (x^4 + x^3 + 6*x^2 +
    5*x + 2, alpha + 6*x^3 + 6*x^2 + 2*x + 6), (x^4 + x^3 + 2*x^2 + 6*x + 6, 
    alpha + x^2 + 6*x + 1), (x^4 + x^3 + 2*x^2 + 6*x + 6, alpha + 6*x^2 + x + 
    6), (x^4 + 6*x^3 + x^2 + 5, alpha + x^3 + 5*x^2 + x + 1), (x^4 + 6*x^3 + x^2
    + 5, alpha + 6*x^3 + 2*x^2 + 6*x + 6), (x^4 + x^3 + 2*x^2 + x + 3, alpha + 
    3*x^3 + 6*x^2 + x + 4), (x^4 + x^3 + 2*x^2 + x + 3, alpha + 4*x^3 + x^2 + 
    6*x + 3), (x^4 + 5*x^2 + 2*x + 5, alpha + 2*x^3 + 3*x^2 + 4*x + 4), (x^4 + 
    5*x^2 + 2*x + 5, alpha + 5*x^3 + 4*x^2 + 3*x + 3), (x^4 + 5*x^2 + 6*x + 5, 
    alpha + x^3 + 4*x^2 + 2), (
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:41:11 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
RandomPlace(F,4)



Output: Magma V2.11-2     Fri Aug  6 2004 10:41:10 on modular  [Seed = 3017894497]
   -------------------------------------

true (x^4 + x^3 + 6*x^2 + x + 4, alpha + 4*x^3 + 3*x + 1)

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:41:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
P=RandomPlace(F,4);
S={P};
SClassGroup(F,S)


Output: Magma V2.11-2     Fri Aug  6 2004 10:41:57 on modular  [Seed = 3152634458]
   -------------------------------------


>> P=RandomPlace(F,4);
    ^
Runtime error in elt< ... >: LHS and RHS of relation constructor are not 
compatible

>> S={P};
   ^
User error: Identifier 'S' has not been declared or assigned

>> SClassGroup(F,S)
                 ^
User error: Identifier 'S' has not been declared or assigned

Total time: 1.209 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:42:25 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Pl:=RandomPlace(F,4);
S:={Pl};
SClassGroup(F,S)


Output: Magma V2.11-2     Fri Aug  6 2004 10:42:24 on modular  [Seed = 2750511655]
   -------------------------------------


>> SClassGroup(F,S)
              ^
Runtime error in 'SClassGroup': Bad argument types
Argument types given: FldFun, SetEnum[BoolElt]

Total time: 1.189 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:42:49 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Pl:=RandomPlace(F,4);
S:=set(Pl);
SClassGroup(F,S)


Output: Magma V2.11-2     Fri Aug  6 2004 10:42:48 on modular  [Seed = 2885251607]
   -------------------------------------


>> S:=set(Pl);
      ^
User error: Identifier 'set' has not been declared or assigned

>> SClassGroup(F,S)
                 ^
User error: Identifier 'S' has not been declared or assigned

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:42:57 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
F<alpha> := FunctionField(y^2 - D);
Pl:=RandomPlace(F,4);
S:=Set(Pl);
SClassGroup(F,S)


Output: Magma V2.11-2     Fri Aug  6 2004 10:42:56 on modular  [Seed = 1342343671]
   -------------------------------------


>> S:=Set(Pl);
         ^
Runtime error in 'Set': Bad argument types
Argument types given: BoolElt

>> SClassGroup(F,S)
                 ^
User error: Identifier 'S' has not been declared or assigned

Total time: 1.209 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:49:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
K<alpha> := FunctionField(y^2 - D);
M:=MaximalOrder(K)

Output: Magma V2.11-2     Fri Aug  6 2004 10:49:58 on modular  [Seed = 2032902840]
   -------------------------------------


>> M:=MaximalOrder(K);
                  ^
Runtime error in 'MaximalOrder': Bad argument types
Argument types given: FldFun

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:50:45 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
K<alpha> := FunctionField(y^2 - D);
M:=MaximalOrderInfinite(K)

Output: Magma V2.11-2     Fri Aug  6 2004 10:50:44 on modular  [Seed = 1613937651]
   -------------------------------------


Total time: 1.210 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug  6 10:56:15 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
f := x^4 +x + 2;
D := 3*f;
K<alpha> := FunctionField(y^2 - D);
Poles(f)

Output: Magma V2.11-2     Fri Aug  6 2004 10:56:14 on modular  [Seed = 508347207]
   -------------------------------------


>> Poles(f);
        ^
Runtime error in 'Poles': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host 80.58.10.42.proxycache.rima-tde.net. (80.58.10.42)
Time: Fri Aug  6 12:13:13 2004

Input: SetAutoColumns(false);
SetColumns(100);
SetEchoInput(true);
Attach("routines.m");
Qx<x>:=PolynomialRing(Rationals());

P2<u,v,w>:=ProjectiveSpace(Rationals(),2);
Q1:=-4*u^2 - 4*v*w + 4*w^2;
Q2:=-2*u^2 + 2*u*w - 4*v*w + 2*w^2;
Q3:=2*u^2 + 4*u*v + 4*v^2;

Factorisation(BadPrimes([Q1,Q2,Q3]));
//Only bad primes are 2,5. That leaves 1,-1,2,-2,5,-5,10,-10 as possible
//values for delta.

//In fact, there are more bad primes for C than there are where Q1,Q2,Q3
//simultaneously vanish:
Factorisation(BadPrimes(DefiningEquations(SingularSubscheme(Curve(P2,Q1*Q3-Q2^2)))));

d:=-1;
pi,xpolmap,J:=Prym(P2,d*Q1,d*Q2,d*Q3);
D<U,V,W,R,S>:=Domain(pi);
Dpl:=Curve(Projection(Projection(D)));
//verify that negative d lead to D(R) empty.
assert HasRealPoints(Dpl) eq false;

d:=2;
pi,xpolmap,J:=Prym(P2,d*Q1,d*Q2,d*Q3);
D<U,V,W,R,S>:=Domain(pi);
assert not(IsLocallySolvable(D,2:AssumeIrreducible,AssumeNonsingular));

d:=5;
pi,xpolmap,J:=Prym(P2,d*Q1,d*Q2,d*Q3);
D<U,V,W,R,S>:=Domain(pi);
assert not(IsLocallySolvable(D,5:AssumeIrreducible,AssumeNonsingular));

d:=10;
pi,xpolmap,J:=Prym(P2,d*Q1,d*Q2,d*Q3);
D<U,V,W,R,S>:=Domain(pi);
assert not(IsLocallySolvable(D,2:AssumeIrreducible,AssumeNonsingular));

//So the only value left is delta=1:
d:=1;
pi,xpolmap,J:=Prym(P2,d*Q1,d*Q2,d*Q3);
D<U,V,W,R,S>:=Domain(pi);
P4:=Ambient(D);
C:=Codomain(pi);

//there are rational points on C and D:
p0:=C![0,1,0];
P0:=D!RationalPoints(p0@@pi)[1];P0;



KJ:=KummerSurface(J);
Km:=Scheme(KJ);
P3<k1,k2,k3,k4>:=Ambient(Km);

Ckm:=KummerImage(pi,xpolmap,J);

//verify that J(Q) is of rank 1 and has no torsion
assert TwoSelmerGroupData(J) eq 1 and TorsionBound(J,10) eq 1;

//Determine a generator of the Mordell-Weil group: First search for some free
//point
pt:=ReducedBasis(RationalPoints(J:Bound:=100))[1];
//Search up to the height bound suggested by that point:
RationalPoints(J:Bound:=Floor(CanonicalHeight(pt)+
                  Exp(HeightConstant(J:Effort:=100,Factor))));
//We see we can take:
g:=[elt<J|x^2 + 4*x - 4, 68*x - 64, 2>];

//As we'll see, a planar model of C will come in handy.
P2K<K1,K2,K3>:=ProjectiveSpace(BaseRing(Km),2);
Cpl:=P2K!!Projection(Ckm,P3![0,0,0,1]);
Cpleq:=DefiningEquation(Cpl);
Cpleq:=LCM([Denominator(c):c in Coefficients(Cpleq)])*Cpleq;
PolynomialRing(Integers(),3)!Cpleq;

//Create the Mordell-Weil group of J abstractly, together with its realisation
G:=AbelianGroup([0]);
mwmap:=map<G->J|a:->&+[Eltseq(a)[i]*g[i]: i in [1]]>;

p:=13;

//compute the reductions of everything mod 13
quot,emb:=Reduction(mwmap,p);
quot:=hom<Domain(quot)->Image(quot)|
     [quot(g):g in OrderedGenerators(Domain(quot))]>;
Kmp:=BaseChange(Km,Coercion(Rationals(),GF(p)));
Ckmp:=Scheme(Ambient(Kmp),
    DefiningEquations(BaseChange(Ckm,Coercion(Rationals(),GF(p)))));
Cplp:=BaseChange(Cpl,Coercion(Rationals(),GF(p)));
Jp:=Codomain(emb);
KJp:=KummerSurface(Jp);
mp:=func<v|
     Scheme(Ckmp,
        [v[1]*Ckmp.2-v[2]*Ckmp.1,
         v[2]*Ckmp.3-v[3]*Ckmp.2,
         v[3]*Ckmp.1-v[1]*Ckmp.3])>;
//We compute Ckmp(GF(13)) by taking Cplp(GF(13)) (the planar model!)
//and taking the GF(13) points above them on Ckmp.
V:=&join[RationalPoints(mp(v)): v in RationalPoints(Cplp)];
print "#of points on Ckmp:",#V;

//We lift the points to Jp(GF(13)) and keep one representative for each.
V:=&join[ #W eq 0 select {} else {W[1]} where
               W:=RationalPoints(Jp,KJp!Eltseq(v)): v in V];
print "#of points on Jacobian (divided by 2):",#V;

//pull points back to abstract group Jp(GF(13))
V:={v@@emb: v in V};
//take only those points in the image of the Mordell-Weil group
V:={Image(quot)!v: v in V | v in Image(quot)};
//include -points as well, since D is symmetric.
V:=V join {-v:v in V};
print "#of intersections with MWgroup:",#V;

//verify it's the generator and - the generator of the mordell-weil group
//that map to these points.
assert {quot(G.1),quot(-G.1)} eq V;
//verify that mod 13, the generator has indeed order 10.
assert Order(quot(G.1)) eq 10;
//Verify that the generator indeed maps onto Ckm:
Ckm!Eltseq(KJ!mwmap(G.1));

//Here, we are lazy: Of course, we should do these computations with limited
//11-adic information. However, numbers are still small enough in this case to do
//the computation over Z.
crd:=Eltseq(KJ!mwmap(11*G.1));

//Get the equations defining Ckm evaluated at crd.
L:=[Integers()|Evaluate(f,crd):f in DefiningEquations(Ckm)];

//indeed, mod 13^2, 11*G.1 does not map onto Ckm.
[L[1] mod 13^2, L[2] mod 13^2];

Output: WARNING: MAGMA command contains unsafe command 'attach', so it will not be executed.

************** MAGMA *****************
Host D5E0B642.kabel.telenet.be. (213.224.182.66)
Time: Fri Aug  6 12:30:34 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug  6 2004 12:30:33 on modular  [Seed = 240975217]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:38:38 2004

Input: Factorization(X^6-1)

Output: Magma V2.11-2     Fri Aug  6 2004 15:38:37 on modular  [Seed = 390432882]
   -------------------------------------


>> Factorization(X^6-1);
                 ^
User error: Identifier 'X' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:40:45 2004

Input: P<x,y> := PolynomialRing(IntegerRing(), 2);
f := &*[x^6-y^6];
Factorization(f);

Output: Magma V2.11-2     Fri Aug  6 2004 15:40:44 on modular  [Seed = 862039255]
   -------------------------------------

[
    <x - y, 1>,
    <x + y, 1>,
    <x^2 - x*y + y^2, 1>,
    <x^2 + x*y + y^2, 1>
]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:40:55 2004

Input: P<x,y> := PolynomialRing(IntegerRing(), 2);
f := &*[x^12-y^6];
Factorization(f);

Output: Magma V2.11-2     Fri Aug  6 2004 15:40:55 on modular  [Seed = 729396404]
   -------------------------------------

[
    <x^2 - y, 1>,
    <x^2 + y, 1>,
    <x^4 - x^2*y + y^2, 1>,
    <x^4 + x^2*y + y^2, 1>
]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:41:22 2004

Input: P<x,y> := PolynomialRing(IntegerRing(), 2);
f := &*[x^120-y^120];
Factorization(f);

Output: Magma V2.11-2     Fri Aug  6 2004 15:41:20 on modular  [Seed = 594656411]
   -------------------------------------

[
    <x - y, 1>,
    <x + y, 1>,
    <x^2 + y^2, 1>,
    <x^2 - x*y + y^2, 1>,
    <x^2 + x*y + y^2, 1>,
    <x^4 + y^4, 1>,
    <x^4 - x^2*y^2 + y^4, 1>,
    <x^4 - x^3*y + x^2*y^2 - x*y^3 + y^4, 1>,
    <x^4 + x^3*y + x^2*y^2 + x*y^3 + y^4, 1>,
    <x^8 - x^4*y^4 + y^8, 1>,
    <x^8 - x^6*y^2 + x^4*y^4 - x^2*y^6 + y^8, 1>,
    <x^8 - x^7*y + x^5*y^3 - x^4*y^4 + x^3*y^5 - x*y^7 + y^8, 1>,
    <x^8 + x^7*y - x^5*y^3 - x^4*y^4 - x^3*y^5 + x*y^7 + y^8, 1>,
    <x^16 - x^12*y^4 + x^8*y^8 - x^4*y^12 + y^16, 1>,
    <x^16 + x^14*y^2 - x^10*y^6 - x^8*y^8 - x^6*y^10 + x^2*y^14 + y^16, 1>,
    <x^32 + x^28*y^4 - x^20*y^12 - x^16*y^16 - x^12*y^20 + x^4*y^28 + y^32, 1>
]

Total time: 1.419 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:41:34 2004

Input: P<x,y> := PolynomialRing(ComplexRing(), 2);
f := &*[x^120-y^120];
Factorization(f);

Output: Magma V2.11-2     Fri Aug  6 2004 15:41:34 on modular  [Seed = 3683206253]
   -------------------------------------


>> P<x,y> := PolynomialRing(ComplexRing(), 2);
                            ^
User error: Identifier 'ComplexRing' has not been declared or assigned

>> f := &*[x^120-y^120];
           ^
User error: Identifier 'x' has not been declared or assigned

>> Factorization(f);;
                 ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:45:59 2004

Input: DicksonFirst(6,-1);

Output: Magma V2.11-2     Fri Aug  6 2004 15:45:59 on modular  [Seed = 3565570683]
   -------------------------------------

$.1^6 + 6*$.1^4 + 9*$.1^2 + 2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:47:19 2004

Input: for i:=1 to 6 do
  DicksonFirst(i,-1);
end for;

Output: Magma V2.11-2     Fri Aug  6 2004 15:47:19 on modular  [Seed = 3449777362]
   -------------------------------------

$.1
$.1^2 + 2
$.1^3 + 3*$.1
$.1^4 + 4*$.1^2 + 2
$.1^5 + 5*$.1^3 + 5*$.1
$.1^6 + 6*$.1^4 + 9*$.1^2 + 2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:48:39 2004

Input: for i:=1 to 6 do
  DicksonSecond(i,-1);
end for;

Output: Magma V2.11-2     Fri Aug  6 2004 15:48:39 on modular  [Seed = 3315033098]
   -------------------------------------

$.1
$.1^2 + 1
$.1^3 + 2*$.1
$.1^4 + 3*$.1^2 + 1
$.1^5 + 4*$.1^3 + 3*$.1
$.1^6 + 5*$.1^4 + 6*$.1^2 + 1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:48:52 2004

Input: for i:=1 to 6 do
  DicksonFirst(i,-1);
end for;

Output: Magma V2.11-2     Fri Aug  6 2004 15:48:52 on modular  [Seed = 4256128001]
   -------------------------------------

$.1
$.1^2 + 2
$.1^3 + 3*$.1
$.1^4 + 4*$.1^2 + 2
$.1^5 + 5*$.1^3 + 5*$.1
$.1^6 + 6*$.1^4 + 9*$.1^2 + 2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ekamel-elama-emuli.stusta.mhn.de. (141.84.69.18)
Time: Fri Aug  6 15:52:51 2004

Input: for i:=1 to 6 do
  Factorization(DicksonFirst(i,-1));
end for;

Output: Magma V2.11-2     Fri Aug  6 2004 15:52:51 on modular  [Seed = 4137965117]
   -------------------------------------

[
    <$.1, 1>
]
[
    <$.1^2 + 2, 1>
]
[
    <$.1, 1>,
    <$.1^2 + 3, 1>
]
[
    <$.1^4 + 4*$.1^2 + 2, 1>
]
[
    <$.1, 1>,
    <$.1^4 + 5*$.1^2 + 5, 1>
]
[
    <$.1^2 + 2, 1>,
    <$.1^4 + 4*$.1^2 + 1, 1>
]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pD9EB7438.dip0.t-ipconnect.de. (217.235.116.56)
Time: Sat Aug  7 05:49:33 2004

Input: ?BadPrimes

Output: Magma V2.11-2     Sat Aug  7 2004 05:49:32 on modular  [Seed = 2329898616]
   -------------------------------------

5 matches:
     1   I   /magma/geometry/conic/local-global/local-global/BadPrimes
     2   I   /magma/geometry/elliptic-curve/rational_curves/four-descent/\
             BadPrimes
     3   I   /magma/geometry/elliptic-curve/rational_curves/\
             rational_curves-local/BadPrimes
     4   I   /magma/geometry/hyperelliptic-curve/2-selmer-group/BadPrimes
     5   I   /magma/geometry/hyperelliptic-curve/2-selmer-group/BadPrimes
To view an entry, type ? followed by the number next to it

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host m111.net195-132-156.noos.fr. (195.132.156.111)
Time: Sat Aug  7 15:17:36 2004

Input: 1+sqrt(2^750)


Output: Magma V2.11-2     Sat Aug  7 2004 15:17:35 on modular  [Seed = 3034636062]
   -------------------------------------


>> 1+sqrt(2^750)
     ^
User error: Identifier 'sqrt' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-69-108-41-75.dsl.sndg02.pacbell.net. (69.108.41.75)
Time: Sat Aug  7 16:36:54 2004

Input: p 100
4 * sumalt(k=0, (-1)^k/(2*k + 1))

Output: Magma V2.11-2     Sat Aug  7 2004 16:36:54 on modular  [Seed = 3938359016]
   -------------------------------------


>> p 100
     ^
User error: bad syntax

>> 4 * sumalt(k=0, (-1)^k/(2*k + 1));
              ^
User error: Identifier 'k' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-69-108-41-75.dsl.sndg02.pacbell.net. (69.108.41.75)
Time: Sat Aug  7 16:37:40 2004

Input: p 100
4 * sumalt(k=0,(-1)^k/(2*k + 1))

Output: Magma V2.11-2     Sat Aug  7 2004 16:37:39 on modular  [Seed = 4071001605]
   -------------------------------------


>> p 100
     ^
User error: bad syntax

>> 4 * sumalt(k=0,(-1)^k/(2*k + 1));
              ^
User error: Identifier 'k' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-69-108-41-75.dsl.sndg02.pacbell.net. (69.108.41.75)
Time: Sat Aug  7 16:37:50 2004

Input: 4 * sumalt(k=0,(-1)^k/(2*k + 1))

Output: Magma V2.11-2     Sat Aug  7 2004 16:37:49 on modular  [Seed = 4205741571]
   -------------------------------------


>> 4 * sumalt(k=0,(-1)^k/(2*k + 1));
              ^
User error: Identifier 'k' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:01:53 2004

Input: Integers(2772)!1/5;

Output: Magma V2.11-2     Sat Aug  7 2004 22:01:52 on modular  [Seed = 323476458]
   -------------------------------------

1109

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:03:37 2004

Input: (Integers(2881)!504)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:03:36 on modular  [Seed = 3938329211]
   -------------------------------------

400

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:04:32 2004

Input: (Integers(2881)!1874)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:04:31 on modular  [Seed = 3803589028]
   -------------------------------------

1902

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:05:04 2004

Input: (Integers(2881)!347)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:05:03 on modular  [Seed = 4205720028]
   -------------------------------------

714

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:05:18 2004

Input: (Integers(2881)!515)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:05:17 on modular  [Seed = 4120985281]
   -------------------------------------

214

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:05:33 2004

Input: (Integers(2881)!2088)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:05:32 on modular  [Seed = 3449358024]
   -------------------------------------

1100

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:05:47 2004

Input: (Integers(2881)!2356)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:05:46 on modular  [Seed = 3314618070]
   -------------------------------------

1904

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:06:03 2004

Input: (Integers(2881)!736)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:06:02 on modular  [Seed = 3716748862]
   -------------------------------------

200

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:06:39 2004

Input: (Integers(2881)!468)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:06:39 on modular  [Seed = 3565166354]
   -------------------------------------

1004

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:27:29 2004

Input: (integers (2881)! 1874)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:27:28 on modular  [Seed = 2664058983]
   -------------------------------------


>> (integers (2881)! 1874)^1109;;
    ^
User error: Identifier 'integers' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:28:09 2004

Input: integers (2772)!1/5;1109=d


Output: Magma V2.11-2     Sat Aug  7 2004 22:28:09 on modular  [Seed = 2529318982]
   -------------------------------------


>> integers (2772)!1/5;1109=d
   ^
User error: Identifier 'integers' has not been declared or assigned

>> integers (2772)!1/5;1109=d
                            ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:28:12 2004

Input: integers (2772)!1/5;1109=d


Output: Magma V2.11-2     Sat Aug  7 2004 22:28:12 on modular  [Seed = 1866179003]
   -------------------------------------


>> integers (2772)!1/5;1109=d
   ^
User error: Identifier 'integers' has not been declared or assigned

>> integers (2772)!1/5;1109=d
                            ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:28:52 2004

Input: integers(2772!1/5;1109=d
(integers(2881)!504)^1109;


Output: Magma V2.11-2     Sat Aug  7 2004 22:28:51 on modular  [Seed = 2016196339]
   -------------------------------------


>> integers(2772!1/5;1109=d
                    ^
User error: bad syntax

>> (integers(2881)!504)^1109;
    ^
User error: Identifier 'integers' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:29:14 2004

Input: integers(2772)!1/5;1109=d
(integers(2881!504)^1109;


Output: Magma V2.11-2     Sat Aug  7 2004 22:29:14 on modular  [Seed = 1881456354]
   -------------------------------------


>> integers(2772)!1/5;1109=d
   ^
User error: Identifier 'integers' has not been declared or assigned

>> (integers(2881!504)^1109;
                           ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:29:33 2004

Input: integers (2772) !1/5; 1109=d
(integers (2881 !504)^1109;


Output: Magma V2.11-2     Sat Aug  7 2004 22:29:32 on modular  [Seed = 1209833772]
   -------------------------------------


>> integers (2772) !1/5; 1109=d
   ^
User error: Identifier 'integers' has not been declared or assigned

>> (integers (2881 !504)^1109;
                             ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:30:06 2004

Input: integers(2772)!1/5;1109=d
(integers(2881!504)^1109;


Output: Magma V2.11-2     Sat Aug  7 2004 22:30:06 on modular  [Seed = 1376158484]
   -------------------------------------


>> integers(2772)!1/5;1109=d
   ^
User error: Identifier 'integers' has not been declared or assigned

>> (integers(2881!504)^1109;
                           ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:30:29 2004

Input: integers(2772)!1/5;1109=d
(integers(2881)!504)^1109;


Output: Magma V2.11-2     Sat Aug  7 2004 22:30:28 on modular  [Seed = 729807367]
   -------------------------------------


>> integers(2772)!1/5;1109=d
   ^
User error: Identifier 'integers' has not been declared or assigned

>> (integers(2881)!504)^1109;
    ^
User error: Identifier 'integers' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:30:59 2004

Input: factorization(2881)!;

Output: Magma V2.11-2     Sat Aug  7 2004 22:30:58 on modular  [Seed = 595063337]
   -------------------------------------


>> factorization(2881)!;;
                       ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:31:05 2004

Input: (Integers(1927)!1631)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:05 on modular  [Seed = 997190202]
   -------------------------------------

901

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:31:09 2004

Input: factorization (2881)!;

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:09 on modular  [Seed = 862446134]
   -------------------------------------


>> factorization (2881)!;;
                        ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:31:14 2004

Input: factorization (2881) ! ;

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:13 on modular  [Seed = 190831122]
   -------------------------------------


>> factorization (2881) ! ;;
                          ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:31:20 2004

Input: (Integers(1927)!902)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:20 on modular  [Seed = 72406292]
   -------------------------------------

410

Total time: 0.590 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:31:20 2004

Input: factorization (2881) !

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:20 on modular  [Seed = 89248789]
   -------------------------------------


>> factorization (2881) !;
                         ^
User error: bad syntax

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:31:29 2004

Input: factorization(2881)!

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:29 on modular  [Seed = 323470074]
   -------------------------------------


>> factorization(2881)!;
                       ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:31:31 2004

Input: factorization(2881)

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:31 on modular  [Seed = 3955177984]
   -------------------------------------


>> factorization(2881);
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:31:42 2004

Input: Factorization(2881)

Output: Magma V2.11-2     Sat Aug  7 2004 22:31:41 on modular  [Seed = 3820433926]
   -------------------------------------

[ <43, 1>, <67, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:32:07 2004

Input: factorization(1927);

Output: Magma V2.11-2     Sat Aug  7 2004 22:32:07 on modular  [Seed = 4238880051]
   -------------------------------------


>> factorization(1927);;
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:32:14 2004

Input: (Integers(2881)!504)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:32:14 on modular  [Seed = 4104135986]
   -------------------------------------

400

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:32:18 2004

Input: Factorization(1927);

Output: Magma V2.11-2     Sat Aug  7 2004 22:32:18 on modular  [Seed = 3432520982]
   -------------------------------------

[ <41, 1>, <47, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:32:54 2004

Input: (Integers(2881)!1874)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:32:54 on modular  [Seed = 3331463032]
   -------------------------------------

1902

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:33:35 2004

Input: (Integers(2881)!0347)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:33:34 on modular  [Seed = 3733589832]
   -------------------------------------

714

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:33:55 2004

Input: (Integers(1927)!902)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:33:54 on modular  [Seed = 2835118290]
   -------------------------------------

410

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:34:09 2004

Input: (Integers(2881)!0515)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:08 on modular  [Seed = 2700374248]
   -------------------------------------

214

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:34:23 2004

Input: (Integers(2881)!2088)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:22 on modular  [Seed = 3102501118]
   -------------------------------------

1100

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:34:32 2004

Input: (Integers(1927)!411)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:32 on modular  [Seed = 2967757024]
   -------------------------------------

1272

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:34:34 2004

Input: (Integers(2881)!2356)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:33 on modular  [Seed = 2296142041]
   -------------------------------------

1904

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:34:43 2004

Input: (Integers(1927)!1273)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:42 on modular  [Seed = 2161397930]
   -------------------------------------

1849

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:34:46 2004

Input: (Integers(2881)!0736)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:46 on modular  [Seed = 2563524790]
   -------------------------------------

200

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:34:58 2004

Input: (Integers(2881)!0468)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:34:57 on modular  [Seed = 2428780713]
   -------------------------------------

1004

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:35:24 2004

Input: (Integers(1927)!1850)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:35:23 on modular  [Seed = 1782495850]
   -------------------------------------

148

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:35:41 2004

Input: (Integers(1927)!149)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:35:40 on modular  [Seed = 1647751797]
   -------------------------------------

1004

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:36:39 2004

Input: (Integers(1927)!1005)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:36:39 on modular  [Seed = 2033035685]
   -------------------------------------

277

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:36:42 2004

Input: (Integers(2881)!1874)^1109;

Output: Magma V2.11-2     Sat Aug  7 2004 22:36:41 on modular  [Seed = 1898291619]
   -------------------------------------

1902

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:36:51 2004

Input: (Integers(1927)!278)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:36:50 on modular  [Seed = 1226676704]
   -------------------------------------

204

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:37:19 2004

Input: (Integers(1927)!205)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:37:18 on modular  [Seed = 1091932660]
   -------------------------------------

1558

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Sat Aug  7 22:37:26 2004

Input: (Integers(1927)!1559)^2;

Output: Magma V2.11-2     Sat Aug  7 2004 22:37:26 on modular  [Seed = 1494059476]
   -------------------------------------

534

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 22:39:28 2004

Input: Factorization (1927)


Output: Magma V2.11-2     Sat Aug  7 2004 22:39:28 on modular  [Seed = 1459848284]
   -------------------------------------

[ <41, 1>, <47, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:13:03 2004

Input: Gcd(1,2)

Output: Magma V2.11-2     Sat Aug  7 2004 23:13:02 on modular  [Seed = 4005180859]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:13:15 2004

Input: Gcd(21,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:13:15 on modular  [Seed = 3870440902]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:13:49 2004

Input: Gcd(651,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:13:48 on modular  [Seed = 4255721210]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:14:20 2004

Input: Gcd(654,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:14:20 on modular  [Seed = 4120981010]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:14:53 2004

Input: Gcd(-729,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:14:52 on modular  [Seed = 3449361931]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:15:21 2004

Input: Gcd(-491,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:15:21 on modular  [Seed = 3297779558]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:16:17 2004

Input: Gcd(862,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:16:16 on modular  [Seed = 3699902135]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:18:08 2004

Input: Gcd(577,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:18:07 on modular  [Seed = 2952492459]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:18:49 2004

Input: Gcd(-1701,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:18:48 on modular  [Seed = 2817752404]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:19:03 2004

Input: Gcd(2,4)

Output: Magma V2.11-2     Sat Aug  7 2004 23:19:02 on modular  [Seed = 3219875186]
   -------------------------------------

2

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:19:39 2004

Input: Gcd(856,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:19:38 on modular  [Seed = 2296140329]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:20:08 2004

Input: Gcd(-727,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:20:07 on modular  [Seed = 2495630872]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:20:10 2004

Input: Gcd(-727,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:20:09 on modular  [Seed = 1832499182]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:20:50 2004

Input: Gcd(-73,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:20:49 on modular  [Seed = 2066720256]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:27:58 2004

Input: Gcd(1559-535,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:27:57 on modular  [Seed = 1965140386]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:28:12 2004

Input: Gcd(1030-535,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:28:11 on modular  [Seed = 1293521388]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:28:23 2004

Input: Gcd(1051-1030,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:28:22 on modular  [Seed = 1158781433]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:28:35 2004

Input: Gcd(431-1051,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:28:34 on modular  [Seed = 1376161498]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:28:50 2004

Input: Gcd(770-431,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:28:49 on modular  [Seed = 712963761]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:29:00 2004

Input: Gcd(1312-770,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:28:59 on modular  [Seed = 578223795]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:29:08 2004

Input: Gcd(534-1312,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:29:07 on modular  [Seed = 980346195]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:29:18 2004

Input: Gcd(1888-534,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:29:17 on modular  [Seed = 845606229]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:29:32 2004

Input: Gcd(1522-1888,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:29:31 on modular  [Seed = 173987195]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:29:41 2004

Input: Gcd(231-1522,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:29:40 on modular  [Seed = 39247180]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:29:51 2004

Input: Gcd(1333-231,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:29:50 on modular  [Seed = 441369950]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:30:01 2004

Input: Gcd(195-1333,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:30:01 on modular  [Seed = 306629953]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:30:47 2004

Input: Gcd(729,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:30:46 on modular  [Seed = 3955176679]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:30:56 2004

Input: Gcd(491,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:30:56 on modular  [Seed = 3820436729]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:31:11 2004

Input: Gcd(1701,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:31:10 on modular  [Seed = 4222559471]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:31:22 2004

Input: Gcd(727,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:31:21 on modular  [Seed = 4087819280]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:31:34 2004

Input: Gcd(73,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:31:33 on modular  [Seed = 3416200244]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:36:26 2004

Input: Gcd(1641-1804,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:36:25 on modular  [Seed = 3331463189]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:36:36 2004

Input: Gcd(863-1641,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:36:35 on modular  [Seed = 3750429046]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:36:45 2004

Input: Gcd(948-863,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:36:45 on modular  [Seed = 3615689072]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:36:55 2004

Input: Gcd(723-948,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:36:54 on modular  [Seed = 2952491282]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:37:05 2004

Input: Gcd(513-723,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:37:04 on modular  [Seed = 2817751341]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:37:13 2004

Input: Gcd(1098-513,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:37:13 on modular  [Seed = 3219874108]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:37:22 2004

Input: Gcd(1230-1098,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:37:21 on modular  [Seed = 3085134124]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:37:37 2004

Input: Gcd(206-1230,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:37:36 on modular  [Seed = 2413522661]
   -------------------------------------

1

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:37:44 2004

Input: Gcd(43-206,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:37:44 on modular  [Seed = 2278778597]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:37:56 2004

Input: Gcd(1005-149,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:37:55 on modular  [Seed = 2680913638]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:38:04 2004

Input: Gcd(278-1005,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:38:03 on modular  [Seed = 2512483556]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:38:13 2004

Input: Gcd(205-278,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:38:12 on modular  [Seed = 1782483747]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:38:27 2004

Input: Gcd(1559-205,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:38:27 on modular  [Seed = 1647739708]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:38:37 2004

Input: Gcd(535-1559,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:38:37 on modular  [Seed = 2049874730]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:38:46 2004

Input: Gcd(1030-535,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:38:45 on modular  [Seed = 1915130714]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:39:24 2004

Input: Gcd(1051-1030,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:39:23 on modular  [Seed = 1243523916]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:39:55 2004

Input: Gcd(21,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:39:54 on modular  [Seed = 1108779941]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:42:27 2004

Input: Gcd(1631-26,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:42:27 on modular  [Seed = 645056104]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:42:52 2004

Input: Gcd(411-677,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:42:51 on modular  [Seed = 1047191144]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:43:34 2004

Input: Gcd(1850-1631,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:43:33 on modular  [Seed = 828756281]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:44:01 2004

Input: Gcd(1005-902,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:44:00 on modular  [Seed = 157149668]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:44:30 2004

Input: Gcd(205-411,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:44:30 on modular  [Seed = 22405618]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sat Aug  7 23:45:09 2004

Input: Gcd(535-1273,1927)

Output: Magma V2.11-2     Sat Aug  7 2004 23:45:08 on modular  [Seed = 424540592]
   -------------------------------------

41

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:02:22 2004

Input: Gcd(1,7)

Output: Magma V2.11-2     Sun Aug  8 2004 00:02:21 on modular  [Seed = 4120973653]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:02:26 2004

Input: Gcd(2,7)

Output: Magma V2.11-2     Sun Aug  8 2004 00:02:25 on modular  [Seed = 3449366897]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:02:30 2004

Input: Gcd(3,7)

Output: Magma V2.11-2     Sun Aug  8 2004 00:02:29 on modular  [Seed = 3314622845]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:02:34 2004

Input: Gcd(4,7)

Output: Magma V2.11-2     Sun Aug  8 2004 00:02:34 on modular  [Seed = 3716757866]
   -------------------------------------

1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:02:39 2004

Input: Gcd(5,7)

Output: Magma V2.11-2     Sun Aug  8 2004 00:02:39 on modular  [Seed = 3582013799]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:02:43 2004

Input: Gcd(6,7)

Output: Magma V2.11-2     Sun Aug  8 2004 00:02:42 on modular  [Seed = 2918795554]
   -------------------------------------

1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-121-218-202.dsl.snfc21.pacbell.net. (68.121.218.202)
Time: Sun Aug  8 00:13:16 2004

Input: Gcd(9,15)

Output: Magma V2.11-2     Sun Aug  8 2004 00:13:15 on modular  [Seed = 3186185355]
   -------------------------------------

3

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma-dual72-73.mtholyoke.edu. (138.110.72.73)
Time: Sun Aug  8 04:10:00 2004

Input: factor(39858075)

Output: Magma V2.11-2     Sun Aug  8 2004 04:09:59 on modular  [Seed = 3449377653]
   -------------------------------------


>> factor(39858075);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (62.60.196.3)
Time: Sun Aug  8 09:32:21 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Sun Aug  8 2004 09:31:54 on modular  [Seed = 1209999990]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.820 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host e123088.upc-e.chello.nl. (213.93.123.88)
Time: Sun Aug  8 15:49:50 2004

Input: 1+3

Output: Magma V2.11-2     Sun Aug  8 2004 15:49:46 on modular  [Seed = 1142130408]
   -------------------------------------

4

Total time: 0.829 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-167-75.dynamic.hinet.net. (220.136.167.75)
Time: Sun Aug  8 22:41:55 2004

Input: factorization(90^64+1)


Output: Magma V2.11-2     Sun Aug  8 2004 22:41:52 on modular  [Seed = 2116672374]
   -------------------------------------


>> factorization(90^64+1)
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-167-75.dynamic.hinet.net. (220.136.167.75)
Time: Sun Aug  8 22:42:13 2004

Input: Factorization(90^64+1)


Output: Magma V2.11-2     Sun Aug  8 2004 22:42:09 on modular  [Seed = 1981928335]
   -------------------------------------

[ <481246721, 1>, <244992517626703646080964629812252137208394851427483099860891\
540495296174703702552603989586455800495729507526348423681, 1> ]

Total time: 4.499 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-167-75.dynamic.hinet.net. (220.136.167.75)
Time: Sun Aug  8 22:42:25 2004

Input: Factorization(86^64+1)


Output: Magma V2.11-2     Sun Aug  8 2004 22:42:24 on modular  [Seed = 1849281414]
   -------------------------------------

[ <78900878834510645468600608760004949814056831637765367937, 1>, 
<81436488526243427856680489618098138294437750338052584204172809607041, 1> ]

Total time: 0.990 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:10:44 2004

Input: Factorization (2881);


Output: Magma V2.11-2     Mon Aug  9 2004 00:10:43 on modular  [Seed = 3432740087]
   -------------------------------------

[ <43, 1>, <67, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:11:00 2004

Input: factorization (2881);


Output: Magma V2.11-2     Mon Aug  9 2004 00:10:59 on modular  [Seed = 3298000111]
   -------------------------------------


>> factorization (2881);
   ^
User error: Identifier 'factorization' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:11:44 2004

Input: Integers(2772)! 1/5;


Output: Magma V2.11-2     Mon Aug  9 2004 00:11:43 on modular  [Seed = 3169518779]
   -------------------------------------

1109

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:12:14 2004

Input: (Integers(2881)! 504)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 00:12:13 on modular  [Seed = 3034778705]
   -------------------------------------

400

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:12:54 2004

Input: (Integers(2881)! 1874)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 00:12:54 on modular  [Seed = 2902135826]
   -------------------------------------

1902

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:14:06 2004

Input: (Integers(2881)! 347)^1109;
(Integers(2881)! 515)^1109;
(Integers(2881)! 2088)^1109;
(Integers(2881)! 2356)^1109;
(Integers(2881)! 736)^1109;
(Integers(2881)! 408)^1109;
(Integers(2881)! 347)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:14:06 on modular  [Seed = 2767396818]
   -------------------------------------

714
214
1100
1904
200
2467
714

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:15:19 2004

Input: 1887^2+1;

Output: Magma V2.11-2     Mon Aug  9 2004 00:15:18 on modular  [Seed = 2630559667]
   -------------------------------------

3560770

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:15:25 2004

Input: 1887^2+1;

Output: Magma V2.11-2     Mon Aug  9 2004 00:15:25 on modular  [Seed = 2495819697]
   -------------------------------------

3560770

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:20:46 2004

Input: (Integers(2881)! 468)^1109 ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:20:45 on modular  [Seed = 1998638481]
   -------------------------------------

1004

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:25:18 2004

Input: SetVerbose("Cunningham", true);
n := 3^429 + 1;
Factorization(n);

Output: Magma V2.11-2     Mon Aug  9 2004 00:25:17 on modular  [Seed = 1832571067]
   -------------------------------------

Cunningham Factorization: a = 3, e = 429, c = 1
Effort: 3
Trial Division
Found prime <2, 2>
Found prime <7, 1>
Found prime <67, 1>
Found prime <79, 1>
Found prime <157, 1>
Found prime <661, 1>
Found prime <859, 1>
Found prime <2887, 1>
Database lookup
Found prime <207344547828773831191, 1>
Aurifeuillian factors
Found prime <176419, 1>
Found prime <25411, 1>
Found prime <10141, 1>
Primality testing 701165388462884713306643307508027898395978016375818531
Found composite 701165388462884713306643307508027898395978016375818531
Found composite 20111901509540782735138419535221095479
Algebraic factors
Found prime <398581, 1>
Primality testing 2395998704896515009570769446878479241856890751873310751281
Found composite 2395998704896515009570769446878479241856890751873310751281
Factoring 701165388462884713306643307508027898395978016375818531
Factoring 20111901509540782735138419535221095479
Factoring 2395998704896515009570769446878479241856890751873310751281
[ <2, 2>, <7, 1>, <67, 1>, <79, 1>, <157, 1>, <661, 1>, <859, 1>, <2887, 1>, 
<10141, 1>, <20593, 1>, <25411, 1>, <53197, 1>, <176419, 1>, <398581, 1>, 
<1680823, 1>, <33531499, 1>, <207344547828773831191, 1>, 
<11965508271567430202429654719873, 1>, <101542507046161705839774632910752277130\
7833, 1>, <45040109496710622959391872603313706446921645052790773, 1> ]

Total time: 0.890 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:26:58 2004

Input: GCD(600,452);

Output: Magma V2.11-2     Mon Aug  9 2004 00:26:58 on modular  [Seed = 1527572274]
   -------------------------------------

4

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:27:53 2004

Input: Integers(1927)! (1887^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:27:52 on modular  [Seed = 1392832352]
   -------------------------------------

1601

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:28:09 2004

Input: Integers(1927)! (2^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:28:08 on modular  [Seed = 1260189544]
   -------------------------------------

5

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:28:13 2004

Input: Integers(1927)! (5^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:28:13 on modular  [Seed = 1125449573]
   -------------------------------------

26

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:28:14 2004

Input: Integers(1927)! (5^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:28:13 on modular  [Seed = 1092025703]
   -------------------------------------

26

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:28:20 2004

Input: Integers(1927)! (26^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:28:19 on modular  [Seed = 862228267]
   -------------------------------------

677

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:28:27 2004

Input: Integers(1927)! (677^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:28:26 on modular  [Seed = 729585466]
   -------------------------------------

1631

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:28:37 2004

Input: Integers(1927)! (1631^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:28:36 on modular  [Seed = 594845484]
   -------------------------------------

902

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:29:04 2004

Input: Integers(1927)! (902^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:29:04 on modular  [Seed = 306556665]
   -------------------------------------

411

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:29:18 2004

Input: Integers(1927)! (411^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:29:17 on modular  [Seed = 173913839]
   -------------------------------------

1273

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:29:38 2004

Input: Integers(1927)! (41273^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:29:37 on modular  [Seed = 39173835]
   -------------------------------------

238

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:29:43 2004

Input: Integers(1927)! (1273^2+1) ;

Output: Magma V2.11-2     Mon Aug  9 2004 00:29:42 on modular  [Seed = 4205659703]
   -------------------------------------

1850

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:31:19 2004

Input: Integers(1927)! (1273^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(411-677,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:31:19 on modular  [Seed = 4037496732]
   -------------------------------------

1850
1
1
1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:31:50 2004

Input: Integers(1927)! (1273^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(1850-1631,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:31:50 on modular  [Seed = 3887093930]
   -------------------------------------

1850
1
1
1

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:32:15 2004

Input: Integers(1927)! (1850^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(1850-1631,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:32:14 on modular  [Seed = 3750256874]
   -------------------------------------

149
1
1
1

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:32:24 2004

Input: Integers(1927)! (149^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(1850-1631,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:32:23 on modular  [Seed = 3615516923]
   -------------------------------------

1005
1
1
1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:32:47 2004

Input: Integers(1927)! (149^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(105-902,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:32:46 on modular  [Seed = 3331422675]
   -------------------------------------

1005
1
1
1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:33:04 2004

Input: Integers(1927)! (1005^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(105-902,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:33:03 on modular  [Seed = 3202941370]
   -------------------------------------

278
1
1
1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:33:16 2004

Input: Integers(1927)! (278^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(105-902,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:33:15 on modular  [Seed = 3068201286]
   -------------------------------------

205
1
1
1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:33:36 2004

Input: Integers(1927)! (278^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(205-411,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:33:35 on modular  [Seed = 2935558474]
   -------------------------------------

205
1
1
1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:33:57 2004

Input: Integers(1927)! (205^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(205-411,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:33:56 on modular  [Seed = 2800818537]
   -------------------------------------

1559
1
1
1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:34:27 2004

Input: Factorization(1927);
Integers(1927)! (1559^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(205-411,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:34:27 on modular  [Seed = 2663981366]
   -------------------------------------

[ <41, 1>, <47, 1> ]
535
1
1
1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:34:30 2004

Input: Factorization(1927);
Integers(1927)! (1559^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(205-411,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:34:30 on modular  [Seed = 2529241403]
   -------------------------------------

[ <41, 1>, <47, 1> ]
535
1
1
1

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:34:58 2004

Input: Factorization(1927);
Integers(1927)! (1559^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(535-1273,1927);

Output: Magma V2.11-2     Mon Aug  9 2004 00:34:57 on modular  [Seed = 2396598532]
   -------------------------------------

[ <41, 1>, <47, 1> ]
535
1
1
41

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-114-209.Reshall.Berkeley.EDU. (169.229.114.209)
Time: Mon Aug  9 00:35:20 2004

Input: Factorization(1927);
Integers(1927)! (1559^2+1) ;
GCD(26-5,1927);
GCD(1631-26,1927);
GCD(535-1273,1927);
1273-535;

Output: Magma V2.11-2     Mon Aug  9 2004 00:35:19 on modular  [Seed = 2066531590]
   -------------------------------------

[ <41, 1>, <47, 1> ]
535
1
1
41
738

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:48:22 2004

Input: (Integers(2772)!504)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:48:21 on modular  [Seed = 1075184431]
   -------------------------------------

1512

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:52:13 2004

Input: (Integers(2081)!504)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:52:13 on modular  [Seed = 1047035321]
   -------------------------------------

636

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:54:00 2004

Input: (Integers(2881)!504)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:53:59 on modular  [Seed = 878868009]
   -------------------------------------

400

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:55:08 2004

Input: (Integers(2881)!1874)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:55:07 on modular  [Seed = 746221309]
   -------------------------------------

1902

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:55:58 2004

Input: (Integers(2881)!0347)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:55:58 on modular  [Seed = 628320129]
   -------------------------------------

714

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:56:03 2004

Input: (Integers(2881)!347)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:56:02 on modular  [Seed = 491478917]
   -------------------------------------

714

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:56:57 2004

Input: (Integers(2881)!515)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:56:57 on modular  [Seed = 173821801]
   -------------------------------------

214

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:57:50 2004

Input: (Integers(2881)!2088)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:57:49 on modular  [Seed = 5653815]
   -------------------------------------

1100

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:58:27 2004

Input: (Integers(2881)!504)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:58:26 on modular  [Seed = 4239047156]
   -------------------------------------

400

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:58:57 2004

Input: (Integers(2881)!2356)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:58:57 on modular  [Seed = 4104302879]
   -------------------------------------

1904

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 00:59:51 2004

Input: (Integers(2881)!736)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 00:59:51 on modular  [Seed = 3971656017]
   -------------------------------------

200

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 01:00:16 2004

Input: (Integers(2881)!468)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 01:00:15 on modular  [Seed = 3416100462]
   -------------------------------------

1004

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 01:03:46 2004

Input: (Integers(2537)!95)^937;


Output: Magma V2.11-2     Mon Aug  9 2004 01:03:45 on modular  [Seed = 3231089675]
   -------------------------------------

1520

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 01:04:30 2004

Input: (Integers(2881)!504)^1109;


Output: Magma V2.11-2     Mon Aug  9 2004 01:04:29 on modular  [Seed = 3102669855]
   -------------------------------------

400

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-68-122-2-122.dsl.pltn13.pacbell.net. (68.122.2.122)
Time: Mon Aug  9 01:07:52 2004

Input: (Integers(2537)!1648)^937;


Output: Magma V2.11-2     Mon Aug  9 2004 01:07:51 on modular  [Seed = 2868702583]
   -------------------------------------

111

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:10:21 2004

Input: (Integer(2881)!504)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:10:20 on modular  [Seed = 812016641]
   -------------------------------------


>> (Integer(2881)!504)^1109;;
    ^
User error: Identifier 'Integer' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:10:36 2004

Input: (Integers(2881)!504)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:10:35 on modular  [Seed = 729644813]
   -------------------------------------

400

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:11:20 2004

Input: (Integers(2881)!1874)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:11:20 on modular  [Seed = 594900950]
   -------------------------------------

1902

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:11:38 2004

Input: (Integers(2881)!347)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:11:38 on modular  [Seed = 441208573]
   -------------------------------------

714

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:11:48 2004

Input: (Integers(2881)!515)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:11:47 on modular  [Seed = 306464460]
   -------------------------------------

214

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:11:57 2004

Input: (Integers(2881)!2088)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:11:57 on modular  [Seed = 173825754]
   -------------------------------------

1100

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:12:09 2004

Input: (Integers(2881)!2356)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:12:08 on modular  [Seed = 39081671]
   -------------------------------------

1904

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:12:24 2004

Input: (Integers(2881)!736)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:12:23 on modular  [Seed = 4205620800]
   -------------------------------------

200

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host u5-68-116.Rescomp.Berkeley.EDU. (169.229.68.116)
Time: Mon Aug  9 02:12:35 2004

Input: (Integers(2881)!468)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 02:12:34 on modular  [Seed = 4070876765]
   -------------------------------------

1004

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 02:46:45 2004

Input: Factorisation(4386607);

Output: Magma V2.11-2     Mon Aug  9 2004 02:46:44 on modular  [Seed = 2852123904]
   -------------------------------------

[ <1453, 1>, <3019, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 03:36:46 2004

Input: Factorisation(2881);

Output: Magma V2.11-2     Mon Aug  9 2004 03:36:45 on modular  [Seed = 1731268502]
   -------------------------------------

[ <43, 1>, <67, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 03:48:00 2004

Input: Integers(2772)! 1/5;

Output: Magma V2.11-2     Mon Aug  9 2004 03:47:59 on modular  [Seed = 1192307220]
   -------------------------------------

1109

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:07:40 2004

Input: (Integers(2881)! 504)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:07:39 on modular  [Seed = 4154558016]
   -------------------------------------

400

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:10:09 2004

Input: (Integers(2881)! 1874)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:10:09 on modular  [Seed = 3836908793]
   -------------------------------------

1902

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:11:21 2004

Input: (Integers(2881)! 347)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:11:20 on modular  [Seed = 3716918537]
   -------------------------------------

714

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:11:26 2004

Input: (Integers(2881)! 0347)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:11:25 on modular  [Seed = 3582174471]
   -------------------------------------

714

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:12:02 2004

Input: (Integers(2881)! 0515)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:12:01 on modular  [Seed = 3449535840]
   -------------------------------------

214

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:12:38 2004

Input: (Integers(2881)! 2088)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:12:37 on modular  [Seed = 3314791756]
   -------------------------------------

1100

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:13:32 2004

Input: (Integers(2356)! 2088)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:13:31 on modular  [Seed = 3186347754]
   -------------------------------------

916

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:14:40 2004

Input: (Integers(2881)! 2356)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:14:39 on modular  [Seed = 3051603622]
   -------------------------------------

1904

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:15:00 2004

Input: (Integers(2881)! 0736)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:15:00 on modular  [Seed = 2918964821]
   -------------------------------------

200

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:15:28 2004

Input: (Integers(2881)! 0468)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 04:15:28 on modular  [Seed = 2800801146]
   -------------------------------------

1004

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:34:38 2004

Input: 458330%1927;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:35:30 2004

Input: Integers(458330)!1927;

Output: Magma V2.11-2     Mon Aug  9 2004 04:35:29 on modular  [Seed = 2033127255]
   -------------------------------------

1927

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:35:59 2004

Input: Integers(1927)!458330;

Output: Magma V2.11-2     Mon Aug  9 2004 04:35:58 on modular  [Seed = 1898383200]
   -------------------------------------

1631

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:37:51 2004

Input: Integers(1927)!26^2;

Output: Magma V2.11-2     Mon Aug  9 2004 04:37:51 on modular  [Seed = 1748901576]
   -------------------------------------

676

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:38:04 2004

Input: Integers(1927)!677^2;

Output: Magma V2.11-2     Mon Aug  9 2004 04:38:04 on modular  [Seed = 1577593037]
   -------------------------------------

1630

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:38:14 2004

Input: Integers(1927)!1631^2;

Output: Magma V2.11-2     Mon Aug  9 2004 04:38:14 on modular  [Seed = 1442848991]
   -------------------------------------

901

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:38:51 2004

Input: Integers(1927)!902^2;

Output: Magma V2.11-2     Mon Aug  9 2004 04:38:51 on modular  [Seed = 1310209834]
   -------------------------------------

410

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:39:23 2004

Input: Integers(1927)!411^2;

Output: Magma V2.11-2     Mon Aug  9 2004 04:39:22 on modular  [Seed = 1175469827]
   -------------------------------------

1272

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:41:27 2004

Input: Integers(1927)!411^2;
Factorisation(1605);

Output: Magma V2.11-2     Mon Aug  9 2004 04:41:26 on modular  [Seed = 712791011]
   -------------------------------------

1272
[ <3, 1>, <5, 1>, <107, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:41:41 2004

Input: Integers(1927)!411^2;
Factorisation(1605);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:41:41 on modular  [Seed = 578050968]
   -------------------------------------

1272
[ <3, 1>, <5, 1>, <107, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:46:18 2004

Input: Integers(1927)!411^2;
Factorisation(707);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:46:18 on modular  [Seed = 173830831]
   -------------------------------------

1272
[ <7, 1>, <101, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:46:47 2004

Input: Integers(1927)!411^2 +1;
Factorisation(707);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:46:46 on modular  [Seed = 22509960]
   -------------------------------------

1273
[ <7, 1>, <101, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:46:57 2004

Input: Integers(1927)!1273^2 +1;
Factorisation(707);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:46:57 on modular  [Seed = 4189028999]
   -------------------------------------

1850
[ <7, 1>, <101, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:47:44 2004

Input: Integers(1927)!1273^2 +1;
Factorisation(1439);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:47:43 on modular  [Seed = 4054289057]
   -------------------------------------

1850
[ <1439, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:48:09 2004

Input: Integers(1927)!1850^2 +1;
Factorisation(1439);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:48:08 on modular  [Seed = 3921646302]
   -------------------------------------

149
[ <1439, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:48:25 2004

Input: Integers(1927)!149^2 +1;
Factorisation(1439);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:48:24 on modular  [Seed = 3786906310]
   -------------------------------------

1005
[ <1439, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:48:51 2004

Input: Integers(1927)!149^2 +1;
Factorisation(1082);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:48:50 on modular  [Seed = 3650069205]
   -------------------------------------

1005
[ <2, 1>, <541, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:49:09 2004

Input: Integers(1927)!1005^2 +1;
Factorisation(1082);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:49:08 on modular  [Seed = 3515329066]
   -------------------------------------

278
[ <2, 1>, <541, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:49:21 2004

Input: Integers(1927)!278^2 +1;
Factorisation(1082);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:49:20 on modular  [Seed = 3382686246]
   -------------------------------------

205
[ <2, 1>, <541, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:49:43 2004

Input: Integers(1927)!278^2 +1;
Factorisation(1127);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:49:42 on modular  [Seed = 3247946264]
   -------------------------------------

205
[ <7, 2>, <23, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:50:24 2004

Input: Integers(1927)!205^2 +1;
Factorisation(1127);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:50:23 on modular  [Seed = 3119497737]
   -------------------------------------

1559
[ <7, 2>, <23, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:50:38 2004

Input: Integers(1927)!1559^2 +1;
Factorisation(1127);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:50:38 on modular  [Seed = 2902120205]
   -------------------------------------

535
[ <7, 2>, <23, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:51:05 2004

Input: Integers(1927)!1559^2 +1;
Factorisation(330);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:51:04 on modular  [Seed = 2767380259]
   -------------------------------------

535
[ <2, 1>, <3, 1>, <5, 1>, <11, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:51:17 2004

Input: Integers(1927)!5^2 +1;
Factorisation(330);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:51:17 on modular  [Seed = 2630543078]
   -------------------------------------

26
[ <2, 1>, <3, 1>, <5, 1>, <11, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:51:24 2004

Input: Integers(1927)!26^2 +1;
Factorisation(330);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:51:24 on modular  [Seed = 2495803111]
   -------------------------------------

677
[ <2, 1>, <3, 1>, <5, 1>, <11, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:51:34 2004

Input: Integers(1927)!677^2 +1;
Factorisation(330);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:51:33 on modular  [Seed = 2363160294]
   -------------------------------------

1631
[ <2, 1>, <3, 1>, <5, 1>, <11, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:51:53 2004

Input: Integers(1927)!677^2 +1;
Factorisation(1605);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:51:52 on modular  [Seed = 2228420307]
   -------------------------------------

1631
[ <3, 1>, <5, 1>, <107, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:52:44 2004

Input: Integers(1927)!535^2 +1;
Factorisation(1605);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:52:44 on modular  [Seed = 2099971935]
   -------------------------------------

1030
[ <3, 1>, <5, 1>, <107, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:53:32 2004

Input: Integers(1927)!535^2 +1;
Factorisation(1661);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:53:31 on modular  [Seed = 1931807110]
   -------------------------------------

1030
[ <11, 1>, <151, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:53:58 2004

Input: Integers(1927)!535^2 +1;
Factorisation(219);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:53:57 on modular  [Seed = 1799164336]
   -------------------------------------

1030
[ <3, 1>, <73, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:54:21 2004

Input: Integers(1927)!535^2 +1;
Factorisation(103);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:54:21 on modular  [Seed = 1664424352]
   -------------------------------------

1030
[ <103, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:55:03 2004

Input: Integers(1927)!535^2 +1;
Factorisation(1721);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:55:03 on modular  [Seed = 1527587266]
   -------------------------------------

1030
[ <1721, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 04:55:45 2004

Input: Integers(1927)!535^2 +1;
Factorisation(1189);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 04:55:44 on modular  [Seed = 1342582078]
   -------------------------------------

1030
[ <29, 1>, <41, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 05:32:05 2004

Input: Integers(15)!11^2;
Factorisation(1189);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 05:32:04 on modular  [Seed = 289871099]
   -------------------------------------

1
[ <29, 1>, <41, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 05:32:30 2004

Input: Integers(15)!12^2;
Factorisation(1189);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 05:32:29 on modular  [Seed = 157224154]
   -------------------------------------

9
[ <29, 1>, <41, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 05:32:42 2004

Input: Integers(15)!13^2;
Factorisation(1189);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 05:32:41 on modular  [Seed = 22480070]
   -------------------------------------

4
[ <29, 1>, <41, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ckc-109-100.Reshall.Berkeley.EDU. (169.229.109.100)
Time: Mon Aug  9 05:32:53 2004

Input: Integers(15)!14^2;
Factorisation(1189);
Factorisation(1927);

Output: Magma V2.11-2     Mon Aug  9 2004 05:32:52 on modular  [Seed = 4189060163]
   -------------------------------------

1
[ <29, 1>, <41, 1> ]
[ <41, 1>, <47, 1> ]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:09:28 2004

Input: (Integers(2881!504)^1109;

Output: Magma V2.11-2     Mon Aug  9 2004 12:09:28 on modular  [Seed = 2546038573]
   -------------------------------------


>> (Integers(2881!504)^1109;;
                           ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:09:36 2004

Input: (Integers(2881!504)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:09:35 on modular  [Seed = 2680782626]
   -------------------------------------


>> (Integers(2881!504)^1109;
                           ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:09:50 2004

Input: (Integers(2881)!504)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:09:50 on modular  [Seed = 2817607531]
   -------------------------------------

400

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:11:20 2004

Input: (Integers(2881)!347)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:11:19 on modular  [Seed = 3018150038]
   -------------------------------------

714

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:11:44 2004

Input: (Integers(2881)!2088)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:11:43 on modular  [Seed = 3152894086]
   -------------------------------------

1100

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:12:00 2004

Input: (Integers(2881)!0736)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:11:59 on modular  [Seed = 3281330318]
   -------------------------------------

200

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:13:04 2004

Input: (Integers(2881)!1874)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:13:04 on modular  [Seed = 3416074329]
   -------------------------------------

1902

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:13:18 2004

Input: (Integers(2881)!0515)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:13:17 on modular  [Seed = 3548721228]
   -------------------------------------

214

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:13:30 2004

Input: (Integers(2881)!2356)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:13:30 on modular  [Seed = 3683465331]
   -------------------------------------

1904

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:13:42 2004

Input: (Integers(2881)!468)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:13:42 on modular  [Seed = 3820290135]
   -------------------------------------

1004

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:15:06 2004

Input: (Integers(2881)!347)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:15:05 on modular  [Seed = 3955034592]
   -------------------------------------

714

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:15:16 2004

Input: (Integers(2881)!2008)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:15:16 on modular  [Seed = 4087681509]
   -------------------------------------

1567

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:15:24 2004

Input: (Integers(2881)!2088)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:15:23 on modular  [Seed = 4222425570]
   -------------------------------------

1100

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:15:51 2004

Input: (Integers(2772)!504)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:15:51 on modular  [Seed = 122807605]
   -------------------------------------

1512

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:16:07 2004

Input: (Integers(2772)!347)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:16:06 on modular  [Seed = 157281098]
   -------------------------------------

695

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:16:39 2004

Input: Integers(2772)!1/5

Output: Magma V2.11-2     Mon Aug  9 2004 12:16:39 on modular  [Seed = 306507888]
   -------------------------------------

1109

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host info-190-31.Lib.Berkeley.EDU. (128.32.78.171)
Time: Mon Aug  9 12:18:44 2004

Input: (Integers(2881)!515)^1109

Output: Magma V2.11-2     Mon Aug  9 2004 12:18:43 on modular  [Seed = 611501762]
   -------------------------------------

214

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:10:32 2004

Input: Factorize(11111);

Output: Magma V2.11-2     Mon Aug  9 2004 20:10:31 on modular  [Seed = 628913753]
   -------------------------------------


>> Factorize(11111);;
   ^
User error: Identifier 'Factorize' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:10:40 2004

Input: Factorization(11111);

Output: Magma V2.11-2     Mon Aug  9 2004 20:10:39 on modular  [Seed = 1029992009]
   -------------------------------------

[ <41, 1>, <271, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:10:45 2004

Input: Factorization(1111111);

Output: Magma V2.11-2     Mon Aug  9 2004 20:10:45 on modular  [Seed = 896296635]
   -------------------------------------

[ <239, 1>, <4649, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:10:51 2004

Input: Factorization(111111111);

Output: Magma V2.11-2     Mon Aug  9 2004 20:10:50 on modular  [Seed = 1293164236]
   -------------------------------------

[ <3, 2>, <37, 1>, <333667, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:10:55 2004

Input: Factorization(11111111111);

Output: Magma V2.11-2     Mon Aug  9 2004 20:10:54 on modular  [Seed = 1159468737]
   -------------------------------------

[ <21649, 1>, <513239, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:18:59 2004

Input: Factorization(12321);

Output: Magma V2.11-2     Mon Aug  9 2004 20:18:58 on modular  [Seed = 1764768784]
   -------------------------------------

[ <3, 2>, <37, 2> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host www-cache5.usyd.edu.au. (129.78.64.105)
Time: Mon Aug  9 20:19:22 2004

Input: Factorization(123454321);

Output: Magma V2.11-2     Mon Aug  9 2004 20:19:22 on modular  [Seed = 1965826292]
   -------------------------------------

[ <41, 2>, <271, 2> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 04:26:24 2004

Input: Q := RationalField();
M := RMatrixSpace(Q, 8, 8) ! 
[  2,  0,  0,  0,  0,  0,  0,  0,
  -1,  1,  0,  0,  0,  0,  0,  0,
   0,  1, -1,  0,  0,  0,  0,  0,
   0,  0,  1, -1,  0,  0,  0,  0,
   0,  0,  0,  1, -1,  0,  0,  0,
   0,  0,  0,  0,  1, -1,  0,  0,
   0,  0,  0,  0,  0,  1, -1,  0,
 1/2,1/2,1/2,1/2,1/2,1/2,1/2,1/2
];

E8 := LatticeWithBasis(M);
QE8 := GramMatrix(E8);
E8Gram := LatticeWithGram(QE8);

Output: Magma V2.11-2     Tue Aug 10 2004 04:26:24 on modular  [Seed = 123650233]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 04:27:05 2004

Input: Q := RationalField();
M := RMatrixSpace(Q, 8, 8) ! 
[  2,  0,  0,  0,  0,  0,  0,  0,
  -1,  1,  0,  0,  0,  0,  0,  0,
   0,  1, -1,  0,  0,  0,  0,  0,
   0,  0,  1, -1,  0,  0,  0,  0,
   0,  0,  0,  1, -1,  0,  0,  0,
   0,  0,  0,  0,  1, -1,  0,  0,
   0,  0,  0,  0,  0,  1, -1,  0,
 1/2,1/2,1/2,1/2,1/2,1/2,1/2,1/2
];

E8 := LatticeWithBasis(M);
QE8 := GramMatrix(E8);
E8Gram := LatticeWithGram(QE8);
VoronoiCell(E8);

Output: Magma V2.11-2     Tue Aug 10 2004 04:26:44 on modular  [Seed = 406970322]
   -------------------------------------



************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:02:22 2004

Input: L := Lattice("D",4);
H := Holes(L);


Output: Magma V2.11-2     Tue Aug 10 2004 06:02:21 on modular  [Seed = 4104988887]
   -------------------------------------


Total time: 0.639 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:02:32 2004

Input: L := Lattice("D",4);
H := Holes(L);
H;

Output: Magma V2.11-2     Tue Aug 10 2004 06:02:31 on modular  [Seed = 323669818]
   -------------------------------------

[
    (-1/2 -1/2  1/2 -1/2),
    ( 1/2 -1/2  1/2  1/2),
    (-1/2 -1/2  1/2  1/2),
    ( 1/2 -1/2 -1/2  1/2),
    (-1/2 -1/2 -1/2  1/2),
    ( 0 -1  0  0),
    (-1/2  1/2  1/2  1/2),
    (1/2 1/2 1/2 1/2),
    ( 1/2 -1/2 -1/2 -1/2),
    (-1/2 -1/2 -1/2 -1/2),
    (0 0 1 0),
    (-1  0  0  0),
    ( 0  0  0 -1),
    (0 0 0 1),
    ( 0  0 -1  0),
    (-1/2  1/2 -1/2 -1/2),
    (-1/2  1/2  1/2 -1/2),
    (1 0 0 0),
    (-1/2  1/2 -1/2  1/2),
    ( 1/2  1/2  1/2 -1/2),
    ( 1/2  1/2 -1/2  1/2),
    ( 1/2  1/2 -1/2 -1/2),
    (0 1 0 0),
    ( 1/2 -1/2  1/2 -1/2)
]

Total time: 0.649 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:02:52 2004

Input: L := Lattice("D",4);
H := Holes(L);
H[1];

Output: Magma V2.11-2     Tue Aug 10 2004 06:02:51 on modular  [Seed = 457361217]
   -------------------------------------

(-1/2 -1/2  1/2 -1/2)

Total time: 0.639 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:03:00 2004

Input: L := Lattice("D",4);
H := Holes(L);
#H[1];

Output: Magma V2.11-2     Tue Aug 10 2004 06:02:59 on modular  [Seed = 56287041]
   -------------------------------------


>> #H[1];;
   ^
Runtime error in '#': Bad argument types
Argument types given: ModTupFldElt

Total time: 0.639 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:03:09 2004

Input: L := Lattice("D",4);
H := Holes(L);
#(H[1]);

Output: Magma V2.11-2     Tue Aug 10 2004 06:03:09 on modular  [Seed = 189978439]
   -------------------------------------


>> #(H[1]);;
   ^
Runtime error in '#': Bad argument types
Argument types given: ModTupFldElt

Total time: 0.630 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:03:17 2004

Input: L := Lattice("D",4);
H := Holes(L);
Length(H[1]);

Output: Magma V2.11-2     Tue Aug 10 2004 06:03:16 on modular  [Seed = 862646086]
   -------------------------------------


>> Length(H[1]);;
         ^
Runtime error in 'Length': Bad argument types
Argument types given: ModTupFldElt

Total time: 0.679 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:04:23 2004

Input: L := Lattice("D",4);
H := Holes(L);
H[1][2];

Output: Magma V2.11-2     Tue Aug 10 2004 06:04:20 on modular  [Seed = 979625615]
   -------------------------------------

-1/2

Total time: 0.840 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:06:05 2004

Input: L := Lattice("D",4);
H := Holes(L);
Size(H[1]);

Output: Magma V2.11-2     Tue Aug 10 2004 06:06:05 on modular  [Seed = 612236088]
   -------------------------------------


>> Size(H[1]);;
       ^
Runtime error in 'Size': Bad argument types
Argument types given: ModTupFldElt

Total time: 0.620 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:09:22 2004

Input: L := Lattice("D",4);
H := Holes(L);
NumberOfColumns(H[1]);

Output: Magma V2.11-2     Tue Aug 10 2004 06:09:21 on modular  [Seed = 779612654]
   -------------------------------------

4

Total time: 0.620 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:09:56 2004

Input: L' := Lattice("D",4);
H := Holes(L);
NumberOfColumns(H[1]);

Output: Magma V2.11-2     Tue Aug 10 2004 06:09:56 on modular  [Seed = 1443858867]
   -------------------------------------


>> L' := Lattice("D",4);
                        ^
User error: Unexpected newline in literal identifier

>> H := Holes(L);
              ^
User error: Identifier 'L' has not been declared or assigned

>> NumberOfColumns(H[1]);;
                   ^
User error: Identifier 'H' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:11:40 2004

Input: L := Lattice("D",4);
H := Holes(L);
Sort(H);

Output: Magma V2.11-2     Tue Aug 10 2004 06:11:39 on modular  [Seed = 1193187597]
   -------------------------------------


>> Sort(H);;
       ^
Runtime error in 'Sort': No comparison algorithm for sequence elts

Total time: 0.620 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host proxy7-m.huji.ac.il. (128.139.226.37)
Time: Tue Aug 10 06:15:38 2004

Input: L := Lattice("D",4);
H := Holes(L);
?Sort;


Output: Magma V2.11-2     Tue Aug 10 2004 06:15:37 on modular  [Seed = 1932169771]
   -------------------------------------

4 matches:
     1   I   /magma/aggregate/sequence/detail/operation/modification/Sort
     2   I   /magma/aggregate/sequence/detail/operation/modification/Sort
     3   I   /magma/geometry/brandt-modules/ModBrdt:Subspaces/SortDecomposition
     4   I   /magma/geometry/modular-symbol/decomposition/SortDecomposition
To view an entry, type ? followed by the number next to it

Total time: 0.620 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (83.146.13.223)
Time: Tue Aug 10 06:53:56 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Tue Aug 10 2004 06:53:54 on modular  [Seed = 1193193237]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.639 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 06:55:15 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
ShortVectors(L1,6);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Tue Aug 10 2004 06:55:05 on modular  [Seed = 1881774313]
   -------------------------------------


Current total memory usage: 92.2MB, failed memory request: 3.7MB
System Error: User memory limit has been reached

Current total memory usage: 92.2MB, failed memory request: 3.7MB
System Error: User memory limit has been reached

Current total memory usage: 92.2MB, failed memory request: 3.7MB
System Error: User memory limit has been reached

Total time: 9.819 seconds, Total memory usage: 96.71MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 06:57:58 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
ShortVectors(L1,1,3);

Output: Magma V2.11-2     Tue Aug 10 2004 06:57:57 on modular  [Seed = 2032177756]
   -------------------------------------

[
    <(1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0), 2>,
    <(1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1), 2>,
    <(1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0), 2>,
    <(1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0), 2>,
    <(1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0), 2>,
    <(1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0), 2>,
    <(1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0), 2>,
    <( 1  0  0  1 -1  0  0  0  0  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  1 -1  0  0  0  0  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  1 -1  0  0  0  0  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  1 -1  0  0  0  0  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  1 -1  0  0  0  1  0  0  0  0  0  0  1), 2>,
    <( 1  0  0  1 -1  0  0  0  1  0  0  0  1  0  0  0), 2>,
    <( 1  0  0  1 -1  0  0  0  1  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  1 -1  0  0  0  1  0  1  0  0  0  0  0), 2>,
    <( 1  0  0  1 -1  0  0  0  1  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  1 -1  0  0  0  1  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  1 -1  0  1  0  0  0  0  0  0  0  0  1), 2>,
    <( 1  0  0  1 -1  0  1  0  0  0  0  0  1  0  0  0), 2>,
    <( 1  0  0  1 -1  0  1  0  0  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  1 -1  0  1  0  0  0  1  0  0  0  0  0), 2>,
    <( 1  0  0  1 -1  0  1  0  0  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  1 -1  0  1  0  0  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  1 -1  0  1  0  1  0  0  0  0  0  0  0), 2>,
    <( 1  0  0  1 -1  0  1  0  1  0  0  0  0  0  0  1), 2>,
    <( 1  0  0  1 -1  0  1  0  1  0  0  0  1  0  0  0), 2>,
    <( 1  0  0  1 -1  0  1  0  1  0  1  0  0  0  0  0), 2>,
    <(1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1), 2>,
    <(1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0), 2>,
    <(1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1), 2>,
    <(1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0), 2>,
    <(1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1), 2>,
    <(1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0), 2>,
    <(1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0), 2>,
    <(1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1), 2>,
    <(1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0), 2>,
    <(1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0), 2>,
    <(1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0), 2>,
    <(1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1), 2>,
    <(1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0), 2>,
    <(1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0), 2>,
    <(1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0), 2>,
    <( 1  0  0  2 -2  0  0  0  1  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  2 -2  0  1  0  0  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  2 -2  0  1  0  1  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  2 -2  0  1  0  1  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  2 -2  0  1  0  1  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  2 -2  0  1  0  1  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  0  0  0  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  0  0  1  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  0  0  1  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  2 -1  0  0  0  1  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  2 -1  0  0  0  1  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  0  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  0  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  0  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  2 -1  0  1  0  0  0  1  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  1  0  0  0  0  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  1  0  0  0  1  0  0  0), 2>,
    <( 1  0  0  2 -1  0  1  0  1  0  0  0  1  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  1  0  1  0  0  0  0  0), 2>,
    <( 1  0  0  2 -1  0  1  0  1  0  1  0  0  0  0  1), 2>,
    <( 1  0  0  2 -1  0  1  0  1  0  1  0  1  0  0  0), 2>,
    <( 1  0  0  3 -2  0  1  0  1  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  2 -2  0  1  0  1  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  2 -1  0  0  0  1  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  2 -1  0  1  0  0  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  2 -1  0  1  0  1  0  0  0  1  0  0  1), 2>,
    <( 2  0  0  2 -1  0  1  0  1  0  1  0  0  0  0  1), 2>,
    <( 2  0  0  2 -1  0  1  0  1  0  1  0  1  0  0  0), 2>,
    <( 2  0  0  2 -1  0  1  0  1  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  3 -2  0  1  0  1  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  3 -2  0  1  0  1  0  1  0  1  0  0  2), 2>,
    <( 2  0  0  3 -2  0  1  0  1  0  1  0  2  0  0  1), 2>,
    <( 2  0  0  3 -2  0  1  0  1  0  2  0  1  0  0  1), 2>,
    <( 2  0  0  3 -2  0  1  0  2  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  3 -2  0  2  0  1  0  1  0  1  0  0  1), 2>,
    <( 2  0  0  3 -1  0  1  0  1  0  1  0  1  0  0  1), 2>,
    <( 0  1 -3  0  0 -2  0  1  0  1  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -2  0  0  0  1  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -2  0  1  0  0  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -2  0  1  0  1  0  0  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -2  0  1  0  1  0  1  0  0 -1  0), 2>,
    <( 0  1 -2  0  0 -2  0  1  0  1  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -2  0  1  0  1  0  1  0  1  0  0), 2>,
    <( 0  1 -2  0  0 -1  0  0  0  0  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  0  0  1  0  0  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  0  0  1  0  1  0  0 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  0  0  1  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  0  0  1  0  1  0  1  0  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  0  0  0  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  0  0  1  0  0 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  0  0  1  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  0  0  1  0  1  0  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  1  0  0  0  0 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  1  0  0  0  1 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  1  0  0  0  1  0  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  1  0  1  0  0 -1  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  1  0  1  0  0  0  0), 2>,
    <( 0  1 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  0  0  0  0  1 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  0  0  1  0  0 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  0  0  1  0  1 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  0  0  1  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  1  0  0  0  0 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  1  0  0  0  1 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  1  0  0  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  1  0  1  0  0 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  0  0  1  0  1  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  0  0  0  0  0 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  0  0  0  0  1 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  0  0  0  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  0  0  1  0  0 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  0  0  1  0  0  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  0  0  1  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  1  0  0  0  0 -1  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  1  0  0  0  0  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  1  0  0  0  1  0  0), 2>,
    <( 0  1 -1  0  0 -1  0  1  0  1  0  1  0  0  0  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  0  0  0  0  1 -1  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  0  0  0  0  1  0  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  0  0  1  0  0 -1  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  0  0  1  0  0  0  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  0  0  1  0  1  0  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  1  0  0  0  0 -1  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  1  0  0  0  0  0  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  1  0  0  0  1  0  0), 2>,
    <( 0  1 -1  0  0  0  0  0  0  1  0  1  0  0  0  0), 2>,
    <( 0  1 -1  0  0  0  0  1  0  0  0  0  0  0 -1  0), 2>,
    <( 0  1 -1  0  0  0  0  1  0  0  0  0  0  0  0  0), 2>,
    <( 0  1 -1  0  0  0  0  1  0  0  0  0  0  1  0  0), 2>,
    <( 0  1 -1  0  0  0  0  1  0  0  0  1  0  0  0  0), 2>,
    <( 0  1 -1  0  0  0  0  1  0  1  0  0  0  0  0  0), 2>,
    <( 0  1  0  0  0  0  0  0  0  0  0  0  0  0 -1  0), 2>,
    <(0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0), 2>,
    <(0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0), 2>,
    <(0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0), 2>,
    <(0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0), 2>,
    <(0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0), 2>,
    <(0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0), 2>,
    <( 0  2 -3  0  0 -2  0  1  0  1  0  1  0  1 -2  0), 2>,
    <( 0  2 -3  0  0 -2  0  1  0  1  0  1  0  1 -1  0), 2>,
    <( 0  2 -3  0  0 -2  0  1  0  1  0  1  0  2 -1  0), 2>,
    <( 0  2 -3  0  0 -2  0  1  0  1  0  2  0  1 -1  0), 2>,
    <( 0  2 -3  0  0 -2  0  1  0  2  0  1  0  1 -1  0), 2>,
    <( 0  2 -3  0  0 -2  0  2  0  1  0  1  0  1 -1  0), 2>,
    <( 0  2 -3  0  0 -1  0  1  0  1  0  1  0  1 -1  0), 2>,
    <( 0  2 -2  0  0 -2  0  1  0  1  0  1  0  1 -1  0), 2>,
    <( 0  2 -2  0  0 -1  0  0  0  1  0  1  0  1 -1  0), 2>,
    <( 0  2 -2  0  0 -1  0  1  0  0  0  1  0  1 -1  0), 2>,
    <( 0  2 -2  0  0 -1  0  1  0  1  0  0  0  1 -1  0), 2>,
    <( 0  2 -2  0  0 -1  0  1  0  1  0  1  0  0 -1  0), 2>,
    <( 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1 -1  0), 2>,
    <( 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0), 2>,
    <( 0  0  1  0  0  0  0 -1  0  0  0  0  0  0  0  0), 2>,
    <( 0  0  1  0  0  0  0  0  0 -1  0  0  0  0  0  0), 2>,
    <( 0  0  1  0  0  0  0  0  0  0  0 -1  0  0  0  0), 2>,
    <( 0  0  1  0  0  0  0  0  0  0  0  0  0 -1  0  0), 2>,
    <(0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0), 2>,
    <(0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0), 2>,
    <( 0  0  1  0  0  1  0 -1  0 -1  0  0  0  0  0  0), 2>,
    <( 0  0  1  0  0  1  0 -1  0  0  0 -1  0  0  0  0), 2>,
    <( 0  0  1  0  0  1  0 -1  0  0  0  0  0 -1  0  0), 2>,
    <( 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  0  0), 2>,
    <( 0  0  1  0  0  1  0 -1  0  0  0  0  0  0  1  0), 2>,
    <( 0  0  1  0  0  1  0  0  0 -1  0 -1  0  0  0  0), 2>,
    <( 0  0  1  0  0  1  0  0  0 -1  0  0  0 -1  0  0), 2>,
    <( 0  0  1  0  0  1  0  0  0 -1  0  0  0  0  0  0), 2>,
    <( 0  0  1  0  0  1  0  0  0 -1  0  0  0  0  1  0), 2>,
    <( 0  0  1  0  0  1  0  0  0  0  0 -1  0 -1  0  0), 2>,
    <( 0  0  1  0  0  1  0  0  0  0  0 -1
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 06:58:19 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
ShortVectors(L1,0,1);

Output: Magma V2.11-2     Tue Aug 10 2004 06:58:18 on modular  [Seed = 1631095355]
   -------------------------------------


>> ShortVectors(L1,0,1);;
               ^
Runtime error in 'ShortVectors': Argument 2 must be positive

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 06:58:31 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
ShortVectors(L1,0);

Output: Magma V2.11-2     Tue Aug 10 2004 06:58:31 on modular  [Seed = 1764786734]
   -------------------------------------


>> ShortVectors(L1,0);;
               ^
Runtime error in 'ShortVectors': Argument 2 must be positive

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 06:58:47 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
ShortVectors(L1,3,5);

Output: Magma V2.11-2     Tue Aug 10 2004 06:58:44 on modular  [Seed = 2445834981]
   -------------------------------------

[
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  0 -1  0  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  0 -1  0  1), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  0  0  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  0  0  1  1), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  1 -1  0  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0 -1  1  0  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0  0  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0  0  0 -1  1  1), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  0  0  1 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  1 -1  0 -1  0  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  1 -1  0  0  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0 -1  1  0  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0  0  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0  0  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  0  0  1  0 -1  0  0  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  0  0  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  1 -1  0 -1  0 -1  0  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  1 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  1 -1  0 -1  0  0  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  1 -1  0  0  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0 -1  1  0  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0  0  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0  0  0 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  0  0  1  0  0  0 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0  0  0 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  0  0  1 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  1 -1  0 -1  0 -1  0 -1  0  0), 4>,
    <( 1 -2  2  0  0  1  1 -1  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  1 -1  0 -1  0 -1  0  0  1  0), 4>,
    <( 1 -2  2  0  0  1  1 -1  0 -1  0  0  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  1 -1  0  0  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  1  1  0  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  2  0 -1  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  2  0 -1  0 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  0  0  2  0 -1  0 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  0  0  2  0 -1  0 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  2  0 -1  1 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  0  2  1 -1  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  1  1  0 -1  0 -1  0 -1  0 -1  0  0), 4>,
    <( 1 -2  2  0  1  1  0 -1  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  1  1  0 -1  0 -1  0 -1  0  0  1  0), 4>,
    <( 1 -2  2  0  1  1  0 -1  0 -1  0  0  0 -1  1  0), 4>,
    <( 1 -2  2  0  1  1  0 -1  0  0  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  1  1  0  0  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  0  1  2  0 -1  0 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  0 -1  1 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  0 -1  1  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  0  0  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  0 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  0  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  1 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  1 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  1  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1 -1  1  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1  0  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1  0  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0 -1  1  0  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0  0  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0  0  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0  0  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  0  0  1 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  0 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  0  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  1 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  1 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  1  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0 -1  1  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0  0  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0  0  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  0  0  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  0 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  0 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  0  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  0  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  1 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1 -1  1  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1  0  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1  0  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1 -1  1  0  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1  0  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1  0  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1  0  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1  0  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1  0  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0 -1  1  0  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0  0  0 -1  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0  0  0 -1  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0  0  0 -1  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0  0  0 -1  1 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0  0  1 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0  0  1 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0  0  1 -1  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0  0  1 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  0  0  1 -1  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  0  0  1 -1  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  0 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  0  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  1 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  1 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  1  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0 -1  1  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0  0  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0  0  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  0  0  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  0 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  0 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  0  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  0  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  1 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1 -1  1  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1  0  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1  0  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0 -1  1  0  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0  0  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0  0  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0  0  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0  0  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0  0  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  0  0  1 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  0 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  0 -1  0  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  0  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  0  0  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  1 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0 -1  1  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0  0  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0  0  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  0  0  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  1 -1  0 -1  0  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  1 -1  0  0  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1 -1  1  0  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1  0  0 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1  0  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1  0  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1 -1  1  0  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1  0  0 -1  0 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1  0  0 -1  0 -1  1 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1  0  0 -1  0 -1  1 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1  0  0 -1  1 -1  0 -1  1  0), 4>,
    <( 1 -2  2  1 -1  1  1  0  0 -1  1 -1  0 -1  1  1), 4>,
    <( 1 -2  2  1 -1  1  1  0  0 -1  1 -1
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 06:59:11 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
ShortVectors(L1,5,7);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Tue Aug 10 2004 06:59:01 on modular  [Seed = 2579526396]
   -------------------------------------


Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Total time: 9.729 seconds, Total memory usage: 100.00MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:00:18 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
S1:=ShortVectors(L1,5,7);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Tue Aug 10 2004 07:00:08 on modular  [Seed = 3035455260]
   -------------------------------------


Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Total time: 9.709 seconds, Total memory usage: 100.00MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:00:33 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
S1:=ShortVectors(L1,3,5);#S1;

Output: Magma V2.11-2     Tue Aug 10 2004 07:00:32 on modular  [Seed = 3185858173]
   -------------------------------------

30960

Total time: 1.139 seconds, Total memory usage: 9.75MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:00:51 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
S1:=ShortVectors(L1,3,5);
#S1;

Output: Magma V2.11-2     Tue Aug 10 2004 07:00:49 on modular  [Seed = 2784775767]
   -------------------------------------

30960

Total time: 1.129 seconds, Total memory usage: 9.75MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:01:08 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
S1:=ShortVectors(L1,3,5);

Output: Magma V2.11-2     Tue Aug 10 2004 07:01:07 on modular  [Seed = 2918467150]
   -------------------------------------


Total time: 1.139 seconds, Total memory usage: 9.75MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:01:20 2004

Input: EHUT1:=Matrix(RationalField(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
#ShortVectors(L1,3,5);

Output: Magma V2.11-2     Tue Aug 10 2004 07:01:19 on modular  [Seed = 3582737978]
   -------------------------------------

30960

Total time: 1.179 seconds, Total memory usage: 9.75MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:07:36 2004

Input: T:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
T4:=LatticeWithGram(T);
IsPositiveDefinite(T4);
T4 eq Dual(T4);

Output: Magma V2.11-2     Tue Aug 10 2004 07:07:35 on modular  [Seed = 3750113976]
   -------------------------------------


>> ,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
                                                              ^
User error: bad syntax

>> T4:=LatticeWithGram(T);
                       ^
User error: Identifier 'T' has not been declared or assigned

>> IsPositiveDefinite(T4);
                      ^
User error: Identifier 'T4' has not been declared or assigned

>> T4 eq Dual(T4);;
   ^
User error: Identifier 'T4' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:08:10 2004

Input: T4:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
G4:=LatticeWithGram(T4);
IsPositiveDefinite(G4);
G4 eq Dual(G4);

Output: Magma V2.11-2     Tue Aug 10 2004 07:08:10 on modular  [Seed = 3381666883]
   -------------------------------------


>> 1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
                                                               ^
User error: bad syntax

>> G4:=LatticeWithGram(T4);
                       ^
User error: Identifier 'T4' has not been declared or assigned

>> IsPositiveDefinite(G4);
                      ^
User error: Identifier 'G4' has not been declared or assigned

>> G4 eq Dual(G4);;
   ^
User error: Identifier 'G4' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:09:16 2004

Input: T4:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1,0, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
G4:=LatticeWithGram(T4);
IsPositiveDefinite(G4);
G4 eq Dual(G4);

Output: Magma V2.11-2     Tue Aug 10 2004 07:09:16 on modular  [Seed = 4054326333]
   -------------------------------------


>> ,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
                                                                 ^
User error: bad syntax

>> G4:=LatticeWithGram(T4);
                       ^
User error: Identifier 'T4' has not been declared or assigned

>> IsPositiveDefinite(G4);
                      ^
User error: Identifier 'G4' has not been declared or assigned

>> G4 eq Dual(G4);;
   ^
User error: Identifier 'G4' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:12:12 2004

Input: Gram4d:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1,0, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
Gitter4d:=LatticeWithGram(Gram4d);
IsPositiveDefinite(Gitter4d);
Gitter4d eq Dual(Gitter4d);

Output: Magma V2.11-2     Tue Aug 10 2004 07:12:11 on modular  [Seed = 4204992097]
   -------------------------------------


>> -1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
                                                                     ^
User error: bad syntax

>> Gitter4d:=LatticeWithGram(Gram4d);
                             ^
User error: Identifier 'Gram4d' has not been declared or assigned

>> IsPositiveDefinite(Gitter4d);
                      ^
User error: Identifier 'Gitter4d' has not been declared or assigned

>> Gitter4d eq Dual(Gitter4d);;
   ^
User error: Identifier 'Gitter4d' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:12:27 2004

Input: Gram4d:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1,0, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);


Output: Magma V2.11-2     Tue Aug 10 2004 07:12:26 on modular  [Seed = 3803909736]
   -------------------------------------


>> -1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2);
                                                                     ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:12:44 2004

Input: Gram4d:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1,0, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2]);


Output: Magma V2.11-2     Tue Aug 10 2004 07:12:43 on modular  [Seed = 3937601105]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:13:09 2004

Input: Gram4d:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1,0, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2]);
Gitter4d:=LatticeWithGram(Gram4d);
IsPositiveDefinite(Gitter4d);
Gitter4d eq Dual(Gitter4d);

Output: Magma V2.11-2     Tue Aug 10 2004 07:13:08 on modular  [Seed = 289996230]
   -------------------------------------


>> IsPositiveDefinite(Gitter4d);
                     ^
Runtime error in 'IsPositiveDefinite': Bad argument types
Argument types given: Lat
true

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host demeter.matha.RWTH-Aachen.DE. (134.130.164.53)
Time: Tue Aug 10 07:13:27 2004

Input: Gram4d:=Matrix(RationalField(),8,8,[2,0,1,1,0,1,1,0, 0,2,-1,1,-1,0,0,1, 1,-1,2,0,1,1,1,0, 1,1,0,2,-1,1,0,1, 0,-1,1,-1,2,0,1,0, 1,0,1,1,0,2,0,1, 1,0,1,0,1,0,2,0, 0,1,0,1,0,1,0,2]);
Gitter4d:=LatticeWithGram(Gram4d);
IsPositiveDefinite(Gram4d);
Gitter4d eq Dual(Gitter4d);

Output: Magma V2.11-2     Tue Aug 10 2004 07:13:26 on modular  [Seed = 423687644]
   -------------------------------------

true
true

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ti121210a080-1323.bb.online.no. (80.212.5.43)
Time: Tue Aug 10 08:57:56 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Tue Aug 10 2004 08:57:55 on modular  [Seed = 4238703548]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host dpvc-129-44-218-5.syr.east.verizon.net. (129.44.218.5)
Time: Tue Aug 10 09:01:45 2004

Input: what's the deal here?

Output: Magma V2.11-2     Tue Aug 10 2004 09:01:44 on modular  [Seed = 423665459]
   -------------------------------------


>> what's the deal here?;
                         ^
User error: Unexpected newline in literal identifier

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host clarke.maths.warwick.ac.uk. (137.205.232.91)
Time: Tue Aug 10 10:51:08 2004

Input: Factorisation(211)

Output: Magma V2.11-2     Tue Aug 10 2004 10:51:07 on modular  [Seed = 3699735829]
   -------------------------------------

[ <211, 1> ]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host clarke.maths.warwick.ac.uk. (137.205.232.91)
Time: Tue Aug 10 10:56:34 2004

Input: Factorisation(279)

Output: Magma V2.11-2     Tue Aug 10 2004 10:56:33 on modular  [Seed = 3364973563]
   -------------------------------------

[ <3, 2>, <31, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host clarke.maths.warwick.ac.uk. (137.205.232.91)
Time: Tue Aug 10 10:58:11 2004

Input: Factorisation(611)

Output: Magma V2.11-2     Tue Aug 10 2004 10:58:10 on modular  [Seed = 4037628769]
   -------------------------------------

[ <13, 1>, <47, 1> ]

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 0x503ef1cb.odnxx1.adsl-dhcp.tele.dk. (80.62.241.203)
Time: Wed Aug 11 07:23:30 2004

Input: getuid

Output: WARNING: MAGMA command contains unsafe command 'getuid', so it will not be executed.

************** MAGMA *****************
Host 0x503ef1cb.odnxx1.adsl-dhcp.tele.dk. (80.62.241.203)
Time: Wed Aug 11 07:23:38 2004

Input: GETUID

Output: WARNING: MAGMA command contains unsafe command 'getuid', so it will not be executed.

************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Wed Aug 11 09:57:01 2004

Input: Q5:=pAdicField(5,50);
Q5x<x>:=PolynomialRing(Q5);
TRE:=TotallyRamifiedExtension(Q5,x^4+5);
MinimalPolynomial(TRE!0);

Output: Magma V2.11-2     Wed Aug 11 2004 09:56:57 on modular  [Seed = 4004874840]
   -------------------------------------

O(1)

Total time: 0.699 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Wed Aug 11 09:57:25 2004

Input: Q5:=pAdicField(5,50);
Q5x<x>:=PolynomialRing(Q5);
TRE:=TotallyRamifiedExtension(Q5,x^4+5);
MinimalPolynomial(TRE!0);
2+2;

Output: Magma V2.11-2     Wed Aug 11 2004 09:57:25 on modular  [Seed = 3871179327]
   -------------------------------------

O(1)
4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Wed Aug 11 13:29:32 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 224*x^14 + 22592*x^12 - 1340416*x^10 + 51269632*x^8 - 1332215808*x^6 + 24168628224*x^4 - 285380444160*x^2 + 1761205026816));


Output: Magma V2.11-2     Wed Aug 11 2004 13:29:19 on modular  [Seed = 189799749]
   -------------------------------------

67 16

Total time: 11.520 seconds, Total memory usage: 6.42MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Wed Aug 11 13:37:33 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 + 28*x^14 + 324*x^12 + 2008*x^10 + 7212*x^8 + 15160*x^6 + 17936*x^4 + 10800*x^2 + 2500));


Output: Magma V2.11-2     Wed Aug 11 2004 13:37:25 on modular  [Seed = 340724832]
   -------------------------------------

69 16

Total time: 7.429 seconds, Total memory usage: 6.63MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:26:17 2004

Input: Delta:=q;
for i from 1 to 10 do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:26:16 on modular  [Seed = 3202718551]
   -------------------------------------


>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i from 1 to 10 do Delta:=Delta*(1-q^i)^24; end for;;
         ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:26:48 2004

Input: Delta:=q;
for i in [1...10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:26:47 on modular  [Seed = 2262672192]
   -------------------------------------


>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1...10] do Delta:=Delta*(1-q^i)^24; end for;;
                ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:26:53 2004

Input: Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:26:53 on modular  [Seed = 2396367682]
   -------------------------------------


>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:27:13 2004

Input: local q;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:27:13 on modular  [Seed = 2530063030]
   -------------------------------------


>> local q;
   ^
User error: bad syntax

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:28:18 2004

Input: q parameter;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:28:18 on modular  [Seed = 2663758589]
   -------------------------------------


>> q parameter;
     ^
User error: bad syntax

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:29:08 2004

Input: Z:=RingofIntegers;
q!Z;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:29:08 on modular  [Seed = 3871195827]
   -------------------------------------


>> Z:=RingofIntegers;
      ^
User error: Identifier 'RingofIntegers' has not been declared or assigned

>> q!Z;
   ^
User error: Identifier 'q' has not been declared or assigned

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:29:36 2004

Input: ZZ:=Ring(Z);
q!Z;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:29:36 on modular  [Seed = 4004891231]
   -------------------------------------


>> ZZ:=Ring(Z);
            ^
User error: Identifier 'Z' has not been declared or assigned

>> q!Z;
   ^
User error: Identifier 'q' has not been declared or assigned

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:29:52 2004

Input: ZZ:=Ring(integers);
q!Z;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:29:52 on modular  [Seed = 4138586743]
   -------------------------------------


>> ZZ:=Ring(integers);
            ^
User error: Identifier 'integers' has not been declared or assigned

>> q!Z;
   ^
User error: Identifier 'q' has not been declared or assigned

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:30:06 2004

Input: ZZ:=Ring(Integers);
q!Z;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:30:05 on modular  [Seed = 4272282226]
   -------------------------------------


>> ZZ:=Ring(Integers);
           ^
Runtime error in 'Ring': Bad argument types
Argument types given: Intrinsic

>> q!Z;
   ^
User error: Identifier 'q' has not been declared or assigned

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:31:19 2004

Input: Z:=IntegerRing();
q!Z;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:31:19 on modular  [Seed = 3381849375]
   -------------------------------------


>> q!Z;
   ^
User error: Identifier 'q' has not been declared or assigned

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:31:50 2004

Input: Z:=IntegerRing();
q:=Z!;
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:31:49 on modular  [Seed = 3515545318]
   -------------------------------------


>> q:=Z!;
        ^
User error: bad syntax

>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:33:44 2004

Input: Z:=IntegerRing();
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:33:44 on modular  [Seed = 3649240688]
   -------------------------------------


>> Delta:=q;
          ^
User error: Identifier 'q' has not been declared or assigned

>> for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;;
                                       ^
User error: Identifier 'q' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:35:46 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:35:46 on modular  [Seed = 578356224]
   -------------------------------------


Total time: 0.689 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:37:22 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,2);

Output: Magma V2.11-2     Wed Aug 11 2004 14:37:21 on modular  [Seed = 779421807]
   -------------------------------------

-24

Total time: 0.689 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:37:30 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,2000);

Output: Magma V2.11-2     Wed Aug 11 2004 14:37:30 on modular  [Seed = 913117308]
   -------------------------------------

0

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:38:04 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10000] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,2000);

Output: Magma V2.11-2     Wed Aug 11 2004 14:37:44 on modular  [Seed = 1046812774]
   -------------------------------------



************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:39:50 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..1000] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,1000);

Output: Magma V2.11-2     Wed Aug 11 2004 14:39:29 on modular  [Seed = 139669193]
   -------------------------------------



************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:40:35 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..100] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,100);

Output: Magma V2.11-2     Wed Aug 11 2004 14:40:14 on modular  [Seed = 1664633421]
   -------------------------------------



************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:41:16 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..50] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,50);

Output: Magma V2.11-2     Wed Aug 11 2004 14:40:56 on modular  [Seed = 1815561588]
   -------------------------------------



************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:41:51 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..50] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);

Output: Magma V2.11-2     Wed Aug 11 2004 14:41:31 on modular  [Seed = 1949261071]
   -------------------------------------



************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:42:26 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..50] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,1);

Output: Magma V2.11-2     Wed Aug 11 2004 14:42:05 on modular  [Seed = 2082952481]
   -------------------------------------



************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:43:09 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,1);

Output: Magma V2.11-2     Wed Aug 11 2004 14:43:09 on modular  [Seed = 1142910425]
   -------------------------------------

1

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:43:15 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);

Output: Magma V2.11-2     Wed Aug 11 2004 14:43:15 on modular  [Seed = 1276601775]
   -------------------------------------

-115920

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:44:11 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
Isprime(7);

Output: Magma V2.11-2     Wed Aug 11 2004 14:44:10 on modular  [Seed = 1410301327]
   -------------------------------------

-115920

>> Isprime(7);;
   ^
User error: Identifier 'Isprime' has not been declared or assigned

Total time: 0.689 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:44:25 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);

Output: Magma V2.11-2     Wed Aug 11 2004 14:44:24 on modular  [Seed = 2717550985]
   -------------------------------------

-115920
true

Total time: 0.669 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:46:07 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);
for j in [1..2] do if t:=3+2^i; IsPrime(t) then Factor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end do;

Output: Magma V2.11-2     Wed Aug 11 2004 14:46:06 on modular  [Seed = 2867954404]
   -------------------------------------

-115920
true

>> for j in [1..2] do if t:=3+2^i; IsPrime(t) then Factor(Coefficient(Delta,3)
                          ^
User error: bad syntax

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:46:24 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);
for j in [1..2] do if t:=Z!(3+2^i); IsPrime(t) then Factor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end do;

Output: Magma V2.11-2     Wed Aug 11 2004 14:46:23 on modular  [Seed = 3001653997]
   -------------------------------------

-115920
true

>> for j in [1..2] do if t:=Z!(3+2^i); IsPrime(t) then Factor(Coefficient(Delt
                          ^
User error: bad syntax

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:46:52 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);
for j in [1..2] do  t:=Z!(3+2^i); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end do;

Output: Magma V2.11-2     Wed Aug 11 2004 14:46:51 on modular  [Seed = 3135345153]
   -------------------------------------

-115920
true

>> ctor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end do;;
                                                              ^
User error: bad syntax

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:47:04 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);
for j in [1..2] do  t:=Z!(3+2^i); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:47:03 on modular  [Seed = 2195302917]
   -------------------------------------

-115920
true

>> for j in [1..2] do  t:=Z!(3+2^i); if IsPrime(t) then Factor(Coefficient(Del
                                 ^
User error: Identifier 'i' has not been declared or assigned

Total time: 0.669 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:47:31 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:47:30 on modular  [Seed = 2328994408]
   -------------------------------------

-115920
true

>> ctor(Coefficient(Delta,3)-Coeffcient(Delta,t));end if; end for;;
                             ^
User error: Identifier 'Coeffcient' has not been declared or assigned

Total time: 0.689 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:48:21 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:48:20 on modular  [Seed = 2462693958]
   -------------------------------------

-115920
true

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:48:58 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7);Factor(12);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:48:57 on modular  [Seed = 2596385187]
   -------------------------------------

-115920
true

>> IsPrime(7);Factor(12);
                    ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngIntElt

Total time: 0.669 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:50:58 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 12 Modulo 3;
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:50:57 on modular  [Seed = 3820537938]
   -------------------------------------

-115920
true

>> IsPrime(7); 12 Modulo 3;
                  ^
User error: bad syntax

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:51:10 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); Modulo(12, 3);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:51:09 on modular  [Seed = 3954229334]
   -------------------------------------

-115920
true

>> IsPrime(7); Modulo(12, 3);
               ^
User error: Identifier 'Modulo' has not been declared or assigned

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:53:54 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); IntegerFactorization(12);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:53:54 on modular  [Seed = 4121878423]
   -------------------------------------

-115920
true

>> IsPrime(7); IntegerFactorization(12);
               ^
User error: Identifier 'IntegerFactorization' has not been declared or assigned

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:54:02 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); IntegerFactor(12);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:54:01 on modular  [Seed = 4255569815]
   -------------------------------------

-115920
true

>> IsPrime(7); IntegerFactor(12);
               ^
User error: Identifier 'IntegerFactor' has not been declared or assigned

Total time: 0.679 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:54:32 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(12,1);M;

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:54:31 on modular  [Seed = 3332238465]
   -------------------------------------

-115920
true

>> M:=ModularSymbols(12,1);M;
                    ^
Runtime error in 'ModularSymbols': Argument 2 (1) should be >= 2

>> M:=ModularSymbols(12,1);M;
                           ^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.689 seconds, Total memory usage: 3.54MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:54:58 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:54:57 on modular  [Seed = 3465929836]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

Total time: 0.740 seconds, Total memory usage: 3.64MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:55:19 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:55:19 on modular  [Seed = 3599629409]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

Total time: 0.760 seconds, Total memory usage: 3.88MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:55:37 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:55:36 on modular  [Seed = 3750032727]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field

Total time: 0.760 seconds, Total memory usage: 3.88MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:56:51 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C);

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:56:50 on modular  [Seed = 612306677]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field

Total time: 0.889 seconds, Total memory usage: 4.38MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:57:09 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C);
f;

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:57:08 on modular  [Seed = 745996555]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + O(q^8)
]

Total time: 0.870 seconds, Total memory usage: 4.38MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:57:42 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C,10000);
f;

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:57:21 on modular  [Seed = 879696134]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:57:43 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C,200);
f;

for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:57:41 on modular  [Seed = 979441468]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 
        12830688*q^22 + 18643272*q^23 + 21288960*q^24 - 25499225*q^25 + 
        13865712*q^26 - 73279080*q^27 + 24647168*q^28 + 128406630*q^29 - 
        29211840*q^30 - 52843168*q^31 - 196706304*q^32 + 134722224*q^33 + 
        165742416*q^34 - 80873520*q^35 + 167282496*q^36 - 182213314*q^37 - 
        255874080*q^38 - 145589976*q^39 + 408038400*q^40 + 308120442*q^41 + 
        101267712*q^42 - 17125708*q^43 - 786948864*q^44 - 548895690*q^45 - 
        447438528*q^46 + 2687348496*q^47 + 248758272*q^48 - 1696965207*q^49 + 
        611981400*q^50 - 1740295368*q^51 + 850430336*q^52 - 1596055698*q^53 + 
        1758697920*q^54 + 2582175960*q^55 - 1414533120*q^56 + 2686677840*q^57 - 
        3081759120*q^58 - 5189203740*q^59 - 1791659520*q^60 + 6956478662*q^61 + 
        1268236032*q^62 + 1902838392*q^63 + 2699296768*q^64 - 2790474540*q^65 - 
        3233333376*q^66 - 15481826884*q^67 + 10165534848*q^68 + 4698104544*q^69 
        + 1940964480*q^70 + 9791485272*q^71 - 9600560640*q^72 + 1463791322*q^73 
        + 4373119536*q^74 - 6425804700*q^75 - 15693610240*q^76 - 8951543328*q^77
        + 3494159424*q^78 + 38116845680*q^79 + 4767866880*q^80 + 1665188361*q^81
        - 7394890608*q^82 - 29335099668*q^83 + 6211086336*q^84 - 
        33355661220*q^85 + 411016992*q^86 + 32358470760*q^87 + 45164021760*q^88 
        - 24992917110*q^89 + 13173496560*q^90 + 9673645072*q^91 - 
        27442896384*q^92 - 13316478336*q^93 - 64496363904*q^94 + 
        51494658600*q^95 - 49569988608*q^96 + 75013568546*q^97 + 
        40727164968*q^98 - 60754911516*q^99 + 37534859200*q^100 + 
        81742959102*q^101 + 41767088832*q^102 - 225755128648*q^103 - 
        48807306240*q^104 - 20380127040*q^105 + 38305336752*q^106 + 
        90241258356*q^107 + 107866805760*q^108 + 73482676310*q^109 - 
        61972223040*q^110 - 45917755128*q^111 - 16528605184*q^112 - 
        85146862638*q^113 - 64480268160*q^114 + 90047003760*q^115 - 
        189014559360*q^116 + 65655879534*q^117 + 124540889760*q^118 + 
        115632958896*q^119 + 102825676800*q^120 + 498319933*q^121 - 
        166955487888*q^122 + 77646351384*q^123 + 77785143296*q^124 - 
        359001100500*q^125 - 45668121408*q^126 - 262717201024*q^127 + 
        338071388160*q^128 - 4315678416*q^129 + 66971388960*q^130 + 
        631528759932*q^131 - 198311113728*q^132 - 178514816480*q^133 + 
        371563845216*q^134 - 353937956400*q^135 - 583413304320*q^136 - 
        297198746214*q^137 - 112754509056*q^138 + 596793577940*q^139 + 
        119045821440*q^140 + 677211820992*q^141 - 234995646528*q^142 - 
        308865667656*q^143 - 112181096448*q^144 + 620204022900*q^145 - 
        35130991728*q^146 - 427635232164*q^147 + 268217998208*q^148 - 
        1115433620850*q^149 + 154219312800*q^150 - 824447297848*q^151 + 
        900676761600*q^152 + 784811057562*q^153 + 214837039872*q^154 - 
        255232501440*q^155 + 214308444672*q^156 + 1315116754406*q^157 - 
        914804296320*q^158 - 402206035896*q^159 - 950091448320*q^160 - 
        312162946368*q^161 - 39964520664*q^162 - 357832759588*q^163 - 
        453553290624*q^164 + 650708341920*q^165 + 704042392032*q^166 + 
        2754833892216*q^167 - 356462346240*q^168 - 1458379197393*q^169 + 
        800535869280*q^170 - 1211595753060*q^171 + 25209042176*q^172 - 
        950387449578*q^173 - 776603298240*q^174 + 426959023400*q^175 + 
        527734751232*q^176 - 1307679342480*q^177 + 599830010640*q^178 + 
        1681384224780*q^179 + 807974455680*q^180 - 996774496018*q^181 - 
        232167481728*q^182 + 1753032622824*q^183 + 1574983618560*q^184 - 
        880090306620*q^185 + 319595480064*q^186 - 3691995187608*q^187 - 
        3955776986112*q^188 + 1226984915520*q^189 - 1235871806400*q^190 + 
        2762403350592*q^191 + 680222785536*q^192 + 5442387685442*q^193 - 
        1800325645104*q^194 - 703199584080*q^195 + 2497932784704*q^196 - 
        2876091504354*q^197 + 1458117876384*q^198 + 728391402200*q^199 + 
        O(q^200)
]

Total time: 1.699 seconds, Total memory usage: 5.49MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:58:42 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C,200);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:58:40 on modular  [Seed = 73345351]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 
        12830688*q^22 + 18643272*q^23 + 21288960*q^24 - 25499225*q^25 + 
        13865712*q^26 - 73279080*q^27 + 24647168*q^28 + 128406630*q^29 - 
        29211840*q^30 - 52843168*q^31 - 196706304*q^32 + 134722224*q^33 + 
        165742416*q^34 - 80873520*q^35 + 167282496*q^36 - 182213314*q^37 - 
        255874080*q^38 - 145589976*q^39 + 408038400*q^40 + 308120442*q^41 + 
        101267712*q^42 - 17125708*q^43 - 786948864*q^44 - 548895690*q^45 - 
        447438528*q^46 + 2687348496*q^47 + 248758272*q^48 - 1696965207*q^49 + 
        611981400*q^50 - 1740295368*q^51 + 850430336*q^52 - 1596055698*q^53 + 
        1758697920*q^54 + 2582175960*q^55 - 1414533120*q^56 + 2686677840*q^57 - 
        3081759120*q^58 - 5189203740*q^59 - 1791659520*q^60 + 6956478662*q^61 + 
        1268236032*q^62 + 1902838392*q^63 + 2699296768*q^64 - 2790474540*q^65 - 
        3233333376*q^66 - 15481826884*q^67 + 10165534848*q^68 + 4698104544*q^69 
        + 1940964480*q^70 + 9791485272*q^71 - 9600560640*q^72 + 1463791322*q^73 
        + 4373119536*q^74 - 6425804700*q^75 - 15693610240*q^76 - 8951543328*q^77
        + 3494159424*q^78 + 38116845680*q^79 + 4767866880*q^80 + 1665188361*q^81
        - 7394890608*q^82 - 29335099668*q^83 + 6211086336*q^84 - 
        33355661220*q^85 + 411016992*q^86 + 32358470760*q^87 + 45164021760*q^88 
        - 24992917110*q^89 + 13173496560*q^90 + 9673645072*q^91 - 
        27442896384*q^92 - 13316478336*q^93 - 64496363904*q^94 + 
        51494658600*q^95 - 49569988608*q^96 + 75013568546*q^97 + 
        40727164968*q^98 - 60754911516*q^99 + 37534859200*q^100 + 
        81742959102*q^101 + 41767088832*q^102 - 225755128648*q^103 - 
        48807306240*q^104 - 20380127040*q^105 + 38305336752*q^106 + 
        90241258356*q^107 + 107866805760*q^108 + 73482676310*q^109 - 
        61972223040*q^110 - 45917755128*q^111 - 16528605184*q^112 - 
        85146862638*q^113 - 64480268160*q^114 + 90047003760*q^115 - 
        189014559360*q^116 + 65655879534*q^117 + 124540889760*q^118 + 
        115632958896*q^119 + 102825676800*q^120 + 498319933*q^121 - 
        166955487888*q^122 + 77646351384*q^123 + 77785143296*q^124 - 
        359001100500*q^125 - 45668121408*q^126 - 262717201024*q^127 + 
        338071388160*q^128 - 4315678416*q^129 + 66971388960*q^130 + 
        631528759932*q^131 - 198311113728*q^132 - 178514816480*q^133 + 
        371563845216*q^134 - 353937956400*q^135 - 583413304320*q^136 - 
        297198746214*q^137 - 112754509056*q^138 + 596793577940*q^139 + 
        119045821440*q^140 + 677211820992*q^141 - 234995646528*q^142 - 
        308865667656*q^143 - 112181096448*q^144 + 620204022900*q^145 - 
        35130991728*q^146 - 427635232164*q^147 + 268217998208*q^148 - 
        1115433620850*q^149 + 154219312800*q^150 - 824447297848*q^151 + 
        900676761600*q^152 + 784811057562*q^153 + 214837039872*q^154 - 
        255232501440*q^155 + 214308444672*q^156 + 1315116754406*q^157 - 
        914804296320*q^158 - 402206035896*q^159 - 950091448320*q^160 - 
        312162946368*q^161 - 39964520664*q^162 - 357832759588*q^163 - 
        453553290624*q^164 + 650708341920*q^165 + 704042392032*q^166 + 
        2754833892216*q^167 - 356462346240*q^168 - 1458379197393*q^169 + 
        800535869280*q^170 - 1211595753060*q^171 + 25209042176*q^172 - 
        950387449578*q^173 - 776603298240*q^174 + 426959023400*q^175 + 
        527734751232*q^176 - 1307679342480*q^177 + 599830010640*q^178 + 
        1681384224780*q^179 + 807974455680*q^180 - 996774496018*q^181 - 
        232167481728*q^182 + 1753032622824*q^183 + 1574983618560*q^184 - 
        880090306620*q^185 + 319595480064*q^186 - 3691995187608*q^187 - 
        3955776986112*q^188 + 1226984915520*q^189 - 1235871806400*q^190 + 
        2762403350592*q^191 + 680222785536*q^192 + 5442387685442*q^193 - 
        1800325645104*q^194 - 703199584080*q^195 + 2497932784704*q^196 - 
        2876091504354*q^197 + 1458117876384*q^198 + 728391402200*q^199 + 
        O(q^200)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 1.679 seconds, Total memory usage: 5.49MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:59:14 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=Z<q>!qExpansionBasis(C,200);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:59:13 on modular  [Seed = 207036846]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field

>> f:=Z<q>!qExpansionBasis(C,200);
       ^
User error: bad syntax

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,139);
               ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.760 seconds, Total memory usage: 3.88MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 14:59:37 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=Z<q>!(qExpansionBasis(C,200));
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 14:59:36 on modular  [Seed = 340736431]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field

>> f:=Z<q>!(qExpansionBasis(C,200));
       ^
User error: bad syntax

>> f;
   ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,139);
               ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.760 seconds, Total memory usage: 3.88MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:00:05 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
Delta:=q;
for i in [1..10] do Delta:=Delta*(1-q^i)^24; end for;
Coefficient(Delta,10);
IsPrime(7); 
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C,200);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:00:03 on modular  [Seed = 1898601697]
   -------------------------------------

-115920
true
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 
        12830688*q^22 + 18643272*q^23 + 21288960*q^24 - 25499225*q^25 + 
        13865712*q^26 - 73279080*q^27 + 24647168*q^28 + 128406630*q^29 - 
        29211840*q^30 - 52843168*q^31 - 196706304*q^32 + 134722224*q^33 + 
        165742416*q^34 - 80873520*q^35 + 167282496*q^36 - 182213314*q^37 - 
        255874080*q^38 - 145589976*q^39 + 408038400*q^40 + 308120442*q^41 + 
        101267712*q^42 - 17125708*q^43 - 786948864*q^44 - 548895690*q^45 - 
        447438528*q^46 + 2687348496*q^47 + 248758272*q^48 - 1696965207*q^49 + 
        611981400*q^50 - 1740295368*q^51 + 850430336*q^52 - 1596055698*q^53 + 
        1758697920*q^54 + 2582175960*q^55 - 1414533120*q^56 + 2686677840*q^57 - 
        3081759120*q^58 - 5189203740*q^59 - 1791659520*q^60 + 6956478662*q^61 + 
        1268236032*q^62 + 1902838392*q^63 + 2699296768*q^64 - 2790474540*q^65 - 
        3233333376*q^66 - 15481826884*q^67 + 10165534848*q^68 + 4698104544*q^69 
        + 1940964480*q^70 + 9791485272*q^71 - 9600560640*q^72 + 1463791322*q^73 
        + 4373119536*q^74 - 6425804700*q^75 - 15693610240*q^76 - 8951543328*q^77
        + 3494159424*q^78 + 38116845680*q^79 + 4767866880*q^80 + 1665188361*q^81
        - 7394890608*q^82 - 29335099668*q^83 + 6211086336*q^84 - 
        33355661220*q^85 + 411016992*q^86 + 32358470760*q^87 + 45164021760*q^88 
        - 24992917110*q^89 + 13173496560*q^90 + 9673645072*q^91 - 
        27442896384*q^92 - 13316478336*q^93 - 64496363904*q^94 + 
        51494658600*q^95 - 49569988608*q^96 + 75013568546*q^97 + 
        40727164968*q^98 - 60754911516*q^99 + 37534859200*q^100 + 
        81742959102*q^101 + 41767088832*q^102 - 225755128648*q^103 - 
        48807306240*q^104 - 20380127040*q^105 + 38305336752*q^106 + 
        90241258356*q^107 + 107866805760*q^108 + 73482676310*q^109 - 
        61972223040*q^110 - 45917755128*q^111 - 16528605184*q^112 - 
        85146862638*q^113 - 64480268160*q^114 + 90047003760*q^115 - 
        189014559360*q^116 + 65655879534*q^117 + 124540889760*q^118 + 
        115632958896*q^119 + 102825676800*q^120 + 498319933*q^121 - 
        166955487888*q^122 + 77646351384*q^123 + 77785143296*q^124 - 
        359001100500*q^125 - 45668121408*q^126 - 262717201024*q^127 + 
        338071388160*q^128 - 4315678416*q^129 + 66971388960*q^130 + 
        631528759932*q^131 - 198311113728*q^132 - 178514816480*q^133 + 
        371563845216*q^134 - 353937956400*q^135 - 583413304320*q^136 - 
        297198746214*q^137 - 112754509056*q^138 + 596793577940*q^139 + 
        119045821440*q^140 + 677211820992*q^141 - 234995646528*q^142 - 
        308865667656*q^143 - 112181096448*q^144 + 620204022900*q^145 - 
        35130991728*q^146 - 427635232164*q^147 + 268217998208*q^148 - 
        1115433620850*q^149 + 154219312800*q^150 - 824447297848*q^151 + 
        900676761600*q^152 + 784811057562*q^153 + 214837039872*q^154 - 
        255232501440*q^155 + 214308444672*q^156 + 1315116754406*q^157 - 
        914804296320*q^158 - 402206035896*q^159 - 950091448320*q^160 - 
        312162946368*q^161 - 39964520664*q^162 - 357832759588*q^163 - 
        453553290624*q^164 + 650708341920*q^165 + 704042392032*q^166 + 
        2754833892216*q^167 - 356462346240*q^168 - 1458379197393*q^169 + 
        800535869280*q^170 - 1211595753060*q^171 + 25209042176*q^172 - 
        950387449578*q^173 - 776603298240*q^174 + 426959023400*q^175 + 
        527734751232*q^176 - 1307679342480*q^177 + 599830010640*q^178 + 
        1681384224780*q^179 + 807974455680*q^180 - 996774496018*q^181 - 
        232167481728*q^182 + 1753032622824*q^183 + 1574983618560*q^184 - 
        880090306620*q^185 + 319595480064*q^186 - 3691995187608*q^187 - 
        3955776986112*q^188 + 1226984915520*q^189 - 1235871806400*q^190 + 
        2762403350592*q^191 + 680222785536*q^192 + 5442387685442*q^193 - 
        1800325645104*q^194 - 703199584080*q^195 + 2497932784704*q^196 - 
        2876091504354*q^197 + 1458117876384*q^198 + 728391402200*q^199 + 
        O(q^200)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 1.659 seconds, Total memory usage: 5.49MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:01:00 2004

Input: M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C,200);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:00:58 on modular  [Seed = 2015581617]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 
        12830688*q^22 + 18643272*q^23 + 21288960*q^24 - 25499225*q^25 + 
        13865712*q^26 - 73279080*q^27 + 24647168*q^28 + 128406630*q^29 - 
        29211840*q^30 - 52843168*q^31 - 196706304*q^32 + 134722224*q^33 + 
        165742416*q^34 - 80873520*q^35 + 167282496*q^36 - 182213314*q^37 - 
        255874080*q^38 - 145589976*q^39 + 408038400*q^40 + 308120442*q^41 + 
        101267712*q^42 - 17125708*q^43 - 786948864*q^44 - 548895690*q^45 - 
        447438528*q^46 + 2687348496*q^47 + 248758272*q^48 - 1696965207*q^49 + 
        611981400*q^50 - 1740295368*q^51 + 850430336*q^52 - 1596055698*q^53 + 
        1758697920*q^54 + 2582175960*q^55 - 1414533120*q^56 + 2686677840*q^57 - 
        3081759120*q^58 - 5189203740*q^59 - 1791659520*q^60 + 6956478662*q^61 + 
        1268236032*q^62 + 1902838392*q^63 + 2699296768*q^64 - 2790474540*q^65 - 
        3233333376*q^66 - 15481826884*q^67 + 10165534848*q^68 + 4698104544*q^69 
        + 1940964480*q^70 + 9791485272*q^71 - 9600560640*q^72 + 1463791322*q^73 
        + 4373119536*q^74 - 6425804700*q^75 - 15693610240*q^76 - 8951543328*q^77
        + 3494159424*q^78 + 38116845680*q^79 + 4767866880*q^80 + 1665188361*q^81
        - 7394890608*q^82 - 29335099668*q^83 + 6211086336*q^84 - 
        33355661220*q^85 + 411016992*q^86 + 32358470760*q^87 + 45164021760*q^88 
        - 24992917110*q^89 + 13173496560*q^90 + 9673645072*q^91 - 
        27442896384*q^92 - 13316478336*q^93 - 64496363904*q^94 + 
        51494658600*q^95 - 49569988608*q^96 + 75013568546*q^97 + 
        40727164968*q^98 - 60754911516*q^99 + 37534859200*q^100 + 
        81742959102*q^101 + 41767088832*q^102 - 225755128648*q^103 - 
        48807306240*q^104 - 20380127040*q^105 + 38305336752*q^106 + 
        90241258356*q^107 + 107866805760*q^108 + 73482676310*q^109 - 
        61972223040*q^110 - 45917755128*q^111 - 16528605184*q^112 - 
        85146862638*q^113 - 64480268160*q^114 + 90047003760*q^115 - 
        189014559360*q^116 + 65655879534*q^117 + 124540889760*q^118 + 
        115632958896*q^119 + 102825676800*q^120 + 498319933*q^121 - 
        166955487888*q^122 + 77646351384*q^123 + 77785143296*q^124 - 
        359001100500*q^125 - 45668121408*q^126 - 262717201024*q^127 + 
        338071388160*q^128 - 4315678416*q^129 + 66971388960*q^130 + 
        631528759932*q^131 - 198311113728*q^132 - 178514816480*q^133 + 
        371563845216*q^134 - 353937956400*q^135 - 583413304320*q^136 - 
        297198746214*q^137 - 112754509056*q^138 + 596793577940*q^139 + 
        119045821440*q^140 + 677211820992*q^141 - 234995646528*q^142 - 
        308865667656*q^143 - 112181096448*q^144 + 620204022900*q^145 - 
        35130991728*q^146 - 427635232164*q^147 + 268217998208*q^148 - 
        1115433620850*q^149 + 154219312800*q^150 - 824447297848*q^151 + 
        900676761600*q^152 + 784811057562*q^153 + 214837039872*q^154 - 
        255232501440*q^155 + 214308444672*q^156 + 1315116754406*q^157 - 
        914804296320*q^158 - 402206035896*q^159 - 950091448320*q^160 - 
        312162946368*q^161 - 39964520664*q^162 - 357832759588*q^163 - 
        453553290624*q^164 + 650708341920*q^165 + 704042392032*q^166 + 
        2754833892216*q^167 - 356462346240*q^168 - 1458379197393*q^169 + 
        800535869280*q^170 - 1211595753060*q^171 + 25209042176*q^172 - 
        950387449578*q^173 - 776603298240*q^174 + 426959023400*q^175 + 
        527734751232*q^176 - 1307679342480*q^177 + 599830010640*q^178 + 
        1681384224780*q^179 + 807974455680*q^180 - 996774496018*q^181 - 
        232167481728*q^182 + 1753032622824*q^183 + 1574983618560*q^184 - 
        880090306620*q^185 + 319595480064*q^186 - 3691995187608*q^187 - 
        3955776986112*q^188 + 1226984915520*q^189 - 1235871806400*q^190 + 
        2762403350592*q^191 + 680222785536*q^192 + 5442387685442*q^193 - 
        1800325645104*q^194 - 703199584080*q^195 + 2497932784704*q^196 - 
        2876091504354*q^197 + 1458117876384*q^198 + 728391402200*q^199 + 
        O(q^200)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Del
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 1.540 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:03:05 2004

Input: Q:=RationalField;
Q<q>:=PolynomialRing(q);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
C;
f:=qExpansionBasis(C,200);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:03:03 on modular  [Seed = 1142908928]
   -------------------------------------


>> Q<q>:=PolynomialRing(q);
                        ^
User error: Identifier 'q' has not been declared or assigned
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
Modular symbols space for Gamma_0(1) of weight 12 and dimension 2 over Rational 
Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 
        12830688*q^22 + 18643272*q^23 + 21288960*q^24 - 25499225*q^25 + 
        13865712*q^26 - 73279080*q^27 + 24647168*q^28 + 128406630*q^29 - 
        29211840*q^30 - 52843168*q^31 - 196706304*q^32 + 134722224*q^33 + 
        165742416*q^34 - 80873520*q^35 + 167282496*q^36 - 182213314*q^37 - 
        255874080*q^38 - 145589976*q^39 + 408038400*q^40 + 308120442*q^41 + 
        101267712*q^42 - 17125708*q^43 - 786948864*q^44 - 548895690*q^45 - 
        447438528*q^46 + 2687348496*q^47 + 248758272*q^48 - 1696965207*q^49 + 
        611981400*q^50 - 1740295368*q^51 + 850430336*q^52 - 1596055698*q^53 + 
        1758697920*q^54 + 2582175960*q^55 - 1414533120*q^56 + 2686677840*q^57 - 
        3081759120*q^58 - 5189203740*q^59 - 1791659520*q^60 + 6956478662*q^61 + 
        1268236032*q^62 + 1902838392*q^63 + 2699296768*q^64 - 2790474540*q^65 - 
        3233333376*q^66 - 15481826884*q^67 + 10165534848*q^68 + 4698104544*q^69 
        + 1940964480*q^70 + 9791485272*q^71 - 9600560640*q^72 + 1463791322*q^73 
        + 4373119536*q^74 - 6425804700*q^75 - 15693610240*q^76 - 8951543328*q^77
        + 3494159424*q^78 + 38116845680*q^79 + 4767866880*q^80 + 1665188361*q^81
        - 7394890608*q^82 - 29335099668*q^83 + 6211086336*q^84 - 
        33355661220*q^85 + 411016992*q^86 + 32358470760*q^87 + 45164021760*q^88 
        - 24992917110*q^89 + 13173496560*q^90 + 9673645072*q^91 - 
        27442896384*q^92 - 13316478336*q^93 - 64496363904*q^94 + 
        51494658600*q^95 - 49569988608*q^96 + 75013568546*q^97 + 
        40727164968*q^98 - 60754911516*q^99 + 37534859200*q^100 + 
        81742959102*q^101 + 41767088832*q^102 - 225755128648*q^103 - 
        48807306240*q^104 - 20380127040*q^105 + 38305336752*q^106 + 
        90241258356*q^107 + 107866805760*q^108 + 73482676310*q^109 - 
        61972223040*q^110 - 45917755128*q^111 - 16528605184*q^112 - 
        85146862638*q^113 - 64480268160*q^114 + 90047003760*q^115 - 
        189014559360*q^116 + 65655879534*q^117 + 124540889760*q^118 + 
        115632958896*q^119 + 102825676800*q^120 + 498319933*q^121 - 
        166955487888*q^122 + 77646351384*q^123 + 77785143296*q^124 - 
        359001100500*q^125 - 45668121408*q^126 - 262717201024*q^127 + 
        338071388160*q^128 - 4315678416*q^129 + 66971388960*q^130 + 
        631528759932*q^131 - 198311113728*q^132 - 178514816480*q^133 + 
        371563845216*q^134 - 353937956400*q^135 - 583413304320*q^136 - 
        297198746214*q^137 - 112754509056*q^138 + 596793577940*q^139 + 
        119045821440*q^140 + 677211820992*q^141 - 234995646528*q^142 - 
        308865667656*q^143 - 112181096448*q^144 + 620204022900*q^145 - 
        35130991728*q^146 - 427635232164*q^147 + 268217998208*q^148 - 
        1115433620850*q^149 + 154219312800*q^150 - 824447297848*q^151 + 
        900676761600*q^152 + 784811057562*q^153 + 214837039872*q^154 - 
        255232501440*q^155 + 214308444672*q^156 + 1315116754406*q^157 - 
        914804296320*q^158 - 402206035896*q^159 - 950091448320*q^160 - 
        312162946368*q^161 - 39964520664*q^162 - 357832759588*q^163 - 
        453553290624*q^164 + 650708341920*q^165 + 704042392032*q^166 + 
        2754833892216*q^167 - 356462346240*q^168 - 1458379197393*q^169 + 
        800535869280*q^170 - 1211595753060*q^171 + 25209042176*q^172 - 
        950387449578*q^173 - 776603298240*q^174 + 426959023400*q^175 + 
        527734751232*q^176 - 1307679342480*q^177 + 599830010640*q^178 + 
        1681384224780*q^179 + 807974455680*q^180 - 996774496018*q^181 - 
        232167481728*q^182 + 1753032622824*q^183 + 1574983618560*q^184 - 
        880090306620*q^185 + 319595480064*q^186 - 3691995187608*q^187 - 
        3955776986112*q^188 + 1226984915520*q^189 - 1235871806400*q^190 + 
        2762403350592*q^191 + 680222785536*q^192 + 5442387685442*q^193 - 
        1800325645104*q^194 - 703199584080*q^195 + 2497932784704*q^196 - 
        2876091504354*q^197 + 1458117876384*q^198 + 728391402200*q^199 + 
        O(q^200)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Del
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 1.550 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:03:28 2004

Input: Q:=RationalField;
Q<q>:=PolynomialRing(q);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,200);
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:03:26 on modular  [Seed = 1276600337]
   -------------------------------------


>> Q<q>:=PolynomialRing(q);
                        ^
User error: Identifier 'q' has not been declared or assigned
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Del
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 1.540 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:03:44 2004

Input: Q:=RationalField;
Q<q>:=PolynomialRing(Q);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,200);
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:03:42 on modular  [Seed = 1410300153]
   -------------------------------------


>> Q<q>:=PolynomialRing(Q);
                       ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: Intrinsic
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Del
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 1.540 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:06:01 2004

Input: Q:=RationalField;
Q<q>:==PolynomialRing(Q);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,200);
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:06:00 on modular  [Seed = 2734263705]
   -------------------------------------


>> Q<q>:==PolynomialRing(Q);
         ^
User error: bad syntax
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Del
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 1.540 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:06:08 2004

Input: Q:=RationalField;
Q<q>:=PolynomialRing(Q);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,200);
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Delta,3)-Coefficient(Delta,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:06:07 on modular  [Seed = 2867955094]
   -------------------------------------


>> Q<q>:=PolynomialRing(Q);
                       ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: Intrinsic
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(Del
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 1.550 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:07:51 2004

Input: Z:=RationalField;
Z<q>:=PolynomialRing(Z);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,200);
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:07:49 on modular  [Seed = 3001654548]
   -------------------------------------


>> Z<q>:=PolynomialRing(Z);
                       ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: Intrinsic
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                           ^
Runtime error in '!': Illegal coercion

Total time: 1.540 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:08:11 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,200);
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:08:09 on modular  [Seed = 3101923074]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 1.540 seconds, Total memory usage: 5.03MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:09:32 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:09:31 on modular  [Seed = 2161880904]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 + O(q^20)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.730 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:13:02 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);
g:=1+2*q;Coefficient(g,1);
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);
f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:13:01 on modular  [Seed = 2413076753]
   -------------------------------------

2
Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 + O(q^20)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:13:25 2004

Input: M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);
Z:=RationalField();
Z<q>:=PolynomialRing(Z);
g:=1+2*q;Coefficient(g,1);

f;
Coefficient(f,139);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:13:24 on modular  [Seed = 2546776416]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
2
[
    q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 
        84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 
        577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 
        2727432*q^18 + 10661420*q^19 + O(q^20)
]

>> Coefficient(f,139);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:13:43 2004

Input: M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);
Z:=RationalField();
Z<q>:=PolynomialRing(Z);
g:=1+2*q;Coefficient(g,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:13:42 on modular  [Seed = 2680467802]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field
2

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.750 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:13:55 2004

Input: M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);
Z:=RationalField();
Z<q>:=PolynomialRing(Z);
g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:13:54 on modular  [Seed = 3887909174]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> g:=1+2*q;Coefficient(f,1);
                       ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:15:11 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);

M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=Z<q>!(qExpansionBasis(C,20));
g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:15:10 on modular  [Seed = 4004896755]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> f:=Z<q>!(qExpansionBasis(C,20));
       ^
User error: bad syntax

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.620 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:15:36 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);

M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=Z<q>;
g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:15:36 on modular  [Seed = 4121871502]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> f:=Z<q>;
       ^
User error: bad syntax

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.620 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:15:47 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);

M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f in Z<q>;
g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:15:47 on modular  [Seed = 4255567037]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> f in Z<q>;
         ^
User error: bad syntax

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.620 seconds, Total memory usage: 3.26MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:16:10 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z);

M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:16:09 on modular  [Seed = 3315528863]
   -------------------------------------

Full modular symbols space for Gamma_0(1) of weight 12 and dimension 3 over 
Rational Field

>> g:=1+2*q;Coefficient(f,1);
                       ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:19:58 2004

Input: Z:=RationalField();
Z<q>:=PowerSequence(Z)

M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:19:58 on modular  [Seed = 3548963758]
   -------------------------------------


>> M:=ModularSymbols(1,12);M;
   ^
User error: bad syntax

>> C:=CuspidalSubspace(M);
                       ^
User error: Identifier 'M' has not been declared or assigned

>> f:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
          ^
User error: Identifier 'q' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:20:55 2004

Input: Z:=RationalField();
Z<q>:=PolynomialRing(Z)

M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f!Z<q>;
f:=qExpansionBasis(C,20);

g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:20:54 on modular  [Seed = 779427482]
   -------------------------------------


>> M:=ModularSymbols(1,12);M;
   ^
User error: bad syntax

>> C:=CuspidalSubspace(M);
                       ^
User error: Identifier 'M' has not been declared or assigned

>> f!Z<q>;
      ^
User error: bad syntax

>> f:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
          ^
User error: Identifier 'q' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:21:44 2004

Input: Z:=RationalInteger();
Z<q>:=PolynomialRing(Z)
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f!Z<q>;
f:=qExpansionBasis(C,20);

g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:21:44 on modular  [Seed = 896402911]
   -------------------------------------


>> Z:=RationalInteger();
      ^
User error: Identifier 'RationalInteger' has not been declared or assigned

>> M:=ModularSymbols(1,12);M;
   ^
User error: bad syntax

>> C:=CuspidalSubspace(M);
                       ^
User error: Identifier 'M' has not been declared or assigned

>> f!Z<q>;
      ^
User error: bad syntax

>> f:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
          ^
User error: Identifier 'q' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:22:08 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z)
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f!Z<q>;
f:=qExpansionBasis(C,20);

g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:22:08 on modular  [Seed = 1030098431]
   -------------------------------------


>> M:=ModularSymbols(1,12);M;
   ^
User error: bad syntax

>> C:=CuspidalSubspace(M);
                       ^
User error: Identifier 'M' has not been declared or assigned

>> f!Z<q>;
      ^
User error: bad syntax

>> f:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
          ^
User error: Identifier 'q' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:22:25 2004

Input: Z:=IntegerRing();
Z<q>:=PolynomialRing(Z)
M:=ModularSymbols(1,12);M;
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

g:=1+2*q;Coefficient(f,1);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:22:24 on modular  [Seed = 90060247]
   -------------------------------------


>> M:=ModularSymbols(1,12);M;
   ^
User error: bad syntax

>> C:=CuspidalSubspace(M);
                       ^
User error: Identifier 'M' has not been declared or assigned

>> f:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
          ^
User error: Identifier 'q' has not been declared or assigned

>> g:=1+2*q;Coefficient(f,1);
                        ^
User error: Identifier 'f' has not been declared or assigned

>> Coefficient(f,13);
               ^
User error: Identifier 'f' has not been declared or assigned

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                           ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:23:34 2004

Input: M:=ModularSymbols(1,12);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

Z:=IntegerRing();
Z<q>:=PolynomialRing(Z)
f!Z<q>;
Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:23:33 on modular  [Seed = 323493892]
   -------------------------------------


>> f!Z<q>;
   ^
User error: bad syntax

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                                                                          ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:27:31 2004

Input: M:=ModularSymbols(1,12);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

Z:=IntegerRing();
Z<q>:=PolynomialRing(Z);
f!Z<q>;
Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:27:31 on modular  [Seed = 507849759]
   -------------------------------------


>> f!Z<q>;
      ^
User error: bad syntax

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.750 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:28:00 2004

Input: M:=ModularSymbols(1,12);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

Coefficient(f,13);
for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3)-Coefficient(f,t));end if; end for;

Output: Magma V2.11-2     Wed Aug 11 2004 15:27:59 on modular  [Seed = 1715295355]
   -------------------------------------


>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> for j in [1..2] do  t:=Z!(3+2^j); if IsPrime(t) then Factor(Coefficient(f,3
                          ^
User error: Identifier 'Z' has not been declared or assigned

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:28:19 2004

Input: M:=ModularSymbols(1,12);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

Coefficient(f,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:28:18 on modular  [Seed = 1848990751]
   -------------------------------------


>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:30:16 2004

Input: Q:=RationalField();
M:=ModularSymbols(1,12);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

Coefficient(f,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:30:15 on modular  [Seed = 1982678163]
   -------------------------------------


>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.750 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:31:04 2004

Input: Q:=RationalField();

M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,20);

Coefficient(f,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:31:04 on modular  [Seed = 2133085605]
   -------------------------------------

Rational Field

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:31:46 2004

Input: Q:=RationalField();

M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,5000);

Coefficient(f,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:31:26 on modular  [Seed = 1193046635]
   -------------------------------------

Rational Field


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:35:29 2004

Input: Q:=RationalField();
Q<q>:=PolynomialRing(Q);g;

M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);

Coefficient(f,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:35:28 on modular  [Seed = 1276606574]
   -------------------------------------


>> Q<q>:=PolynomialRing(Q);g;
                           ^
User error: Identifier 'g' has not been declared or assigned
Rational Field

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.789 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:35:41 2004

Input: Q:=RationalField();
Q<q>:=PolynomialRing(Q);g:=0;

M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);

Coefficient(f,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:35:41 on modular  [Seed = 1427005818]
   -------------------------------------

Rational Field

>> Coefficient(f,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.789 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:35:52 2004

Input: Q:=RationalField();
Q<q>:=PolynomialRing(Q);g:=0;

M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
g:=f;
Coefficient(g,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:35:51 on modular  [Seed = 2734266007]
   -------------------------------------

Rational Field

>> Coefficient(g,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:36:08 2004

Input: Q:=RationalField();
Q<q>:=PolynomialRing(Q);g:=0;
Coeff(g,1);
M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
g:=f;
Coefficient(g,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:36:07 on modular  [Seed = 2867961519]
   -------------------------------------


>> Coeff(g,1);
   ^
User error: Identifier 'Coeff' has not been declared or assigned
Rational Field

>> Coefficient(g,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:36:15 2004

Input: Q:=RationalField();
Q<q>:=PolynomialRing(Q);g:=0;
Coefficient(g,1);
M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
g:=f;
Coefficient(g,13);


Output: Magma V2.11-2     Wed Aug 11 2004 15:36:14 on modular  [Seed = 3001648830]
   -------------------------------------


>> Coefficient(g,1);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: RngIntElt, RngIntElt
Rational Field

>> Coefficient(g,13);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:36:53 2004

Input: Q:=RationalField();
Q<q>:=PolynomialRing(Q);g:=1+2*q;
Coefficient(g,1);
M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
g:=f;
Coefficient(g,2);


Output: Magma V2.11-2     Wed Aug 11 2004 15:36:52 on modular  [Seed = 3135344332]
   -------------------------------------

2
Rational Field

>> Coefficient(g,2);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:37:17 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
Q:=RationalField();
Q<q>:=PolynomialRing(Q);g:=1+2*q;
Coefficient(g,1);

g:=f;
Coefficient(g,2);


Output: Magma V2.11-2     Wed Aug 11 2004 15:37:16 on modular  [Seed = 2195306188]
   -------------------------------------

Rational Field
2

>> Coefficient(g,2);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.789 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:39:26 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
HeckeOperator(C,3);


Output: Magma V2.11-2     Wed Aug 11 2004 15:39:25 on modular  [Seed = 2295577671]
   -------------------------------------

Rational Field
[252   0]
[  0 252]

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:44:58 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
HeckeOperator(C,3);
PowerSeries(C);

Output: Magma V2.11-2     Wed Aug 11 2004 15:44:57 on modular  [Seed = 3937524977]
   -------------------------------------

Rational Field
[252   0]
[  0 252]
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 84480*q^8 - 
    113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 577738*q^13 + 
    401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 2727432*q^18 + 
    10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 12830688*q^22 + 18643272*q^23 
    + 21288960*q^24 - 25499225*q^25 + 13865712*q^26 - 73279080*q^27 + 
    24647168*q^28 + 128406630*q^29 - 29211840*q^30 - 52843168*q^31 - 
    196706304*q^32 + 134722224*q^33 + 165742416*q^34 - 80873520*q^35 + 
    167282496*q^36 - 182213314*q^37 - 255874080*q^38 - 145589976*q^39 + 
    408038400*q^40 + 308120442*q^41 + 101267712*q^42 - 17125708*q^43 - 
    786948864*q^44 - 548895690*q^45 - 447438528*q^46 + 2687348496*q^47 + 
    248758272*q^48 - 1696965207*q^49 + O(q^50)

Total time: 0.789 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:45:17 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
HeckeOperator(C,3);
PowerSeries(C);
Coefficient(f,2);

Output: Magma V2.11-2     Wed Aug 11 2004 15:45:16 on modular  [Seed = 4071212188]
   -------------------------------------

Rational Field
[252   0]
[  0 252]
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 84480*q^8 - 
    113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 577738*q^13 + 
    401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 2727432*q^18 + 
    10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 12830688*q^22 + 18643272*q^23 
    + 21288960*q^24 - 25499225*q^25 + 13865712*q^26 - 73279080*q^27 + 
    24647168*q^28 + 128406630*q^29 - 29211840*q^30 - 52843168*q^31 - 
    196706304*q^32 + 134722224*q^33 + 165742416*q^34 - 80873520*q^35 + 
    167282496*q^36 - 182213314*q^37 - 255874080*q^38 - 145589976*q^39 + 
    408038400*q^40 + 308120442*q^41 + 101267712*q^42 - 17125708*q^43 - 
    786948864*q^44 - 548895690*q^45 - 447438528*q^46 + 2687348496*q^47 + 
    248758272*q^48 - 1696965207*q^49 + O(q^50)

>> Coefficient(f,2);;
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 0.789 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:45:51 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
HeckeOperator(C,3);
PowerSeries(C);
Coefficient(f,2);
Eigenvalues(C,2);

Output: Magma V2.11-2     Wed Aug 11 2004 15:45:50 on modular  [Seed = 4221619639]
   -------------------------------------

Rational Field
[252   0]
[  0 252]
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 84480*q^8 - 
    113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 577738*q^13 + 
    401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 2727432*q^18 + 
    10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 12830688*q^22 + 18643272*q^23 
    + 21288960*q^24 - 25499225*q^25 + 13865712*q^26 - 73279080*q^27 + 
    24647168*q^28 + 128406630*q^29 - 29211840*q^30 - 52843168*q^31 - 
    196706304*q^32 + 134722224*q^33 + 165742416*q^34 - 80873520*q^35 + 
    167282496*q^36 - 182213314*q^37 - 255874080*q^38 - 145589976*q^39 + 
    408038400*q^40 + 308120442*q^41 + 101267712*q^42 - 17125708*q^43 - 
    786948864*q^44 - 548895690*q^45 - 447438528*q^46 + 2687348496*q^47 + 
    248758272*q^48 - 1696965207*q^49 + O(q^50)

>> Coefficient(f,2);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> Eigenvalues(C,2);;
              ^
Runtime error in 'Eigenvalues': Bad argument types
Argument types given: ModSym, RngIntElt

Total time: 0.789 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:46:03 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
HeckeOperator(C,3);
PowerSeries(C);
Coefficient(f,2);
Eigenvalue(C,2);

Output: Magma V2.11-2     Wed Aug 11 2004 15:46:02 on modular  [Seed = 3281581467]
   -------------------------------------

Rational Field
[252   0]
[  0 252]
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 84480*q^8 - 
    113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 577738*q^13 + 
    401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 2727432*q^18 + 
    10661420*q^19 - 7109760*q^20 - 4219488*q^21 - 12830688*q^22 + 18643272*q^23 
    + 21288960*q^24 - 25499225*q^25 + 13865712*q^26 - 73279080*q^27 + 
    24647168*q^28 + 128406630*q^29 - 29211840*q^30 - 52843168*q^31 - 
    196706304*q^32 + 134722224*q^33 + 165742416*q^34 - 80873520*q^35 + 
    167282496*q^36 - 182213314*q^37 - 255874080*q^38 - 145589976*q^39 + 
    408038400*q^40 + 308120442*q^41 + 101267712*q^42 - 17125708*q^43 - 
    786948864*q^44 - 548895690*q^45 - 447438528*q^46 + 2687348496*q^47 + 
    248758272*q^48 - 1696965207*q^49 + O(q^50)

>> Coefficient(f,2);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> Eigenvalue(C,2);;
   ^
User error: Identifier 'Eigenvalue' has not been declared or assigned

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:46:16 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qExpansionBasis(C,50);
HeckeOperator(C,3);
Eigenvalue(C,2);

Output: Magma V2.11-2     Wed Aug 11 2004 15:46:16 on modular  [Seed = 3415276897]
   -------------------------------------

Rational Field
[252   0]
[  0 252]

>> Eigenvalue(C,2);;
   ^
User error: Identifier 'Eigenvalue' has not been declared or assigned

Total time: 0.779 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:46:58 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qIntegralBasis(C,5);
HeckeOperator(C,3);
Coefficient(f,2);
Eigenvalue(C,2);

Output: Magma V2.11-2     Wed Aug 11 2004 15:46:57 on modular  [Seed = 3548964160]
   -------------------------------------

Rational Field
[252   0]
[  0 252]

>> Coefficient(f,2);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> Eigenvalue(C,2);;
   ^
User error: Identifier 'Eigenvalue' has not been declared or assigned

Total time: 0.740 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host long.math.iastate.edu. (129.186.52.128)
Time: Wed Aug 11 15:48:28 2004

Input: M:=ModularSymbols(1,12);
BaseField(M);
C:=CuspidalSubspace(M);
f:=qIntegralBasis(C,5);
HeckeEigenvalue(C,3);
Coefficient(f,2);
Eigenvalue(C,2);

Output: Magma V2.11-2     Wed Aug 11 2004 15:48:27 on modular  [Seed = 3682657010]
   -------------------------------------

Rational Field

>> HeckeEigenvalue(C,3);
   ^
User error: Identifier 'HeckeEigenvalue' has not been declared or assigned

>> Coefficient(f,2);
              ^
Runtime error in 'Coefficient': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

>> Eigenvalue(C,2);;
   ^
User error: Identifier 'Eigenvalue' has not been declared or assigned

Total time: 0.720 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host c-24-7-68-216.client.comcast.net. (24.7.68.216)
Time: Thu Aug 12 02:49:57 2004

Input: (Integers(79)!2)^40;

Output: Magma V2.11-2     Thu Aug 12 2004 02:49:56 on modular  [Seed = 3068978314]
   -------------------------------------

2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma3-529b.postech.ac.kr. (141.223.33.172)
Time: Thu Aug 12 03:30:19 2004

Input: G:=ShepardTodd(9);


Output: Magma V2.11-2     Thu Aug 12 2004 03:30:19 on modular  [Seed = 3415316072]
   -------------------------------------


>> G:=ShepardTodd(9);
      ^
User error: Identifier 'ShepardTodd' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ma3-529b.postech.ac.kr. (141.223.33.172)
Time: Thu Aug 12 03:30:53 2004

Input: G:=ShephardTodd(9);
Order(G);
CompositionFactors(G);



Output: Magma V2.11-2     Thu Aug 12 2004 03:30:52 on modular  [Seed = 3298728256]
   -------------------------------------

192
    G
    |  Cyclic(2)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1

Total time: 0.600 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host ma3-529b.postech.ac.kr. (141.223.33.172)
Time: Thu Aug 12 04:24:32 2004

Input: G:=ShephardTodd(9);
Order(G);
CompositionFactors(G);

C:=ExtendCode(QRCode(GF(2),47));
G:=AutomorphismGroup(C);
ConjugacyClass(G);


Output: Magma V2.11-2     Thu Aug 12 2004 04:24:11 on modular  [Seed = 1142828100]
   -------------------------------------

192
    G
    |  Cyclic(2)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1


************** MAGMA *****************
Host ma3-529b.postech.ac.kr. (141.223.33.172)
Time: Thu Aug 12 04:27:58 2004

Input: G:=ShephardTodd(9);
Order(G);
CompositionFactors(G);

C:=ExtendCode(QRCode(GF(2),47));
G:=AutomorphismGroup(C);
ConjugacyClass(G);


Output: Magma V2.11-2     Thu Aug 12 2004 04:27:37 on modular  [Seed = 1342847106]
   -------------------------------------

192
    G
    |  Cyclic(2)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Thu Aug 12 05:10:07 2004

Input: Q5:=pAdicField(5,50);
Q5x<x>:=PolynomialRing(Q5);
TRE:=TotallyRamifiedExtension(Q5,x^4+5);
MinimalPolynomial(TRE!0);
2+2;

Output: Magma V2.11-2     Thu Aug 12 2004 05:10:06 on modular  [Seed = 4221667646]
   -------------------------------------

O(1)
4

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (149.156.65.173)
Time: Thu Aug 12 07:04:04 2004

Input: a:=2;
b:=3;
print a+b;

Output: Magma V2.11-2     Thu Aug 12 2004 07:04:01 on modular  [Seed = 3298741064]
   -------------------------------------

5

Total time: 0.659 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Aug 13 06:35:53 2004

Input: //bash-2.05b$ magma -n
//Magma V2.11-2     Thu Jul 22 2004 12:28:26 on celery   [Seed = 79421586]
//Type ? for help.  Type <Ctrl>-D to quit.

cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
"Discriminant(F,1)";


//Magma: Internal error
//Please mail this entire run [**WITH THE FOLLOWING LINES**]
   // to magma-bugs@maths.usyd.edu.au
//Version date: Fri May 28 14:46:51 EST 2004
//Initial seed: 79421586
//Time to this point: 0.34
//Segmentation fault

///////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////

cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
"Points(S)";


Output: Magma V2.11-2     Fri Aug 13 2004 06:35:50 on modular  [Seed = 357092782]
   -------------------------------------

Discriminant(F,1)
Points(S)

Total time: 0.669 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Aug 13 06:36:34 2004

Input: //bash-2.05b$ magma -n
//Magma V2.11-2     Thu Jul 22 2004 12:28:26 on celery   [Seed = 79421586]
//Type ? for help.  Type <Ctrl>-D to quit.

cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
R<X,Y,Z,W>:=PolynomialRing(cu,4);
F:=X^2+z^2/(u^2-z*u+z^2);
Discriminant(F,1);


//Magma: Internal error
//Please mail this entire run [**WITH THE FOLLOWING LINES**]
   // to magma-bugs@maths.usyd.edu.au
//Version date: Fri May 28 14:46:51 EST 2004
//Initial seed: 79421586
//Time to this point: 0.34
//Segmentation fault

///////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////

cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
"Points(S)";


Output: Magma V2.11-2     Fri Aug 13 2004 06:36:34 on modular  [Seed = 223401347]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 223401347
Time to this point: 0.6
Segmentation fault
Points(S)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Aug 13 06:37:04 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
"Points(S)";


Output: Magma V2.11-2     Fri Aug 13 2004 06:37:04 on modular  [Seed = 89710057]
   -------------------------------------

Points(S)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache3.nottingham.ac.uk. (128.243.220.41)
Time: Fri Aug 13 06:37:11 2004

Input: cyc<z>:=CyclotomicField(8);
cu<u>:=FunctionField(cyc);
P<X,Y,Z,W>:=ProjectiveSpace(cu,3);
eqns:=[X-z^3*W,Y+z^3*Z,Z^3+Z*W^2+(-z*u^3-z^3*u)*W^3];
S:=Scheme(P,eqns);
Points(S);


Output: Magma V2.11-2     Fri Aug 13 2004 06:37:10 on modular  [Seed = 2099291543]
   -------------------------------------



Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to magma-bugs@maths.usyd.edu.au
Version date: Fri May 28 14:46:51 EST 2004
Initial seed: 2099291543
Time to this point: 0.62
Internal error in fact_sep() at dpoly/nfact.c, line 1843

Total time: 0.579 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Fri Aug 13 06:48:59 2004

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
for i:=10 to 20 do 
FindGroupOrder2(319546020820551643220672513,i);
end for;

Output: Magma V2.11-2     Fri Aug 13 2004 06:48:49 on modular  [Seed = 1560314096]
   -------------------------------------

[ <2, 2>, <3, 1>, <29, 1>, <83, 1>, <443, 1>, <24973093965378171439, 1> ]
[ <2, 3>, <3, 2>, <11257, 1>, <394255945461748102769, 1> ]
[ <2, 3>, <3, 1>, <1321, 1>, <10079044310514955142971, 1> ]
[ <2, 4>, <3, 4>, <5, 1>, <23, 1>, <53, 1>, <3517, 1>, <45641, 1>, 
<252015459497, 1> ]
[ <2, 2>, <3, 1>, <2383, 1>, <602713, 1>, <18540334550860691, 1> ]
[ <2, 2>, <3, 1>, <27943, 1>, <77591, 1>, <12281963089824023, 1> ]
[ <2, 2>, <3, 1>, <5, 1>, <149, 1>, <3923, 1>, <4327, 1>, <1528939, 1>, 
<1377211159, 1> ]
[ <2, 2>, <3, 1>, <7, 1>, <3804119295482931902604349, 1> ]
[ <2, 2>, <3, 1>, <221401, 1>, <91990309, 1>, <1307466324841, 1> ]
[ <2, 2>, <3, 1>, <277, 1>, <503, 1>, <191119241722062987331, 1> ]
[ <2, 3>, <3, 2>, <13, 2>, <31, 1>, <61, 1>, <1873, 1>, <7414551850101419, 1> ]

Total time: 9.559 seconds, Total memory usage: 5.18MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Fri Aug 13 06:51:39 2004

Input: exit;

Output: Magma V2.11-2     Fri Aug 13 2004 06:51:39 on modular  [Seed = 1443596881]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Fri Aug 13 06:51:50 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug 13 2004 06:51:49 on modular  [Seed = 1309905463]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Fri Aug 13 06:51:55 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug 13 2004 06:51:55 on modular  [Seed = 1176214065]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Fri Aug 13 06:52:02 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug 13 2004 06:52:01 on modular  [Seed = 3202573011]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host cache1.nottingham.ac.uk. (128.243.220.21)
Time: Fri Aug 13 06:52:08 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug 13 2004 06:52:07 on modular  [Seed = 3068881629]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 213.219.184.47.adslpower.by.edpnet.be. (213.219.184.47)
Time: Fri Aug 13 15:09:44 2004

Input: test

Output: Magma V2.11-2     Fri Aug 13 2004 15:09:43 on modular  [Seed = 1242962686]
   -------------------------------------


>> test;
   ^
User error: Identifier 'test' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 213.219.184.47.adslpower.by.edpnet.be. (213.219.184.47)
Time: Fri Aug 13 15:10:06 2004

Input: 2+3

Output: Magma V2.11-2     Fri Aug 13 2004 15:10:05 on modular  [Seed = 1476659990]
   -------------------------------------

5

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (211.98.130.10)
Time: Sat Aug 14 06:57:38 2004

Input: p[9]

Output: Magma V2.11-2     Sat Aug 14 2004 06:57:37 on modular  [Seed = 2496144894]
   -------------------------------------


>> p[9];
   ^
User error: Identifier 'p' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ppp19a-90070708-088.pt.lu. (213.166.54.88)
Time: Sat Aug 14 10:12:23 2004

Input: 2+4

Output: Magma V2.11-2     Sat Aug 14 2004 10:12:22 on modular  [Seed = 307056281]
   -------------------------------------

6

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host host224-55.pool80182.interbusiness.it. (80.182.55.224)
Time: Sat Aug 14 10:27:35 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Sat Aug 14 2004 10:27:34 on modular  [Seed = 3382094290]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-67-171-55-190.client.comcast.net. (67.171.55.190)
Time: Sat Aug 14 23:08:05 2004

Input: 1+2

Output: Magma V2.11-2     Sat Aug 14 2004 23:08:04 on modular  [Seed = 1029877754]
   -------------------------------------

3

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-67-171-55-190.client.comcast.net. (67.171.55.190)
Time: Sat Aug 14 23:08:42 2004

Input: pi

Output: Magma V2.11-2     Sat Aug 14 2004 23:08:41 on modular  [Seed = 745782982]
   -------------------------------------


>> pi;
   ^
User error: Identifier 'pi' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-67-171-55-190.client.comcast.net. (67.171.55.190)
Time: Sat Aug 14 23:09:07 2004

Input: pi = 3.141592653589793

Output: Magma V2.11-2     Sat Aug 14 2004 23:09:06 on modular  [Seed = 3565897301]
   -------------------------------------


>> pi = 3.141592653589793;
   ^
User error: Identifier 'pi' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-67-171-55-190.client.comcast.net. (67.171.55.190)
Time: Sat Aug 14 23:09:34 2004

Input: mod5

Output: Magma V2.11-2     Sat Aug 14 2004 23:09:33 on modular  [Seed = 3699592801]
   -------------------------------------


>> mod5;
   ^
User error: Identifier 'mod5' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-67-171-55-190.client.comcast.net. (67.171.55.190)
Time: Sat Aug 14 23:10:01 2004

Input: 9876543210123456789876543210123456789876543210+1

Output: Magma V2.11-2     Sat Aug 14 2004 23:10:00 on modular  [Seed = 3298513311]
   -------------------------------------

9876543210123456789876543210123456789876543211

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host sven.edvz.uni-linz.ac.at. (140.78.198.112)
Time: Sun Aug 15 06:17:58 2004

Input: 12^89


Output: Magma V2.11-2     Sun Aug 15 2004 06:17:54 on modular  [Seed = 3415585485]
   -------------------------------------

1114630437411196002603821792971106239963355619747736851305940080331488249670804\
256571506663882752

Total time: 0.730 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (157.88.83.6)
Time: Mon Aug 16 04:25:30 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Mon Aug 16 2004 04:25:29 on modular  [Seed = 3884370430]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (157.88.83.6)
Time: Mon Aug 16 04:25:43 2004

Input: 12+23;


Output: Magma V2.11-2     Mon Aug 16 2004 04:25:42 on modular  [Seed = 4019110153]
   -------------------------------------

35

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (157.88.83.6)
Time: Mon Aug 16 04:25:58 2004

Input: sim(ty);


Output: Magma V2.11-2     Mon Aug 16 2004 04:25:57 on modular  [Seed = 4170831373]
   -------------------------------------


>> sim(ty);
       ^
User error: Identifier 'ty' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (157.88.83.6)
Time: Mon Aug 16 04:26:08 2004

Input: sim(3);


Output: Magma V2.11-2     Mon Aug 16 2004 04:26:07 on modular  [Seed = 3231837759]
   -------------------------------------


>> sim(3);
   ^
User error: Identifier 'sim' has not been declared or assigned

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (144.122.136.68)
Time: Mon Aug 16 06:21:01 2004

Input: ? load 

Output: WARNING: MAGMA command contains unsafe command 'load', so it will not be executed.

************** MAGMA *****************
Host 3(NXDOMAIN) (144.122.136.68)
Time: Mon Aug 16 06:21:22 2004

Input: 2^13

Output: Magma V2.11-2     Mon Aug 16 2004 06:21:21 on modular  [Seed = 3867618596]
   -------------------------------------

8192

Total time: 0.590 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 11:43:25 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Mon Aug 16 2004 11:43:22 on modular  [Seed = 2313690871]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.639 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 13:00:15 2004

Input: F := IntegerRing();
P<x> := PolynomialRing(Z);
Factorization(x^12 - x^8 -x^4 +1);

Output: Magma V2.11-2     Mon Aug 16 2004 13:00:14 on modular  [Seed = 4120140940]
   -------------------------------------


>> P<x> := PolynomialRing(Z);
                          ^
User error: Identifier 'Z' has not been declared or assigned

>> Factorization(x^12 - x^8 -x^4 +1);;
                 ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 13:00:34 2004

Input: Z := IntegerRing();
P<x> := PolynomialRing(Z);
Factorization(x^12 - x^8 -x^4 +1);

Output: Magma V2.11-2     Mon Aug 16 2004 13:00:33 on modular  [Seed = 4254880939]
   -------------------------------------

[
    <x - 1, 2>,
    <x + 1, 2>,
    <x^2 + 1, 2>,
    <x^4 + 1, 1>
]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 13:21:38 2004

Input: "Factorial of 12 is", Factorial(12);


Output: Magma V2.11-2     Mon Aug 16 2004 13:21:38 on modular  [Seed = 2730692327]
   -------------------------------------

Factorial of 12 is 479001600

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host United-Defense-LP-1065659.cust-rtr.pacbell.net. (69.104.229.186)
Time: Mon Aug 16 13:28:23 2004

Input: (a1*x^2 + a1*x) / x

Output: Magma V2.11-2     Mon Aug 16 2004 13:28:23 on modular  [Seed = 2212637779]
   -------------------------------------


>> (a1*x^2 + a1*x) / x;
    ^
User error: Identifier 'a1' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host United-Defense-LP-1065659.cust-rtr.pacbell.net. (69.104.229.186)
Time: Mon Aug 16 13:29:22 2004

Input: (a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0) / (b2*x^2 + b1*x + b0)

Output: Magma V2.11-2     Mon Aug 16 2004 13:29:21 on modular  [Seed = 2566469390]
   -------------------------------------


>> (a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0) / (b2*x^2 + b1*x + b0);
    ^
User error: Identifier 'a4' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host United-Defense-LP-1065659.cust-rtr.pacbell.net. (69.104.229.186)
Time: Mon Aug 16 13:30:43 2004

Input: (a4*x^4 + a3*x^3 + a2*x^2 + a1*x) / (x+1)

Output: Magma V2.11-2     Mon Aug 16 2004 13:30:42 on modular  [Seed = 2132726107]
   -------------------------------------


>> (a4*x^4 + a3*x^3 + a2*x^2 + a1*x) / (x+1);
    ^
User error: Identifier 'a4' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 13:35:21 2004

Input: a:= 10;
b := 7;
a := b;
b := a;
b; 

Output: Magma V2.11-2     Mon Aug 16 2004 13:35:21 on modular  [Seed = 1126363772]
   -------------------------------------

7

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:00:25 2004

Input: c=1 + 0*i;
Parent(c)

Output: Magma V2.11-2     Mon Aug 16 2004 14:00:25 on modular  [Seed = 3867627961]
   -------------------------------------


>> c=1 + 0*i;
           ^
User error: Identifier 'i' has not been declared or assigned

>> Parent(c);
          ^
User error: Identifier 'c' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:00:47 2004

Input: C<i> := ComplexField();
c=1 + 0*i;
Parent(c)

Output: Magma V2.11-2     Mon Aug 16 2004 14:00:46 on modular  [Seed = 4002372038]
   -------------------------------------


>> c=1 + 0*i;
   ^
User error: Identifier 'c' has not been declared or assigned

>> Parent(c);
          ^
User error: Identifier 'c' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:00:56 2004

Input: C<i> := ComplexField();
c :=1 + 0*i;
Parent(c)

Output: Magma V2.11-2     Mon Aug 16 2004 14:00:56 on modular  [Seed = 4153819337]
   -------------------------------------

Complex Field

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:01:03 2004

Input: D<i> := ComplexField();
c :=1 + 0*i;
Parent(c)

Output: Magma V2.11-2     Mon Aug 16 2004 14:01:02 on modular  [Seed = 4288563399]
   -------------------------------------

Complex Field

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:01:50 2004

Input: C := ComplexField();
c :=1 + 0*i;
Parent(c)

Output: Magma V2.11-2     Mon Aug 16 2004 14:01:49 on modular  [Seed = 3349573676]
   -------------------------------------


>> c :=1 + 0*i;
             ^
User error: Identifier 'i' has not been declared or assigned

>> Parent(c);
          ^
User error: Identifier 'c' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:02:23 2004

Input: C := ComplexField();
c := C ! 37

Output: Magma V2.11-2     Mon Aug 16 2004 14:02:22 on modular  [Seed = 3433921284]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:02:26 2004

Input: C := ComplexField();
c := C ! 37;

Output: Magma V2.11-2     Mon Aug 16 2004 14:02:26 on modular  [Seed = 3568657152]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:02:33 2004

Input: C := ComplexField();
c := C ! 37;
c;

Output: Magma V2.11-2     Mon Aug 16 2004 14:02:32 on modular  [Seed = 3703401218]
   -------------------------------------

37

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:35:05 2004

Input: C<i> = ComplexField();
C;

Output: Magma V2.11-2     Mon Aug 16 2004 14:35:04 on modular  [Seed = 1745475416]
   -------------------------------------


>> C<i> = ComplexField();
        ^
User error: bad syntax

>> C;;
   ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:35:13 2004

Input: C<i> := ComplexField();
C;

Output: Magma V2.11-2     Mon Aug 16 2004 14:35:12 on modular  [Seed = 1610735465]
   -------------------------------------

Complex Field

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:39:52 2004

Input: C<i> := ComplexField();
C;
Category(C);

Output: Magma V2.11-2     Mon Aug 16 2004 14:39:51 on modular  [Seed = 1913900140]
   -------------------------------------

Complex Field
FldPr

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 14:41:04 2004

Input: ListCategories();

Output: Magma V2.11-2     Mon Aug 16 2004 14:41:03 on modular  [Seed = 1581244552]
   -------------------------------------

Aff                   GrpFPDcos             PlaneLnSet
Alg                   GrpFPDcosElt          PlaneProj
AlgAss                GrpFPElt              PlanePt
AlgAssElt             GrpFPExtProc          PlanePtSet
AlgBas                GrpFPHomsProc         PlcCrv
AlgBasElt             GrpFPLixProc          PlcCrvElt
AlgBasGrpP            GrpFPTietzeProc       PlcEnum
AlgChtr               GrpFPTietzeProcOld    PlcFun
AlgChtrElt            GrpFrml               PlcFunElt
AlgClff               GrpFrmlElt            PlcNum
AlgClffElt            GrpGPC                PlcNumElt
AlgElt                GrpGPCElt             PowAut
AlgExt                GrpGen                PowAutSch
AlgExtElt             GrpGenElt             PowClsGrp
AlgFP                 GrpLie                PowGSetEnum
AlgFPElt              GrpLieElt             PowGrpAlgSub
AlgFPEltOld           GrpMat                PowIdl
AlgFPG                GrpMatBSGS            PowIsoSch
AlgFPGElt             GrpMatElt             PowMap
AlgFPLie              GrpMatProj            PowMapAut
AlgFPLieElt           GrpMatProjElt         PowMapSch
AlgFPOld              GrpPC                 PowModTupRng
AlgFr                 GrpPCElt              PowSeqEnum
AlgFrElt              GrpPCRepnProc         PowSetEnum
AlgGen                GrpPCpQuotientProc    PowSetFormal
AlgGenElt             GrpPSL2               PowSetIndx
AlgGrp                GrpPSL2Elt            PowSetMulti
AlgGrpElt             GrpPerm               PowStr
AlgGrpSub             GrpPermBSGS           PowerGroup
AlgLie                GrpPermBasim          Prj
AlgLieElt             GrpPermCox            PrjProd
AlgMat                GrpPermDcosElt        PrjScrl
AlgMatElt             GrpPermElt            Process
AlgQuat               GrpPermLcosElt        Program
AlgQuatElt            GrpPermRcosElt        Pt
AlgQuatOrd            GrpPermTransProc      PtEll
AlgQuatOrdElt         GrpRWS                PtHyp
AlgSym                GrpRWSElt             QuadBin
AlgSymElt             GrpRandProc           QuadBinElt
AnHcJac               GrpSLP                Rec
Any                   GrpSLPElt             RecField
ArrAssoc              Grph                  RecFrmt
Aut                   GrphDir               Ref
AutCrvEll             GrphEdge              RegExp
Bool                  GrphEdgeSet           RegExpAlg
BoolElt               GrphMult              Rel
Cat                   GrphMultDir           RelElt
ClsGrp                GrphMultUnd           Rng
Clstr                 GrphNet               RngCyc
Code                  GrphRes               RngCycElt
CodeAdd               GrphResVert           RngDiff
CodeLin               GrphSpl               RngDiffElt
CodeLinFld            GrphSplVert           RngDiffOp
CodeLinRng            GrphUnd               RngDiffOpElt
CodeQuantum           GrphVert              RngDiffOpLIdl
Cop                   GrphVertSet           RngDiffOpRIdl
CopElt                Hackobj               RngElt
CosetGeom             HatHat                RngFrm
Crv                   HomCrvEll             RngFrmElt
CrvCon                HomGrp                RngFunG
CrvEll                HomGrpFrml            RngFunGElt
CrvEllOld             HomGrpProc            RngFunOrd
CrvEllPtOld           HomModAbVar           RngFunOrdElt
CrvHyp                HomPicCrv             RngFunOrdG
CrvHypOld             IO                    RngFunOrdGElt
CrvHypPtOld           IOPipe                RngFunOrdIdl
CrvMod                IOSocket              RngGal
CrvRat                Inc                   RngGalElt
Crypt                 IncBlk                RngHck
CryptKey              IncBlkSet             RngHckElt
CryptTxt              IncGeom               RngHckIdl
Cyc                   IncLsp                RngInt
DB                    IncNsp                RngIntElt
DBAtlas               IncPt                 RngIntEltFact
DBAtlasKeyMatRep      IncPtSet              RngIntRes
DBAtlasKeyPermRep     Infty                 RngIntResElt
DBUser                Intrinsic             RngInvar
DiffFun               IsoCrvEll             RngMPol
DiffFunElt            JacCrv                RngMPolElt
DivCrv                JacHyp                RngMPolLoc
DivCrvElt             JacHypPt              RngMPolRes
DivFun                JacHypSng             RngMPolResElt
DivFunElt             LP                    RngMPolSub
DivNum                Lat                   RngMSer
DivNumElt             LatElt                RngMSerElt
Dsgn                  LatEnumProc           RngOrd
ECat                  LatKant               RngOrdElt
Empty                 LinearSys             RngOrdFracIdl
ExtRe                 List                  RngOrdIdl
ExtReElt              MPI                   RngOrdRes
FSA                   MPol                  RngOrdResElt
Fbr                   MPolElt               RngPad
File                  Map                   RngPadElt
Fld                   MapAutSch             RngPadRes
FldAC                 MapChn                RngPadResElt
FldACElt              MapCrvEll             RngPadResExt
FldAb                 MapGrpFrml            RngPadResExtElt
FldAbFun              MapIsoCrvEll          RngPowLaz
FldAlg                MapIsoSch             RngPowLazElt
FldAlgElt             MapModAbVar           RngQuad
FldCom                MapPicCrv             RngQuadElt
FldComElt             MapSch                RngQuadFracIdl
FldCyc                Mod                   RngQuadIdl
FldCycElt             ModAbVar              RngReSub
FldElt                ModAbVarElt           RngReSubElt
FldFin                ModAbVarHomol         RngRelK
FldFinElt             ModAbVarLSer          RngRelKElt
FldFun                ModAbVarSubGrp        RngSLPol
FldFunElt             ModAlg                RngSLPolElt
FldFunG               ModAlgElt             RngSer
FldFunGElt            ModBrdt               RngSerElt
FldFunOrd             ModBrdtElt            RngSerLaur
FldFunOrdElt          ModCoho               RngSerLaurElt
FldFunRat             ModComplex            RngSerPow
FldFunRatElt          ModCpx                RngSerPowElt
FldFunRatMElt         ModDed                RngSerPuis
FldFunRatUElt         ModDedElt             RngSerPuisElt
FldNum                ModED                 RngUPol
FldNumElt             ModEDElt              RngUPolElt
FldNumG               ModElt                RngUPolRes
FldNumGElt            ModExt                RngUPolResElt
FldOrd                ModExtElt             RngVal
FldOrdElt             ModFld                RngValElt
FldPad                ModFldElt             RngWitt
FldPadElt             ModFrm                RngWittElt
FldPr                 ModFrmElt             RootDtm
FldPrElt              ModGrp                RootSys
FldQuad               ModGrpElt             SQProc
FldQuadElt            ModMPol               Sch
FldRat                ModMPolElt            SchGrpEll
FldRatElt             ModMatFld             SeqEnum
FldRe                 ModMatFldElt          Set
FldReElt              ModMatGrp             SetCart
FldResLst             ModMatGrpElt          SetCsp
FldResLstElt          ModMatRng             SetCspElt
GRBskt                ModMatRngElt          SetEnum
GRCY                  ModRng                SetFormal
GRCrvK                ModRngElt             SetGIndx
GRCrvS                ModSS                 SetIndx
GRFano                ModSSElt              SetMulti
GRK3                  ModSym                SetPt
GRPtS                 ModSymElt             SetPtEll
GRSch                 ModTheta              SetPtHyp
GRx                   ModThetaElt           Setq
GSet                  ModTupFld             SgpFP
GSetEnum              ModTupFldElt          SgpFPElt
GenMPol               ModTupRng             SolRepProc
GenMPolElt            ModTupRngElt          SpcFld
GenMPolG              MonDivLst             SpcFldElt
GenMPolGElt           MonFP                 SpcHyp
GenMPolRes            MonFPElt              SpcHypArc
GenMPolResElt         MonOrd                SpcHypElt
Grp                   MonOrdElt             SpcHypPgon
GrpAb                 MonPlc                SpcRng
GrpAbElt              MonPlcElt             SpcRngElt
GrpAbGen              MonRWS                SrfKum
GrpAbGenElt           MonRWSElt             SrfKumPt
GrpAtc                MonStg                Str
GrpAtcElt             MonStgElt             Strm
GrpAtlas              MonTbl                SubFldLat
GrpAtlasBiffed        Mtrx                  SubFldLatElt
GrpAuto               MtrxS                 SubGrpLat
GrpAutoElt            MtrxSpcElt            SubGrpLatElt
GrpBB                 MtrxSprs              SubModLat
GrpBBElt              MtrxSprsStr           SubModLatElt
GrpBrd                MultiRet              SymAlgQuat
GrpBrdClassProc       NFSProc               SymCrvEll
GrpBrdElt             NFldCom               SymFry
GrpCayg               NFldComElt            SymGen
GrpCaygElt            NFldRe                SymGenLoc
GrpDrch               NFldReElt             SymKod
GrpDrchElt            NwtnPgon              Tbl
GrpDrchEltNew         NwtnPgonFace          Thue
GrpDrchNew            PackageRef            Tup
GrpElt                PicCrv                Unassign
GrpFP                 PicCrvElt             UndefRef
GrpFPCos              PicHypSng             UnusedMapCrvEll
GrpFPCosElt           PicHypSngElt          UserProgram
GrpFPCosetEnumProc    Plane                 UserProgramShell
GrpFPCox              PlaneAff              VarAbMod
GrpFPCoxElt           PlaneLn               VarargNum

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pcmeyers.psi.utoronto.ca. (128.100.221.95)
Time: Mon Aug 16 15:00:05 2004

Input: C<i> := ComplexField();
C;
Category(C);

Output: Magma V2.11-2     Mon Aug 16 2004 15:00:05 on modular  [Seed = 107365210]
   -------------------------------------

Complex Field
FldPr

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (146.244.28.235)
Time: Mon Aug 16 15:47:12 2004

Input: 1+1;


Output: Magma V2.11-2     Mon Aug 16 2004 15:47:12 on modular  [Seed = 1728522575]
   -------------------------------------

2

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (146.244.28.235)
Time: Mon Aug 16 15:47:33 2004

Input: GolayCode(GF(2),true);



Output: Magma V2.11-2     Mon Aug 16 2004 15:47:32 on modular  [Seed = 2132750659]
   -------------------------------------

[24, 12, 8] "Extended Golay Code" Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:19:26 2004

Input: ?sin

Output: Magma V2.11-2     Tue Aug 17 2004 05:19:25 on modular  [Seed = 2713791821]
   -------------------------------------

3 matches:
     1   I   /magma/ring-field-algebra/real-complex/transcendental/\
             trigonometric/Sin
     2   I   /magma/ring-field-algebra/real-complex/transcendental/\
             trigonometric/Sin
     3   I   /magma/ring-field-algebra/series-power-Laurent/transcendental/\
             trigonometric/Sin
To view an entry, type ? followed by the number next to it

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:19:56 2004

Input: Sin (1/10)

Output: Magma V2.11-2     Tue Aug 17 2004 05:19:55 on modular  [Seed = 2848531811]
   -------------------------------------

0.099833416646828152306814198405

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:20:24 2004

Input: ?sin

Output: Magma V2.11-2     Tue Aug 17 2004 05:20:24 on modular  [Seed = 2195852843]
   -------------------------------------

3 matches:
     1   I   /magma/ring-field-algebra/real-complex/transcendental/\
             trigonometric/Sin
     2   I   /magma/ring-field-algebra/real-complex/transcendental/\
             trigonometric/Sin
     3   I   /magma/ring-field-algebra/series-power-Laurent/transcendental/\
             trigonometric/Sin
To view an entry, type ? followed by the number next to it

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:20:47 2004

Input: ?inverse

Output: Magma V2.11-2     Tue Aug 17 2004 05:20:47 on modular  [Seed = 2330592788]
   -------------------------------------

50 matches:
     1   O   /magma/group
     2   O   /magma/ring-field-algebra
     3   S   /magma/mapping/detail/operation/inverse
     4   S   /magma/ring-field-algebra/real-complex/transcendental/\
             inverse-hyperbolic
     5   S   /magma/ring-field-algebra/real-complex/transcendental/\
             inverse-trigonometric
     6   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/transforms/krawchouk/InverseKrawchouk
     7   I   /magma/combinatorial-geometrical-incidence/\
             error-correcting-linear-code/transforms/mattson-solomon/\
             InverseMattsonSolomonTransform
     8   I   /magma/combinatorial-geometrical-incidence/tableaux-chap/\
             tableaux/tableaux-operations/InverseJeuDeTaquin
     9   I   /magma/combinatorial-geometrical-incidence/tableaux-chap/\
             tableaux/tableaux-operations/InverseRowInsert
    10   I   /magma/combinatorial-geometrical-incidence/tableaux-chap/\
             tableaux/tableaux-operations/InverseRowInsert
    11   I   /magma/combinatorial-geometrical-incidence/tableaux-chap/\
             tableaux/tableaux-rsk/InverseRSKCorrespondenceDoubleWord
    12   I   /magma/combinatorial-geometrical-incidence/tableaux-chap/\
             tableaux/tableaux-rsk/InverseRSKCorrespondenceMatrix
    13   I   /magma/combinatorial-geometrical-incidence/tableaux-chap/\
             tableaux/tableaux-rsk/InverseRSKCorrespondenceSingleWord
    14   I   /magma/geometry/hyperelliptic-curve/transforms/\
             isomorphism-arithmetic/Inverse
    15   I   /magma/geometry/modular-forms/complements/\
             subsec_left_and_right_inverses/LeftInverse
    16   I   /magma/geometry/modular-forms/complements/\
             subsec_left_and_right_inverses/LeftInverseMorphism
    17   I   /magma/geometry/modular-forms/complements/\
             subsec_left_and_right_inverses/RightInverse
    18   I   /magma/geometry/modular-forms/complements/\
             subsec_left_and_right_inverses/RightInverseMorphism
    19   I   /magma/geometry/modular-forms/morphisms/subsec_arithmetic/Inverse
    20   I   /magma/geometry/schemes/maps/maps-attributes/maps-trivial/\
             AllInverseDefiningPolynomials
    21   I   /magma/geometry/schemes/maps/maps-attributes/maps-trivial/\
             FactoredInverseDefiningPolynomials
    22   I   /magma/geometry/schemes/maps/maps-attributes/maps-trivial/\
             InverseDefiningPolynomials
    23   I   /magma/geometry/schemes/maps/maps-creation/Inverse
    24   I   /magma/group/automatic/arithmetic/arithmetic/Inverse
    25   I   /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\
             Inverse
    26   I   /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\
             Inverse
    27   I   /magma/group/matrix/finitely_presented_group/matrices-words/\
             InverseWordMap
    28   I   /magma/group/permutation/presentations/word-group/InverseWordMap
    29   I   /magma/group/rewrite-system/arithmetic/arithmetic/Inverse
    30   I   /magma/mapping/detail/operation/inverse/HasKnownInverse
    31   I   /magma/mapping/detail/operation/inverse/Inverse
    32   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\
             InverseMod
    33   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\
             InverseMod
    34   I   /magma/ring-field-algebra/integer/arithmetic-function/\
             EulerPhiInverse
    35   I   /magma/ring-field-algebra/integer/arithmetic-function/\
             EulerPhiInverse
    36   I   /magma/ring-field-algebra/integer/arithmetic-function/\
             FactoredEulerPhiInverse
    37   I   /magma/ring-field-algebra/integer/arithmetic-function/\
             FactoredEulerPhiInverse
    38   I   /magma/ring-field-algebra/integer/modular/modular-arithmetic/\
             Modinv
    39   I   /magma/ring-field-algebra/local/elt-roots/InverseRoot
    40   I   /magma/ring-field-algebra/local/elt-roots/InverseRoot
    41   I   /magma/ring-field-algebra/local/elt-roots/InverseRoot
    42   I   /magma/ring-field-algebra/local/elt-roots/InverseRoot
    43   I   /magma/ring-field-algebra/local/elt-roots/InverseRoot
    44   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    45   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    46   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    47   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    48   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    49   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
    50   I   /magma/ring-field-algebra/local/elt-roots/InverseSquareRoot
To view an entry, type ? followed by the number next to it

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:21:36 2004

Input: ?5

Output: Magma V2.11-2     Tue Aug 17 2004 05:21:35 on modular  [Seed = 1947532059]
   -------------------------------------

No numbers are defined

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:21:59 2004

Input: ?inverse-trigonometric

Output: Magma V2.11-2     Tue Aug 17 2004 05:21:59 on modular  [Seed = 2082272059]
   -------------------------------------

===============================================================================
PATH: /magma/ring-field-algebra/real-complex/transcendental/\
      inverse-trigonometric
KIND: Section
===============================================================================
Inverse Trigonometric Functions.

The inverse trigonometric functions are all available for arbitrary free
(real or complex) argument, as well as for restricted real arguments of
fixed precision.  The principal values are chosen as indicated.

We mention the power series expansions for the inverse of the sine and
tangent functions (for | z| <= 1): eqalign( arcsin(z)&=sum_(n=0)^Infinity
bigl(prod_(k=1)^(2n) k^(( - 1)^(k - 1))bigr)(z^(2n + 1)/2n + 1), cr
arctan(z)&=sum_(n=1)^Infinity( - 1)^n(z^(2n + 1)/2n + 1).cr) The important
relations with the logarithmic function include eqalign(
arcsin(z)&=(1/i)log(i z + Sqrt(1 - z^2)), cr arccos(z)&=(1/i)log(z +
Sqrt(z^2 - 1)), cr arctan(z)&=(1/2i)log((1 + i z/1 - i z)).cr)

Intrinsics:

    [+1] Arcsin
    [+2] Arcsin
    [+3] Arccos
    [+4] Arccos
    [+5] Arctan
    [+6] Arctan
    [+7] Arctan
    [+8] Arccot
    [+9] Arcsec
    [+10] Arccosec
===============================================================================

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:22:34 2004

Input: ?arcsin

Output: Magma V2.11-2     Tue Aug 17 2004 05:22:33 on modular  [Seed = 1678043981]
   -------------------------------------

3 matches:
     1   I   /magma/ring-field-algebra/real-complex/transcendental/\
             inverse-trigonometric/Arcsin
     2   I   /magma/ring-field-algebra/real-complex/transcendental/\
             inverse-trigonometric/Arcsin
     3   I   /magma/ring-field-algebra/series-power-Laurent/transcendental/\
             trigonometric/Arcsin
To view an entry, type ? followed by the number next to it

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:22:49 2004

Input: Arcsin(1/10)

Output: Magma V2.11-2     Tue Aug 17 2004 05:22:48 on modular  [Seed = 1812783988]
   -------------------------------------

0.1001674211615597963455231794503205692194

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:26:25 2004

Input: 10^2 - (0.5)^2

Output: Magma V2.11-2     Tue Aug 17 2004 05:26:24 on modular  [Seed = 1496962921]
   -------------------------------------

99.750000000000000000000000000000000000000

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:28:04 2004

Input: (10^2 - (0.5)^2)^(1/2)

Output: Magma V2.11-2     Tue Aug 17 2004 05:28:03 on modular  [Seed = 1092734866]
   -------------------------------------

9.987492177719089457890191164029143598779

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:29:27 2004

Input: 2*Arcsin(0.5/10)

Output: Magma V2.11-2     Tue Aug 17 2004 05:29:26 on modular  [Seed = 1244316876]
   -------------------------------------

0.1000417136115400293254887736381614286303

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host socspe010.sgn.suntory.co.jp. (202.248.85.3)
Time: Tue Aug 17 05:32:02 2004

Input: 9.987*25

Output: Magma V2.11-2     Tue Aug 17 2004 05:32:02 on modular  [Seed = 861119185]
   -------------------------------------

249.67499999999999999999999999741

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Tue Aug 17 12:45:28 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^12 - 40*x^10 - 28*x^9 + 514*x^8 + 696*x^7 - 2082*x^6 - 4316*x^5 - 756*x^4 + 2228*x^3 + 1074*x^2 + 136*x + 1));


Output: Magma V2.11-2     Tue Aug 17 2004 12:45:16 on modular  [Seed = 4036200344]
   -------------------------------------

21 12

Total time: 1.099 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Tue Aug 17 12:47:52 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^12 - 68*x^10 + 1082*x^8 - 6712*x^6 + 17256*x^4 - 16800*x^2 + 5000));


Output: Magma V2.11-2     Tue Aug 17 2004 12:47:50 on modular  [Seed = 4187655739]
   -------------------------------------

29 12

Total time: 1.230 seconds, Total memory usage: 3.46MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 14:03:01 2004

Input: Arcsin (3/5)

Output: Magma V2.11-2     Tue Aug 17 2004 14:03:00 on modular  [Seed = 6490403]
   -------------------------------------

0.643501108793284386802809228701166766702

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 14:03:34 2004

Input: Sin (3/5)

Output: Magma V2.11-2     Tue Aug 17 2004 14:03:34 on modular  [Seed = 4153736950]
   -------------------------------------

0.56464247339503535720094544563

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 14:06:54 2004

Input: Arcsin (0.56464247339503535720094544563)

Output: Magma V2.11-2     Tue Aug 17 2004 14:06:53 on modular  [Seed = 4187681203]
   -------------------------------------

0.5999999999999999999999999999652772683094999343731

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 14:07:59 2004

Input: Sin 30

Output: Magma V2.11-2     Tue Aug 17 2004 14:07:58 on modular  [Seed = 3766741225]
   -------------------------------------


>> Sin 30;
       ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 14:08:24 2004

Input: Sin(30)

Output: Magma V2.11-2     Tue Aug 17 2004 14:08:23 on modular  [Seed = 3602243126]
   -------------------------------------

-0.988031624092861789987748907253330460452

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 14:10:06 2004

Input: Sin (3) /Cos(4)

Output: Magma V2.11-2     Tue Aug 17 2004 14:10:05 on modular  [Seed = 3686323025]
   -------------------------------------

-0.215897476171213281847314766373

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 18:01:43 2004

Input: Arcsin (Sin(30))

Output: Magma V2.11-2     Tue Aug 17 2004 18:01:42 on modular  [Seed = 2983358606]
   -------------------------------------

-1.4159265358979323846264338325284012669000364310241

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 18:02:42 2004

Input: Arcsin (30) * Sin (30)

Output: Magma V2.11-2     Tue Aug 17 2004 18:02:41 on modular  [Seed = 2848614481]
   -------------------------------------

-1.55199644588226338022358749407 - 4.0450673397530112863741409977824*i

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 18:13:57 2004

Input: Sin (3/5);
Sin (6/10)

Output: Magma V2.11-2     Tue Aug 17 2004 18:13:57 on modular  [Seed = 2650693569]
   -------------------------------------

0.56464247339503535720094544563
0.56464247339503535720094544563

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host E167085.ppp.dion.ne.jp. (210.238.167.85)
Time: Tue Aug 17 18:20:32 2004

Input: Arcsin (3/5)

Output: Magma V2.11-2     Tue Aug 17 2004 18:20:32 on modular  [Seed = 2048507826]
   -------------------------------------

0.643501108793284386802809228701166766702

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host dhcp228.math.leidenuniv.nl. (132.229.228.228)
Time: Wed Aug 18 09:36:04 2004

Input: S:=CuspForms(10,6);
NewformDecomposition(S);

Output: Magma V2.11-2     Wed Aug 18 2004 09:36:01 on modular  [Seed = 1278105101]
   -------------------------------------


>> NewformDecomposition(S);;
                       ^
Runtime error in 'NewformDecomposition': Bad argument types
Argument types given: ModFrm

Total time: 0.610 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host xdsl-81-173-179-188.netcologne.de. (81.173.179.188)
Time: Wed Aug 18 12:50:10 2004

Input: 1/2

Output: Magma V2.11-2     Wed Aug 18 2004 12:50:09 on modular  [Seed = 39898049]
   -------------------------------------

1/2

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host xdsl-81-173-179-188.netcologne.de. (81.173.179.188)
Time: Wed Aug 18 12:50:24 2004

Input: x=2x+3

Output: Magma V2.11-2     Wed Aug 18 2004 12:50:24 on modular  [Seed = 174638040]
   -------------------------------------


>> x=2x+3;
      ^
User error: Invalid hexadecimal integer

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host xdsl-81-173-179-188.netcologne.de. (81.173.179.188)
Time: Wed Aug 18 12:50:39 2004

Input: y=2x+3

Output: Magma V2.11-2     Wed Aug 18 2004 12:50:38 on modular  [Seed = 326228687]
   -------------------------------------


>> y=2x+3;
      ^
User error: Invalid hexadecimal integer

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host a82-92-30-202.adsl.xs4all.nl. (82.92.30.202)
Time: Wed Aug 18 16:02:31 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Wed Aug 18 2004 16:02:27 on modular  [Seed = 776788734]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host az-foothills2b-173.losaca.adelphia.net. (24.53.228.173)
Time: Wed Aug 18 20:17:21 2004

Input: 5443

Output: Magma V2.11-2     Wed Aug 18 2004 20:17:20 on modular  [Seed = 3467411032]
   -------------------------------------

5443

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 82-33-77-2.cable.ubr02.trow.blueyonder.co.uk. (82.33.77.2)
Time: Thu Aug 19 04:21:02 2004

Input: IdentifySimple(SL(2,5));

Output: Magma V2.11-2     Thu Aug 19 2004 04:21:01 on modular  [Seed = 2229380963]
   -------------------------------------

true [* <17, 5, 0> *]

Total time: 0.659 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host 3(NXDOMAIN) (80.120.10.197)
Time: Thu Aug 19 04:36:22 2004

Input: 2+2


Output: Magma V2.11-2     Thu Aug 19 2004 04:36:21 on modular  [Seed = 2882440228]
   -------------------------------------

4

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.184.135.51)
Time: Thu Aug 19 12:09:34 2004

Input: f= a + bt
df/dt

Output: Magma V2.11-2     Thu Aug 19 2004 12:09:30 on modular  [Seed = 1446234109]
   -------------------------------------


>> df/dt;
   ^
User error: bad syntax

Total time: 0.620 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.184.135.51)
Time: Thu Aug 19 12:09:34 2004

Input: f= a + bt
df/dt

Output: Magma V2.11-2     Thu Aug 19 2004 12:09:33 on modular  [Seed = 1480444404]
   -------------------------------------


>> df/dt;
   ^
User error: bad syntax

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (200.184.135.51)
Time: Thu Aug 19 12:09:56 2004

Input: f= a + bt
g = df/dt

Output: Magma V2.11-2     Thu Aug 19 2004 12:09:55 on modular  [Seed = 1176754052]
   -------------------------------------


>> g = df/dt;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:53:54 2004

Input: M := ModularSymbols(3,25);
C := CuspidalSubspace(M);
qExpansionBasis(C);


Output: Magma V2.11-2     Thu Aug 19 2004 16:53:53 on modular  [Seed = 575041617]
   -------------------------------------

[]

Total time: 0.639 seconds, Total memory usage: 3.61MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:54:08 2004

Input: M := ModularSymbols(3,25);
C := CuspidalSubspace(M);
qExpansionBasis(C,3);


Output: Magma V2.11-2     Thu Aug 19 2004 16:54:07 on modular  [Seed = 709785687]
   -------------------------------------

[]

Total time: 0.620 seconds, Total memory usage: 3.61MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:54:15 2004

Input: M := ModularSymbols(3,25);
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,3);


Output: Magma V2.11-2     Thu Aug 19 2004 16:54:14 on modular  [Seed = 1379270710]
   -------------------------------------


Total time: 0.620 seconds, Total memory usage: 3.61MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:54:20 2004

Input: M := ModularSymbols(3,25);
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,3);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:54:19 on modular  [Seed = 1514014771]
   -------------------------------------

[]

Total time: 0.620 seconds, Total memory usage: 3.61MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:55:06 2004

Input: M := ModularSymbols(3,25,+1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,3);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:55:05 on modular  [Seed = 1109790969]
   -------------------------------------

Full modular symbols space for Gamma_0(3) of weight 25 and dimension 0 over 
Rational Field
[]

Total time: 0.610 seconds, Total memory usage: 3.61MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:55:12 2004

Input: M := ModularSymbols(3,25,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,3);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:55:12 on modular  [Seed = 1244535016]
   -------------------------------------

Full modular symbols space for Gamma_0(3) of weight 25 and dimension 0 over 
Rational Field
[]

Total time: 0.610 seconds, Total memory usage: 3.61MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:55:21 2004

Input: M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,3);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:55:20 on modular  [Seed = 1914052824]
   -------------------------------------

Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.630 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:55:54 2004

Input: M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:55:53 on modular  [Seed = 2065639856]
   -------------------------------------

Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:56:53 2004

Input:  G<a> := DirichletGroup(5);  G; 
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:56:52 on modular  [Seed = 1661417061]
   -------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:57:02 2004

Input:  G<a> := DirichletGroup(5);  #G; 
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:57:01 on modular  [Seed = 1796161124]
   -------------------------------------

2
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:57:07 2004

Input:  G<a> := DirichletGroup(-5);  #G; 
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:57:06 on modular  [Seed = 2482488994]
   -------------------------------------


>>  G<a> := DirichletGroup(-5);  #G; 
                          ^
Runtime error in 'DirichletGroup': Argument 1 (-5) should be >= 1

>>  G<a> := DirichletGroup(-5);  #G; 
                                  ^
User error: Identifier 'G' has not been declared or assigned
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:57:19 2004

Input:  G<a> := DirichletGroup(5);  #G; 
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:57:18 on modular  [Seed = 2617233063]
   -------------------------------------

2
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:57:44 2004

Input:  G<a> := DirichletGroup(25);  #G; 
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:57:43 on modular  [Seed = 2213009110]
   -------------------------------------

2
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 16:58:49 2004

Input: G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 16:58:48 on modular  [Seed = 2347752976]
   -------------------------------------

4
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.679 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:00:37 2004

Input: G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(25,3,G<a>);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:00:37 on modular  [Seed = 3265697573]
   -------------------------------------

4

>> M := ModularSymbols(25,3,G<a>);
                             ^
User error: bad syntax

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M);
                         ^
User error: Identifier 'M' has not been declared or assigned

>> B:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:02:36 2004

Input: G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(25,3,1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:02:36 on modular  [Seed = 3417284533]
   -------------------------------------

4
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.620 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:02:42 2004

Input: G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(25,3,0);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:02:41 on modular  [Seed = 4086802320]
   -------------------------------------

4
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.630 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:02:50 2004

Input: G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(25,3,-1);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:02:49 on modular  [Seed = 4221546384]
   -------------------------------------

4
Full modular symbols space for Gamma_0(25) of weight 3 and dimension 0 over 
Rational Field
[]

Total time: 0.610 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:04:01 2004

Input: G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(G<a>,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:04:00 on modular  [Seed = 3766793266]
   -------------------------------------

4

>> M := ModularSymbols(G<a>,3);
                        ^
User error: bad syntax

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M);
                         ^
User error: Identifier 'M' has not been declared or assigned

>> B:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:08:23 2004

Input:  G<a> := DirichletGroup(5,CyclotomicField(EulerPhi(5)));
conductor(a);
G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(G<a>,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:08:22 on modular  [Seed = 3968383800]
   -------------------------------------


>> conductor(a);
   ^
User error: Identifier 'conductor' has not been declared or assigned
4

>> M := ModularSymbols(G<a>,3);
                        ^
User error: bad syntax

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M);
                         ^
User error: Identifier 'M' has not been declared or assigned

>> B:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:08:30 2004

Input:  G<a> := DirichletGroup(5,CyclotomicField(EulerPhi(5)));
Conductor(a);
G<a> := DirichletGroup(5,GF(5));
 #G;
M := ModularSymbols(G<a>,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:08:29 on modular  [Seed = 326583499]
   -------------------------------------

5
4

>> M := ModularSymbols(G<a>,3);
                        ^
User error: bad syntax

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M);
                         ^
User error: Identifier 'M' has not been declared or assigned

>> B:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:08:39 2004

Input:  G<a> := DirichletGroup(5,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(G<a>,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:08:38 on modular  [Seed = 461327576]
   -------------------------------------

5
4

>> M := ModularSymbols(G<a>,3);
                        ^
User error: bad syntax

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M);
                         ^
User error: Identifier 'M' has not been declared or assigned

>> B:=qExpansionBasis(C,20);
                      ^
User error: Identifier 'C' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:09:07 2004

Input:  G<a> := DirichletGroup(5,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:09:06 on modular  [Seed = 57103588]
   -------------------------------------

5
4
Full modular symbols space of level 5, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 4 and degree 2
[]

Total time: 0.649 seconds, Total memory usage: 3.52MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:09:37 2004

Input:  G<a> := DirichletGroup(5,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,2);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:09:37 on modular  [Seed = 191847695]
   -------------------------------------

5
4
Full modular symbols space of level 5, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 4 and degree 2
[]

Total time: 0.669 seconds, Total memory usage: 3.52MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:10:01 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,2);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:10:00 on modular  [Seed = 861365518]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
[
    q + O(q^2)
]

Total time: 1.310 seconds, Total memory usage: 4.02MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:10:14 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:10:12 on modular  [Seed = 996109594]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
[
    q - zeta_4*q^4 - 3*q^6 + 6*zeta_4*q^9 - 3*q^11 - 12*zeta_4*q^14 + 11*q^16 + 
        5*zeta_4*q^19 + O(q^20),
    q^2 + zeta_4*q^3 - 4*q^7 - 5*zeta_4*q^8 + q^12 + 6*zeta_4*q^13 + 11*q^17 + 
        6*zeta_4*q^18 + O(q^20)
]

Total time: 1.349 seconds, Total memory usage: 4.02MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:10:51 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,20);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:10:50 on modular  [Seed = 591885676]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
[
    q - zeta_4*q^4 - 3*q^6 + 6*zeta_4*q^9 - 3*q^11 - 12*zeta_4*q^14 + 11*q^16 + 
        5*zeta_4*q^19 + O(q^20),
    q^2 + zeta_4*q^3 - 4*q^7 - 5*zeta_4*q^8 + q^12 + 6*zeta_4*q^13 + 11*q^17 + 
        6*zeta_4*q^18 + O(q^20)
]

Total time: 1.320 seconds, Total memory usage: 4.02MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:11:25 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:11:24 on modular  [Seed = 709786691]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
[
    q - zeta_4*q^4 - 3*q^6 + 6*zeta_4*q^9 - 3*q^11 - 12*zeta_4*q^14 + 11*q^16 + 
        5*zeta_4*q^19 + 12*q^21 + 15*zeta_4*q^24 - 18*q^26 - 30*zeta_4*q^29 - 
        38*q^31 + 33*zeta_4*q^34 + 6*q^36 - 18*zeta_4*q^39 + 57*q^41 + 
        3*zeta_4*q^44 + 42*q^46 - zeta_4*q^49 - 33*q^51 - 45*zeta_4*q^54 - 
        60*q^56 + 90*zeta_4*q^59 - 28*q^61 - 71*zeta_4*q^64 + 9*q^66 + 
        42*zeta_4*q^69 + 42*q^71 + 48*zeta_4*q^74 + 5*q^76 - 80*zeta_4*q^79 - 
        9*q^81 - 12*zeta_4*q^84 + 12*q^86 - 15*zeta_4*q^89 + 72*q^91 + 
        18*zeta_4*q^94 + 27*q^96 - 18*zeta_4*q^99 + O(q^100),
    q^2 + zeta_4*q^3 - 4*q^7 - 5*zeta_4*q^8 + q^12 + 6*zeta_4*q^13 + 11*q^17 + 
        6*zeta_4*q^18 - 3*q^22 - 14*zeta_4*q^23 - 15*q^27 + 4*zeta_4*q^28 - 
        9*q^32 - 3*zeta_4*q^33 + 16*q^37 + 5*zeta_4*q^38 + 12*q^42 - 
        4*zeta_4*q^43 + 6*q^47 + 11*zeta_4*q^48 + 6*q^52 + 26*zeta_4*q^53 - 
        5*q^57 - 30*zeta_4*q^58 - 38*q^62 - 24*zeta_4*q^63 - 39*q^67 - 
        11*zeta_4*q^68 + 30*q^72 + 11*zeta_4*q^73 + 12*q^77 - 18*zeta_4*q^78 + 
        57*q^82 + 91*zeta_4*q^83 + 30*q^87 + 15*zeta_4*q^88 - 14*q^92 - 
        38*zeta_4*q^93 - 44*q^97 - zeta_4*q^98 + O(q^100)
]

Total time: 1.520 seconds, Total memory usage: 4.32MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:12:50 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,100);
B;
zeta;

Output: Magma V2.11-2     Thu Aug 19 2004 17:12:48 on modular  [Seed = 1176637570]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
[
    q - zeta_4*q^4 - 3*q^6 + 6*zeta_4*q^9 - 3*q^11 - 12*zeta_4*q^14 + 11*q^16 + 
        5*zeta_4*q^19 + 12*q^21 + 15*zeta_4*q^24 - 18*q^26 - 30*zeta_4*q^29 - 
        38*q^31 + 33*zeta_4*q^34 + 6*q^36 - 18*zeta_4*q^39 + 57*q^41 + 
        3*zeta_4*q^44 + 42*q^46 - zeta_4*q^49 - 33*q^51 - 45*zeta_4*q^54 - 
        60*q^56 + 90*zeta_4*q^59 - 28*q^61 - 71*zeta_4*q^64 + 9*q^66 + 
        42*zeta_4*q^69 + 42*q^71 + 48*zeta_4*q^74 + 5*q^76 - 80*zeta_4*q^79 - 
        9*q^81 - 12*zeta_4*q^84 + 12*q^86 - 15*zeta_4*q^89 + 72*q^91 + 
        18*zeta_4*q^94 + 27*q^96 - 18*zeta_4*q^99 + O(q^100),
    q^2 + zeta_4*q^3 - 4*q^7 - 5*zeta_4*q^8 + q^12 + 6*zeta_4*q^13 + 11*q^17 + 
        6*zeta_4*q^18 - 3*q^22 - 14*zeta_4*q^23 - 15*q^27 + 4*zeta_4*q^28 - 
        9*q^32 - 3*zeta_4*q^33 + 16*q^37 + 5*zeta_4*q^38 + 12*q^42 - 
        4*zeta_4*q^43 + 6*q^47 + 11*zeta_4*q^48 + 6*q^52 + 26*zeta_4*q^53 - 
        5*q^57 - 30*zeta_4*q^58 - 38*q^62 - 24*zeta_4*q^63 - 39*q^67 - 
        11*zeta_4*q^68 + 30*q^72 + 11*zeta_4*q^73 + 12*q^77 - 18*zeta_4*q^78 + 
        57*q^82 + 91*zeta_4*q^83 + 30*q^87 + 15*zeta_4*q^88 - 14*q^92 - 
        38*zeta_4*q^93 - 44*q^97 - zeta_4*q^98 + O(q^100)
]

>> zeta;;
   ^
User error: Identifier 'zeta' has not been declared or assigned

Total time: 1.500 seconds, Total memory usage: 4.32MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:13:11 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,100);
B;
zeta_4;

Output: Magma V2.11-2     Thu Aug 19 2004 17:13:10 on modular  [Seed = 1311381693]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
[
    q - zeta_4*q^4 - 3*q^6 + 6*zeta_4*q^9 - 3*q^11 - 12*zeta_4*q^14 + 11*q^16 + 
        5*zeta_4*q^19 + 12*q^21 + 15*zeta_4*q^24 - 18*q^26 - 30*zeta_4*q^29 - 
        38*q^31 + 33*zeta_4*q^34 + 6*q^36 - 18*zeta_4*q^39 + 57*q^41 + 
        3*zeta_4*q^44 + 42*q^46 - zeta_4*q^49 - 33*q^51 - 45*zeta_4*q^54 - 
        60*q^56 + 90*zeta_4*q^59 - 28*q^61 - 71*zeta_4*q^64 + 9*q^66 + 
        42*zeta_4*q^69 + 42*q^71 + 48*zeta_4*q^74 + 5*q^76 - 80*zeta_4*q^79 - 
        9*q^81 - 12*zeta_4*q^84 + 12*q^86 - 15*zeta_4*q^89 + 72*q^91 + 
        18*zeta_4*q^94 + 27*q^96 - 18*zeta_4*q^99 + O(q^100),
    q^2 + zeta_4*q^3 - 4*q^7 - 5*zeta_4*q^8 + q^12 + 6*zeta_4*q^13 + 11*q^17 + 
        6*zeta_4*q^18 - 3*q^22 - 14*zeta_4*q^23 - 15*q^27 + 4*zeta_4*q^28 - 
        9*q^32 - 3*zeta_4*q^33 + 16*q^37 + 5*zeta_4*q^38 + 12*q^42 - 
        4*zeta_4*q^43 + 6*q^47 + 11*zeta_4*q^48 + 6*q^52 + 26*zeta_4*q^53 - 
        5*q^57 - 30*zeta_4*q^58 - 38*q^62 - 24*zeta_4*q^63 - 39*q^67 - 
        11*zeta_4*q^68 + 30*q^72 + 11*zeta_4*q^73 + 12*q^77 - 18*zeta_4*q^78 + 
        57*q^82 + 91*zeta_4*q^83 + 30*q^87 + 15*zeta_4*q^88 - 14*q^92 - 
        38*zeta_4*q^93 - 44*q^97 - zeta_4*q^98 + O(q^100)
]

>> zeta_4;;
   ^
User error: Identifier 'zeta_4' has not been declared or assigned

Total time: 1.520 seconds, Total memory usage: 4.32MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:18:05 2004

Input:  G<a> := DirichletGroup(25,CyclotomicField(EulerPhi(5)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C,100);
B;
zeta_4;

Output: Magma V2.11-2     Thu Aug 19 2004 17:18:04 on modular  [Seed = 2498808973]
   -------------------------------------

5
4
Full modular symbols space of level 25, weight 3, character a, and dimension 10 
over Cyclotomic Field of order 4 and degree 2
q + a*q^2 + zeta_4*a*q^3 - zeta_4*q^4 - 3*q^6 - 4*a*q^7 - 5*zeta_4*a*q^8 + 
    6*zeta_4*q^9 - 3*q^11 + a*q^12 + 6*zeta_4*a*q^13 - 12*zeta_4*q^14 + 11*q^16 
    + 11*a*q^17 + 6*zeta_4*a*q^18 + 5*zeta_4*q^19 + 12*q^21 - 3*a*q^22 - 
    14*zeta_4*a*q^23 + 15*zeta_4*q^24 - 18*q^26 - 15*a*q^27 + 4*zeta_4*a*q^28 - 
    30*zeta_4*q^29 - 38*q^31 - 9*a*q^32 - 3*zeta_4*a*q^33 + 33*zeta_4*q^34 + 
    6*q^36 + 16*a*q^37 + 5*zeta_4*a*q^38 - 18*zeta_4*q^39 + 57*q^41 + 12*a*q^42 
    - 4*zeta_4*a*q^43 + 3*zeta_4*q^44 + 42*q^46 + 6*a*q^47 + 11*zeta_4*a*q^48 - 
    zeta_4*q^49 - 33*q^51 + 6*a*q^52 + 26*zeta_4*a*q^53 - 45*zeta_4*q^54 - 
    60*q^56 - 5*a*q^57 - 30*zeta_4*a*q^58 + 90*zeta_4*q^59 - 28*q^61 - 38*a*q^62
    - 24*zeta_4*a*q^63 - 71*zeta_4*q^64 + 9*q^66 - 39*a*q^67 - 11*zeta_4*a*q^68 
    + 42*zeta_4*q^69 + 42*q^71 + 30*a*q^72 + 11*zeta_4*a*q^73 + 48*zeta_4*q^74 +
    5*q^76 + 12*a*q^77 - 18*zeta_4*a*q^78 - 80*zeta_4*q^79 - 9*q^81 + 57*a*q^82 
    + 91*zeta_4*a*q^83 - 12*zeta_4*q^84 + 12*q^86 + 30*a*q^87 + 15*zeta_4*a*q^88
    - 15*zeta_4*q^89 + 72*q^91 - 14*a*q^92 - 38*zeta_4*a*q^93 + 18*zeta_4*q^94 +
    27*q^96 - 44*a*q^97 - zeta_4*a*q^98 - 18*zeta_4*q^99 + O(q^100)

>> zeta_4;;
   ^
User error: Identifier 'zeta_4' has not been declared or assigned

Total time: 1.500 seconds, Total memory usage: 4.32MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:36:49 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C,100);
B;
zeta_4;

Output: Magma V2.11-2     Thu Aug 19 2004 17:36:47 on modular  [Seed = 2764110046]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenform(C,100);
                ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

>> zeta_4;;
   ^
User error: Identifier 'zeta_4' has not been declared or assigned

Total time: 1.859 seconds, Total memory usage: 4.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:37:19 2004

Input:  G<a,b> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C,100);
B;
zeta_4;

Output: Magma V2.11-2     Thu Aug 19 2004 17:37:18 on modular  [Seed = 2898849847]
   -------------------------------------


>>  G<a,b> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
     ^
Runtime error in 'AssignNames': Argument 2 must have length 1

>> Conductor(a);
             ^
User error: Identifier 'a' has not been declared or assigned
6

>> M := ModularSymbols(a,3);
                       ^
User error: Identifier 'a' has not been declared or assigned

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M);
                         ^
User error: Identifier 'M' has not been declared or assigned

>> B:=qEigenform(C,100);
                 ^
User error: Identifier 'C' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

>> zeta_4;;
   ^
User error: Identifier 'zeta_4' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:37:29 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C,100);
B;
zeta_4;

Output: Magma V2.11-2     Thu Aug 19 2004 17:37:28 on modular  [Seed = 3568339033]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenform(C,100);
                ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

>> zeta_4;;
   ^
User error: Identifier 'zeta_4' has not been declared or assigned

Total time: 0.679 seconds, Total memory usage: 3.59MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:38:53 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,100);
B;
zeta_4;

Output: Magma V2.11-2     Thu Aug 19 2004 17:38:52 on modular  [Seed = 3315702076]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2
[]

>> zeta_4;;
   ^
User error: Identifier 'zeta_4' has not been declared or assigned

Total time: 0.699 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:39:08 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qExpansionBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:39:08 on modular  [Seed = 3450442020]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2
[]

Total time: 0.679 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:39:36 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:39:35 on modular  [Seed = 4119964408]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2
[]

Total time: 0.669 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:39:56 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:39:53 on modular  [Seed = 4237861824]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    q - 6*q^15 - q^16 - 3*q^22 + 6*q^23 + 12*q^29 - 12*q^30 + 12*q^36 + 2*q^37 +
        q^43 + 27*q^44 - 6*q^50 - 33*q^51 - 27*q^57 - 12*q^58 - 37*q^64 + 
        42*q^65 - 6*q^71 + 9*q^72 + 42*q^78 - 56*q^79 + 78*q^85 - 3*q^86 + 
        54*q^92 + 72*q^93 - 21*q^99 + O(q^100),
    q^2 - 7*q^16 + q^18 - 2*q^23 - 7*q^25 + 19*q^30 + 19*q^32 + 7*q^37 - 21*q^39
        - 20*q^44 - 6*q^46 + 5*q^51 + 40*q^53 + q^58 - 35*q^60 - 56*q^65 + 
        11*q^67 - 6*q^72 - 35*q^74 + 85*q^79 + 73*q^81 + 35*q^86 - 27*q^88 - 
        30*q^93 - 59*q^95 + O(q^100),
    q^3 - q^12 - 2*q^13 - 9*q^17 + 5*q^19 + 10*q^20 + 5*q^24 - 8*q^26 - 14*q^27 
        + 16*q^31 + 2*q^33 - 8*q^34 - 5*q^38 + 6*q^40 + 36*q^41 - 4*q^45 - 
        6*q^47 - 18*q^48 - 8*q^52 + 10*q^54 - 24*q^55 - 11*q^59 - 22*q^61 + 
        12*q^62 - 2*q^66 + 17*q^68 + 28*q^69 - 7*q^73 + 5*q^75 + 18*q^80 - 
        3*q^82 - 40*q^83 + 44*q^87 - 5*q^89 - 2*q^90 + 6*q^94 - 23*q^96 + 
        42*q^97 + O(q^100),
    q^4 + q^11 + 2*q^15 - q^16 - 15*q^18 - 12*q^22 + 6*q^23 + 15*q^25 + 26*q^29 
        - 12*q^30 + 18*q^32 - 18*q^36 + 2*q^37 - 14*q^39 - 18*q^43 + 27*q^44 - 
        28*q^46 + 38*q^50 - 33*q^51 + 24*q^53 - 26*q^57 - 12*q^58 + 28*q^60 + 
        38*q^64 + 42*q^65 - 94*q^67 - 74*q^71 + 9*q^72 + 64*q^74 + 42*q^78 - 
        56*q^79 + 4*q^81 + 30*q^85 - 3*q^86 + 23*q^88 - 28*q^92 + 72*q^93 - 
        10*q^95 + 20*q^99 + O(q^100),
    q^5 - 3*q^12 - q^13 + 2*q^19 + 5*q^20 - 3*q^26 - 7*q^27 + 7*q^33 - 4*q^34 + 
        5*q^40 + 18*q^41 - 10*q^47 - 9*q^48 + q^54 - 12*q^55 - 23*q^61 + 6*q^62 
        + 23*q^68 + 14*q^69 + 3*q^75 + 5*q^82 - 20*q^83 - q^90 - 20*q^96 + 
        21*q^97 + O(q^100),
    q^6 + q^12 - 2*q^13 - 5*q^19 - 4*q^20 + 8*q^26 + 8*q^27 - 2*q^33 + 7*q^34 - 
        6*q^40 - 13*q^41 + 6*q^47 - 3*q^48 - 10*q^54 + 10*q^55 + 22*q^61 - 
        8*q^62 - 17*q^68 - 6*q^69 - 5*q^75 + 7*q^76 + 3*q^82 + 9*q^83 + 5*q^89 +
        23*q^96 - 7*q^97 + O(q^100),
    q^8 + q^11 - 3*q^15 - q^16 - 5*q^18 - q^22 + 6*q^23 + 9*q^25 + 9*q^29 - 
        12*q^30 - 8*q^32 - 2*q^36 + 2*q^37 + 7*q^39 - 10*q^43 + 27*q^44 - 4*q^46
        + 4*q^50 - 33*q^51 - 14*q^53 + 4*q^57 - 12*q^58 + 35*q^60 - q^64 + 
        42*q^65 - 39*q^67 - 3*q^71 + 9*q^72 + 41*q^74 - 7*q^78 - 56*q^79 - 
        52*q^81 + 11*q^85 - 3*q^86 + 26*q^88 + 2*q^92 + 72*q^93 + 33*q^95 + q^99
        + O(q^100),
    q^9 + q^11 + q^15 - 4*q^16 - 4*q^18 - 6*q^22 + 4*q^23 + 2*q^25 + 13*q^29 + 
        q^30 + 11*q^32 - 9*q^36 - q^37 - 14*q^39 - 9*q^43 + 2*q^44 - 10*q^46 + 
        19*q^50 - 13*q^51 + 26*q^53 - 13*q^57 + 13*q^58 + 19*q^64 - 28*q^67 - 
        37*q^71 - q^72 + 6*q^74 + 21*q^78 - 7*q^79 + 21*q^81 + 15*q^85 - 9*q^86 
        - q^88 - 14*q^92 + 22*q^93 - 26*q^95 + 10*q^99 + O(q^100),
    q^10 - q^12 - q^13 - 4*q^17 + 5*q^19 + 5*q^20 + 3*q^24 - 8*q^26 - 7*q^27 + 
        6*q^31 + 2*q^33 - 4*q^34 - 8*q^38 + 6*q^40 + 18*q^41 - q^45 - 6*q^47 - 
        9*q^48 + q^52 + 10*q^54 - 12*q^55 + 5*q^59 - 22*q^61 + 6*q^62 + 3*q^66 +
        17*q^68 + 14*q^69 - 13*q^73 + 5*q^75 - 3*q^80 - 3*q^82 - 20*q^83 + 
        14*q^87 - 5*q^89 - q^90 + 2*q^94 - 23*q^96 + 21*q^97 + O(q^100),
    2*q^11 + q^15 - q^16 - 9*q^18 - 6*q^22 + 6*q^23 + 11*q^25 + 13*q^29 - 
        12*q^30 + 3*q^32 - 9*q^36 + 2*q^37 - 7*q^39 - 9*q^43 + 27*q^44 - 14*q^46
        + 19*q^50 - 33*q^51 + 12*q^53 - 13*q^57 - 12*q^58 + 35*q^60 + 19*q^64 + 
        42*q^65 - 67*q^67 - 37*q^71 + 9*q^72 + 47*q^74 + 21*q^78 - 56*q^79 - 
        31*q^81 + 15*q^85 - 3*q^86 + 25*q^88 - 14*q^92 + 72*q^93 + 7*q^95 + 
        10*q^99 + O(q^100)
]

Total time: 2.380 seconds, Total memory usage: 4.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:40:41 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenformBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:40:40 on modular  [Seed = 276057948]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenformBasis(C,100);
      ^
User error: Identifier 'qEigenformBasis' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.000 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:40:53 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:40:52 on modular  [Seed = 427640425]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenform(C,100);
                ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.800 seconds, Total memory usage: 4.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:41:10 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:41:08 on modular  [Seed = 23420513]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    q - 6*q^15 - q^16 - 3*q^22 + 6*q^23 + 12*q^29 - 12*q^30 + 12*q^36 + 2*q^37 +
        q^43 + 27*q^44 - 6*q^50 - 33*q^51 - 27*q^57 - 12*q^58 - 37*q^64 + 
        42*q^65 - 6*q^71 + 9*q^72 + 42*q^78 - 56*q^79 + 78*q^85 - 3*q^86 + 
        54*q^92 + 72*q^93 - 21*q^99 + O(q^100),
    q^2 - 7*q^16 + q^18 - 2*q^23 - 7*q^25 + 19*q^30 + 19*q^32 + 7*q^37 - 21*q^39
        - 20*q^44 - 6*q^46 + 5*q^51 + 40*q^53 + q^58 - 35*q^60 - 56*q^65 + 
        11*q^67 - 6*q^72 - 35*q^74 + 85*q^79 + 73*q^81 + 35*q^86 - 27*q^88 - 
        30*q^93 - 59*q^95 + O(q^100),
    q^3 - q^12 - 2*q^13 - 9*q^17 + 5*q^19 + 10*q^20 + 5*q^24 - 8*q^26 - 14*q^27 
        + 16*q^31 + 2*q^33 - 8*q^34 - 5*q^38 + 6*q^40 + 36*q^41 - 4*q^45 - 
        6*q^47 - 18*q^48 - 8*q^52 + 10*q^54 - 24*q^55 - 11*q^59 - 22*q^61 + 
        12*q^62 - 2*q^66 + 17*q^68 + 28*q^69 - 7*q^73 + 5*q^75 + 18*q^80 - 
        3*q^82 - 40*q^83 + 44*q^87 - 5*q^89 - 2*q^90 + 6*q^94 - 23*q^96 + 
        42*q^97 + O(q^100),
    q^4 + q^11 + 2*q^15 - q^16 - 15*q^18 - 12*q^22 + 6*q^23 + 15*q^25 + 26*q^29 
        - 12*q^30 + 18*q^32 - 18*q^36 + 2*q^37 - 14*q^39 - 18*q^43 + 27*q^44 - 
        28*q^46 + 38*q^50 - 33*q^51 + 24*q^53 - 26*q^57 - 12*q^58 + 28*q^60 + 
        38*q^64 + 42*q^65 - 94*q^67 - 74*q^71 + 9*q^72 + 64*q^74 + 42*q^78 - 
        56*q^79 + 4*q^81 + 30*q^85 - 3*q^86 + 23*q^88 - 28*q^92 + 72*q^93 - 
        10*q^95 + 20*q^99 + O(q^100),
    q^5 - 3*q^12 - q^13 + 2*q^19 + 5*q^20 - 3*q^26 - 7*q^27 + 7*q^33 - 4*q^34 + 
        5*q^40 + 18*q^41 - 10*q^47 - 9*q^48 + q^54 - 12*q^55 - 23*q^61 + 6*q^62 
        + 23*q^68 + 14*q^69 + 3*q^75 + 5*q^82 - 20*q^83 - q^90 - 20*q^96 + 
        21*q^97 + O(q^100),
    q^6 + q^12 - 2*q^13 - 5*q^19 - 4*q^20 + 8*q^26 + 8*q^27 - 2*q^33 + 7*q^34 - 
        6*q^40 - 13*q^41 + 6*q^47 - 3*q^48 - 10*q^54 + 10*q^55 + 22*q^61 - 
        8*q^62 - 17*q^68 - 6*q^69 - 5*q^75 + 7*q^76 + 3*q^82 + 9*q^83 + 5*q^89 +
        23*q^96 - 7*q^97 + O(q^100),
    q^8 + q^11 - 3*q^15 - q^16 - 5*q^18 - q^22 + 6*q^23 + 9*q^25 + 9*q^29 - 
        12*q^30 - 8*q^32 - 2*q^36 + 2*q^37 + 7*q^39 - 10*q^43 + 27*q^44 - 4*q^46
        + 4*q^50 - 33*q^51 - 14*q^53 + 4*q^57 - 12*q^58 + 35*q^60 - q^64 + 
        42*q^65 - 39*q^67 - 3*q^71 + 9*q^72 + 41*q^74 - 7*q^78 - 56*q^79 - 
        52*q^81 + 11*q^85 - 3*q^86 + 26*q^88 + 2*q^92 + 72*q^93 + 33*q^95 + q^99
        + O(q^100),
    q^9 + q^11 + q^15 - 4*q^16 - 4*q^18 - 6*q^22 + 4*q^23 + 2*q^25 + 13*q^29 + 
        q^30 + 11*q^32 - 9*q^36 - q^37 - 14*q^39 - 9*q^43 + 2*q^44 - 10*q^46 + 
        19*q^50 - 13*q^51 + 26*q^53 - 13*q^57 + 13*q^58 + 19*q^64 - 28*q^67 - 
        37*q^71 - q^72 + 6*q^74 + 21*q^78 - 7*q^79 + 21*q^81 + 15*q^85 - 9*q^86 
        - q^88 - 14*q^92 + 22*q^93 - 26*q^95 + 10*q^99 + O(q^100),
    q^10 - q^12 - q^13 - 4*q^17 + 5*q^19 + 5*q^20 + 3*q^24 - 8*q^26 - 7*q^27 + 
        6*q^31 + 2*q^33 - 4*q^34 - 8*q^38 + 6*q^40 + 18*q^41 - q^45 - 6*q^47 - 
        9*q^48 + q^52 + 10*q^54 - 12*q^55 + 5*q^59 - 22*q^61 + 6*q^62 + 3*q^66 +
        17*q^68 + 14*q^69 - 13*q^73 + 5*q^75 - 3*q^80 - 3*q^82 - 20*q^83 + 
        14*q^87 - 5*q^89 - q^90 + 2*q^94 - 23*q^96 + 21*q^97 + O(q^100),
    2*q^11 + q^15 - q^16 - 9*q^18 - 6*q^22 + 6*q^23 + 11*q^25 + 13*q^29 - 
        12*q^30 + 3*q^32 - 9*q^36 + 2*q^37 - 7*q^39 - 9*q^43 + 27*q^44 - 14*q^46
        + 19*q^50 - 33*q^51 + 12*q^53 - 13*q^57 - 12*q^58 + 35*q^60 + 19*q^64 + 
        42*q^65 - 67*q^67 - 37*q^71 + 9*q^72 + 47*q^74 + 21*q^78 - 56*q^79 - 
        31*q^81 + 15*q^85 - 3*q^86 + 25*q^88 - 14*q^92 + 72*q^93 + 7*q^95 + 
        10*q^99 + O(q^100)
]

Total time: 2.379 seconds, Total memory usage: 4.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:41:47 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:41:46 on modular  [Seed = 158160519]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2
[]

Total time: 0.679 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:41:59 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:41:57 on modular  [Seed = 827682432]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2
[
    q - 9*q^5 - 4*q^6 + 13*q^7 + 4*q^8 + 10*q^10 - 6*q^11 - 6*q^12 + 2*q^13 - 
        6*q^14 - 3*q^15 - 4*q^16 - 6*q^17 + 5*q^19 + 6*q^20 - 12*q^21 - 12*q^22 
        + 15*q^23 + 4*q^24 + 24*q^25 + 28*q^26 + 3*q^27 - 8*q^28 - 6*q^30 - 
        44*q^31 - 8*q^32 + 33*q^33 - 14*q^34 - 21*q^35 + 24*q^36 - 31*q^37 - 
        6*q^38 - 24*q^39 - 16*q^40 + 18*q^41 - 2*q^42 - 14*q^43 + 18*q^44 + 
        60*q^45 + 30*q^46 + 33*q^47 + 12*q^48 + 27*q^49 - 28*q^50 + 27*q^51 - 
        32*q^52 - 24*q^53 - 18*q^54 - 33*q^55 + 8*q^56 + 3*q^57 + 12*q^58 + 
        24*q^59 - 12*q^60 - 135*q^61 + 16*q^62 - 36*q^63 + 8*q^64 - 42*q^65 - 
        18*q^66 + 90*q^67 - 6*q^68 - 9*q^69 + 98*q^70 + 54*q^71 - 24*q^72 + 
        74*q^73 - 62*q^74 - 18*q^75 - 2*q^76 + 42*q^77 + 12*q^78 + 55*q^79 + 
        24*q^80 - 108*q^81 - 28*q^82 - 60*q^83 + 30*q^84 + 39*q^85 + 12*q^86 - 
        12*q^87 + 36*q^88 + 33*q^89 + 36*q^90 + 46*q^91 - 66*q^92 - 69*q^93 - 
        62*q^94 - 18*q^95 + 8*q^96 - 30*q^97 - 132*q^98 - 72*q^99 + O(q^100),
    q^2 - 6*q^5 - 3*q^6 + 9*q^7 + 2*q^8 + 6*q^9 - 6*q^11 - 6*q^12 - 6*q^13 + 
        5*q^14 + 3*q^15 + 3*q^19 + 12*q^20 - 18*q^21 - 9*q^22 - 9*q^23 + 24*q^25
        + 18*q^26 + 9*q^27 - 12*q^28 - 6*q^29 - 9*q^30 - 8*q^32 + 36*q^33 - 
        15*q^34 - 21*q^35 + 12*q^36 - 24*q^37 - 24*q^39 - 6*q^40 + 30*q^41 - 
        3*q^42 - 6*q^43 + 6*q^44 + 30*q^46 + 3*q^47 + 12*q^48 + 30*q^49 - 2*q^50
        + 21*q^51 - 24*q^53 - 9*q^54 - 45*q^55 - 2*q^56 + 12*q^58 - 12*q^60 - 
        96*q^61 - 21*q^62 + 30*q^63 + 42*q^65 + 90*q^67 - 12*q^68 - 18*q^69 + 
        42*q^70 + 30*q^71 - 62*q^74 - 30*q^75 - 6*q^76 + 42*q^77 - 6*q^78 + 
        15*q^79 - 108*q^81 - 6*q^82 + 12*q^83 + 24*q^84 + 24*q^85 - 2*q^86 + 
        36*q^88 + 72*q^89 + 72*q^90 - 36*q^91 - 18*q^92 - 24*q^93 - 18*q^95 + 
        12*q^96 - 78*q^97 - 65*q^98 - 54*q^99 + O(q^100),
    q^3 - 4*q^5 - q^6 + 5*q^7 + 2*q^8 + q^10 - 3*q^11 - 4*q^12 - 2*q^13 + 2*q^14
        + 3*q^15 + 2*q^17 + 2*q^19 + 4*q^20 - 10*q^21 - 9*q^22 - 2*q^24 + 
        12*q^25 + 12*q^26 + 3*q^27 - 2*q^28 - 6*q^29 - 15*q^31 - 4*q^32 + 
        24*q^33 - 5*q^34 - 14*q^35 + 12*q^36 - q^38 - 12*q^39 - 4*q^40 + 10*q^41
        - 11*q^42 - 6*q^43 + 6*q^45 + 15*q^46 + 2*q^47 + 4*q^48 + 26*q^49 - 
        2*q^50 - 4*q^52 - 12*q^53 - 6*q^54 - 15*q^55 + 2*q^56 + 25*q^59 - 6*q^60
        - 64*q^61 - 7*q^62 + 12*q^63 + 15*q^66 + 45*q^67 - 8*q^68 - 6*q^69 + 
        35*q^70 + 30*q^71 - 16*q^73 - 31*q^74 - 20*q^75 - 2*q^76 - 6*q^78 + 
        8*q^80 - 54*q^81 - 4*q^82 + 4*q^83 + 4*q^84 + 24*q^85 + 18*q^87 + 
        18*q^88 + 48*q^89 + 24*q^90 + 8*q^91 - 18*q^92 - 29*q^94 - 9*q^95 + 
        8*q^96 - 26*q^97 - 40*q^98 - 54*q^99 + O(q^100),
    2*q^4 - 3*q^5 - 5*q^6 + 7*q^7 + 2*q^8 + 5*q^10 - 12*q^11 - 6*q^12 + 10*q^13 
        + 3*q^15 - 4*q^16 - 3*q^17 + 12*q^18 + q^19 - 21*q^21 - 9*q^22 + 15*q^23
        + 2*q^24 + 10*q^25 + 8*q^26 - 3*q^27 - 6*q^29 - 6*q^30 - 22*q^31 - 
        4*q^32 + 39*q^33 - 13*q^34 + 21*q^35 + 12*q^36 - 31*q^37 - 3*q^38 - 
        18*q^39 + 4*q^40 + 6*q^41 - 7*q^42 - 6*q^43 + 18*q^44 + 30*q^45 - 3*q^46
        - 27*q^47 + 12*q^48 - 14*q^49 - 2*q^50 + 27*q^51 - 16*q^52 + 27*q^53 - 
        21*q^55 - 14*q^56 + 12*q^58 + 12*q^59 - 24*q^60 - 57*q^61 + 53*q^62 - 
        42*q^65 - 9*q^66 + 74*q^67 - 18*q^68 + 49*q^70 + 30*q^71 - 24*q^72 + 
        37*q^73 - 79*q^74 - 42*q^75 + 2*q^76 + 21*q^77 - 6*q^78 + 55*q^79 + 
        12*q^80 - 63*q^81 + 16*q^82 - 132*q^83 + 42*q^84 + 24*q^85 + 12*q^86 - 
        6*q^87 + 30*q^88 + 111*q^89 + 56*q^91 - 18*q^92 - 69*q^93 - 31*q^94 + 
        6*q^95 + 16*q^96 + 18*q^97 - 84*q^98 - 54*q^99 + O(q^100)
]

Total time: 1.379 seconds, Total memory usage: 4.28MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:42:57 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);


Output: Magma V2.11-2     Thu Aug 19 2004 17:42:55 on modular  [Seed = 962422514]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2

Total time: 1.389 seconds, Total memory usage: 4.28MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:43:07 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B.1


Output: Magma V2.11-2     Thu Aug 19 2004 17:43:06 on modular  [Seed = 591887581]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2

>> B.1
    ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 1.349 seconds, Total memory usage: 4.28MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:43:15 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B.1;


Output: Magma V2.11-2     Thu Aug 19 2004 17:43:14 on modular  [Seed = 726627533]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2

>> B.1;
    ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[RngSerPowElt], RngIntElt

Total time: 1.379 seconds, Total memory usage: 4.28MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:43:23 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:43:21 on modular  [Seed = 1547174833]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2
[
    q - 9*q^5 - 4*q^6 + 13*q^7 + 4*q^8 + 10*q^10 - 6*q^11 - 6*q^12 + 2*q^13 - 
        6*q^14 - 3*q^15 - 4*q^16 - 6*q^17 + 5*q^19 + 6*q^20 - 12*q^21 - 12*q^22 
        + 15*q^23 + 4*q^24 + 24*q^25 + 28*q^26 + 3*q^27 - 8*q^28 - 6*q^30 - 
        44*q^31 - 8*q^32 + 33*q^33 - 14*q^34 - 21*q^35 + 24*q^36 - 31*q^37 - 
        6*q^38 - 24*q^39 - 16*q^40 + 18*q^41 - 2*q^42 - 14*q^43 + 18*q^44 + 
        60*q^45 + 30*q^46 + 33*q^47 + 12*q^48 + 27*q^49 - 28*q^50 + 27*q^51 - 
        32*q^52 - 24*q^53 - 18*q^54 - 33*q^55 + 8*q^56 + 3*q^57 + 12*q^58 + 
        24*q^59 - 12*q^60 - 135*q^61 + 16*q^62 - 36*q^63 + 8*q^64 - 42*q^65 - 
        18*q^66 + 90*q^67 - 6*q^68 - 9*q^69 + 98*q^70 + 54*q^71 - 24*q^72 + 
        74*q^73 - 62*q^74 - 18*q^75 - 2*q^76 + 42*q^77 + 12*q^78 + 55*q^79 + 
        24*q^80 - 108*q^81 - 28*q^82 - 60*q^83 + 30*q^84 + 39*q^85 + 12*q^86 - 
        12*q^87 + 36*q^88 + 33*q^89 + 36*q^90 + 46*q^91 - 66*q^92 - 69*q^93 - 
        62*q^94 - 18*q^95 + 8*q^96 - 30*q^97 - 132*q^98 - 72*q^99 + O(q^100),
    q^2 - 6*q^5 - 3*q^6 + 9*q^7 + 2*q^8 + 6*q^9 - 6*q^11 - 6*q^12 - 6*q^13 + 
        5*q^14 + 3*q^15 + 3*q^19 + 12*q^20 - 18*q^21 - 9*q^22 - 9*q^23 + 24*q^25
        + 18*q^26 + 9*q^27 - 12*q^28 - 6*q^29 - 9*q^30 - 8*q^32 + 36*q^33 - 
        15*q^34 - 21*q^35 + 12*q^36 - 24*q^37 - 24*q^39 - 6*q^40 + 30*q^41 - 
        3*q^42 - 6*q^43 + 6*q^44 + 30*q^46 + 3*q^47 + 12*q^48 + 30*q^49 - 2*q^50
        + 21*q^51 - 24*q^53 - 9*q^54 - 45*q^55 - 2*q^56 + 12*q^58 - 12*q^60 - 
        96*q^61 - 21*q^62 + 30*q^63 + 42*q^65 + 90*q^67 - 12*q^68 - 18*q^69 + 
        42*q^70 + 30*q^71 - 62*q^74 - 30*q^75 - 6*q^76 + 42*q^77 - 6*q^78 + 
        15*q^79 - 108*q^81 - 6*q^82 + 12*q^83 + 24*q^84 + 24*q^85 - 2*q^86 + 
        36*q^88 + 72*q^89 + 72*q^90 - 36*q^91 - 18*q^92 - 24*q^93 - 18*q^95 + 
        12*q^96 - 78*q^97 - 65*q^98 - 54*q^99 + O(q^100),
    q^3 - 4*q^5 - q^6 + 5*q^7 + 2*q^8 + q^10 - 3*q^11 - 4*q^12 - 2*q^13 + 2*q^14
        + 3*q^15 + 2*q^17 + 2*q^19 + 4*q^20 - 10*q^21 - 9*q^22 - 2*q^24 + 
        12*q^25 + 12*q^26 + 3*q^27 - 2*q^28 - 6*q^29 - 15*q^31 - 4*q^32 + 
        24*q^33 - 5*q^34 - 14*q^35 + 12*q^36 - q^38 - 12*q^39 - 4*q^40 + 10*q^41
        - 11*q^42 - 6*q^43 + 6*q^45 + 15*q^46 + 2*q^47 + 4*q^48 + 26*q^49 - 
        2*q^50 - 4*q^52 - 12*q^53 - 6*q^54 - 15*q^55 + 2*q^56 + 25*q^59 - 6*q^60
        - 64*q^61 - 7*q^62 + 12*q^63 + 15*q^66 + 45*q^67 - 8*q^68 - 6*q^69 + 
        35*q^70 + 30*q^71 - 16*q^73 - 31*q^74 - 20*q^75 - 2*q^76 - 6*q^78 + 
        8*q^80 - 54*q^81 - 4*q^82 + 4*q^83 + 4*q^84 + 24*q^85 + 18*q^87 + 
        18*q^88 + 48*q^89 + 24*q^90 + 8*q^91 - 18*q^92 - 29*q^94 - 9*q^95 + 
        8*q^96 - 26*q^97 - 40*q^98 - 54*q^99 + O(q^100),
    2*q^4 - 3*q^5 - 5*q^6 + 7*q^7 + 2*q^8 + 5*q^10 - 12*q^11 - 6*q^12 + 10*q^13 
        + 3*q^15 - 4*q^16 - 3*q^17 + 12*q^18 + q^19 - 21*q^21 - 9*q^22 + 15*q^23
        + 2*q^24 + 10*q^25 + 8*q^26 - 3*q^27 - 6*q^29 - 6*q^30 - 22*q^31 - 
        4*q^32 + 39*q^33 - 13*q^34 + 21*q^35 + 12*q^36 - 31*q^37 - 3*q^38 - 
        18*q^39 + 4*q^40 + 6*q^41 - 7*q^42 - 6*q^43 + 18*q^44 + 30*q^45 - 3*q^46
        - 27*q^47 + 12*q^48 - 14*q^49 - 2*q^50 + 27*q^51 - 16*q^52 + 27*q^53 - 
        21*q^55 - 14*q^56 + 12*q^58 + 12*q^59 - 24*q^60 - 57*q^61 + 53*q^62 - 
        42*q^65 - 9*q^66 + 74*q^67 - 18*q^68 + 49*q^70 + 30*q^71 - 24*q^72 + 
        37*q^73 - 79*q^74 - 42*q^75 + 2*q^76 + 21*q^77 - 6*q^78 + 55*q^79 + 
        12*q^80 - 63*q^81 + 16*q^82 - 132*q^83 + 42*q^84 + 24*q^85 + 12*q^86 - 
        6*q^87 + 30*q^88 + 111*q^89 + 56*q^91 - 18*q^92 - 69*q^93 - 31*q^94 + 
        6*q^95 + 16*q^96 + 18*q^97 - 84*q^98 - 54*q^99 + O(q^100)
]

Total time: 1.419 seconds, Total memory usage: 4.28MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:44:14 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
PowerSeries(C); 


Output: Magma V2.11-2     Thu Aug 19 2004 17:44:12 on modular  [Seed = 1142954620]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2
q + (1/3*(-zeta_6 - 1)*a - zeta_6)*q^2 + a*q^3 + (2*zeta_6 - 2)*q^4 + ((2*zeta_6
    - 2)*a + (3*zeta_6 - 6))*q^5 + (zeta_6*a - 2*zeta_6 + 1)*q^6 + ((-3*zeta_6 +
    2)*a - 2*zeta_6 + 6)*q^7 + (1/3*(-2*zeta_6 + 4)*a + 2)*q^8 + ((-2*zeta_6 - 
    2)*a - 6*zeta_6)*q^9 + (a + (5*zeta_6 + 5))*q^10 + ((2*zeta_6 - 1)*a - 
    6*zeta_6 + 6)*q^11 + (2*zeta_6 - 2)*a*q^12 + (2*zeta_6*a + (16*zeta_6 - 
    8))*q^13 + (1/3*(-5*zeta_6 + 1)*a - 5*zeta_6 - 6)*q^14 + ((-zeta_6 + 2)*a - 
    6)*q^15 - 4*zeta_6*q^16 + (2*a - 3*zeta_6 - 3)*q^17 + (12*zeta_6 - 12)*q^18 
    + ((-zeta_6 + 1)*a - 2*zeta_6 + 4)*q^19 + (-4*zeta_6*a - 12*zeta_6 + 6)*q^20
    + ((6*zeta_6 - 4)*a - 3*zeta_6 + 9)*q^21 + ((3*zeta_6 - 6)*a - 3)*q^22 + 
    ((3*zeta_6 + 3)*a + 24*zeta_6)*q^23 + (-2*a + (2*zeta_6 + 2))*q^24 + 
    ((-8*zeta_6 + 4)*a - 14*zeta_6 + 14)*q^25 + ((-6*zeta_6 + 6)*a - 10*zeta_6 +
    20)*q^26 + (-3*zeta_6*a - 12*zeta_6 + 6)*q^27 + ((4*zeta_6 + 2)*a + 
    (12*zeta_6 - 8))*q^28 + ((2*zeta_6 - 4)*a + 6)*q^29 + ((3*zeta_6 + 3)*a + 
    3*zeta_6)*q^30 + (-15*a - 22*zeta_6 - 22)*q^31 + (1/3*(8*zeta_6 - 4)*a + 
    (4*zeta_6 - 4))*q^32 + ((-12*zeta_6 + 12)*a + (3*zeta_6 - 6))*q^33 + 
    (5*zeta_6*a + (2*zeta_6 - 1))*q^34 + ((7*zeta_6 - 7)*a + (42*zeta_6 - 
    42))*q^35 + ((-4*zeta_6 + 8)*a + 12)*q^36 + ((8*zeta_6 + 8)*a - 
    7*zeta_6)*q^37 + (-a - 3*zeta_6 - 3)*q^38 + ((8*zeta_6 - 4)*a + (6*zeta_6 - 
    6))*q^39 + ((2*zeta_6 - 2)*a + (10*zeta_6 - 20))*q^40 + (-10*zeta_6*a - 
    24*zeta_6 + 12)*q^41 + ((zeta_6 - 10)*a - 4*zeta_6 + 5)*q^42 + ((2*zeta_6 - 
    4)*a - 8)*q^43 + ((-2*zeta_6 - 2)*a + 12*zeta_6)*q^44 + (6*a + (30*zeta_6 + 
    30))*q^45 + ((-10*zeta_6 + 5)*a - 33*zeta_6 + 33)*q^46 + ((-zeta_6 + 1)*a - 
    30*zeta_6 + 60)*q^47 - 4*zeta_6*a*q^48 + ((-10*zeta_6 + 16)*a - 44*zeta_6 + 
    41)*q^49 + (1/3*(2*zeta_6 - 4)*a - 26)*q^50 + ((-7*zeta_6 - 7)*a + 
    6*zeta_6)*q^51 + (-4*a - 16*zeta_6 - 16)*q^52 + ((8*zeta_6 - 4)*a + 
    (51*zeta_6 - 51))*q^53 + ((3*zeta_6 - 3)*a + (9*zeta_6 - 18))*q^54 + 
    (15*zeta_6*a + (24*zeta_6 - 12))*q^55 + (1/3*(2*zeta_6 + 8)*a - 12*zeta_6 + 
    22)*q^56 + 3*q^57 + (-4*zeta_6 - 4)*a*q^58 + (25*a + (12*zeta_6 + 12))*q^59 
    + ((4*zeta_6 - 2)*a - 12*zeta_6 + 12)*q^60 + ((32*zeta_6 - 32)*a + 
    (39*zeta_6 - 78))*q^61 + (7*zeta_6*a + (74*zeta_6 - 37))*q^62 + ((-10*zeta_6
    + 2)*a - 30*zeta_6 - 36)*q^63 + 8*q^64 + ((-14*zeta_6 - 14)*a - 
    84*zeta_6)*q^65 + (15*a - 9*zeta_6 - 9)*q^66 + ((-30*zeta_6 + 15)*a - 
    16*zeta_6 + 16)*q^67 + ((4*zeta_6 - 4)*a - 6*zeta_6 + 12)*q^68 + (6*zeta_6*a
    + (18*zeta_6 - 9))*q^69 + ((-14*zeta_6 + 21)*a + (7*zeta_6 + 49))*q^70 + 
    ((-10*zeta_6 + 20)*a + 24)*q^71 - 24*zeta_6*q^72 + (-16*a + (37*zeta_6 + 
    37))*q^73 + (1/3*(62*zeta_6 - 31)*a - 17*zeta_6 + 17)*q^74 + ((10*zeta_6 - 
    10)*a - 12*zeta_6 + 24)*q^75 + (2*zeta_6*a + (8*zeta_6 - 4))*q^76 + 
    ((-14*zeta_6 - 14)*a - 21*zeta_6 + 21)*q^77 + ((2*zeta_6 - 4)*a + 18)*q^78 +
    ((-5*zeta_6 - 5)*a + 40*zeta_6)*q^79 + (8*a + (12*zeta_6 + 12))*q^80 + 
    ((36*zeta_6 - 18)*a + (45*zeta_6 - 45))*q^81 + ((2*zeta_6 - 2)*a + 
    (22*zeta_6 - 44))*q^82 + (-4*zeta_6*a - 144*zeta_6 + 72)*q^83 + ((-8*zeta_6 
    - 4)*a + (18*zeta_6 - 12))*q^84 + ((-8*zeta_6 + 16)*a + 15)*q^85 + 
    (1/3*(2*zeta_6 + 2)*a + 14*zeta_6)*q^86 + (18*a - 6*zeta_6 - 6)*q^87 + 
    ((-12*zeta_6 + 6)*a - 6*zeta_6 + 6)*q^88 + ((-24*zeta_6 + 24)*a + (39*zeta_6
    - 78))*q^89 + (-24*zeta_6*a - 72*zeta_6 + 36)*q^90 + ((12*zeta_6 + 20)*a + 
    (92*zeta_6 - 10))*q^91 + ((6*zeta_6 - 12)*a - 48)*q^92 + ((8*zeta_6 + 8)*a -
    45*zeta_6)*q^93 + (-29*a - 31*zeta_6 - 31)*q^94 + ((6*zeta_6 - 3)*a + 
    (24*zeta_6 - 24))*q^95 + ((-4*zeta_6 + 4)*a + (4*zeta_6 - 8))*q^96 + 
    (26*zeta_6*a + (96*zeta_6 - 48))*q^97 + (1/3*(65*zeta_6 - 55)*a - 19*zeta_6 
    - 48)*q^98 + ((18*zeta_6 - 36)*a - 18)*q^99 + O(q^100)

Total time: 1.399 seconds, Total memory usage: 4.28MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:45:41 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
PowerSeries(C); 


Output: Magma V2.11-2     Thu Aug 19 2004 17:45:40 on modular  [Seed = 1294537693]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2

PowerSeries(
    M: Modular symbols space of level 7, weight 3, character a, and...
)
qEigenform(
    M: Modular symbols space of level 7, weight 3, character a, and...
)
In file "/usr/local/magma/package/Geometry/ModSym/qexpansion.m", line 159, 
column 21:
>>    return qEigenform(M,prec);
                       ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

Total time: 0.709 seconds, Total memory usage: 3.59MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:46:20 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
PowerSeries(C,20); 


Output: Magma V2.11-2     Thu Aug 19 2004 17:46:19 on modular  [Seed = 1897213902]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2

PowerSeries(
    M: Modular symbols space of level 7, weight 3, character a, and...,
    prec: 20
)
In file "/usr/local/magma/package/Geometry/ModSym/qexpansion.m", line 148, 
column 21:
>>    return qEigenform(M,prec);
                       ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

Total time: 0.689 seconds, Total memory usage: 3.59MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:46:47 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);

PowerSeries(C,20); 


Output: Magma V2.11-2     Thu Aug 19 2004 17:46:46 on modular  [Seed = 2031953835]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2

PowerSeries(
    M: Modular symbols space of level 7, weight 3, character a, and...,
    prec: 20
)
In file "/usr/local/magma/package/Geometry/ModSym/qexpansion.m", line 148, 
column 21:
>>    return qEigenform(M,prec);
                       ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

Total time: 0.679 seconds, Total memory usage: 3.59MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:47:00 2004

Input:  G<a> := DirichletGroup(7,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:47:00 on modular  [Seed = 1627733921]
   -------------------------------------

7
6
Full modular symbols space of level 7, weight 3, character a, and dimension 2 
over Cyclotomic Field of order 6 and degree 2
[]

Total time: 0.679 seconds, Total memory usage: 3.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:48:19 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qIntegralBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:48:17 on modular  [Seed = 1779305311]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    q - 6*q^15 - q^16 - 3*q^22 + 6*q^23 + 12*q^29 - 12*q^30 + 12*q^36 + 2*q^37 +
        q^43 + 27*q^44 - 6*q^50 - 33*q^51 - 27*q^57 - 12*q^58 - 37*q^64 + 
        42*q^65 - 6*q^71 + 9*q^72 + 42*q^78 - 56*q^79 + 78*q^85 - 3*q^86 + 
        54*q^92 + 72*q^93 - 21*q^99 + O(q^100),
    q^2 - 7*q^16 + q^18 - 2*q^23 - 7*q^25 + 19*q^30 + 19*q^32 + 7*q^37 - 21*q^39
        - 20*q^44 - 6*q^46 + 5*q^51 + 40*q^53 + q^58 - 35*q^60 - 56*q^65 + 
        11*q^67 - 6*q^72 - 35*q^74 + 85*q^79 + 73*q^81 + 35*q^86 - 27*q^88 - 
        30*q^93 - 59*q^95 + O(q^100),
    q^3 - q^12 - 2*q^13 - 9*q^17 + 5*q^19 + 10*q^20 + 5*q^24 - 8*q^26 - 14*q^27 
        + 16*q^31 + 2*q^33 - 8*q^34 - 5*q^38 + 6*q^40 + 36*q^41 - 4*q^45 - 
        6*q^47 - 18*q^48 - 8*q^52 + 10*q^54 - 24*q^55 - 11*q^59 - 22*q^61 + 
        12*q^62 - 2*q^66 + 17*q^68 + 28*q^69 - 7*q^73 + 5*q^75 + 18*q^80 - 
        3*q^82 - 40*q^83 + 44*q^87 - 5*q^89 - 2*q^90 + 6*q^94 - 23*q^96 + 
        42*q^97 + O(q^100),
    q^4 + q^11 + 2*q^15 - q^16 - 15*q^18 - 12*q^22 + 6*q^23 + 15*q^25 + 26*q^29 
        - 12*q^30 + 18*q^32 - 18*q^36 + 2*q^37 - 14*q^39 - 18*q^43 + 27*q^44 - 
        28*q^46 + 38*q^50 - 33*q^51 + 24*q^53 - 26*q^57 - 12*q^58 + 28*q^60 + 
        38*q^64 + 42*q^65 - 94*q^67 - 74*q^71 + 9*q^72 + 64*q^74 + 42*q^78 - 
        56*q^79 + 4*q^81 + 30*q^85 - 3*q^86 + 23*q^88 - 28*q^92 + 72*q^93 - 
        10*q^95 + 20*q^99 + O(q^100),
    q^5 - 3*q^12 - q^13 + 2*q^19 + 5*q^20 - 3*q^26 - 7*q^27 + 7*q^33 - 4*q^34 + 
        5*q^40 + 18*q^41 - 10*q^47 - 9*q^48 + q^54 - 12*q^55 - 23*q^61 + 6*q^62 
        + 23*q^68 + 14*q^69 + 3*q^75 + 5*q^82 - 20*q^83 - q^90 - 20*q^96 + 
        21*q^97 + O(q^100),
    q^6 + q^12 - 2*q^13 - 5*q^19 - 4*q^20 + 8*q^26 + 8*q^27 - 2*q^33 + 7*q^34 - 
        6*q^40 - 13*q^41 + 6*q^47 - 3*q^48 - 10*q^54 + 10*q^55 + 22*q^61 - 
        8*q^62 - 17*q^68 - 6*q^69 - 5*q^75 + 7*q^76 + 3*q^82 + 9*q^83 + 5*q^89 +
        23*q^96 - 7*q^97 + O(q^100),
    q^8 + q^11 - 3*q^15 - q^16 - 5*q^18 - q^22 + 6*q^23 + 9*q^25 + 9*q^29 - 
        12*q^30 - 8*q^32 - 2*q^36 + 2*q^37 + 7*q^39 - 10*q^43 + 27*q^44 - 4*q^46
        + 4*q^50 - 33*q^51 - 14*q^53 + 4*q^57 - 12*q^58 + 35*q^60 - q^64 + 
        42*q^65 - 39*q^67 - 3*q^71 + 9*q^72 + 41*q^74 - 7*q^78 - 56*q^79 - 
        52*q^81 + 11*q^85 - 3*q^86 + 26*q^88 + 2*q^92 + 72*q^93 + 33*q^95 + q^99
        + O(q^100),
    q^9 + q^11 + q^15 - 4*q^16 - 4*q^18 - 6*q^22 + 4*q^23 + 2*q^25 + 13*q^29 + 
        q^30 + 11*q^32 - 9*q^36 - q^37 - 14*q^39 - 9*q^43 + 2*q^44 - 10*q^46 + 
        19*q^50 - 13*q^51 + 26*q^53 - 13*q^57 + 13*q^58 + 19*q^64 - 28*q^67 - 
        37*q^71 - q^72 + 6*q^74 + 21*q^78 - 7*q^79 + 21*q^81 + 15*q^85 - 9*q^86 
        - q^88 - 14*q^92 + 22*q^93 - 26*q^95 + 10*q^99 + O(q^100),
    q^10 - q^12 - q^13 - 4*q^17 + 5*q^19 + 5*q^20 + 3*q^24 - 8*q^26 - 7*q^27 + 
        6*q^31 + 2*q^33 - 4*q^34 - 8*q^38 + 6*q^40 + 18*q^41 - q^45 - 6*q^47 - 
        9*q^48 + q^52 + 10*q^54 - 12*q^55 + 5*q^59 - 22*q^61 + 6*q^62 + 3*q^66 +
        17*q^68 + 14*q^69 - 13*q^73 + 5*q^75 - 3*q^80 - 3*q^82 - 20*q^83 + 
        14*q^87 - 5*q^89 - q^90 + 2*q^94 - 23*q^96 + 21*q^97 + O(q^100),
    2*q^11 + q^15 - q^16 - 9*q^18 - 6*q^22 + 6*q^23 + 11*q^25 + 13*q^29 - 
        12*q^30 + 3*q^32 - 9*q^36 + 2*q^37 - 7*q^39 - 9*q^43 + 27*q^44 - 14*q^46
        + 19*q^50 - 33*q^51 + 12*q^53 - 13*q^57 - 12*q^58 + 35*q^60 + 19*q^64 + 
        42*q^65 - 67*q^67 - 37*q^71 + 9*q^72 + 47*q^74 + 21*q^78 - 56*q^79 - 
        31*q^81 + 15*q^85 - 3*q^86 + 25*q^88 - 14*q^92 + 72*q^93 + 7*q^95 + 
        10*q^99 + O(q^100)
]

Total time: 2.370 seconds, Total memory usage: 4.49MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:48:44 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenBasis(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:48:43 on modular  [Seed = 2465657789]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenBasis(C,100);
      ^
User error: Identifier 'qEigenBasis' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.000 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:49:14 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:49:12 on modular  [Seed = 2600401878]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenform(C,100);
                ^
Runtime error in 'qEigenform': Argument 1 must correspond to a single 
Galois-conjugacy class of newforms.

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.830 seconds, Total memory usage: 4.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:49:34 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);
B:=qEigenform(C.1,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:49:33 on modular  [Seed = 2196169723]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenform(C.1,100);
                ^
Runtime error in 'qEigenform': Bad argument types
Argument types given: ModSymElt, RngIntElt

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.000 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:49:54 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M);Decompose(C);
B:=qEigenform(C.1,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:49:53 on modular  [Seed = 2347756062]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> C := CuspidalSubspace(M);Decompose(C);
                            ^
User error: Identifier 'Decompose' has not been declared or assigned

>> B:=qEigenform(C.1,100);
                ^
Runtime error in 'qEigenform': Bad argument types
Argument types given: ModSymElt, RngIntElt

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.990 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:50:53 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C);
B:=qEigenform(D.1,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:50:52 on modular  [Seed = 3168328980]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> C := CuspidalSubspace(M); D := Decomposition(C);
                                               ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: ModSym

>> B:=qEigenform(D.1,100);
                 ^
User error: Identifier 'D' has not been declared or assigned

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.010 seconds, Total memory usage: 3.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:51:15 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);
B:=qEigenform(D.1,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:51:13 on modular  [Seed = 2764096865]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2

>> B:=qEigenform(D.1,100);
                  ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[ModSym], RngIntElt

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.449 seconds, Total memory usage: 3.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:51:28 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;
B:=qEigenform(D.1,100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:51:26 on modular  [Seed = 2898840934]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 49, weight 3, character a, and dimension 2 
    over Cyclotomic Field of order 6 and degree 2,
    Modular symbols space of level 49, weight 3, character a, and dimension 8 
    over Cyclotomic Field of order 6 and degree 2
]

>> B:=qEigenform(D.1,100);
                  ^
Runtime error in '.': Bad argument types
Argument types given: SeqEnum[ModSym], RngIntElt

>> B;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 1.449 seconds, Total memory usage: 3.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:51:49 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;
B:=qEigenform(D[1],100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:51:47 on modular  [Seed = 3568350515]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 49, weight 3, character a, and dimension 2 
    over Cyclotomic Field of order 6 and degree 2,
    Modular symbols space of level 49, weight 3, character a, and dimension 8 
    over Cyclotomic Field of order 6 and degree 2
]
q + 3*zeta_6*q^2 + (5*zeta_6 - 5)*q^4 - 3*q^8 - 9*zeta_6*q^9 + (-6*zeta_6 + 
    6)*q^11 + 11*zeta_6*q^16 + (-27*zeta_6 + 27)*q^18 + 18*q^22 - 18*zeta_6*q^23
    + (25*zeta_6 - 25)*q^25 - 54*q^29 + (45*zeta_6 - 45)*q^32 + 45*q^36 + 
    38*zeta_6*q^37 + 58*q^43 + 30*zeta_6*q^44 + (-54*zeta_6 + 54)*q^46 - 75*q^50
    + (-6*zeta_6 + 6)*q^53 - 162*zeta_6*q^58 - 91*q^64 + (-118*zeta_6 + 
    118)*q^67 + 114*q^71 + 27*zeta_6*q^72 + (114*zeta_6 - 114)*q^74 + 
    94*zeta_6*q^79 + (81*zeta_6 - 81)*q^81 + 174*zeta_6*q^86 + (18*zeta_6 - 
    18)*q^88 + 90*q^92 - 54*q^99 + O(q^100)

Total time: 2.120 seconds, Total memory usage: 4.39MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:53:29 2004

Input:  G<a> := DirichletGroup(49,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;
B:=qEigenform(D[2],100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:53:27 on modular  [Seed = 3753623452]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 49, weight 3, character a, and dimension 2 
    over Cyclotomic Field of order 6 and degree 2,
    Modular symbols space of level 49, weight 3, character a, and dimension 8 
    over Cyclotomic Field of order 6 and degree 2
]
q + (1/1297*(-64*zeta_6 + 78)*a^3 + 1/1297*(74*zeta_6 + 153)*a^2 + 
    1/1297*(-388*zeta_6 - 662)*a + 1/1297*(-2756*zeta_6 + 927))*q^2 + 
    (1/1297*(-64*zeta_6 + 78)*a^3 + 1/1297*(74*zeta_6 + 153)*a^2 + 
    1/1297*(-388*zeta_6 - 1959)*a + 1/1297*(-2756*zeta_6 + 927))*q^3 + 
    (1/1297*(-28*zeta_6 - 128)*a^3 + 1/1297*(-454*zeta_6 + 148)*a^2 + 
    1/1297*(2100*zeta_6 - 776)*a + 1/1297*(-233*zeta_6 - 1621))*q^4 + 
    (1/1297*(7*zeta_6 + 32)*a^3 + 1/1297*(-535*zeta_6 - 37)*a^2 + 
    1/1297*(-1822*zeta_6 + 1491)*a + 1/1297*(6219*zeta_6 - 6404))*q^5 + 
    (1/1297*(-46*zeta_6 - 25)*a^3 + 1/1297*(-190*zeta_6 - 498)*a^2 + 
    1/1297*(856*zeta_6 - 719)*a + 1/1297*(8233*zeta_6 - 2941))*q^6 + 
    (1/1297*(-234*zeta_6 + 42)*a^3 + 1/1297*(-459*zeta_6 + 681)*a^2 + 
    1/1297*(1986*zeta_6 - 3150)*a + 1/1297*(-2781*zeta_6 - 2893))*q^8 + 
    (1/1297*(-64*zeta_6 + 78)*a^3 + 1/1297*(74*zeta_6 + 153)*a^2 + 
    1/1297*(-388*zeta_6 - 662)*a + 1/1297*(-162*zeta_6 + 927))*q^9 + 
    (1/1297*(89*zeta_6 - 149)*a^3 + 1/1297*(424*zeta_6 - 841)*a^2 + 
    1/1297*(1107*zeta_6 + 2096)*a + 1/1297*(5697*zeta_6 + 4365))*q^10 + 
    (1/1297*(70*zeta_6 + 320)*a^3 + 1/1297*(1135*zeta_6 - 370)*a^2 + 
    1/1297*(-5250*zeta_6 + 1940)*a + 1/1297*(-66*zeta_6 + 4701))*q^11 + 
    (1/1297*(-92*zeta_6 - 50)*a^3 + 1/1297*(917*zeta_6 + 301)*a^2 + 
    1/1297*(5603*zeta_6 - 5329)*a + 1/1297*(-13365*zeta_6 + 10979))*q^12 + 
    (1/1297*(124*zeta_6 + 11)*a^3 + 1/1297*(343*zeta_6 + 1568)*a^2 + 
    1/1297*(-221*zeta_6 + 1769)*a + 1/1297*(-22870*zeta_6 + 6067))*q^13 + 
    (1/1297*(780*zeta_6 - 140)*a^3 + 1/1297*(1530*zeta_6 - 2270)*a^2 + 
    1/1297*(-6620*zeta_6 + 10500)*a + 1/1297*(9270*zeta_6 + 2726))*q^15 + 
    (1/1297*(768*zeta_6 - 936)*a^3 + 1/1297*(-888*zeta_6 - 1836)*a^2 + 
    1/1297*(4656*zeta_6 + 7944)*a + 1/1297*(21399*zeta_6 - 11124))*q^16 + 
    (1/1297*(220*zeta_6 - 106)*a^3 + 1/1297*(-2362*zeta_6 + 1987)*a^2 + 
    1/1297*(-936*zeta_6 + 9247)*a + 1/1297*(2016*zeta_6 - 25803))*q^17 + (zeta_6
    - 1)*q^18 + (1/1297*(369*zeta_6 - 166)*a^3 + 1/1297*(2370*zeta_6 - 1024)*a^2
    + 1/1297*(-4329*zeta_6 + 7262)*a + 1/1297*(-14022*zeta_6 + 28357))*q^19 + 
    (1/1297*(24*zeta_6 + 295)*a^3 + 1/1297*(945*zeta_6 - 868)*a^2 + 
    1/1297*(-10879*zeta_6 + 1221)*a + 1/1297*(-912*zeta_6 + 10839))*q^20 + 
    (1/1297*(-234*zeta_6 + 42)*a^3 + 1/1297*(-459*zeta_6 + 681)*a^2 + 
    1/1297*(1986*zeta_6 - 3150)*a + 1/1297*(-2781*zeta_6 - 11972))*q^22 + 
    (1/1297*(-512*zeta_6 + 624)*a^3 + 1/1297*(592*zeta_6 + 1224)*a^2 + 
    1/1297*(-3104*zeta_6 - 5296)*a + 1/1297*(-3890*zeta_6 + 7416))*q^23 + 
    (1/1297*(-53*zeta_6 - 57)*a^3 + 1/1297*(1642*zeta_6 - 1758)*a^2 + 
    1/1297*(1381*zeta_6 - 3507)*a + 1/1297*(3311*zeta_6 + 17730))*q^24 + 
    (1/1297*(-28*zeta_6 - 128)*a^3 + 1/1297*(-454*zeta_6 + 148)*a^2 + 
    1/1297*(2100*zeta_6 - 776)*a + 1/1297*(7549*zeta_6 - 9403))*q^25 + 
    (1/1297*(-589*zeta_6 + 272)*a^3 + 1/1297*(-3899*zeta_6 + 1631)*a^2 + 
    1/1297*(6562*zeta_6 - 11321)*a + 1/1297*(23679*zeta_6 - 46652))*q^26 + 
    (1/1297*(-144*zeta_6 - 473)*a^3 + 1/1297*(-1779*zeta_6 + 20)*a^2 + 
    1/1297*(17285*zeta_6 - 3435)*a + 1/1297*(21036*zeta_6 - 22233))*q^27 + 
    (1/1297*(-1092*zeta_6 + 196)*a^3 + 1/1297*(-2142*zeta_6 + 3178)*a^2 + 
    1/1297*(9268*zeta_6 - 14700)*a + 1/1297*(-12978*zeta_6 + 13304))*q^29 + 
    (1/1297*(-512*zeta_6 + 624)*a^3 + 1/1297*(592*zeta_6 + 1224)*a^2 + 
    1/1297*(-3104*zeta_6 - 5296)*a + 1/1297*(-35018*zeta_6 + 7416))*q^30 + 
    (1/1297*(-490*zeta_6 + 354)*a^3 + 1/1297*(3728*zeta_6 - 2598)*a^2 + 
    1/1297*(434*zeta_6 - 18768)*a + 1/1297*(-9914*zeta_6 + 41022))*q^31 + 
    (1/1297*(42*zeta_6 + 192)*a^3 + 1/1297*(681*zeta_6 - 222)*a^2 + 
    1/1297*(-3150*zeta_6 + 1164)*a + 1/1297*(-31427*zeta_6 + 34208))*q^32 + 
    (1/1297*(191*zeta_6 + 132)*a^3 + 1/1297*(-2369*zeta_6 - 639)*a^2 + 
    1/1297*(-13028*zeta_6 + 12149)*a + 1/1297*(32949*zeta_6 - 28362))*q^33 + 
    (1/1297*(-194*zeta_6 - 331)*a^3 + 1/1297*(-1478*zeta_6 - 1198)*a^2 + 
    1/1297*(11956*zeta_6 - 3709)*a + 1/1297*(32015*zeta_6 - 19847))*q^34 + 
    (1/1297*(-234*zeta_6 + 42)*a^3 + 1/1297*(-459*zeta_6 + 681)*a^2 + 
    1/1297*(1986*zeta_6 - 3150)*a + 1/1297*(-2781*zeta_6 + 4889))*q^36 + 
    (1/1297*(-512*zeta_6 + 624)*a^3 + 1/1297*(592*zeta_6 + 1224)*a^2 + 
    1/1297*(-3104*zeta_6 - 5296)*a + 1/1297*(-22048*zeta_6 + 7416))*q^37 + 
    (1/1297*(-392*zeta_6 + 802)*a^3 + 1/1297*(-3762*zeta_6 + 5963)*a^2 + 
    1/1297*(-6916*zeta_6 - 6973)*a + 1/1297*(-31796*zeta_6 - 39555))*q^38 + 
    (1/1297*(-392*zeta_6 - 1792)*a^3 + 1/1297*(-6356*zeta_6 + 2072)*a^2 + 
    1/1297*(29400*zeta_6 - 10864)*a + 1/1297*(33054*zeta_6 - 59010))*q^39 + 
    (1/1297*(461*zeta_6 - 116)*a^3 + 1/1297*(1453*zeta_6 - 1325)*a^2 + 
    1/1297*(-9932*zeta_6 + 12591)*a + 1/1297*(-657*zeta_6 + 17378))*q^40 + 
    (1/1297*(22*zeta_6 + 1027)*a^3 + 1/1297*(3136*zeta_6 - 3822)*a^2 + 
    1/1297*(-37966*zeta_6 + 3389)*a + 1/1297*(8243*zeta_6 + 34903))*q^41 + 
    (1/1297*(1638*zeta_6 - 294)*a^3 + 1/1297*(3213*zeta_6 - 4767)*a^2 + 
    1/1297*(-13902*zeta_6 + 22050)*a + 1/1297*(19467*zeta_6 + 13766))*q^43 + 
    (1/1297*(-576*zeta_6 + 702)*a^3 + 1/1297*(666*zeta_6 + 1377)*a^2 + 
    1/1297*(-3492*zeta_6 - 5958)*a + 1/1297*(15403*zeta_6 + 8343))*q^44 + 
    (1/1297*(167*zeta_6 - 163)*a^3 + 1/1297*(-720*zeta_6 + 229)*a^2 + 
    1/1297*(445*zeta_6 + 5740)*a + 1/1297*(5327*zeta_6 - 8073))*q^45 + 
    (1/1297*(-28*zeta_6 - 128)*a^3 + 1/1297*(-454*zeta_6 + 148)*a^2 + 
    1/1297*(2100*zeta_6 - 776)*a + 1/1297*(14034*zeta_6 - 15888))*q^46 + 
    (1/1297*(-496*zeta_6 - 44)*a^3 + 1/1297*(1222*zeta_6 + 1510)*a^2 + 
    1/1297*(19042*zeta_6 - 20046)*a + 1/1297*(-30438*zeta_6 + 14642))*q^47 + 
    (1/1297*(426*zeta_6 - 276)*a^3 + 1/1297*(237*zeta_6 + 6642)*a^2 + 
    1/1297*(10851*zeta_6 + 5136)*a + 1/1297*(-82335*zeta_6 + 10488))*q^48 + 
    (1/1297*(546*zeta_6 - 98)*a^3 + 1/1297*(1071*zeta_6 - 1589)*a^2 + 
    1/1297*(-4634*zeta_6 + 7350)*a + 1/1297*(6489*zeta_6 + 15397))*q^50 + 
    (1/1297*(2624*zeta_6 - 3198)*a^3 + 1/1297*(-3034*zeta_6 - 6273)*a^2 + 
    1/1297*(15908*zeta_6 + 27142)*a + 1/1297*(36473*zeta_6 - 38007))*q^51 + 
    (1/1297*(601*zeta_6 - 773)*a^3 + 1/1297*(-168*zeta_6 - 2065)*a^2 + 
    1/1297*(4211*zeta_6 + 17768)*a + 1/1297*(27745*zeta_6 - 3051))*q^52 + 
    (1/1297*(756*zeta_6 + 3456)*a^3 + 1/1297*(12258*zeta_6 - 3996)*a^2 + 
    1/1297*(-56700*zeta_6 + 20952)*a + 1/1297*(-62450*zeta_6 + 112508))*q^53 + 
    (1/1297*(717*zeta_6 - 428)*a^3 + 1/1297*(6345*zeta_6 - 1937)*a^2 + 
    1/1297*(-3192*zeta_6 + 10051)*a + 1/1297*(-46701*zeta_6 + 75926))*q^54 + 
    (1/1297*(-76*zeta_6 - 718)*a^3 + 1/1297*(-2344*zeta_6 + 1884)*a^2 + 
    1/1297*(26452*zeta_6 - 3218)*a + 1/1297*(5482*zeta_6 - 27190))*q^55 + 
    (1/1297*(-1950*zeta_6 + 350)*a^3 + 1/1297*(-3825*zeta_6 + 5675)*a^2 + 
    1/1297*(16550*zeta_6 - 26250)*a + 1/1297*(-23175*zeta_6 - 70368))*q^57 + 
    (1/1297*(-128*zeta_6 + 156)*a^3 + 1/1297*(148*zeta_6 + 306)*a^2 + 
    1/1297*(-776*zeta_6 - 1324)*a + 1/1297*(12646*zeta_6 + 1854))*q^58 + 
    (1/1297*(1149*zeta_6 - 1603)*a^3 + 1/1297*(1306*zeta_6 - 5888)*a^2 + 
    1/1297*(9803*zeta_6 + 32029)*a + 1/1297*(58801*zeta_6 + 11628))*q^59 + 
    (1/1297*(196*zeta_6 + 896)*a^3 + 1/1297*(3178*zeta_6 - 1036)*a^2 + 
    1/1297*(-14700*zeta_6 + 5432)*a + 1/1297*(47026*zeta_6 - 34048))*q^60 + 
    (1/1297*(-1723*zeta_6 + 276)*a^3 + 1/1297*(-2831*zeta_6 + 5031)*a^2 + 
    1/1297*(44920*zeta_6 - 53125)*a + 1/1297*(-26613*zeta_6 - 33834))*q^61 + 
    (1/1297*(176*zeta_6 + 434)*a^3 + 1/1297*(1742*zeta_6 + 552)*a^2 + 
    1/1297*(-15794*zeta_6 + 3766)*a + 1/1297*(-27440*zeta_6 + 22418))*q^62 + 
    (1/1297*(1716*zeta_6 - 308)*a^3 + 1/1297*(3366*zeta_6 - 4994)*a^2 + 
    1/1297*(-14564*zeta_6 + 23100)*a + 1/1297*(20394*zeta_6 - 10345))*q^64 + 
    (1/1297*(896*zeta_6 - 1092)*a^3 + 1/1297*(-1036*zeta_6 - 2142)*a^2 + 
    1/1297*(5432*zeta_6 + 9268)*a + 1/1297*(93058*zeta_6 - 12978))*q^65 + 
    (1/1297*(395*zeta_6 - 603)*a^3 + 1/1297*(1124*zeta_6 - 2829)*a^2 + 
    1/1297*(4097*zeta_6 + 10206)*a + 1/1297*(22603*zeta_6 + 11241))*q^66 + 
    (1/1297*(-420*zeta_6 - 1920)*a^3 + 1/1297*(-6810*zeta_6 + 2220)*a^2 + 
    1/1297*(31500*zeta_6 - 11640)*a + 1/1297*(396*zeta_6 - 28206))*q^67 + 
    (1/1297*(1368*zeta_6 - 46)*a^3 + 1/1297*(-609*zeta_6 - 4081)*a^2 + 
    1/1297*(-44235*zeta_6 + 48845)*a + 1/1297*(53073*zeta_6 - 7331))*q^68 + 
    (1/1297*(-172*zeta_6 + 696)*a^3 + 1/1297*(1658*zeta_6 - 5020)*a^2 + 
    1/1297*(-26010*zeta_6 - 320)*a + 1/1297*(40258*zeta_6 + 15056))*q^69 + 
    (1/1297*(-2184*zeta_6 + 392)*a^3 + 1/1297*(-4284*zeta_6 + 6356)*a^2 + 
    1/1297*(18536*zeta_6 - 29400)*a + 1/1297*(-25956*zeta_6 - 66776))*q^71 + 
    (1/1297*(-128*zeta_6 + 156)*a^3 + 1/1297*(148*zeta_6 + 306)*a^2 + 
    1/1297*(-776*zeta_6 - 1324)*a + 1/1297*(3567*zeta_6 + 1854))*q^72 + 
    (1/1297*(-709*zeta_6 + 1391)*a^3 + 1/1297*(-6030*zeta_6 + 9862)*a^2 + 
    1/1297*(-11675*zeta_6 - 13535)*a + 1/1297*(-54769*zeta_6 - 63234))*q^73 + 
    (1/1297*(-224*zeta_6 - 1024)*a^3 + 1/1297*(-3632*zeta_6 + 1184)*a^2 + 
    1/1297*(16800*zeta_6 - 6208)*a + 1/1297*(39640*zeta_6 - 54472))*q^74 + 
    (1/1297*(376*zeta_6 - 134)*a^3 + 1/1297*(1835*zeta_6 - 1061)*a^2 + 
    1/1297*(-6151*zeta_6 + 8753)*a + 1/1297*(-7803*zeta_6 + 21953))*q^75 + 
    (1/1297*(-322*zeta_6 - 175)*a^3 + 1/1297*(-1330*zeta_6 - 3486)*a^2 + 
    1/1297*(5992*zeta_6 - 5033)*a + 1/1297*(57631*zeta_6 - 20587))*q^76 + 
    (1/1297*(3276*zeta_6 - 588)*a^3 + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:54:45 2004

Input:  G<a> := DirichletGroup(7^3,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;
B:=qEigenform(D[2],100);
B;


Output: Magma V2.11-2     Thu Aug 19 2004 17:54:24 on modular  [Seed = 3349391171]
   -------------------------------------

7
6
Full modular symbols space of level 343, weight 3, character a, and dimension 
130 over Cyclotomic Field of order 6 and degree 2


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:55:16 2004

Input:  G<a> := DirichletGroup(7^3,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:54:56 on modular  [Seed = 3484135275]
   -------------------------------------

7
6
Full modular symbols space of level 343, weight 3, character a, and dimension 
130 over Cyclotomic Field of order 6 and degree 2


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:55:35 2004

Input:  G<a> := DirichletGroup(7^2,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:55:33 on modular  [Seed = 4153644854]
   -------------------------------------

7
6
Full modular symbols space of level 49, weight 3, character a, and dimension 18 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 49, weight 3, character a, and dimension 2 
    over Cyclotomic Field of order 6 and degree 2,
    Modular symbols space of level 49, weight 3, character a, and dimension 8 
    over Cyclotomic Field of order 6 and degree 2
]

Total time: 1.439 seconds, Total memory usage: 3.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:55:44 2004

Input:  G<a> := DirichletGroup(14,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:55:43 on modular  [Seed = 4288388916]
   -------------------------------------

7
6
Full modular symbols space of level 14, weight 3, character a, and dimension 8 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 14, weight 3, character a, and dimension 4 
    over Cyclotomic Field of order 6 and degree 2
]

Total time: 0.909 seconds, Total memory usage: 3.88MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:55:53 2004

Input:  G<a> := DirichletGroup(21,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:55:52 on modular  [Seed = 3766779932]
   -------------------------------------


>>  G<a> := DirichletGroup(21,CyclotomicField(EulerPhi(7)));
     ^
Runtime error in 'AssignNames': Argument 2 must have length 2

>> Conductor(a);
             ^
User error: Identifier 'a' has not been declared or assigned
12

>> M := ModularSymbols(a,3);
                       ^
User error: Identifier 'a' has not been declared or assigned

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M); D := Decomposition(C,3);D;
                         ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M); D := Decomposition(C,3);D;
                                                ^
User error: Identifier 'C' has not been declared or assigned

>> C := CuspidalSubspace(M); D := Decomposition(C,3);D;
                                                     ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:56:09 2004

Input:  G<a,b> := DirichletGroup(21,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:56:08 on modular  [Seed = 393443320]
   -------------------------------------

3
12
Full modular symbols space of level 21, weight 3, character a, and dimension 12 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 21, weight 3, character a, and dimension 8 
    over Cyclotomic Field of order 6 and degree 2
]

Total time: 1.040 seconds, Total memory usage: 3.83MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:56:20 2004

Input:  G<a> := DirichletGroup(28,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:56:19 on modular  [Seed = 511343882]
   -------------------------------------


>>  G<a> := DirichletGroup(28,CyclotomicField(EulerPhi(7)));
     ^
Runtime error in 'AssignNames': Argument 2 must have length 2

>> Conductor(a);
             ^
User error: Identifier 'a' has not been declared or assigned
12

>> M := ModularSymbols(a,3);
                       ^
User error: Identifier 'a' has not been declared or assigned

>> M;
   ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M); D := Decomposition(C,3);D;
                         ^
User error: Identifier 'M' has not been declared or assigned

>> C := CuspidalSubspace(M); D := Decomposition(C,3);D;
                                                ^
User error: Identifier 'C' has not been declared or assigned

>> C := CuspidalSubspace(M); D := Decomposition(C,3);D;
                                                     ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:56:26 2004

Input:  G<a,b> := DirichletGroup(28,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:56:25 on modular  [Seed = 107111704]
   -------------------------------------

4
12
Full modular symbols space of level 28, weight 3, character a, and dimension 16 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 28, weight 3, character a, and dimension 12 
    over Cyclotomic Field of order 6 and degree 2
]

Total time: 1.240 seconds, Total memory usage: 3.89MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Thu Aug 19 17:57:06 2004

Input:  G<a,b> := DirichletGroup(42,CyclotomicField(EulerPhi(7)));
Conductor(a);
 #G;
M := ModularSymbols(a,3);
M;
C := CuspidalSubspace(M); D := Decomposition(C,3);D;


Output: Magma V2.11-2     Thu Aug 19 2004 17:57:05 on modular  [Seed = 241855784]
   -------------------------------------

3
12
Full modular symbols space of level 42, weight 3, character a, and dimension 32 
over Cyclotomic Field of order 6 and degree 2
[
    Modular symbols space of level 42, weight 3, character a, and dimension 24 
    over Cyclotomic Field of order 6 and degree 2
]

Total time: 1.480 seconds, Total memory usage: 4.55MB


************** MAGMA *****************
Host chello212186080191.chello.pl. (212.186.80.191)
Time: Thu Aug 19 19:38:22 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug 19 2004 19:38:21 on modular  [Seed = 928206796]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host adsl-66-143-164-62.dsl.austtx.swbell.net. (66.143.164.62)
Time: Thu Aug 19 20:16:09 2004

Input: 2x-1/4(-3x + 2x)

Output: Magma V2.11-2     Thu Aug 19 2004 20:16:09 on modular  [Seed = 1728275640]
   -------------------------------------


>> 2x-1/4(-3x + 2x);
    ^
User error: Invalid hexadecimal integer

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 12-216-42-157.client.mchsi.com. (12.216.42.157)
Time: Thu Aug 19 23:38:58 2004

Input: G<a> := DirichletGroup(11,CyclotomicField(EulerPhi(11)));
G;
Conductor(a); D :=Decomposition(C,3);D; 
 

Output: Magma V2.11-2     Thu Aug 19 2004 23:38:57 on modular  [Seed = 158153280]
   -------------------------------------

Group of Dirichlet characters of modulus 11 over Cyclotomic Field of order 10 
and degree 4
11

>> Conductor(a); D :=Decomposition(C,3);D; 
                                   ^
User error: Identifier 'C' has not been declared or assigned

>> Conductor(a); D :=Decomposition(C,3);D; 
                                        ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 12-216-42-157.client.mchsi.com. (12.216.42.157)
Time: Thu Aug 19 23:39:50 2004

Input: G<a> := DirichletGroup(11,CyclotomicField(EulerPhi(11)));
G;
Conductor(a); 
M := ModularSymbols(a,3);
C := CuspidalSubspace(M); 
D :=Decomposition(C,3);D; 
 

Output: Magma V2.11-2     Thu Aug 19 2004 23:39:50 on modular  [Seed = 57094301]
   -------------------------------------

Group of Dirichlet characters of modulus 11 over Cyclotomic Field of order 10 
and degree 4
11
[
    Modular symbols space of level 11, weight 3, character a, and dimension 2 
    over Cyclotomic Field of order 10 and degree 4
]

Total time: 0.769 seconds, Total memory usage: 3.72MB


************** MAGMA *****************
Host 12-216-42-157.client.mchsi.com. (12.216.42.157)
Time: Thu Aug 19 23:40:59 2004

Input: G<a> := DirichletGroup(121,CyclotomicField(EulerPhi(11)));
G;
Conductor(a); 
M := ModularSymbols(a,3);
C := CuspidalSubspace(M); 
D :=Decomposition(C,3);D; 
 

Output: Magma V2.11-2     Thu Aug 19 2004 23:40:39 on modular  [Seed = 776609153]
   -------------------------------------

Group of Dirichlet characters of modulus 121 over Cyclotomic Field of order 10 
and degree 4
11


************** MAGMA *****************
Host 12-216-42-157.client.mchsi.com. (12.216.42.157)
Time: Thu Aug 19 23:42:24 2004

Input: G<a> := DirichletGroup(13,CyclotomicField(EulerPhi(13)));
G;
Conductor(a); 
M := ModularSymbols(a,3);
C := CuspidalSubspace(M); 
D :=Decomposition(C,3);D; 
 

Output: Magma V2.11-2     Thu Aug 19 2004 23:42:23 on modular  [Seed = 658707744]
   -------------------------------------

Group of Dirichlet characters of modulus 13 over Cyclotomic Field of order 12 
and degree 4
13
[
    Modular symbols space of level 13, weight 3, character a, and dimension 2 
    over Cyclotomic Field of order 12 and degree 4
]

Total time: 0.789 seconds, Total memory usage: 3.77MB


************** MAGMA *****************
Host 12-216-42-157.client.mchsi.com. (12.216.42.157)
Time: Thu Aug 19 23:43:14 2004

Input: G<a> := DirichletGroup(121,CyclotomicField(EulerPhi(11)));
G;
Conductor(a); 
M := ModularSymbols(a,3);
C := CuspidalSubspace(M); 
D :=Decomposition(C,3);D; 
 

Output: Magma V2.11-2     Thu Aug 19 2004 23:42:53 on modular  [Seed = 1597730170]
   -------------------------------------

Group of Dirichlet characters of modulus 121 over Cyclotomic Field of order 10 
and degree 4
11


************** MAGMA *****************
Host YahooBB221085250049.bbtec.net. (221.85.250.49)
Time: Fri Aug 20 00:26:05 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug 20 2004 00:26:04 on modular  [Seed = 2549328851]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host heidelberg.bund.de. (194.95.179.177)
Time: Fri Aug 20 08:35:31 2004

Input: 3+5;

Output: Magma V2.11-2     Fri Aug 20 2004 08:35:28 on modular  [Seed = 1193539145]
   -------------------------------------

8

Total time: 0.679 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host heidelberg.bund.de. (194.95.179.177)
Time: Fri Aug 20 08:35:31 2004

Input: 3+5;

Output: Magma V2.11-2     Fri Aug 20 2004 08:35:29 on modular  [Seed = 1159853130]
   -------------------------------------

8

Total time: 0.629 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Fri Aug 20 10:29:46 2004

Input: mapToM2Z_N:=function(a,N,x,y);
return GL(2,quo<Integers()|ideal<Integers()|N>>)![a[1]+a[2]*x+a[4]*y,a[2]*y-a[3]-a[4]*x,a[2]*y+a[3]-a[4]*x,a[1]-a[2]*x-a[4]*y];
end function;

findCosets:=function(N,x,y);
myODgen:=[[a/2,b/2,c/2,d/2]: a,b,c,d in [-2..2]| a^2+b^2+c^2+d^2 eq 4];
ZmodN:=quo<Integers()|ideal<Integers()|N>>;
stuff_N:=[mapToM2Z_N(a,N,x,y): a in myODgen];
ODStar_N:=sub<GL(2,ZmodN)|stuff_N>;
ZmodNstar:=[a: a in ZmodN| IsInvertible(a)];
bigX_N:=[Vector([x1,x2]): x1,x2 in quo<Integers()|ideal<Integers()|N>> | x1 in ZmodNstar or x2 in ZmodNstar];
return [a: a in {Orbit(ODStar_N,bigX_N[i]): i in [1..#bigX_N]}];
end function;

makeLifts:=function(nicecosets);
temp:=[];
for i:=1 to #nicecosets do
nc:=[a: a in nicecosets[i]];possibles:=[a: a in nc| a[2] eq 0];
temp:=temp cat
[GL(2,BaseRing(Parent(possibles[1])))![possibles[1][1],0,0,1/(possibles[1][1])]];
end for;
return temp;
end function;


Output: Magma V2.11-2     Fri Aug 20 2004 10:29:46 on modular  [Seed = 2932467029]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Fri Aug 20 10:30:32 2004

Input: mapToM2Z_N:=function(a,N,x,y);
return GL(2,quo<Integers()|ideal<Integers()|N>>)![a[1]+a[2]*x+a[4]*y,a[2]*y-a[3]-a[4]*x,a[2]*y+a[3]-a[4]*x,a[1]-a[2]*x-a[4]*y];
end function;

findCosets:=function(N,x,y);
myODgen:=[[a/2,b/2,c/2,d/2]: a,b,c,d in [-2..2]| a^2+b^2+c^2+d^2 eq 4];
ZmodN:=quo<Integers()|ideal<Integers()|N>>;
stuff_N:=[mapToM2Z_N(a,N,x,y): a in myODgen];
ODStar_N:=sub<GL(2,ZmodN)|stuff_N>;
ZmodNstar:=[a: a in ZmodN| IsInvertible(a)];
bigX_N:=[Vector([x1,x2]): x1,x2 in quo<Integers()|ideal<Integers()|N>> | x1 in ZmodNstar or x2 in ZmodNstar];
return [a: a in {Orbit(ODStar_N,bigX_N[i]): i in [1..#bigX_N]}];
end function;

makeLifts:=function(nicecosets);
temp:=[];
for i:=1 to #nicecosets do
nc:=[a: a in nicecosets[i]];possibles:=[a: a in nc| a[2] eq 0];
temp:=temp cat
[GL(2,BaseRing(Parent(possibles[1])))![possibles[1][1],0,0,1/(possibles[1][1])]];
end for;
return temp;
end function;

 #findCosets(9,4,1);

Output: Magma V2.11-2     Fri Aug 20 2004 10:30:31 on modular  [Seed = 3135107228]
   -------------------------------------

3

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Fri Aug 20 10:30:55 2004

Input: mapToM2Z_N:=function(a,N,x,y);
return GL(2,quo<Integers()|ideal<Integers()|N>>)![a[1]+a[2]*x+a[4]*y,a[2]*y-a[3]-a[4]*x,a[2]*y+a[3]-a[4]*x,a[1]-a[2]*x-a[4]*y];
end function;

findCosets:=function(N,x,y);
myODgen:=[[a/2,b/2,c/2,d/2]: a,b,c,d in [-2..2]| a^2+b^2+c^2+d^2 eq 4];
ZmodN:=quo<Integers()|ideal<Integers()|N>>;
stuff_N:=[mapToM2Z_N(a,N,x,y): a in myODgen];
ODStar_N:=sub<GL(2,ZmodN)|stuff_N>;
ZmodNstar:=[a: a in ZmodN| IsInvertible(a)];
bigX_N:=[Vector([x1,x2]): x1,x2 in quo<Integers()|ideal<Integers()|N>> | x1 in ZmodNstar or x2 in ZmodNstar];
return [a: a in {Orbit(ODStar_N,bigX_N[i]): i in [1..#bigX_N]}];
end function;

makeLifts:=function(nicecosets);
temp:=[];
for i:=1 to #nicecosets do
nc:=[a: a in nicecosets[i]];possibles:=[a: a in nc| a[2] eq 0];
temp:=temp cat
[GL(2,BaseRing(Parent(possibles[1])))![possibles[1][1],0,0,1/(possibles[1][1])]];
end for;
return temp;
end function;

 #findCosets(9,4,1);
makeLifts(findCosets(9,4,1));

Output: Magma V2.11-2     Fri Aug 20 2004 10:30:54 on modular  [Seed = 2246234042]
   -------------------------------------

3
[
    [2 0]
    [0 5],

    [1 0]
    [0 1],

    [4 0]
    [0 7]
]

Total time: 0.620 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pallas.mpim-bonn.mpg.de. (192.68.254.5)
Time: Fri Aug 20 10:55:34 2004

Input: mapToM2Z_N:=function(a,N,x,y);
return GL(2,quo<Integers()|ideal<Integers()|N>>)![a[1]+a[2]*x+a[4]*y,a[2]*y-a[3]-a[4]*x,a[2]*y+a[3]-a[4]*x,a[1]-a[2]*x-a[4]*y];
end function;

findCosets:=function(N,x,y);
myODgen:=[[a/2,b/2,c/2,d/2]: a,b,c,d in [-2..2]| a^2+b^2+c^2+d^2 eq 4];
ZmodN:=quo<Integers()|ideal<Integers()|N>>;
stuff_N:=[mapToM2Z_N(a,N,x,y): a in myODgen];
ODStar_N:=sub<GL(2,ZmodN)|stuff_N>;
ZmodNstar:=[a: a in ZmodN| IsInvertible(a)];
bigX_N:=[Vector([x1,x2]): x1,x2 in quo<Integers()|ideal<Integers()|N>> | x1 in ZmodNstar or x2 in ZmodNstar];
return [a: a in {Orbit(ODStar_N,bigX_N[i]): i in [1..#bigX_N]}];
end function;

makeLifts:=function(nicecosets);
temp:=[];
for i:=1 to #nicecosets do
nc:=[a: a in nicecosets[i]];possibles:=[a: a in nc| a[2] eq 0];
temp:=temp cat
[GL(2,BaseRing(Parent(possibles[1])))![possibles[1][1],0,0,1/(possibles[1][1])]];
end for;
return temp;
end function;

 #findCosets(5,2,0);
makeLifts(findCosets(5,2,0));

Output: Magma V2.11-2     Fri Aug 20 2004 10:55:34 on modular  [Seed = 4053180470]
   -------------------------------------

1
[
    [1 0]
    [0 1]
]

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host n1-129-P11.teoc.pl. (212.160.197.129)
Time: Fri Aug 20 16:41:32 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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x1+x2+x5+x6+x8+x9+x10+x16+x19+x21+x22+x23+x24+x25+x1*x2+x1*x4+x1*x5+x1*x6+x1*x7+x1*x8+x1*x11+x1*x15+x1*x16+x1*x17+x1*x19+x1*x20+x1*x23+x2*x3+x2*x8+x2*x10+x2*x13+x2*x15+x2*x17+x2*x21+x2*x22+x2*x23+x2*x25+x3*x4+x3*x11+x3*x12+x3*x13+x3*x14+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x25+x4*x7+x4*x11+x4*x13+x4*x18+x4*x20+x4*x22+x4*x24+x4*x25+x5*x7+x5*x9+x5*x12+x5*x14+x5*x17+x6*x7+x6*x8+x6*x9+x6*x10+x6*x11+x6*x13+x6*x15+x6*x20+x6*x21+x6*x22+x6*x24+x7*x10+x7*x12+x7*x15+x7*x16+x7*x18+x7*x20+x7*x22+x7*x23+x7*x25+x8*x11+x8*x12+x8*x13+x8*x16+x8*x17+x8*x19+x8*x21+x9*x10+x9*x15+x9*x16+x9*x20+x9*x23+x10*x12+x10*x13+x10*x16+x10*x19+x10*x20+x10*x22+x10*x23+x10*x24+x11*x14+x11*x20+x11*x21+x11*x22+x11*x23+x11*x24+x11*x25+x12*x18+x12*x22+x12*x23+x13*x15+x13*x17+x13*x18+x13*x20+x13*x21+x13*x23+x13*x24+x13*x25+x14*x15+x14*x21+x14*x23+x14*x25+x15*x16+x15*x17+x15*x19+x15*x20+x15*x21+x15*x22+x15*x23+x16*x17+x16*x19+x16*x22+x16*x23+x16*x24+x17*x21+x17*x22+x17*x23+x17*x24+x18*x21+x19*x20+x19*x22+x19*x24+x20*x22+x20*x23+x20*x24+x20*x25+x21*x24+x22*x23+x22*x24+x22*x25+x23*x24+x23*x25
];

SetVerbose("Groebner", 1);
time G := GroebnerBasis(B);
G;

Output: Magma V2.11-2     Fri Aug 20 2004 16:41:04 on modular  [Seed = 2983629171]
   -------------------------------------

********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2)
Rank: 25
Order: Graded Reverse Lexicographical (bit vector word)
Reduced exponents (bit vector)
Initial length: 50
Inhomogeneous
Matrix kind: Packed GF(2)
Datum size: 0
No rewrite rules

*******
STEP 1
Basis length: 25, queue length: 76, step degree: 2, num pairs: 20
0 field pair(s)
Number of pair polynomials: 20, at 326 column(s), 0.000
Symbolic reduction time: 0.000
20 + 5 = 25 rows / 326 columns, 48.687% / 48.855% (158.72/r)
0.000 + 0.000 + 0.000 = 0.000 [20]
Queue insertion time: 0.000
Step 1 time: 0.000, mat/total time: 0.000/0.000, memory: 6.4MB

*******
STEP 2
Basis length: 45, queue length: 185, step degree: 3, num pairs: 185
50 field pair(s)
Number of pair polynomials: 148, at 2066 column(s), 0.010
Symbolic reduction time: 0.010
148 + 505 = 653 rows / 2626 columns, 6.271% / 10.507% (164.68/r)
0.020 + 0.000 + 0.009 = 0.030 [145]
Queue insertion time: 0.029
Step 2 time: 0.090, mat/total time: 0.030/0.090, memory: 6.4MB

*******
STEP 3
Basis length: 190, queue length: 1805, step degree: 4, num pairs: 1805
435 field pair(s)
Number of pair polynomials: 1805, at 14192 column(s), 0.619
Symbolic reduction time: 0.499
1805 + 6146 = 7951 rows / 14546 columns, 4.081% / 6.6175% (593.63/r)
4.939 + 0.000 + 1.879 = 6.830 [949]
Queue insertion time: 1.480
Step 3 time: 9.469, mat/total time: 6.870/9.560, memory: 24.2MB

*******
STEP 4
Basis length: 1139, queue length: 17208, step degree: 4, num pairs: 974
150 field pair(s)
Number of pair polynomials: 974, at 13904 column(s), 0.539
Symbolic reduction time: 1.210
974 + 6751 = 7725 rows / 13926 columns, 6.5841% / 10.083% (916.9/r)
2.750 + 0.010 + 1.249 = 4.010 [974]


************** MAGMA *****************
Host n1-129-P11.teoc.pl. (212.160.197.129)
Time: Fri Aug 20 16:42:28 2004

Input: P<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25> := PolynomialRing(GF(2), 25, "grevlex");

B := [
x1^2+x1, x2^2+x2, x3^2+x3, x4^2+x4, x5^2+x5, x6^2+x6, x7^2+x7, x8^2+x8, x9^2+x9, x10^2+x10, x11^2+x11, x12^2+x12, x13^2+x13, x14^2+x14, x15^2+x15, x16^2+x16, x17^2+x17, x18^2+x18, x19^2+x19, x20^2+x20, x21^2+x21, x22^2+x22, x23^2+x23, x24^2+x24, x25^2+x25,
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x1+x3+x5+x6+x9+x11+x12+x15+x16+x17+x21+x22+x23+x25+x1*x2+x1*x4+x1*x8+x1*x10+x1*x12+x1*x13+x1*x16+x1*x17+x1*x19+x1*x20+x1*x22+x1*x24+x1*x25+x2*x4+x2*x6+x2*x7+x2*x10+x2*x14+x2*x19+x2*x20+x2*x21+x2*x22+x2*x23+x2*x24+x2*x25+x3*x11+x3*x12+x3*x13+x3*x17+x3*x18+x3*x19+x3*x23+x4*x6+x4*x8+x4*x10+x4*x11+x4*x12+x4*x13+x4*x15+x4*x22+x5*x6+x5*x7+x5*x9+x5*x10+x5*x11+x5*x12+x5*x13+x5*x14+x5*x15+x5*x17+x5*x18+x5*x23+x6*x7+x6*x8+x6*x10+x6*x11+x6*x12+x6*x15+x6*x16+x6*x17+x6*x21+x6*x24+x7*x9+x7*x11+x7*x12+x7*x17+x7*x18+x7*x19+x7*x22+x7*x23+x7*x24+x8*x10+x8*x13+x8*x15+x8*x16+x8*x19+x8*x20+x8*x24+x8*x25+x9*x10+x9*x11+x9*x13+x9*x14+x9*x15+x9*x16+x9*x17+x9*x18+x9*x24+x9*x25+x10*x12+x10*x13+x10*x17+x10*x19+x10*x22+x10*x24+x10*x25+x11*x13+x11*x14+x11*x20+x11*x23+x11*x24+x11*x25+x12*x14+x12*x15+x12*x17+x12*x18+x12*x19+x12*x20+x12*x24+x13*x17+x13*x21+x14*x15+x14*x19+x14*x22+x14*x24+x14*x25+x15*x17+x15*x18+x15*x20+x15*x23+x16*x19+x16*x21+x16*x22+x16*x25+x17*x18+x17*x20+x17*x21+x17*x23+x17*x25+x18*x21+x18*x22+x18*x25+x19*x20+x19*x22+x20*x21+x20*x23+x20*x24+x20*x25+x21*x22+x21*x23+x21*x24+x21*x25+x22*x23+x22*x24+x23*x25,
x1+x2+x5+x6+x8+x9+x10+x16+x19+x21+x22+x23+x24+x25+x1*x2+x1*x4+x1*x5+x1*x6+x1*x7+x1*x8+x1*x11+x1*x15+x1*x16+x1*x17+x1*x19+x1*x20+x1*x23+x2*x3+x2*x8+x2*x10+x2*x13+x2*x15+x2*x17+x2*x21+x2*x22+x2*x23+x2*x25+x3*x4+x3*x11+x3*x12+x3*x13+x3*x14+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x25+x4*x7+x4*x11+x4*x13+x4*x18+x4*x20+x4*x22+x4*x24+x4*x25+x5*x7+x5*x9+x5*x12+x5*x14+x5*x17+x6*x7+x6*x8+x6*x9+x6*x10+x6*x11+x6*x13+x6*x15+x6*x20+x6*x21+x6*x22+x6*x24+x7*x10+x7*x12+x7*x15+x7*x16+x7*x18+x7*x20+x7*x22+x7*x23+x7*x25+x8*x11+x8*x12+x8*x13+x8*x16+x8*x17+x8*x19+x8*x21+x9*x10+x9*x15+x9*x16+x9*x20+x9*x23+x10*x12+x10*x13+x10*x16+x10*x19+x10*x20+x10*x22+x10*x23+x10*x24+x11*x14+x11*x20+x11*x21+x11*x22+x11*x23+x11*x24+x11*x25+x12*x18+x12*x22+x12*x23+x13*x15+x13*x17+x13*x18+x13*x20+x13*x21+x13*x23+x13*x24+x13*x25+x14*x15+x14*x21+x14*x23+x14*x25+x15*x16+x15*x17+x15*x19+x15*x20+x15*x21+x15*x22+x15*x23+x16*x17+x16*x19+x16*x22+x16*x23+x16*x24+x17*x21+x17*x22+x17*x23+x17*x24+x18*x21+x19*x20+x19*x22+x19*x24+x20*x22+x20*x23+x20*x24+x20*x25+x21*x24+x22*x23+x22*x24+x22*x25+x23*x24+x23*x25
];

SetVerbose("Groebner", 1);
time G := GroebnerBasis(B);
G;

Output: Magma V2.11-2     Fri Aug 20 2004 16:42:07 on modular  [Seed = 3201932675]
   -------------------------------------

********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2)
Rank: 25
Order: Graded Reverse Lexicographical (bit vector word)
Reduced exponents (bit vector)
Initial length: 50
Inhomogeneous
Matrix kind: Packed GF(2)
Datum size: 0
No rewrite rules

*******
STEP 1
Basis length: 25, queue length: 76, step degree: 2, num pairs: 20
0 field pair(s)
Number of pair polynomials: 20, at 326 column(s), 0.000
Symbolic reduction time: 0.000
20 + 5 = 25 rows / 326 columns, 48.687% / 48.855% (158.72/r)
0.000 + 0.000 + 0.000 = 0.000 [20]
Queue insertion time: 0.000
Step 1 time: 0.000, mat/total time: 0.000/0.009, memory: 6.4MB

*******
STEP 2
Basis length: 45, queue length: 185, step degree: 3, num pairs: 185
50 field pair(s)
Number of pair polynomials: 148, at 2066 column(s), 0.010
Symbolic reduction time: 0.010
148 + 505 = 653 rows / 2626 columns, 6.271% / 10.507% (164.68/r)
0.030 + 0.000 + 0.010 = 0.040 [145]
Queue insertion time: 0.019
Step 2 time: 0.080, mat/total time: 0.040/0.089, memory: 6.4MB

*******
STEP 3
Basis length: 190, queue length: 1805, step degree: 4, num pairs: 1805
435 field pair(s)
Number of pair polynomials: 1805, at 14192 column(s), 0.629
Symbolic reduction time: 0.499
1805 + 6146 = 7951 rows / 14546 columns, 4.081% / 6.6175% (593.63/r)
4.929 + 0.000 + 1.870 = 6.810 [949]
Queue insertion time: 1.479
Step 3 time: 9.459, mat/total time: 6.860/9.549, memory: 24.2MB

*******
STEP 4
Basis length: 1139, queue length: 17208, step degree: 4, num pairs: 974
150 field pair(s)
Number of pair polynomials: 974, at 13904 column(s), 0.550
Symbolic reduction time: 1.209
974 + 6751 = 7725 rows / 13926 columns, 6.5841% / 10.083% (916.9/r)
2.750 + 0.000 + 1.260 = 4.019 [974]


************** MAGMA *****************
Host connector.propel.com. (67.72.98.54)
Time: Fri Aug 20 17:22:31 2004

Input: P=S/((P/R)*(1-(1/((1+(R/P))^(N*2)))))

Output: Magma V2.11-2     Fri Aug 20 2004 17:22:30 on modular  [Seed = 3299077744]
   -------------------------------------


>> P=S/((P/R)*(1-(1/((1+(R/P))^(N*2)))));
     ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 00:32:36 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 44*x^14 + 701*x^12 - 5126*x^10 + 19117*x^8 - 37360*x^6 + 36884*x^4 - 16600*x^2 + 2500));


Output: Magma V2.11-2     Sat Aug 21 2004 00:32:29 on modular  [Seed = 1897324549]
   -------------------------------------

177 16

Total time: 6.350 seconds, Total memory usage: 5.61MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 00:36:00 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 60*x^14 - 32*x^13 + 1216*x^12 + 504*x^11 - 11812*x^10 - 960*x^9 + 58602*x^8 - 16432*x^7 - 137024*x^6 + 72048*x^5 + 130496*x^4 - 84808*x^3 - 34528*x^2 + 23272*x + 142));


Output: Magma V2.11-2     Sat Aug 21 2004 00:35:52 on modular  [Seed = 1277942861]
   -------------------------------------

165 16

Total time: 8.090 seconds, Total memory usage: 5.93MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 00:59:31 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup( x^16 - 8*x^15 - 28*x^14 + 336*x^13 + 128*x^12 - 5424*x^11 + 2520*x^10 + 43168*x^9 - 28488*x^8 - 182544*x^7 + 98948*x^6 + 402576*x^5 - 108796*x^4 - 405664*x^3 - 3360*x^2 + 120800*x + 15625));


Output: Magma V2.11-2     Sat Aug 21 2004 00:59:24 on modular  [Seed = 3135057215]
   -------------------------------------

177 16

Total time: 6.690 seconds, Total memory usage: 5.73MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 02:09:35 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 90*x^14 + 3000*x^12 - 50400*x^10 + 474570*x^8 - 2570400*x^6 + 7706475*x^4 - 11113200*x^2 + 4862025));


Output: Magma V2.11-2     Sat Aug 21 2004 02:09:29 on modular  [Seed = 1796001114]
   -------------------------------------

70 16

Total time: 6.270 seconds, Total memory usage: 7.12MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 02:14:13 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 8*x^15 - 12*x^14 + 224*x^13 - 206*x^12 - 2040*x^11 + 3496*x^10 + 7512*x^9 - 17161*x^8 - 9736*x^7 + 32928*x^6 + 712*x^5 - 22930*x^4 + 1296*x^3 + 5180*x^2 + 744*x + 9));


Output: Magma V2.11-2     Sat Aug 21 2004 02:14:03 on modular  [Seed = 2032062586]
   -------------------------------------

25 16

Total time: 9.430 seconds, Total memory usage: 7.60MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 02:18:58 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));


Output: Magma V2.11-2     Sat Aug 21 2004 02:18:51 on modular  [Seed = 1964170518]
   -------------------------------------

86 16

Total time: 6.629 seconds, Total memory usage: 5.91MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 02:23:41 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));
R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));


Output: Magma V2.11-2     Sat Aug 21 2004 02:23:28 on modular  [Seed = 1429405213]
   -------------------------------------

86 16
86 16

Total time: 12.760 seconds, Total memory usage: 5.99MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 02:24:11 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));
R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));
R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));
R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 64*x^14 + 1356*x^12 - 11184*x^10 + 44790*x^8 - 94528*x^6 + 104664*x^4 - 54880*x^2 + 9604));


Output: Magma V2.11-2     Sat Aug 21 2004 02:23:50 on modular  [Seed = 2915698419]
   -------------------------------------

86 16
86 16
86 16


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 02:25:24 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 80*x^14 + 2168*x^12 - 23520*x^10 + 104144*x^8 - 186240*x^6 + 129152*x^4 - 35840*x^2 + 3136));


Output: Magma V2.11-2     Sat Aug 21 2004 02:25:18 on modular  [Seed = 2780958275]
   -------------------------------------

98 16

Total time: 5.839 seconds, Total memory usage: 6.00MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:27:10 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 30*x^14 + 282*x^12 - 1242*x^10 + 2901*x^8 - 3672*x^6 + 2376*x^4 - 648*x^2 + 36));


Output: Magma V2.11-2     Sat Aug 21 2004 03:27:04 on modular  [Seed = 574986817]
   -------------------------------------

175 16

Total time: 6.650 seconds, Total memory usage: 5.99MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:28:43 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 32*x^14 + 434*x^12 - 3248*x^10 + 14610*x^8 - 40224*x^6 + 65676*x^4 - 57440*x^2 + 20164));


Output: Magma V2.11-2     Sat Aug 21 2004 03:28:37 on modular  [Seed = 962494903]
   -------------------------------------

113 16

Total time: 6.209 seconds, Total memory usage: 5.99MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:29:36 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 8*x^15 - 12*x^14 + 212*x^13 - 208*x^12 - 1860*x^11 + 4084*x^10 + 5008*x^9 - 22245*x^8 + 8692*x^7 + 41656*x^6 - 54600*x^5 - 1216*x^4 + 48308*x^3 - 38964*x^2 + 12604*x - 1451));


Output: Magma V2.11-2     Sat Aug 21 2004 03:29:26 on modular  [Seed = 827754956]
   -------------------------------------

145 16

Total time: 9.639 seconds, Total memory usage: 6.69MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:30:50 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 28*x^14 + 272*x^12 - 1252*x^10 + 3063*x^8 - 4092*x^6 + 2882*x^4 - 968*x^2 + 121));


Output: Magma V2.11-2     Sat Aug 21 2004 03:30:43 on modular  [Seed = 158249473]
   -------------------------------------

137 16

Total time: 7.469 seconds, Total memory usage: 5.86MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:31:40 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 24*x^14 + 222*x^12 - 1020*x^10 + 2493*x^8 - 3204*x^6 + 1980*x^4 - 468*x^2 + 9));


Output: Magma V2.11-2     Sat Aug 21 2004 03:31:35 on modular  [Seed = 6798204]
   -------------------------------------

114 16

Total time: 5.119 seconds, Total memory usage: 5.97MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:32:56 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 30*x^14 + 351*x^12 - 2022*x^10 + 5988*x^8 - 8802*x^6 + 5823*x^4 - 1386*x^2 + 9));


Output: Magma V2.11-2     Sat Aug 21 2004 03:32:49 on modular  [Seed = 1779290592]
   -------------------------------------

138 16

Total time: 6.629 seconds, Total memory usage: 6.03MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:34:40 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 40*x^14 + 488*x^12 - 2656*x^10 + 6994*x^8 - 8544*x^6 + 4416*x^4 - 864*x^2 + 36));


Output: Magma V2.11-2     Sat Aug 21 2004 03:34:36 on modular  [Seed = 1611127367]
   -------------------------------------

141 16

Total time: 3.980 seconds, Total memory usage: 7.14MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:36:56 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 44*x^14 - 24*x^13 + 628*x^12 + 528*x^11 - 3260*x^10 - 2544*x^9 + 6658*x^8 + 3360*x^7 - 5420*x^6 - 1512*x^5 + 1660*x^4 + 144*x^3 - 140*x^2 + 1));


Output: Magma V2.11-2     Sat Aug 21 2004 03:36:45 on modular  [Seed = 2132329945]
   -------------------------------------

145 16

Total time: 10.170 seconds, Total memory usage: 7.40MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:39:32 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 48*x^14 + 852*x^12 - 7088*x^10 + 30152*x^8 - 66720*x^6 + 74628*x^4 - 36288*x^2 + 3969));


Output: Magma V2.11-2     Sat Aug 21 2004 03:39:26 on modular  [Seed = 1947453809]
   -------------------------------------

106 16

Total time: 5.579 seconds, Total memory usage: 5.96MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:45:23 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 32*x^14 + 378*x^12 - 2088*x^10 + 5778*x^8 - 8432*x^6 + 6426*x^4 - 2312*x^2 + 289));


Output: Magma V2.11-2     Sat Aug 21 2004 03:45:16 on modular  [Seed = 1412688114]
   -------------------------------------

123 16

Total time: 6.299 seconds, Total memory usage: 9.40MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 03:46:19 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 40*x^14 - 16*x^13 + 524*x^12 + 432*x^11 - 2612*x^10 - 3176*x^9 + 4284*x^8 + 6384*x^7 - 2848*x^6 - 5128*x^5 + 928*x^4 + 1744*x^3 - 268*x^2 - 224*x + 49));


Output: Magma V2.11-2     Sat Aug 21 2004 03:46:13 on modular  [Seed = 2747539277]
   -------------------------------------

74 16

Total time: 6.039 seconds, Total memory usage: 7.63MB


************** MAGMA *****************
Host 3(NXDOMAIN) (211.100.105.110)
Time: Sat Aug 21 07:40:54 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Sat Aug 21 2004 07:40:50 on modular  [Seed = 23557358]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.740 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (211.100.105.110)
Time: Sat Aug 21 07:41:15 2004

Input: 1+1

Output: Magma V2.11-2     Sat Aug 21 2004 07:41:15 on modular  [Seed = 309618661]
   -------------------------------------

2

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (211.100.105.110)
Time: Sat Aug 21 07:41:37 2004

Input: 1000!

Output: Magma V2.11-2     Sat Aug 21 2004 07:41:37 on modular  [Seed = 1796021942]
   -------------------------------------


>> 1000!;
        ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (211.100.105.110)
Time: Sat Aug 21 07:41:56 2004

Input: 1000!

Output: Magma V2.11-2     Sat Aug 21 2004 07:41:55 on modular  [Seed = 2082080851]
   -------------------------------------


>> 1000!;
        ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 12:26:45 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 24*x^14 - 16*x^13 + 208*x^12 + 248*x^11 - 728*x^10 - 1200*x^9 + 826*x^8 + 1968*x^7 - 200*x^6 - 1232*x^5 - 4*x^4 + 304*x^3 - 24*x^2 - 16*x + 2));


Output: Magma V2.11-2     Sat Aug 21 2004 12:26:39 on modular  [Seed = 2032095223]
   -------------------------------------

158 16

Total time: 5.230 seconds, Total memory usage: 6.69MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 12:27:50 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 24*x^14 - 8*x^13 + 208*x^12 + 144*x^11 - 800*x^10 - 808*x^9 + 1298*x^8 + 1744*x^7 - 576*x^6 - 1288*x^5 - 128*x^4 + 240*x^3 + 40*x^2 - 8*x - 1));


Output: Magma V2.11-2     Sat Aug 21 2004 12:27:45 on modular  [Seed = 1611028816]
   -------------------------------------

157 16

Total time: 5.570 seconds, Total memory usage: 7.70MB


************** MAGMA *****************
Host h001150025580.ne.client2.attbi.com. (24.218.223.58)
Time: Sat Aug 21 12:29:00 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 28*x^14 + 300*x^12 - 1616*x^10 + 4796*x^8 - 7928*x^6 + 6816*x^4 - 2368*x^2 + 4));


Output: Magma V2.11-2     Sat Aug 21 2004 12:28:56 on modular  [Seed = 1796035090]
   -------------------------------------

115 16

Total time: 4.719 seconds, Total memory usage: 5.83MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Sat Aug 21 13:41:30 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-312*x^14+21294*x^12-466440*x^10+3760419*x^8-13603824*x^6+22936680*x^4-16451136*x^2+4112784));


Output: Magma V2.11-2     Sat Aug 21 2004 13:41:15 on modular  [Seed = 3551861721]
   -------------------------------------

116 16

Total time: 7.890 seconds, Total memory usage: 6.33MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Sat Aug 21 13:54:02 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-112*x^12+848*x^8+137200*x^4+1500625));


Output: Magma V2.11-2     Sat Aug 21 2004 13:53:55 on modular  [Seed = 3383690443]
   -------------------------------------

70 16

Total time: 6.520 seconds, Total memory usage: 6.07MB


************** MAGMA *****************
Host ip68-7-196-184.sd.sd.cox.net. (68.7.196.184)
Time: Sat Aug 21 14:13:45 2004

Input: sin(x)^2 / cos(x)^2 = 1

Output: Magma V2.11-2     Sat Aug 21 2004 14:13:45 on modular  [Seed = 1880531353]
   -------------------------------------


>> sin(x)^2 / cos(x)^2 = 1;
       ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ip68-7-196-184.sd.sd.cox.net. (68.7.196.184)
Time: Sat Aug 21 14:14:09 2004

Input: Factor(x^2 - 12x +2)

Output: Magma V2.11-2     Sat Aug 21 2004 14:14:08 on modular  [Seed = 1644475298]
   -------------------------------------


>> Factor(x^2 - 12x +2);
                  ^
User error: Invalid hexadecimal integer

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ip68-7-196-184.sd.sd.cox.net. (68.7.196.184)
Time: Sat Aug 21 14:14:16 2004

Input: Factor(x^2 - 12*x +2)

Output: Magma V2.11-2     Sat Aug 21 2004 14:14:16 on modular  [Seed = 1779219362]
   -------------------------------------


>> Factor(x^2 - 12*x +2);
          ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 14:42:33 2004

Input: M:=ModularForms(Gamma0(5),2);
M.1;

Output: Magma V2.11-2     Sat Aug 21 2004 14:42:32 on modular  [Seed = 2515747645]
   -------------------------------------

1 + 6*q + 18*q^2 + 24*q^3 + 42*q^4 + 6*q^5 + 72*q^6 + 48*q^7 + O(q^8)

Total time: 0.699 seconds, Total memory usage: 3.87MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 14:42:46 2004

Input: M:=ModularForms(Gamma0(5),2);
M;
M.1;

Output: Magma V2.11-2     Sat Aug 21 2004 14:42:45 on modular  [Seed = 2650491656]
   -------------------------------------

Space of modular forms on Gamma_0(5) of weight 2 and dimension 1 over Integer 
Ring.
1 + 6*q + 18*q^2 + 24*q^3 + 42*q^4 + 6*q^5 + 72*q^6 + 48*q^7 + O(q^8)

Total time: 0.689 seconds, Total memory usage: 3.87MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 14:44:58 2004

Input: M:=ModularForms(Gamma0(5),2);
M;
qExpansion(M.1,20);

Output: Magma V2.11-2     Sat Aug 21 2004 14:44:57 on modular  [Seed = 2279693982]
   -------------------------------------

Space of modular forms on Gamma_0(5) of weight 2 and dimension 1 over Integer 
Ring.
1 + 6*q + 18*q^2 + 24*q^3 + 42*q^4 + 6*q^5 + 72*q^6 + 48*q^7 + 90*q^8 + 78*q^9 +
    18*q^10 + 72*q^11 + 168*q^12 + 84*q^13 + 144*q^14 + 24*q^15 + 186*q^16 + 
    108*q^17 + 234*q^18 + 120*q^19 + O(q^20)

Total time: 0.699 seconds, Total memory usage: 3.87MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 14:54:47 2004

Input: M:=ModularForms(Gamma0(5),2);
M;
qExpansion(M.1,50);

Output: Magma V2.11-2     Sat Aug 21 2004 14:54:46 on modular  [Seed = 4187955903]
   -------------------------------------

Space of modular forms on Gamma_0(5) of weight 2 and dimension 1 over Integer 
Ring.
1 + 6*q + 18*q^2 + 24*q^3 + 42*q^4 + 6*q^5 + 72*q^6 + 48*q^7 + 90*q^8 + 78*q^9 +
    18*q^10 + 72*q^11 + 168*q^12 + 84*q^13 + 144*q^14 + 24*q^15 + 186*q^16 + 
    108*q^17 + 234*q^18 + 120*q^19 + 42*q^20 + 192*q^21 + 216*q^22 + 144*q^23 + 
    360*q^24 + 6*q^25 + 252*q^26 + 240*q^27 + 336*q^28 + 180*q^29 + 72*q^30 + 
    192*q^31 + 378*q^32 + 288*q^33 + 324*q^34 + 48*q^35 + 546*q^36 + 228*q^37 + 
    360*q^38 + 336*q^39 + 90*q^40 + 252*q^41 + 576*q^42 + 264*q^43 + 504*q^44 + 
    78*q^45 + 432*q^46 + 288*q^47 + 744*q^48 + 342*q^49 + O(q^50)

Total time: 0.709 seconds, Total memory usage: 3.87MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:19:01 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
chars;

Output: Magma V2.11-2     Sat Aug 21 2004 15:19:01 on modular  [Seed = 3383699676]
   -------------------------------------

[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.2^2,
    $.1*$.2^2,
    $.2^3,
    $.1*$.2^3
]

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:19:17 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];

Output: Magma V2.11-2     Sat Aug 21 2004 15:19:16 on modular  [Seed = 844419893]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:19:42 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[1],2); MO2a;

Output: Magma V2.11-2     Sat Aug 21 2004 15:19:41 on modular  [Seed = 979163972]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_0(15) of weight 2 and dimension 4 over Integer 
Ring.

Total time: 0.600 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:20:14 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[1],2); MO2a;
E2a:=EisensteinSubspace(MO2a); E2a;

Output: Magma V2.11-2     Sat Aug 21 2004 15:20:13 on modular  [Seed = 393344585]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_0(15) of weight 2 and dimension 4 over Integer 
Ring.
Space of modular forms on Gamma_0(15) of weight 2 and dimension 3 over Integer 
Ring.

Total time: 0.590 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:21:16 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[1],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[1],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:21:15 on modular  [Seed = 494664837]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_0(15) of weight 2 and dimension 3 over Integer 
Ring.
1/12 + q + 3*q^2 + q^3 + 7*q^4 + 6*q^5 + 3*q^6 + 8*q^7 + 15*q^8 + q^9 + 18*q^10 
    + 12*q^11 + 7*q^12 + 14*q^13 + 24*q^14 + 6*q^15 + 31*q^16 + 18*q^17 + 3*q^18
    + 20*q^19 + 42*q^20 + 8*q^21 + 36*q^22 + 24*q^23 + 15*q^24 + 31*q^25 + 
    42*q^26 + q^27 + 56*q^28 + 30*q^29 + 18*q^30 + 32*q^31 + 63*q^32 + 12*q^33 +
    54*q^34 + 48*q^35 + 7*q^36 + 38*q^37 + 60*q^38 + 14*q^39 + 90*q^40 + 42*q^41
    + 24*q^42 + 44*q^43 + 84*q^44 + 6*q^45 + 72*q^46 + 48*q^47 + 31*q^48 + 
    57*q^49 + 93*q^50 + 18*q^51 + 98*q^52 + 54*q^53 + 3*q^54 + 72*q^55 + 
    120*q^56 + 20*q^57 + 90*q^58 + 60*q^59 + 42*q^60 + 62*q^61 + 96*q^62 + 
    8*q^63 + 127*q^64 + 84*q^65 + 36*q^66 + 68*q^67 + 126*q^68 + 24*q^69 + 
    144*q^70 + 72*q^71 + 15*q^72 + 74*q^73 + 114*q^74 + 31*q^75 + 140*q^76 + 
    96*q^77 + 42*q^78 + 80*q^79 + 186*q^80 + q^81 + 126*q^82 + 84*q^83 + 56*q^84
    + 108*q^85 + 132*q^86 + 30*q^87 + 180*q^88 + 90*q^89 + 18*q^90 + 112*q^91 + 
    168*q^92 + 32*q^93 + 144*q^94 + 120*q^95 + 63*q^96 + 98*q^97 + 171*q^98 + 
    12*q^99 + 217*q^100 + 102*q^101 + 54*q^102 + 104*q^103 + 210*q^104 + 
    48*q^105 + 162*q^106 + 108*q^107 + 7*q^108 + 110*q^109 + 216*q^110 + 
    38*q^111 + 248*q^112 + 114*q^113 + 60*q^114 + 144*q^115 + 210*q^116 + 
    14*q^117 + 180*q^118 + 144*q^119 + 90*q^120 + 133*q^121 + 186*q^122 + 
    42*q^123 + 224*q^124 + 156*q^125 + 24*q^126 + 128*q^127 + 255*q^128 + 
    44*q^129 + 252*q^130 + 132*q^131 + 84*q^132 + 160*q^133 + 204*q^134 + 
    6*q^135 + 270*q^136 + 138*q^137 + 72*q^138 + 140*q^139 + 336*q^140 + 
    48*q^141 + 216*q^142 + 168*q^143 + 31*q^144 + 180*q^145 + 222*q^146 + 
    57*q^147 + 266*q^148 + 150*q^149 + 93*q^150 + 152*q^151 + 300*q^152 + 
    18*q^153 + 288*q^154 + 192*q^155 + 98*q^156 + 158*q^157 + 240*q^158 + 
    54*q^159 + 378*q^160 + 192*q^161 + 3*q^162 + 164*q^163 + 294*q^164 + 
    72*q^165 + 252*q^166 + 168*q^167 + 120*q^168 + 183*q^169 + 324*q^170 + 
    20*q^171 + 308*q^172 + 174*q^173 + 90*q^174 + 248*q^175 + 372*q^176 + 
    60*q^177 + 270*q^178 + 180*q^179 + 42*q^180 + 182*q^181 + 336*q^182 + 
    62*q^183 + 360*q^184 + 228*q^185 + 96*q^186 + 216*q^187 + 336*q^188 + 
    8*q^189 + 360*q^190 + 192*q^191 + 127*q^192 + 194*q^193 + 294*q^194 + 
    84*q^195 + 399*q^196 + 198*q^197 + 36*q^198 + 200*q^199 + 465*q^200 + 
    68*q^201 + 306*q^202 + 240*q^203 + 126*q^204 + 252*q^205 + 312*q^206 + 
    24*q^207 + 434*q^208 + 240*q^209 + 144*q^210 + 212*q^211 + 378*q^212 + 
    72*q^213 + 324*q^214 + 264*q^215 + 15*q^216 + 256*q^217 + 330*q^218 + 
    74*q^219 + 504*q^220 + 252*q^221 + 114*q^222 + 224*q^223 + 504*q^224 + 
    31*q^225 + 342*q^226 + 228*q^227 + 140*q^228 + 230*q^229 + 432*q^230 + 
    96*q^231 + 450*q^232 + 234*q^233 + 42*q^234 + 288*q^235 + 420*q^236 + 
    80*q^237 + 432*q^238 + 240*q^239 + 186*q^240 + 242*q^241 + 399*q^242 + q^243
    + 434*q^244 + 342*q^245 + 126*q^246 + 280*q^247 + 480*q^248 + 84*q^249 + 
    468*q^250 + 252*q^251 + 56*q^252 + 288*q^253 + 384*q^254 + 108*q^255 + 
    511*q^256 + 258*q^257 + 132*q^258 + 304*q^259 + 588*q^260 + 30*q^261 + 
    396*q^262 + 264*q^263 + 180*q^264 + 324*q^265 + 480*q^266 + 90*q^267 + 
    476*q^268 + 270*q^269 + 18*q^270 + 272*q^271 + 558*q^272 + 112*q^273 + 
    414*q^274 + 372*q^275 + 168*q^276 + 278*q^277 + 420*q^278 + 32*q^279 + 
    720*q^280 + 282*q^281 + 144*q^282 + 284*q^283 + 504*q^284 + 120*q^285 + 
    504*q^286 + 336*q^287 + 63*q^288 + 307*q^289 + 540*q^290 + 98*q^291 + 
    518*q^292 + 294*q^293 + 171*q^294 + 360*q^295 + 570*q^296 + 12*q^297 + 
    450*q^298 + 336*q^299 + O(q^300)

Total time: 0.659 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:21:42 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[1],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[2],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:21:41 on modular  [Seed = 90432755]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_0(15) of weight 2 and dimension 3 over Integer 
Ring.
1/6 + q + 3*q^2 + 4*q^3 + 7*q^4 + q^5 + 12*q^6 + 8*q^7 + 15*q^8 + 13*q^9 + 
    3*q^10 + 12*q^11 + 28*q^12 + 14*q^13 + 24*q^14 + 4*q^15 + 31*q^16 + 18*q^17 
    + 39*q^18 + 20*q^19 + 7*q^20 + 32*q^21 + 36*q^22 + 24*q^23 + 60*q^24 + q^25 
    + 42*q^26 + 40*q^27 + 56*q^28 + 30*q^29 + 12*q^30 + 32*q^31 + 63*q^32 + 
    48*q^33 + 54*q^34 + 8*q^35 + 91*q^36 + 38*q^37 + 60*q^38 + 56*q^39 + 15*q^40
    + 42*q^41 + 96*q^42 + 44*q^43 + 84*q^44 + 13*q^45 + 72*q^46 + 48*q^47 + 
    124*q^48 + 57*q^49 + 3*q^50 + 72*q^51 + 98*q^52 + 54*q^53 + 120*q^54 + 
    12*q^55 + 120*q^56 + 80*q^57 + 90*q^58 + 60*q^59 + 28*q^60 + 62*q^61 + 
    96*q^62 + 104*q^63 + 127*q^64 + 14*q^65 + 144*q^66 + 68*q^67 + 126*q^68 + 
    96*q^69 + 24*q^70 + 72*q^71 + 195*q^72 + 74*q^73 + 114*q^74 + 4*q^75 + 
    140*q^76 + 96*q^77 + 168*q^78 + 80*q^79 + 31*q^80 + 121*q^81 + 126*q^82 + 
    84*q^83 + 224*q^84 + 18*q^85 + 132*q^86 + 120*q^87 + 180*q^88 + 90*q^89 + 
    39*q^90 + 112*q^91 + 168*q^92 + 128*q^93 + 144*q^94 + 20*q^95 + 252*q^96 + 
    98*q^97 + 171*q^98 + 156*q^99 + 7*q^100 + 102*q^101 + 216*q^102 + 104*q^103 
    + 210*q^104 + 32*q^105 + 162*q^106 + 108*q^107 + 280*q^108 + 110*q^109 + 
    36*q^110 + 152*q^111 + 248*q^112 + 114*q^113 + 240*q^114 + 24*q^115 + 
    210*q^116 + 182*q^117 + 180*q^118 + 144*q^119 + 60*q^120 + 133*q^121 + 
    186*q^122 + 168*q^123 + 224*q^124 + q^125 + 312*q^126 + 128*q^127 + 
    255*q^128 + 176*q^129 + 42*q^130 + 132*q^131 + 336*q^132 + 160*q^133 + 
    204*q^134 + 40*q^135 + 270*q^136 + 138*q^137 + 288*q^138 + 140*q^139 + 
    56*q^140 + 192*q^141 + 216*q^142 + 168*q^143 + 403*q^144 + 30*q^145 + 
    222*q^146 + 228*q^147 + 266*q^148 + 150*q^149 + 12*q^150 + 152*q^151 + 
    300*q^152 + 234*q^153 + 288*q^154 + 32*q^155 + 392*q^156 + 158*q^157 + 
    240*q^158 + 216*q^159 + 63*q^160 + 192*q^161 + 363*q^162 + 164*q^163 + 
    294*q^164 + 48*q^165 + 252*q^166 + 168*q^167 + 480*q^168 + 183*q^169 + 
    54*q^170 + 260*q^171 + 308*q^172 + 174*q^173 + 360*q^174 + 8*q^175 + 
    372*q^176 + 240*q^177 + 270*q^178 + 180*q^179 + 91*q^180 + 182*q^181 + 
    336*q^182 + 248*q^183 + 360*q^184 + 38*q^185 + 384*q^186 + 216*q^187 + 
    336*q^188 + 320*q^189 + 60*q^190 + 192*q^191 + 508*q^192 + 194*q^193 + 
    294*q^194 + 56*q^195 + 399*q^196 + 198*q^197 + 468*q^198 + 200*q^199 + 
    15*q^200 + 272*q^201 + 306*q^202 + 240*q^203 + 504*q^204 + 42*q^205 + 
    312*q^206 + 312*q^207 + 434*q^208 + 240*q^209 + 96*q^210 + 212*q^211 + 
    378*q^212 + 288*q^213 + 324*q^214 + 44*q^215 + 600*q^216 + 256*q^217 + 
    330*q^218 + 296*q^219 + 84*q^220 + 252*q^221 + 456*q^222 + 224*q^223 + 
    504*q^224 + 13*q^225 + 342*q^226 + 228*q^227 + 560*q^228 + 230*q^229 + 
    72*q^230 + 384*q^231 + 450*q^232 + 234*q^233 + 546*q^234 + 48*q^235 + 
    420*q^236 + 320*q^237 + 432*q^238 + 240*q^239 + 124*q^240 + 242*q^241 + 
    399*q^242 + 364*q^243 + 434*q^244 + 57*q^245 + 504*q^246 + 280*q^247 + 
    480*q^248 + 336*q^249 + 3*q^250 + 252*q^251 + 728*q^252 + 288*q^253 + 
    384*q^254 + 72*q^255 + 511*q^256 + 258*q^257 + 528*q^258 + 304*q^259 + 
    98*q^260 + 390*q^261 + 396*q^262 + 264*q^263 + 720*q^264 + 54*q^265 + 
    480*q^266 + 360*q^267 + 476*q^268 + 270*q^269 + 120*q^270 + 272*q^271 + 
    558*q^272 + 448*q^273 + 414*q^274 + 12*q^275 + 672*q^276 + 278*q^277 + 
    420*q^278 + 416*q^279 + 120*q^280 + 282*q^281 + 576*q^282 + 284*q^283 + 
    504*q^284 + 80*q^285 + 504*q^286 + 336*q^287 + 819*q^288 + 307*q^289 + 
    90*q^290 + 392*q^291 + 518*q^292 + 294*q^293 + 684*q^294 + 60*q^295 + 
    570*q^296 + 480*q^297 + 450*q^298 + 336*q^299 + O(q^300)

Total time: 0.659 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:22:09 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[1],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[3],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:22:08 on modular  [Seed = 225176798]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_0(15) of weight 2 and dimension 3 over Integer 
Ring.
7/12 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + 15*q^8 + 13*q^9 + 
    18*q^10 + 12*q^11 + 28*q^12 + 14*q^13 + 24*q^14 + 9*q^15 + 31*q^16 + 18*q^17
    + 39*q^18 + 20*q^19 + 42*q^20 + 32*q^21 + 36*q^22 + 24*q^23 + 60*q^24 + 
    31*q^25 + 42*q^26 + 40*q^27 + 56*q^28 + 30*q^29 + 27*q^30 + 32*q^31 + 
    63*q^32 + 48*q^33 + 54*q^34 + 48*q^35 + 91*q^36 + 38*q^37 + 60*q^38 + 
    56*q^39 + 90*q^40 + 42*q^41 + 96*q^42 + 44*q^43 + 84*q^44 + 18*q^45 + 
    72*q^46 + 48*q^47 + 124*q^48 + 57*q^49 + 93*q^50 + 72*q^51 + 98*q^52 + 
    54*q^53 + 120*q^54 + 72*q^55 + 120*q^56 + 80*q^57 + 90*q^58 + 60*q^59 + 
    63*q^60 + 62*q^61 + 96*q^62 + 104*q^63 + 127*q^64 + 84*q^65 + 144*q^66 + 
    68*q^67 + 126*q^68 + 96*q^69 + 144*q^70 + 72*q^71 + 195*q^72 + 74*q^73 + 
    114*q^74 + 34*q^75 + 140*q^76 + 96*q^77 + 168*q^78 + 80*q^79 + 186*q^80 + 
    121*q^81 + 126*q^82 + 84*q^83 + 224*q^84 + 108*q^85 + 132*q^86 + 120*q^87 + 
    180*q^88 + 90*q^89 + 54*q^90 + 112*q^91 + 168*q^92 + 128*q^93 + 144*q^94 + 
    120*q^95 + 252*q^96 + 98*q^97 + 171*q^98 + 156*q^99 + 217*q^100 + 102*q^101 
    + 216*q^102 + 104*q^103 + 210*q^104 + 72*q^105 + 162*q^106 + 108*q^107 + 
    280*q^108 + 110*q^109 + 216*q^110 + 152*q^111 + 248*q^112 + 114*q^113 + 
    240*q^114 + 144*q^115 + 210*q^116 + 182*q^117 + 180*q^118 + 144*q^119 + 
    135*q^120 + 133*q^121 + 186*q^122 + 168*q^123 + 224*q^124 + 156*q^125 + 
    312*q^126 + 128*q^127 + 255*q^128 + 176*q^129 + 252*q^130 + 132*q^131 + 
    336*q^132 + 160*q^133 + 204*q^134 + 45*q^135 + 270*q^136 + 138*q^137 + 
    288*q^138 + 140*q^139 + 336*q^140 + 192*q^141 + 216*q^142 + 168*q^143 + 
    403*q^144 + 180*q^145 + 222*q^146 + 228*q^147 + 266*q^148 + 150*q^149 + 
    102*q^150 + 152*q^151 + 300*q^152 + 234*q^153 + 288*q^154 + 192*q^155 + 
    392*q^156 + 158*q^157 + 240*q^158 + 216*q^159 + 378*q^160 + 192*q^161 + 
    363*q^162 + 164*q^163 + 294*q^164 + 108*q^165 + 252*q^166 + 168*q^167 + 
    480*q^168 + 183*q^169 + 324*q^170 + 260*q^171 + 308*q^172 + 174*q^173 + 
    360*q^174 + 248*q^175 + 372*q^176 + 240*q^177 + 270*q^178 + 180*q^179 + 
    126*q^180 + 182*q^181 + 336*q^182 + 248*q^183 + 360*q^184 + 228*q^185 + 
    384*q^186 + 216*q^187 + 336*q^188 + 320*q^189 + 360*q^190 + 192*q^191 + 
    508*q^192 + 194*q^193 + 294*q^194 + 126*q^195 + 399*q^196 + 198*q^197 + 
    468*q^198 + 200*q^199 + 465*q^200 + 272*q^201 + 306*q^202 + 240*q^203 + 
    504*q^204 + 252*q^205 + 312*q^206 + 312*q^207 + 434*q^208 + 240*q^209 + 
    216*q^210 + 212*q^211 + 378*q^212 + 288*q^213 + 324*q^214 + 264*q^215 + 
    600*q^216 + 256*q^217 + 330*q^218 + 296*q^219 + 504*q^220 + 252*q^221 + 
    456*q^222 + 224*q^223 + 504*q^224 + 43*q^225 + 342*q^226 + 228*q^227 + 
    560*q^228 + 230*q^229 + 432*q^230 + 384*q^231 + 450*q^232 + 234*q^233 + 
    546*q^234 + 288*q^235 + 420*q^236 + 320*q^237 + 432*q^238 + 240*q^239 + 
    279*q^240 + 242*q^241 + 399*q^242 + 364*q^243 + 434*q^244 + 342*q^245 + 
    504*q^246 + 280*q^247 + 480*q^248 + 336*q^249 + 468*q^250 + 252*q^251 + 
    728*q^252 + 288*q^253 + 384*q^254 + 162*q^255 + 511*q^256 + 258*q^257 + 
    528*q^258 + 304*q^259 + 588*q^260 + 390*q^261 + 396*q^262 + 264*q^263 + 
    720*q^264 + 324*q^265 + 480*q^266 + 360*q^267 + 476*q^268 + 270*q^269 + 
    135*q^270 + 272*q^271 + 558*q^272 + 448*q^273 + 414*q^274 + 372*q^275 + 
    672*q^276 + 278*q^277 + 420*q^278 + 416*q^279 + 720*q^280 + 282*q^281 + 
    576*q^282 + 284*q^283 + 504*q^284 + 180*q^285 + 504*q^286 + 336*q^287 + 
    819*q^288 + 307*q^289 + 540*q^290 + 392*q^291 + 518*q^292 + 294*q^293 + 
    684*q^294 + 360*q^295 + 570*q^296 + 480*q^297 + 450*q^298 + 336*q^299 + 
    O(q^300)

Total time: 0.709 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:23:02 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[5],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[1],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:23:01 on modular  [Seed = 1964217683]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_1(15) with character all conjugates of [$.2^2], 
weight 2, and dimension 4 over Integer Ring.
-1/5 + q - q^2 - 2*q^3 + 3*q^4 + q^5 + 2*q^6 - 6*q^7 - 5*q^8 + 7*q^9 - q^10 + 
    12*q^11 - 6*q^12 - 12*q^13 + 6*q^14 - 2*q^15 + 11*q^16 - 16*q^17 - 7*q^18 + 
    20*q^19 + 3*q^20 + 12*q^21 - 12*q^22 - 22*q^23 + 10*q^24 + q^25 + 12*q^26 - 
    20*q^27 - 18*q^28 + 30*q^29 + 2*q^30 + 32*q^31 - 21*q^32 - 24*q^33 + 16*q^34
    - 6*q^35 + 21*q^36 - 36*q^37 - 20*q^38 + 24*q^39 - 5*q^40 + 42*q^41 - 
    12*q^42 - 42*q^43 + 36*q^44 + 7*q^45 + 22*q^46 - 46*q^47 - 22*q^48 + 43*q^49
    - q^50 + 32*q^51 - 36*q^52 - 52*q^53 + 20*q^54 + 12*q^55 + 30*q^56 - 40*q^57
    - 30*q^58 + 60*q^59 - 6*q^60 + 62*q^61 - 32*q^62 - 42*q^63 + 43*q^64 - 
    12*q^65 + 24*q^66 - 66*q^67 - 48*q^68 + 44*q^69 + 6*q^70 + 72*q^71 - 35*q^72
    - 72*q^73 + 36*q^74 - 2*q^75 + 60*q^76 - 72*q^77 - 24*q^78 + 80*q^79 + 
    11*q^80 + 61*q^81 - 42*q^82 - 82*q^83 + 36*q^84 - 16*q^85 + 42*q^86 - 
    60*q^87 - 60*q^88 + 90*q^89 - 7*q^90 + 72*q^91 - 66*q^92 - 64*q^93 + 46*q^94
    + 20*q^95 + 42*q^96 - 96*q^97 - 43*q^98 + 84*q^99 + 3*q^100 + 102*q^101 - 
    32*q^102 - 102*q^103 + 60*q^104 + 12*q^105 + 52*q^106 - 106*q^107 - 60*q^108
    + 110*q^109 - 12*q^110 + 72*q^111 - 66*q^112 - 112*q^113 + 40*q^114 - 
    22*q^115 + 90*q^116 - 84*q^117 - 60*q^118 + 96*q^119 + 10*q^120 + 133*q^121 
    - 62*q^122 - 84*q^123 + 96*q^124 + q^125 + 42*q^126 - 126*q^127 - 85*q^128 +
    84*q^129 + 12*q^130 + 132*q^131 - 72*q^132 - 120*q^133 + 66*q^134 - 20*q^135
    + 80*q^136 - 136*q^137 - 44*q^138 + 140*q^139 - 18*q^140 + 92*q^141 - 
    72*q^142 - 144*q^143 + 77*q^144 + 30*q^145 + 72*q^146 - 86*q^147 - 108*q^148
    + 150*q^149 + 2*q^150 + 152*q^151 - 100*q^152 - 112*q^153 + 72*q^154 + 
    32*q^155 + 72*q^156 - 156*q^157 - 80*q^158 + 104*q^159 - 21*q^160 + 
    132*q^161 - 61*q^162 - 162*q^163 + 126*q^164 - 24*q^165 + 82*q^166 - 
    166*q^167 - 60*q^168 + 157*q^169 + 16*q^170 + 140*q^171 - 126*q^172 - 
    172*q^173 + 60*q^174 - 6*q^175 + 132*q^176 - 120*q^177 - 90*q^178 + 
    180*q^179 + 21*q^180 + 182*q^181 - 72*q^182 - 124*q^183 + 110*q^184 - 
    36*q^185 + 64*q^186 - 192*q^187 - 138*q^188 + 120*q^189 - 20*q^190 + 
    192*q^191 - 86*q^192 - 192*q^193 + 96*q^194 + 24*q^195 + 129*q^196 - 
    196*q^197 - 84*q^198 + 200*q^199 - 5*q^200 + 132*q^201 - 102*q^202 - 
    180*q^203 + 96*q^204 + 42*q^205 + 102*q^206 - 154*q^207 - 132*q^208 + 
    240*q^209 - 12*q^210 + 212*q^211 - 156*q^212 - 144*q^213 + 106*q^214 - 
    42*q^215 + 100*q^216 - 192*q^217 - 110*q^218 + 144*q^219 + 36*q^220 + 
    192*q^221 - 72*q^222 - 222*q^223 + 126*q^224 + 7*q^225 + 112*q^226 - 
    226*q^227 - 120*q^228 + 230*q^229 + 22*q^230 + 144*q^231 - 150*q^232 - 
    232*q^233 + 84*q^234 - 46*q^235 + 180*q^236 - 160*q^237 - 96*q^238 + 
    240*q^239 - 22*q^240 + 242*q^241 - 133*q^242 - 182*q^243 + 186*q^244 + 
    43*q^245 + 84*q^246 - 240*q^247 - 160*q^248 + 164*q^249 - q^250 + 252*q^251 
    - 126*q^252 - 264*q^253 + 126*q^254 + 32*q^255 + 171*q^256 - 256*q^257 - 
    84*q^258 + 216*q^259 - 36*q^260 + 210*q^261 - 132*q^262 - 262*q^263 + 
    120*q^264 - 52*q^265 + 120*q^266 - 180*q^267 - 198*q^268 + 270*q^269 + 
    20*q^270 + 272*q^271 - 176*q^272 - 144*q^273 + 136*q^274 + 12*q^275 + 
    132*q^276 - 276*q^277 - 140*q^278 + 224*q^279 + 30*q^280 + 282*q^281 - 
    92*q^282 - 282*q^283 + 216*q^284 - 40*q^285 + 144*q^286 - 252*q^287 - 
    147*q^288 + 273*q^289 - 30*q^290 + 192*q^291 - 216*q^292 - 292*q^293 + 
    86*q^294 + 60*q^295 + 180*q^296 - 240*q^297 - 150*q^298 + 264*q^299 + 
    O(q^300)

Total time: 0.960 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:23:36 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[5],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[2],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:23:35 on modular  [Seed = 1644462697]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_1(15) with character all conjugates of [$.2^2], 
weight 2, and dimension 4 over Integer Ring.
-1/5 + q^3 - q^6 - 2*q^9 + 3*q^12 + q^15 + 2*q^18 - 6*q^21 - 5*q^24 + 7*q^27 - 
    q^30 + 12*q^33 - 6*q^36 - 12*q^39 + 6*q^42 - 2*q^45 + 11*q^48 - 16*q^51 - 
    7*q^54 + 20*q^57 + 3*q^60 + 12*q^63 - 12*q^66 - 22*q^69 + 10*q^72 + q^75 + 
    12*q^78 - 20*q^81 - 18*q^84 + 30*q^87 + 2*q^90 + 32*q^93 - 21*q^96 - 24*q^99
    + 16*q^102 - 6*q^105 + 21*q^108 - 36*q^111 - 20*q^114 + 24*q^117 - 5*q^120 +
    42*q^123 - 12*q^126 - 42*q^129 + 36*q^132 + 7*q^135 + 22*q^138 - 46*q^141 - 
    22*q^144 + 43*q^147 - q^150 + 32*q^153 - 36*q^156 - 52*q^159 + 20*q^162 + 
    12*q^165 + 30*q^168 - 40*q^171 - 30*q^174 + 60*q^177 - 6*q^180 + 62*q^183 - 
    32*q^186 - 42*q^189 + 43*q^192 - 12*q^195 + 24*q^198 - 66*q^201 - 48*q^204 +
    44*q^207 + 6*q^210 + 72*q^213 - 35*q^216 - 72*q^219 + 36*q^222 - 2*q^225 + 
    60*q^228 - 72*q^231 - 24*q^234 + 80*q^237 + 11*q^240 + 61*q^243 - 42*q^246 -
    82*q^249 + 36*q^252 - 16*q^255 + 42*q^258 - 60*q^261 - 60*q^264 + 90*q^267 -
    7*q^270 + 72*q^273 - 66*q^276 - 64*q^279 + 46*q^282 + 20*q^285 + 42*q^288 - 
    96*q^291 - 43*q^294 + 84*q^297 + O(q^300)

Total time: 0.760 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:23:55 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[5],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[3],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:23:54 on modular  [Seed = 1779206675]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_1(15) with character all conjugates of [$.2^2], 
weight 2, and dimension 4 over Integer Ring.
q + q^2 + 2*q^3 + 3*q^4 + 5*q^5 + 2*q^6 + 6*q^7 + 5*q^8 + 7*q^9 + 5*q^10 + 
    12*q^11 + 6*q^12 + 12*q^13 + 6*q^14 + 10*q^15 + 11*q^16 + 16*q^17 + 7*q^18 +
    20*q^19 + 15*q^20 + 12*q^21 + 12*q^22 + 22*q^23 + 10*q^24 + 25*q^25 + 
    12*q^26 + 20*q^27 + 18*q^28 + 30*q^29 + 10*q^30 + 32*q^31 + 21*q^32 + 
    24*q^33 + 16*q^34 + 30*q^35 + 21*q^36 + 36*q^37 + 20*q^38 + 24*q^39 + 
    25*q^40 + 42*q^41 + 12*q^42 + 42*q^43 + 36*q^44 + 35*q^45 + 22*q^46 + 
    46*q^47 + 22*q^48 + 43*q^49 + 25*q^50 + 32*q^51 + 36*q^52 + 52*q^53 + 
    20*q^54 + 60*q^55 + 30*q^56 + 40*q^57 + 30*q^58 + 60*q^59 + 30*q^60 + 
    62*q^61 + 32*q^62 + 42*q^63 + 43*q^64 + 60*q^65 + 24*q^66 + 66*q^67 + 
    48*q^68 + 44*q^69 + 30*q^70 + 72*q^71 + 35*q^72 + 72*q^73 + 36*q^74 + 
    50*q^75 + 60*q^76 + 72*q^77 + 24*q^78 + 80*q^79 + 55*q^80 + 61*q^81 + 
    42*q^82 + 82*q^83 + 36*q^84 + 80*q^85 + 42*q^86 + 60*q^87 + 60*q^88 + 
    90*q^89 + 35*q^90 + 72*q^91 + 66*q^92 + 64*q^93 + 46*q^94 + 100*q^95 + 
    42*q^96 + 96*q^97 + 43*q^98 + 84*q^99 + 75*q^100 + 102*q^101 + 32*q^102 + 
    102*q^103 + 60*q^104 + 60*q^105 + 52*q^106 + 106*q^107 + 60*q^108 + 
    110*q^109 + 60*q^110 + 72*q^111 + 66*q^112 + 112*q^113 + 40*q^114 + 
    110*q^115 + 90*q^116 + 84*q^117 + 60*q^118 + 96*q^119 + 50*q^120 + 133*q^121
    + 62*q^122 + 84*q^123 + 96*q^124 + 125*q^125 + 42*q^126 + 126*q^127 + 
    85*q^128 + 84*q^129 + 60*q^130 + 132*q^131 + 72*q^132 + 120*q^133 + 66*q^134
    + 100*q^135 + 80*q^136 + 136*q^137 + 44*q^138 + 140*q^139 + 90*q^140 + 
    92*q^141 + 72*q^142 + 144*q^143 + 77*q^144 + 150*q^145 + 72*q^146 + 86*q^147
    + 108*q^148 + 150*q^149 + 50*q^150 + 152*q^151 + 100*q^152 + 112*q^153 + 
    72*q^154 + 160*q^155 + 72*q^156 + 156*q^157 + 80*q^158 + 104*q^159 + 
    105*q^160 + 132*q^161 + 61*q^162 + 162*q^163 + 126*q^164 + 120*q^165 + 
    82*q^166 + 166*q^167 + 60*q^168 + 157*q^169 + 80*q^170 + 140*q^171 + 
    126*q^172 + 172*q^173 + 60*q^174 + 150*q^175 + 132*q^176 + 120*q^177 + 
    90*q^178 + 180*q^179 + 105*q^180 + 182*q^181 + 72*q^182 + 124*q^183 + 
    110*q^184 + 180*q^185 + 64*q^186 + 192*q^187 + 138*q^188 + 120*q^189 + 
    100*q^190 + 192*q^191 + 86*q^192 + 192*q^193 + 96*q^194 + 120*q^195 + 
    129*q^196 + 196*q^197 + 84*q^198 + 200*q^199 + 125*q^200 + 132*q^201 + 
    102*q^202 + 180*q^203 + 96*q^204 + 210*q^205 + 102*q^206 + 154*q^207 + 
    132*q^208 + 240*q^209 + 60*q^210 + 212*q^211 + 156*q^212 + 144*q^213 + 
    106*q^214 + 210*q^215 + 100*q^216 + 192*q^217 + 110*q^218 + 144*q^219 + 
    180*q^220 + 192*q^221 + 72*q^222 + 222*q^223 + 126*q^224 + 175*q^225 + 
    112*q^226 + 226*q^227 + 120*q^228 + 230*q^229 + 110*q^230 + 144*q^231 + 
    150*q^232 + 232*q^233 + 84*q^234 + 230*q^235 + 180*q^236 + 160*q^237 + 
    96*q^238 + 240*q^239 + 110*q^240 + 242*q^241 + 133*q^242 + 182*q^243 + 
    186*q^244 + 215*q^245 + 84*q^246 + 240*q^247 + 160*q^248 + 164*q^249 + 
    125*q^250 + 252*q^251 + 126*q^252 + 264*q^253 + 126*q^254 + 160*q^255 + 
    171*q^256 + 256*q^257 + 84*q^258 + 216*q^259 + 180*q^260 + 210*q^261 + 
    132*q^262 + 262*q^263 + 120*q^264 + 260*q^265 + 120*q^266 + 180*q^267 + 
    198*q^268 + 270*q^269 + 100*q^270 + 272*q^271 + 176*q^272 + 144*q^273 + 
    136*q^274 + 300*q^275 + 132*q^276 + 276*q^277 + 140*q^278 + 224*q^279 + 
    150*q^280 + 282*q^281 + 92*q^282 + 282*q^283 + 216*q^284 + 200*q^285 + 
    144*q^286 + 252*q^287 + 147*q^288 + 273*q^289 + 150*q^290 + 192*q^291 + 
    216*q^292 + 292*q^293 + 86*q^294 + 300*q^295 + 180*q^296 + 240*q^297 + 
    150*q^298 + 264*q^299 + O(q^300)

Total time: 0.949 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:24:12 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
MO2a:=ModularForms(chars[5],2);
E2a:=EisensteinSubspace(MO2a); E2a;
e2sa:=EisensteinSeries(E2a);
qExpansion(e2sa[4],300);

Output: Magma V2.11-2     Sat Aug 21 2004 15:24:11 on modular  [Seed = 1379185210]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Space of modular forms on Gamma_1(15) with character all conjugates of [$.2^2], 
weight 2, and dimension 4 over Integer Ring.
q^3 + q^6 + 2*q^9 + 3*q^12 + 5*q^15 + 2*q^18 + 6*q^21 + 5*q^24 + 7*q^27 + 5*q^30
    + 12*q^33 + 6*q^36 + 12*q^39 + 6*q^42 + 10*q^45 + 11*q^48 + 16*q^51 + 7*q^54
    + 20*q^57 + 15*q^60 + 12*q^63 + 12*q^66 + 22*q^69 + 10*q^72 + 25*q^75 + 
    12*q^78 + 20*q^81 + 18*q^84 + 30*q^87 + 10*q^90 + 32*q^93 + 21*q^96 + 
    24*q^99 + 16*q^102 + 30*q^105 + 21*q^108 + 36*q^111 + 20*q^114 + 24*q^117 + 
    25*q^120 + 42*q^123 + 12*q^126 + 42*q^129 + 36*q^132 + 35*q^135 + 22*q^138 +
    46*q^141 + 22*q^144 + 43*q^147 + 25*q^150 + 32*q^153 + 36*q^156 + 52*q^159 +
    20*q^162 + 60*q^165 + 30*q^168 + 40*q^171 + 30*q^174 + 60*q^177 + 30*q^180 +
    62*q^183 + 32*q^186 + 42*q^189 + 43*q^192 + 60*q^195 + 24*q^198 + 66*q^201 +
    48*q^204 + 44*q^207 + 30*q^210 + 72*q^213 + 35*q^216 + 72*q^219 + 36*q^222 +
    50*q^225 + 60*q^228 + 72*q^231 + 24*q^234 + 80*q^237 + 55*q^240 + 61*q^243 +
    42*q^246 + 82*q^249 + 36*q^252 + 80*q^255 + 42*q^258 + 60*q^261 + 60*q^264 +
    90*q^267 + 35*q^270 + 72*q^273 + 66*q^276 + 64*q^279 + 46*q^282 + 100*q^285 
    + 42*q^288 + 96*q^291 + 43*q^294 + 84*q^297 + O(q^300)

Total time: 0.740 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:45:51 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
M4a:=ModularSymbols(chars[1],4);
S4a:=CuspidalSubspace(M4a); S4a;


Output: Magma V2.11-2     Sat Aug 21 2004 15:45:50 on modular  [Seed = 3218692322]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Modular symbols space for Gamma_0(15) of weight 4 and dimension 8 over 
Cyclotomic Field of order 8 and degree 4

Total time: 0.829 seconds, Total memory usage: 3.58MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:46:34 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
M4a:=ModularSymbols(chars[1],4);
S4a:=NewSubspace(M4a); S4a;


Output: Magma V2.11-2     Sat Aug 21 2004 15:46:32 on modular  [Seed = 2814459916]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Modular symbols space for Gamma_0(15) of weight 4 and dimension 4 over 
Cyclotomic Field of order 8 and degree 4

Total time: 1.699 seconds, Total memory usage: 3.98MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:47:03 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
M4a:=ModularSymbols(chars[5],4);
S4a:=NewSubspace(M4a); S4a;


Output: Magma V2.11-2     Sat Aug 21 2004 15:47:01 on modular  [Seed = 2949204009]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Modular symbols space of level 15, weight 4, character $.2^2, and dimension 8 
over Cyclotomic Field of order 8 and degree 4

Total time: 1.230 seconds, Total memory usage: 3.73MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:47:12 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
M4a:=ModularSymbols(chars[3],4);
S4a:=NewSubspace(M4a); S4a;


Output: Magma V2.11-2     Sat Aug 21 2004 15:47:11 on modular  [Seed = 2549182491]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Modular symbols space of level 15, weight 4, character $.2, and dimension 0 over
Cyclotomic Field of order 8 and degree 4

Total time: 0.620 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:47:26 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
M4a:=ModularSymbols(chars[7],4);
S4a:=NewSubspace(M4a); S4a;


Output: Magma V2.11-2     Sat Aug 21 2004 15:47:25 on modular  [Seed = 2683926625]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Modular symbols space of level 15, weight 4, character $.2^3, and dimension 0 
over Cyclotomic Field of order 8 and degree 4

Total time: 0.630 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host c-24-14-38-127.client.comcast.net. (24.14.38.127)
Time: Sat Aug 21 15:47:34 2004

Input: G:=DirichletGroup(15,CyclotomicField(8));
chars:=Elements(G);
[Conductor(eps):eps in chars];
M4a:=ModularSymbols(chars[5],4);
S4a:=NewSubspace(M4a); S4a;


Output: Magma V2.11-2     Sat Aug 21 2004 15:47:33 on modular  [Seed = 2279694433]
   -------------------------------------

[ 1, 3, 5, 15, 5, 15, 5, 15 ]
Modular symbols space of level 15, weight 4, character $.2^2, and dimension 8 
over Cyclotomic Field of order 8 and degree 4

Total time: 1.250 seconds, Total memory usage: 3.73MB


************** MAGMA *****************
Host 65-45-165-133-atl-02.cvx.algx.net. (65.45.165.133)
Time: Sat Aug 21 20:28:14 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Sat Aug 21 2004 20:28:14 on modular  [Seed = 2747599370]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 65-45-165-133-atl-02.cvx.algx.net. (65.45.165.133)
Time: Sat Aug 21 20:28:57 2004

Input: x+1/3.14

Output: Magma V2.11-2     Sat Aug 21 2004 20:28:57 on modular  [Seed = 2882339413]
   -------------------------------------


>> x+1/3.14;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 65-45-165-133-atl-02.cvx.algx.net. (65.45.165.133)
Time: Sat Aug 21 20:29:09 2004

Input: 4+1/3.14

Output: Magma V2.11-2     Sat Aug 21 2004 20:29:08 on modular  [Seed = 2482322032]
   -------------------------------------

4.318471337579617834394904458596836868150

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:19:42 2004

Input: F<x,y>:=Group<x,y|x^4,y^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3>;
Order(F);

Output: Magma V2.11-2     Sat Aug 21 2004 21:19:36 on modular  [Seed = 3383721046]
   -------------------------------------

0

Total time: 5.770 seconds, Total memory usage: 18.77MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:20:05 2004

Input: F<x,y>:=Group<x,y|x^4,y^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2>;
Order(F);

Output: Magma V2.11-2     Sat Aug 21 2004 21:20:05 on modular  [Seed = 793352924]
   -------------------------------------

1536

Total time: 0.679 seconds, Total memory usage: 18.78MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:20:25 2004

Input: F<x,y>:=Group<x,y|x^4,y^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2,x*y*x^2*y*x=y*x*y^2*x*y>;
Order(F);

Output: Magma V2.11-2     Sat Aug 21 2004 21:20:24 on modular  [Seed = 393323257]
   -------------------------------------

384

Total time: 0.689 seconds, Total memory usage: 18.69MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:22:18 2004

Input: F<x,y,z>:=Group<x,y,z|x^4,y^4,z^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2,x*y*x^2*y*x=y*x*y^2*x*y,y^2*z^2=z^2*y^2,(y*z)^3=(z*y)^3,y^2*z*y^2*z=z*y^2*z*y^2,y*z*y^2*z*y=z*y*z^2*y*z,x*z=z*x>;
Order(F);

Output: Magma V2.11-2     Sat Aug 21 2004 21:22:12 on modular  [Seed = 477800558]
   -------------------------------------

0

Total time: 5.889 seconds, Total memory usage: 20.06MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:22:58 2004

Input: F<x,y,z>:=Group<x,y,z|x^4,y^4,z^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2,x*y*x^2*y*x=y*x*y^2*x*y,y^2*z^2=z^2*y^2,(y*z)^3=(z*y)^3,y^2*z*y^2*z=z*y^2*z*y^2,y*z*y^2*z*y=z*y*z^2*y*z,x*z=z*x>;
Order(F : CosetLimit:=1000000);

Output: Magma V2.11-2     Sat Aug 21 2004 21:22:50 on modular  [Seed = 73576536]
   -------------------------------------

0

Total time: 8.539 seconds, Total memory usage: 29.08MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:23:10 2004

Input: F<x,y,z>:=Group<x,y,z|x^4,y^4,z^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2,x*y*x^2*y*x=y*x*y^2*x*y,y^2*z^2=z^2*y^2,(y*z)^3=(z*y)^3,y^2*z*y^2*z=z*y^2*z*y^2,y*z*y^2*z*y=z*y*z^2*y*z,x*z=z*x>;
Order(F : CosetLimit:=4000000);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Sat Aug 21 2004 21:23:06 on modular  [Seed = 174898758]
   -------------------------------------


Current total memory usage: 94.9MB, failed memory request: 0.5MB
System Error: User memory limit has been reached

Total time: 4.379 seconds, Total memory usage: 99.54MB


************** MAGMA *****************
Host pD9535557.dip.t-dialin.net. (217.83.85.87)
Time: Sat Aug 21 21:23:42 2004

Input: F<x,y,z>:=Group<x,y,z|x^4,y^4,z^4,x^2*y^2=y^2*x^2,(x*y)^3=(y*x)^3,x^2*y*x^2*y=y*x^2*y*x^2,x*y*x^2*y*x=y*x*y^2*x*y,y^2*z^2=z^2*y^2,(y*z)^3=(z*y)^3,y^2*z*y^2*z=z*y^2*z*y^2,y*z*y^2*z*y=z*y*z^2*y*z,x*z=z*x>;
Order(F : CosetLimit:=3000000);

Output: Magma V2.11-2     Sat Aug 21 2004 21:23:21 on modular  [Seed = 1930807244]
   -------------------------------------



************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Sun Aug 22 13:05:46 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-32*x^14-8*x^13+336*x^12+80*x^11-1496*x^10-104*x^9+3122*x^8-288*x^7-3208*x^6+760*x^5+1552*x^4-592*x^3-256*x^2+152*x-17));


Output: Magma V2.11-2     Sun Aug 22 2004 13:05:35 on modular  [Seed = 3299694501]
   -------------------------------------

159 16

Total time: 5.539 seconds, Total memory usage: 5.99MB


************** MAGMA *****************
Host gw1.btc.transwitch.com. (63.149.68.2)
Time: Sun Aug 22 13:05:58 2004

Input: R<x> := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 120*x^14 + 5508*x^12 - 120440*x^10 + 1263814*x^8 - 5470152*x^6 + 6116356*x^4 - 1624648*x^2 + 9409));


Output: Magma V2.11-2     Sun Aug 22 2004 13:05:52 on modular  [Seed = 1846017374]
   -------------------------------------

157 16

Total time: 5.709 seconds, Total memory usage: 7.67MB


************** MAGMA *****************
Host pD9FAB81E.dip.t-dialin.net. (217.250.184.30)
Time: Sun Aug 22 13:40:35 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
AutomorphismGroup(L1);


Output: Magma V2.11-2     Sun Aug 22 2004 13:40:26 on modular  [Seed = 1012246518]
   -------------------------------------

MatrixGroup(16, Integer Ring) of order 2^29 * 3^10 * 5^4 * 7^2
Generators:
    [ 0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  1  0  0  1  0  0  0  0  0 -1  0  0  1  0]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -1  0 -2  1  0]
    [-1  0  0 -1  1  0  0  0 -1  0  0  0  0  0  0 -1]
    [ 1  0  0  2 -1  0  1  0  1  0  0  0  1  0  0  1]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0]
    [ 1  0  0  1 -1  0  0  0  1  0  0  0  1  0  0  1]
    [ 0 -1  2  0  0  1  0 -1  0 -1  0  0  0 -1  0  0]
    [ 1  0  0  1  0  0  0  0  1  0  0  0  0  0  0  1]
    [ 0 -1  1  0  0  1  0  0  0 -1  0  0  0 -1  0  0]
    [ 1  0  0  1 -1  0  1  0  1  0  0  0  0  0  0  1]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0 -1 -1  0]
    [ 0  0  0  1 -1  0  0  0  1  0  0  0  0  0  0  1]
    [ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  0  0]
    [ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  1  0 -1  0  0  0  0  0]

    [ 0  1 -2  0  0 -2  0  1  0  0  0  1  0  1 -1  0]
    [ 1  0  0  1 -1  0  1  0  1  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0 -1  0  0  0  0  0]
    [ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1 -1  0]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -1  0 -1  1  0]
    [-1  0  0 -2  1  0 -1  0 -1  0 -1  0  0  0  0  0]
    [ 0 -2  3  0  0  2  0 -2  0 -1  0 -1  0 -1  1  0]
    [ 0  0  0  0  0  0  0  0  0  0 -1  0  1  0  0  0]
    [ 0 -2  2  0  0  1  0 -1  0  0  0 -1  0 -1  1  0]
    [ 0  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -2  0 -1  1  0]
    [-2  0  0 -3  2  0 -1  0 -1  0 -2  0 -1  0  0 -1]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -1  0 -2  1  0]
    [-1  0  0 -1  0  0 -1  0  0  0 -1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0 -1]
    [ 0 -2  2  0  0  2  0 -1  0 -1  0 -1  0 -1  1  0]

    [ 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0]
    [-2  0  0 -3  2  0 -1  0 -1  0 -1  0 -1  0  0 -1]

Total time: 8.770 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB81E.dip.t-dialin.net. (217.250.184.30)
Time: Sun Aug 22 13:45:43 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);


Output: Magma V2.11-2     Sun Aug 22 2004 13:45:34 on modular  [Seed = 3450099507]
   -------------------------------------


Total time: 8.760 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB81E.dip.t-dialin.net. (217.250.184.30)
Time: Sun Aug 22 13:47:49 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
Gruppe(100);

Output: Magma V2.11-2     Sun Aug 22 2004 13:47:40 on modular  [Seed = 3602860970]
   -------------------------------------


>> Gruppe(100);;
         ^
Runtime error: Bad argument types
Argument types given: RngIntElt, GrpMat

Total time: 8.780 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB81E.dip.t-dialin.net. (217.250.184.30)
Time: Sun Aug 22 13:50:02 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
print Gruppe(100);

Output: Magma V2.11-2     Sun Aug 22 2004 13:49:53 on modular  [Seed = 3753263710]
   -------------------------------------


>> print Gruppe(100);;
               ^
Runtime error: Bad argument types
Argument types given: RngIntElt, GrpMat

Total time: 8.760 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB81E.dip.t-dialin.net. (217.250.184.30)
Time: Sun Aug 22 13:52:34 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
AutomorphismGroup(L1);

Output: Magma V2.11-2     Sun Aug 22 2004 13:52:25 on modular  [Seed = 3900798193]
   -------------------------------------

MatrixGroup(16, Integer Ring) of order 2^29 * 3^10 * 5^4 * 7^2
Generators:
    [ 0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  1  0  0  1  0  0  0  0  0 -1  0  0  1  0]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -1  0 -2  1  0]
    [-1  0  0 -1  1  0  0  0 -1  0  0  0  0  0  0 -1]
    [ 1  0  0  2 -1  0  1  0  1  0  0  0  1  0  0  1]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0]
    [ 1  0  0  1 -1  0  0  0  1  0  0  0  1  0  0  1]
    [ 0 -1  2  0  0  1  0 -1  0 -1  0  0  0 -1  0  0]
    [ 1  0  0  1  0  0  0  0  1  0  0  0  0  0  0  1]
    [ 0 -1  1  0  0  1  0  0  0 -1  0  0  0 -1  0  0]
    [ 1  0  0  1 -1  0  1  0  1  0  0  0  0  0  0  1]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0 -1 -1  0]
    [ 0  0  0  1 -1  0  0  0  1  0  0  0  0  0  0  1]
    [ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  0  0]
    [ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  1  0 -1  0  0  0  0  0]

    [ 0  1 -2  0  0 -2  0  1  0  0  0  1  0  1 -1  0]
    [ 1  0  0  1 -1  0  1  0  1  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0 -1  0  0  0  0  0]
    [ 0  2 -2  0  0 -1  0  1  0  1  0  1  0  1 -1  0]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -1  0 -1  1  0]
    [-1  0  0 -2  1  0 -1  0 -1  0 -1  0  0  0  0  0]
    [ 0 -2  3  0  0  2  0 -2  0 -1  0 -1  0 -1  1  0]
    [ 0  0  0  0  0  0  0  0  0  0 -1  0  1  0  0  0]
    [ 0 -2  2  0  0  1  0 -1  0  0  0 -1  0 -1  1  0]
    [ 0  0  0 -1  1  0 -1  0  0  0 -1  0  0  0  0  0]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -2  0 -1  1  0]
    [-2  0  0 -3  2  0 -1  0 -1  0 -2  0 -1  0  0 -1]
    [ 0 -2  3  0  0  2  0 -1  0 -1  0 -1  0 -2  1  0]
    [-1  0  0 -1  0  0 -1  0  0  0 -1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0 -1]
    [ 0 -2  2  0  0  2  0 -1  0 -1  0 -1  0 -1  1  0]

    [ 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0]
    [-2  0  0 -3  2  0 -1  0 -1  0 -1  0 -1  0  0 -1]

Total time: 8.750 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB20A.dip.t-dialin.net. (217.250.178.10)
Time: Sun Aug 22 14:21:07 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
NumberingMap(Gruppe);

Output: Magma V2.11-2     Sun Aug 22 2004 14:20:58 on modular  [Seed = 3084784381]
   -------------------------------------

Mapping from: GrpMat: Gruppe to { 1 .. 970864271032320000 }

Total time: 8.819 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB20A.dip.t-dialin.net. (217.250.178.10)
Time: Sun Aug 22 14:23:58 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
Abbildung:=NumberingMap(Gruppe);

Output: Magma V2.11-2     Sun Aug 22 2004 14:23:49 on modular  [Seed = 1194255025]
   -------------------------------------


Total time: 8.860 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB20A.dip.t-dialin.net. (217.250.178.10)
Time: Sun Aug 22 14:26:25 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
5 @@ f;

Output: Magma V2.11-2     Sun Aug 22 2004 14:26:17 on modular  [Seed = 1396373337]
   -------------------------------------

[ 0  2 -2  0  0 -1  0  1  0  0  0  1  0  1 -1  0]
[ 1  0  0  1 -1  0  0  0  1  0  1  0  1  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0]
[ 0 -1  3  0  0  2  0 -1  0 -1  0 -1  0 -1  1  0]
[ 0 -1  1  0  0  1  0 -1  0  0  0  0  0 -1  0  0]
[ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  1]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0]
[-1  0  0 -1  1  0  0  0  0  0 -1  0 -1  0  0  0]
[ 0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[-1  0  0 -1  1  0  0  0 -1  0 -1  0  0  0  0  0]
[ 0 -1  0  0  0  0  0 -1  0  0  0  0  0  0  0  0]
[ 1  0  0  1  0  0  1  0  0  0  0  0  0  0  0  1]
[ 0  0 -1  0  0  0  0  0  0  1  0  0  0  0  0  0]
[-1  0  0 -2  2  0 -1  0 -1  0 -1  0 -1  0  0  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0  0  0  0 -1]
[ 0  0 -1  0  0 -1  0  0  0  1  0  1  0  0  0  0]

Total time: 8.860 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB20A.dip.t-dialin.net. (217.250.178.10)
Time: Sun Aug 22 14:27:14 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
A:=5 @@ f;Det(A);

Output: Magma V2.11-2     Sun Aug 22 2004 14:27:05 on modular  [Seed = 1530068833]
   -------------------------------------


>> A:=5 @@ f;Det(A);;
             ^
User error: Identifier 'Det' has not been declared or assigned

Total time: 8.910 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB20A.dip.t-dialin.net. (217.250.178.10)
Time: Sun Aug 22 14:28:44 2004

Input: EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
L1:=LatticeWithGram(EHUT1);
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
A:=5 @@ f;Determinant(A);

Output: Magma V2.11-2     Sun Aug 22 2004 14:28:35 on modular  [Seed = 1661650931]
   -------------------------------------

1

Total time: 8.879 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:26:57 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A(2k-1,2j-1) ne A(2k,2j) then
                                                               Hilfsvar:=1;
                                                               end if;
                                   if A(2k,2j-1)*A(2k,2j-1)+A(2k-1,2j)*A(2k-1,2j) ne 0 then
                                                                                       Hilfsvar:=1;
                                                                                       end if;
                                   end for;
                     end for;
                     if Hilfsvar neq 1 then Include(~Menge,A);

end for;

#Menge;

Output: Magma V2.11-2     Sun Aug 22 2004 15:26:47 on modular  [Seed = 3669190894]
   -------------------------------------


>>                                    if A(2k-1,2j-1) ne A(2k,2j) then
                                            ^
User error: bad syntax

>>                                                                end if;
                                                                  ^
User error: bad syntax

>>                                    if A(2k,2j-1)*A(2k,2j-1)+A(2k-1,2j)*A(2k
                                            ^
User error: bad syntax

>>                                 end if;
                                   ^
User error: bad syntax

>>                                    end for;
                                      ^
User error: bad syntax

>>                      end for;
                        ^
User error: bad syntax

>>                      if Hilfsvar neq 1 then Include(~Menge,A);
                                    ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

>> #Menge;;
    ^
User error: Identifier 'Menge' has not been declared or assigned

Total time: 8.840 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:29:11 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A(2*k-1,2*j-1) ne A(2*k,2*j) then
                                                                   Hilfsvar:=1;
                                                                   end if;
                                   if A(2*k,2*j-1)*A(2*k,2*j-1)+A(2*k-1,2*j)*A(2*k-1,2*j) ne 0 then
                                                                                               Hilfsvar:=1;
                                                                                               end if;
                                   end for;
                     end for;
                     if Hilfsvar ne 1 then Include(~Menge,A);

end for;

#Menge;


Output: Magma V2.11-2     Sun Aug 22 2004 15:29:02 on modular  [Seed = 3800780895]
   -------------------------------------


>> end for;
       ^
User error: bad syntax

>> #Menge;
    ^
User error: Identifier 'Menge' has not been declared or assigned

Total time: 8.830 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:30:41 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A(2*k-1,2*j-1) ne A(2*k,2*j) then
                                                                   Hilfsvar:=1;
                                                                   end if;
                                   if A(2*k,2*j-1)*A(2*k,2*j-1)+A(2*k-1,2*j)*A(2*k-1,2*j) ne 0 then
                                                                                               Hilfsvar:=1;
                                                                                               end if;
                                   end for;
                     end for;
                     if Hilfsvar ne 1 then Include(~RichtigeElemente,A);

end for;

#RichtigeElemente;

Output: Magma V2.11-2     Sun Aug 22 2004 15:30:32 on modular  [Seed = 3917503730]
   -------------------------------------


>> end for;
       ^
User error: bad syntax
0

Total time: 8.819 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:31:48 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A(2*k-1,2*j-1) ne A(2*k,2*j) then
                                                                   Hilfsvar:=1;
                                                                   end if;
                                   if A(2*k,2*j-1)*A(2*k,2*j-1)+A(2*k-1,2*j)*A(2*k-1,2*j) ne 0 then
                                                                                               Hilfsvar:=1;
                                                                                               end if;
                                   end for;
                     end for;
                     if Hilfsvar ne 1 then 
                                      Include(~RichtigeElemente,A);
                                      end if;
end for;

#RichtigeElemente;

Output: Magma V2.11-2     Sun Aug 22 2004 15:31:40 on modular  [Seed = 4036576559]
   -------------------------------------


>>                                    if A(2*k-1,2*j-1) ne A(2*k,2*j) then
                                          ^
Runtime error: Attempting to call something that is not callable
0

Total time: 8.809 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:36:40 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;
A:= 3535 @@ f;
A(16,16);A(10,2);

Output: Magma V2.11-2     Sun Aug 22 2004 15:36:31 on modular  [Seed = 2213164927]
   -------------------------------------


>> A(16,16);A(10,2);;
    ^
Runtime error in procedure call: Attempting to call something that is not 
callable

>> A(16,16);A(10,2);;
             ^
Runtime error in procedure call: Attempting to call something that is not 
callable

Total time: 8.889 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:37:05 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;
A:= 3535 @@ f;
A;

Output: Magma V2.11-2     Sun Aug 22 2004 15:36:56 on modular  [Seed = 2346860304]
   -------------------------------------

[-1  0  0 -1  1  0 -1  0 -1  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  1  0  0  1  0]
[ 0 -1  1  0  0  0  0 -1  0  0  0  0  0 -1  0  0]
[-1  0  0 -1  1  0 -1  0  0  0  0  0  0  0  0 -1]
[-1  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0 -1]
[ 0  1 -1  0  0 -1  0  0  0  0  0  0  0  1 -1  0]
[ 0  0  0  0 -1  0  1  0  0  0  0  0  0  0  0  0]
[ 0  1 -1  0  0 -1  0  0  0  1  0  0  0  0 -1  0]
[ 0  0  0 -1  0  0  0  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  0  0  0 -1  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 1  0  0  2 -2  0  1  0  1  0  1  0  0  0  0  1]
[ 0  0 -1  0  0 -1  0  0  0  0  0  0  0  0 -1  0]
[ 0  1 -1  0  0  0  0  1  0  0  0  1  0  0  0  0]
[ 1  0  0  1 -1  0  1  0  0  0  1  0  0  0  0  0]

Total time: 8.850 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:38:06 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A(2*k-1,2*j-1) ne A(2*k,2*j) then
                                                                   Hilfsvar:=1;
                                                                   end if;
                                   if A[2*k,2*j-1]*A[2*k,2*j-1]+A[2*k-1,2*j]*A[2*k-1,2*j] ne 0 then
                                                                                               Hilfsvar:=1;
                                                                                               end if;
                                   end for;
                     end for;
                     if Hilfsvar ne 1 then 
                                      Include(~RichtigeElemente,A);
                                      end if;
end for;

#RichtigeElemente;

Output: Magma V2.11-2     Sun Aug 22 2004 15:37:57 on modular  [Seed = 2482644165]
   -------------------------------------


>>                                    if A(2*k-1,2*j-1) ne A(2*k,2*j) then
                                          ^
Runtime error: Attempting to call something that is not callable
0

Total time: 8.809 seconds, Total memory usage: 3.56MB


************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:39:08 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A[2*k-1,2*j-1] ne A[2*k,2*j] then
                                                                   Hilfsvar:=1;
                                                                   end if;
                                   if A[2*k,2*j-1]*A[2*k,2*j-1]+A[2*k-1,2*j]*A[2*k-1,2*j] ne 0 then
                                                                                               Hilfsvar:=1;
                                                                                               end if;
                                   end for;
                     end for;
                     if Hilfsvar ne 1 then 
                                      Include(~RichtigeElemente,A);
                                      end if;
end for;

#RichtigeElemente;

Output: Magma V2.11-2     Sun Aug 22 2004 15:38:47 on modular  [Seed = 2582654621]
   -------------------------------------



************** MAGMA *****************
Host pD9FAB096.dip.t-dialin.net. (217.250.176.150)
Time: Sun Aug 22 15:41:03 2004

Input: C<i>:=ComplexField();
EHUT1:=Matrix(RingOfIntegers(),16,16,[2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1, 0,2,0,0,0,-1,0,-1,0,-1,0,-1,0,-1,1,0, 0,0,2,0,0,0,0,1,0,1,0,1,0,1,-1,0, 0,0,0,2,0,0,-1,0,-1,0,-1,0,-1,0,0,-1, -1,0,0,0,2,0,1,0,1,0,1,0,1,0,0,1, 0,-1,0,0,0,2,0,1,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,2,0,1,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,2,0,1,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,2,0,1,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,2,0,1,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,2,0,1,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,2,0,1,-1,0, -1,0,0,-1,1,0,1,0,1,0,1,0,2,0,0,1, 0,-1,1,0,0,1,0,1,0,1,0,1,0,2,-1,0, 0,1,-1,0,0,-1,0,-1,0,-1,0,-1,0,-1,2,0, -1,0,0,-1,1,0,1,0,1,0,1,0,1,0,0,2]);
Gram1:=Matrix(ComplexField(),8,8,[2,0,-1,-1,-1,-1,-1,-i, 0,2,0,i,i,i,i,-1, -1,0,2,1,1,1,1,i, -1,-i,1,2,1,1,1,i, -1,-i,1,1,2,1,1,i, -1,-i,1,1,1,2,1,i, -1,-i,1,1,1,1,2,i, i,-1,-i,-i,-i,-i,-i,2]);
L1:=LatticeWithGram(EHUT1);
S12:=ShortVectors(L1,2);S12Hilfe:=S12;S12Redux:={ };
Ergebnis1:={ };
ErgebnisMulti1:={* *};
RichtigeElemente:={ };
Gruppe:=AutomorphismGroup(L1);
f:=NumberingMap(Gruppe);
Ordnungf:=#Gruppe;
Hilfsvar:=0;

for i:=1 to Ordnungf do
                     A:=i @@ f;
                     Hilfsvar:=0;
                     for j:=1 to 8 do
                                   for k:=1 to 8 do
                                   if A[2*k-1,2*j-1] ne A[2*k,2*j] then
                                                                   Hilfsvar:=1;
                                                                   end if;
                                   if A[2*k,2*j-1]*A[2*k,2*j-1]+A[2*k-1,2*j]*A[2*k-1,2*j] ne 0 then
                                                                                               Hilfsvar:=1;
                                                                                               end if;
                                   end for;
                     end for;
                     if Hilfsvar ne 1 then 
                                      Include(~RichtigeElemente,A);
                                      end if;
end for;

#RichtigeElemente;

Output: Magma V2.11-2     Sun Aug 22 2004 15:40:43 on modular  [Seed = 3151105091]
   -------------------------------------



************** MAGMA *****************
Host ppp-66-63-133-236.sndg-pm4-1.dialup.nethere.net. (66.63.133.236)
Time: Sun Aug 22 22:54:00 2004

Input: E := EllipticCurve([0,24479776636,0,-163775781014077440000,0]);
E;
G,m := MordellWeilGroup(E);
G;


Output: Magma V2.11-2     Sun Aug 22 2004 22:53:59 on modular  [Seed = 3585984724]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 24479776636*x^2 - 163775781014077440000*x 
over Rational Field
Warning: rank computed (0) is only a lower bound
(It may still be correct, though)
Abelian Group isomorphic to Z/2 + Z/4
Defined on 2 generators
Relations:
    2*G.1 = 0
    4*G.2 = 0

Total time: 0.669 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ppp-66-63-133-236.sndg-pm4-1.dialup.nethere.net. (66.63.133.236)
Time: Sun Aug 22 23:03:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,27837195420673,0,-5480945650502018594279424,0]);
E;
f := P!Reverse([2305,0,-56260949686274,0,343303278924253160058625]);
f;
S := FourDescent(f);
#S;
F := S[1];
pts := Points(F,100);
pts;
X,m := Scheme(F);
X;
m(pts[1]);
Height($1);


Output: Magma V2.11-2     Sun Aug 22 2004 23:02:41 on modular  [Seed = 2533263745]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 27837195420673*x^2 - 
5480945650502018594279424*x over Rational Field
2305*x^4 - 56260949686274*x^2 + 343303278924253160058625


************** MAGMA *****************
Host host165-253.pool80117.interbusiness.it. (80.117.253.165)
Time: Mon Aug 23 02:26:20 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Mon Aug 23 2004 02:26:19 on modular  [Seed = 2516409046]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.529 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:18:33 2004

Input: Hello

Output: Magma V2.11-2     Mon Aug 23 2004 04:18:32 on modular  [Seed = 2550103684]
   -------------------------------------


>> Hello;
   ^
User error: Identifier 'Hello' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:26:55 2004

Input: g := GeneratorPolynomial(F115E10);
g;


Output: Magma V2.11-2     Mon Aug 23 2004 04:26:54 on modular  [Seed = 3051183792]
   -------------------------------------


>> g := GeneratorPolynomial(F115E10);
                            ^
User error: Identifier 'F115E10' has not been declared or assigned

>> g;
   ^
User error: Identifier 'g' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:27:29 2004

Input: h := F115E10
g := GeneratorPolynomial(h);
g;


Output: Magma V2.11-2     Mon Aug 23 2004 04:27:28 on modular  [Seed = 1277470582]
   -------------------------------------


>> g := GeneratorPolynomial(h);
   ^
User error: bad syntax

>> g;
   ^
User error: Identifier 'g' has not been declared or assigned

Total time: 0.510 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:27:49 2004

Input: h := F115E10;
g := GeneratorPolynomial(h);
g;


Output: Magma V2.11-2     Mon Aug 23 2004 04:27:48 on modular  [Seed = 1143779210]
   -------------------------------------


>> h := F115E10;
        ^
User error: Identifier 'F115E10' has not been declared or assigned

>> g := GeneratorPolynomial(h);
                            ^
User error: Identifier 'h' has not been declared or assigned

>> g;
   ^
User error: Identifier 'g' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:30:44 2004

Input: > K<w> := GF(2);
> P<x> := PolynomialRing(K);
> H := HammingCode(K, 3);
> g := GeneratorPolynomial(H);
> g;


Output: Magma V2.11-2     Mon Aug 23 2004 04:30:44 on modular  [Seed = 1563801379]
   -------------------------------------

x^3 + x + 1

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:32:46 2004

Input: > K<w> := GF(F2);
> P<x> := PolynomialRing(K);
> H := HammingCode(K, 3);
> g := GeneratorPolynomial(H);
> g;


Output: Magma V2.11-2     Mon Aug 23 2004 04:32:45 on modular  [Seed = 1778548877]
   -------------------------------------


>>   K<w> := GF(F2);
                ^
User error: Identifier 'F2' has not been declared or assigned

>>   P<x> := PolynomialRing(K);
                            ^
User error: Identifier 'K' has not been declared or assigned

>>   H := HammingCode(K, 3);
                      ^
User error: Identifier 'K' has not been declared or assigned

>>   g := GeneratorPolynomial(H);
                              ^
User error: Identifier 'H' has not been declared or assigned

>>   g;
     ^
User error: Identifier 'g' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 203-217-39-20.dyn.iinet.net.au. (203.217.39.20)
Time: Mon Aug 23 04:33:32 2004

Input: > K<w> := GF(9);
> P<x> := PolynomialRing(K);
> H := HammingCode(K, 3);
> g := GeneratorPolynomial(H);
> g;


Output: Magma V2.11-2     Mon Aug 23 2004 04:33:31 on modular  [Seed = 1661700597]
   -------------------------------------

x^3 + w^6*x + 2

Total time: 0.580 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host ppp147-65.lns1.mel2.internode.on.net. (150.101.147.65)
Time: Mon Aug 23 08:59:47 2004

Input: (x^6 + x^3 + x) / (x^3 + x^2 + 1)

Output: Magma V2.11-2     Mon Aug 23 2004 08:59:45 on modular  [Seed = 3034324921]
   -------------------------------------


>> (x^6 + x^3 + x) / (x^3 + x^2 + 1);
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.649 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ppp147-65.lns1.mel2.internode.on.net. (150.101.147.65)
Time: Mon Aug 23 09:00:43 2004

Input: 6/3


Output: Magma V2.11-2     Mon Aug 23 2004 09:00:42 on modular  [Seed = 1396439142]
   -------------------------------------

2

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ppp147-65.lns1.mel2.internode.on.net. (150.101.147.65)
Time: Mon Aug 23 09:01:36 2004

Input: 1001010 / 1101

Output: Magma V2.11-2     Mon Aug 23 2004 09:01:35 on modular  [Seed = 1628031617]
   -------------------------------------

333670/367

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ppp147-65.lns1.mel2.internode.on.net. (150.101.147.65)
Time: Mon Aug 23 09:01:55 2004

Input: (1001010)/(1101)

Output: Magma V2.11-2     Mon Aug 23 2004 09:01:55 on modular  [Seed = 2031211253]
   -------------------------------------

333670/367

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 09:44:03 2004

Input: C:=LenearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
PermutationGroup(C);


Output: Magma V2.11-2     Mon Aug 23 2004 09:44:02 on modular  [Seed = 3416489511]
   -------------------------------------


>> C:=LenearCode<GF(2), 48 |
                ^
User error: bad syntax

>> 0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
                                             ^
User error: bad syntax

>> PermutationGroup(C);
                    ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 09:44:36 2004

Input: C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
PermutationGroup(C);


Output: Magma V2.11-2     Mon Aug 23 2004 09:44:15 on modular  [Seed = 3282794044]
   -------------------------------------



************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 09:45:17 2004

Input: C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
MinimumWeight(C);


Output: Magma V2.11-2     Mon Aug 23 2004 09:45:16 on modular  [Seed = 3685969528]
   -------------------------------------

12

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 09:50:44 2004

Input: s:=Sym(48)![1, 14, 38, 7, 13, 39, 36, 26, 31, 24, 44, 12, 27, 47, 40, 45, 35, 32, 11, 17, 
    33, 10, 23, 48, 2, 37, 41, 6, 4, 21, 3, 20, 18, 30, 34, 22, 5, 43, 29, 16, 
    15, 25, 46, 9, 8, 42, 28, 19];
e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
t:=Sym(48)![1,  3,  4,  5,  6,  7,  8,  9, 10, 11, 14, 15, 12, 16, 19, 20, 21, 25, 27, 28, 29, 35, 43, 41, 
  2, 23, 44, 39, 24, 48, 37, 22, 17, 38, 18, 46, 13, 26, 33, 31, 36, 40, 32, 42, 34, 45, 47, 30];
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C eq C^s;
C eq C^e;
C eq C^t;


Output: Magma V2.11-2     Mon Aug 23 2004 09:50:44 on modular  [Seed = 3518588586]
   -------------------------------------

false
true
false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 09:51:54 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
WeightDistribution(C);


Output: Magma V2.11-2     Mon Aug 23 2004 09:51:52 on modular  [Seed = 3900727263]
   -------------------------------------

[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 1.999 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:00:16 2004

Input: C:=LenearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
PermutationGroup(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:00:16 on modular  [Seed = 2263760825]
   -------------------------------------


>> C:=LenearCode<GF(2), 24 |
                ^
User error: bad syntax

>> [0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
                                                    ^
User error: bad syntax

>> PermutationGroup(C);
                    ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:00:28 2004

Input: C:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
PermutationGroup(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:00:28 on modular  [Seed = 2650088622]
   -------------------------------------

Permutation group acting on a set of cardinality 24
Order = 138240 = 2^10 * 3^3 * 5
    (5, 13, 6)(7, 14, 20)(8, 17, 19)(9, 21, 22)(10, 11, 12)(15, 23, 16)
    (6, 13)(7, 10)(11, 20)(12, 14)(15, 23)(17, 19)(18, 24)(21, 22)
    (4, 24, 18)(5, 14, 12)(6, 7, 11)(8, 19, 17)(10, 13, 20)(15, 23, 16)
    (3, 12, 5)(4, 18, 24)(6, 10, 19)(7, 8, 23)(11, 15, 13)(16, 17, 20)
    (1, 3)(4, 18)(5, 10)(6, 12)(8, 21)(9, 19)(11, 13)(17, 22)
    (2, 4)(3, 17)(5, 12)(6, 7)(9, 22)(10, 23)(11, 14)(16, 20)
    (2, 6)(4, 23)(5, 15)(7, 11)(10, 14)(12, 24)(13, 16)(18, 20)

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:01:19 2004

Input: C:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
ConjugacyClasses(PermutationGroup(C));


Output: Magma V2.11-2     Mon Aug 23 2004 10:01:18 on modular  [Seed = 2499554677]
   -------------------------------------

Conjugacy Classes
-----------------
[1]     Order 1       Length 1      
        Rep Id($)

[2]     Order 2       Length 18     
        Rep (1, 22)(2, 4)(3, 17)(5, 16)(6, 20)(7, 10)(8, 19)(9, 21)(11, 15)(12, 
            23)(13, 14)(18, 24)

[3]     Order 2       Length 45     
        Rep (3, 8)(5, 16)(6, 12)(7, 10)(11, 15)(13, 14)(17, 19)(20, 23)

[4]     Order 2       Length 180    
        Rep (1, 2)(3, 16)(4, 9)(5, 8)(7, 17)(10, 19)(18, 21)(22, 24)

[5]     Order 2       Length 360    
        Rep (1, 2)(3, 5)(4, 9)(6, 14)(7, 17)(8, 16)(10, 19)(11, 23)(12, 13)(15, 
            20)(18, 22)(21, 24)

[6]     Order 2       Length 360    
        Rep (1, 24)(2, 21)(4, 22)(5, 16)(6, 12)(9, 18)(11, 15)(17, 19)

[7]     Order 2       Length 540    
        Rep (1, 2)(3, 5)(4, 9)(6, 12)(7, 19)(8, 16)(10, 17)(11, 15)(13, 14)(18, 
            21)(20, 23)(22, 24)

[8]     Order 3       Length 128    
        Rep (4, 18, 24)(5, 10, 7)(6, 12, 20)(8, 19, 17)(9, 21, 22)(11, 14, 13)

[9]     Order 3       Length 1920   
        Rep (1, 4, 17)(2, 19, 9)(3, 22, 18)(6, 12, 23)(8, 21, 24)(11, 14, 13)

[10]    Order 3       Length 1920   
        Rep (1, 4, 8)(2, 17, 9)(3, 22, 18)(5, 20, 15)(6, 13, 7)(10, 23, 11)(12, 
            14, 16)(19, 21, 24)

[11]    Order 4       Length 360    
        Rep (1, 2)(3, 19, 8, 17)(4, 9)(5, 7, 16, 10)(6, 20, 12, 23)(11, 13, 15, 
            14)(18, 22)(21, 24)

[12]    Order 4       Length 1080   
        Rep (1, 4, 9, 2)(3, 7)(5, 17)(6, 14, 12, 13)(8, 10)(11, 20, 15, 23)(16, 
            19)(18, 22, 24, 21)

[13]    Order 4       Length 1080   
        Rep (1, 2, 22, 24)(3, 10, 17, 5)(4, 21, 18, 9)(6, 20)(7, 19, 16, 8)(12, 
            23)

[14]    Order 4       Length 1080   
        Rep (1, 4, 21, 24)(2, 22, 18, 9)(3, 7, 19, 5)(6, 12)(8, 10, 17, 16)(11, 
            14)(13, 15)(20, 23)

[15]    Order 4       Length 1440   
        Rep (1, 2, 22, 18)(3, 10, 19, 5)(4, 21, 24, 9)(6, 13, 20, 11)(7, 17, 16,
            8)(12, 14, 23, 15)

[16]    Order 4       Length 1440   
        Rep (1, 2, 3, 16)(4, 8, 5, 9)(6, 13)(7, 22, 24, 17)(10, 21, 18, 19)(11, 
            12)(14, 20)(15, 23)

[17]    Order 4       Length 2160   
        Rep (1, 4, 9, 2)(3, 8)(6, 23, 12, 20)(7, 10)(11, 13, 15, 14)(18, 22, 24,
            21)

[18]    Order 4       Length 4320   
        Rep (1, 2, 8, 16)(3, 5, 9, 4)(6, 12, 23, 20)(7, 21, 24, 17)(10, 22, 18, 
            19)(11, 13, 14, 15)

[19]    Order 4       Length 4320   
        Rep (1, 4, 19, 16)(2, 17, 5, 9)(3, 10, 21, 24)(6, 13, 12, 11)(7, 22, 18,
            8)(14, 23, 15, 20)

[20]    Order 4       Length 4320   
        Rep (1, 2, 3, 16)(4, 8, 5, 9)(7, 21, 24, 19)(10, 22, 18, 17)(11, 14)(12,
            20)

[21]    Order 5       Length 2304   
        Rep (1, 2, 3, 16, 23)(4, 8, 7, 20, 22)(5, 6, 9, 18, 19)(10, 12, 21, 24, 
            17)

[22]    Order 6       Length 5760   
        Rep (1, 2, 3, 22, 24, 8)(4, 19, 21, 18, 17, 9)(5, 23, 11, 16, 6, 13)(7, 
            12, 14, 10, 20, 15)

[23]    Order 6       Length 5760   
        Rep (1, 2, 3, 22, 24, 17)(4, 8, 21, 18, 19, 9)(5, 10)(6, 12, 23)(7, 
            16)(11, 13, 15)

[24]    Order 6       Length 5760   
        Rep (1, 2)(3, 10, 8, 16, 19, 5)(4, 21, 24, 9, 18, 22)(6, 20, 23)(7, 
            17)(11, 15, 14)

[25]    Order 6       Length 11520  
        Rep (1, 2, 3, 16, 23, 15)(4, 17, 7, 6, 14, 9)(5, 20, 13, 22, 18, 19)(8, 
            10, 12, 11, 21, 24)

[26]    Order 6       Length 11520  
        Rep (1, 2, 3, 22, 18, 8)(4, 19, 9)(5, 23, 7, 20, 16, 6)(10, 12)(11, 
            15)(17, 21, 24)

[27]    Order 8       Length 8640   
        Rep (1, 4, 17, 5, 9, 2, 19, 16)(3, 7, 21, 18, 8, 10, 22, 24)(11, 13, 14,
            15)(12, 20)

[28]    Order 10      Length 6912   
        Rep (1, 2, 8, 10, 6, 9, 18, 17, 7, 23)(3, 5, 12, 21, 24, 19, 16, 20, 22,
            4)(11, 15)(13, 14)

[29]    Order 12      Length 11520  
        Rep (1, 24, 8, 21, 2, 19, 22, 4, 3, 9, 18, 17)(5, 6, 10, 20, 7, 12)(11, 
            13, 15, 14)(16, 23)

[30]    Order 12      Length 11520  
        Rep (1, 2, 3, 16)(4, 19, 7, 9, 18, 17, 5, 21, 24, 8, 10, 22)(6, 11, 20, 
            13, 12, 14)(15, 23)

[31]    Order 12      Length 11520  
        Rep (1, 18, 17, 16, 6, 14, 9, 24, 3, 7, 23, 15)(2, 8, 5, 12, 11, 21, 4, 
            19, 10, 20, 13, 22)

[32]    Order 15      Length 9216   
        Rep (1, 2, 3, 16, 23)(4, 17, 5, 20, 21, 18, 8, 10, 6, 22, 24, 19, 7, 12,
            9)(11, 13, 14)

[33]    Order 15      Length 9216   
        Rep (1, 2, 3, 16, 23)(4, 19, 10, 20, 9, 24, 8, 5, 12, 22, 18, 17, 7, 6, 
            21)(11, 14, 13)



Total time: 0.610 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:04:52 2004

Input: C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
PermutationGroup(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:04:32 on modular  [Seed = 2798526105]
   -------------------------------------



************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:14:54 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>
C0 eq C0^e1;
C0 eq C0^e2;
C0 eq C0^e3;


Output: Magma V2.11-2     Mon Aug 23 2004 10:14:53 on modular  [Seed = 3034320422]
   -------------------------------------


>> e3:=:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 2
       ^
User error: bad syntax

>>         48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 
                     ^
User error: bad syntax

>>         38, 36, 21, 35, 42, 28, 7, 16);
                                        ^
User error: bad syntax

>> C0 eq C0^e1;
   ^
User error: bad syntax

>> C0 eq C0^e2;
   ^
User error: Identifier 'C0' has not been declared or assigned

>> C0 eq C0^e3;
   ^
User error: Identifier 'C0' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:15:08 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>
C0 eq C0^e1;
C0 eq C0^e2;
C0 eq C0^e3;


Output: Magma V2.11-2     Mon Aug 23 2004 10:15:08 on modular  [Seed = 1294333935]
   -------------------------------------


>> C0 eq C0^e1;
   ^
User error: bad syntax

>> C0 eq C0^e2;
   ^
User error: Identifier 'C0' has not been declared or assigned

>> C0 eq C0^e3;
   ^
User error: Identifier 'C0' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:16:16 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0 eq C0^e;
C0 eq C0^e1;
C0 eq C0^e2;
C0 eq C0^e3;


Output: Magma V2.11-2     Mon Aug 23 2004 10:16:16 on modular  [Seed = 1110114108]
   -------------------------------------

true
false
false
false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:22:26 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C0 eq C0^e;
C0 eq C0^e1;
C0 eq C0^e2;
C0 eq C0^e3;


Output: Magma V2.11-2     Mon Aug 23 2004 10:22:25 on modular  [Seed = 1695406474]
   -------------------------------------

true
true
true
true

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:23:18 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C0 eq C0^e;
C0 eq C0^e1;
C0 eq C0^e2;
C0 eq C0^e3;
G:=sub<Sym(48)| e1, e2,e3>;


Output: Magma V2.11-2     Mon Aug 23 2004 10:23:17 on modular  [Seed = 2014364899]
   -------------------------------------

true
true
true
true

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:23:35 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C0 eq C0^e;
C0 eq C0^e1;
C0 eq C0^e2;
C0 eq C0^e3;
G:=sub<Sym(48)| e1, e2,e3>;
G;

Output: Magma V2.11-2     Mon Aug 23 2004 10:23:34 on modular  [Seed = 1880673496]
   -------------------------------------

true
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14, 
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31, 
        39)(34, 46)(36, 41)(37, 47)(40, 44)
    (2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 30,
        35, 8, 20, 47, 41, 18, 16, 11)
    (3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37, 
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:30:30 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M:=GeneratorMatrix(C0);
C:=LinearCode(HorizontalJoin([ M, M^e1, M^e2, M^e3]);
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:30:30 on modular  [Seed = 124762575]
   -------------------------------------


>> C:=LinearCode(HorizontalJoin([ M, M^e1, M^e2, M^e3]);
                                                       ^
User error: bad syntax

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:32:22 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M:=GeneratorMatrix(C0);
C:=LinearCode(VerticalJoin([ M, M^e1, M^e2, M^e3]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:32:21 on modular  [Seed = 477405863]
   -------------------------------------


>> C:=LinearCode(VerticalJoin([ M, M^e1, M^e2, M^e3]));
                                    ^
Runtime error in '^': Cannot apply permutation to this object

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:33:58 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);

Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:33:57 on modular  [Seed = 360600590]
   -------------------------------------


>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:34:25 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(HorizontalJoin([ M0, M1, M2, M3]);
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:34:25 on modular  [Seed = 708930325]
   -------------------------------------


>> C:=LinearCode(HorizontalJoin([ M0, M1, M2, M3]);
                                                  ^
User error: bad syntax

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:34:51 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M1, M2, M3]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:34:51 on modular  [Seed = 575235047]
   -------------------------------------

24

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:35:14 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M1, M2, M3]));
C;


Output: Magma V2.11-2     Mon Aug 23 2004 10:35:13 on modular  [Seed = 978418645]
   -------------------------------------

[48, 24] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1
    1 0 1 1 1 1 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0
    1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0
    0 1 0 1 0 0 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1
    0 1 0 1 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1
    0 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0
    0 1 1 1 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0
    1 1 0 1 0 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1
    0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1
    1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1
    1 1 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0
    0 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0
    0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0
    0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0
    0 1 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0
    0 0 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1
    0 1 1 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0
    1 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1
    1 0 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1
    0 1 0 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0
    1 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1
    1 1 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0
    0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0
    1 0 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1
    1 0 1 1 0 1 0 0]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:35:39 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M1, M2, M3]));
WeightDistribution(C);



Output: Magma V2.11-2     Mon Aug 23 2004 10:35:37 on modular  [Seed = 844723141]
   -------------------------------------

[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 2.000 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:37:52 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
G:=sub<Sym(48) | e1, e2, e3>;
ConjugacyClasses(G);


Output: Magma V2.11-2     Mon Aug 23 2004 10:37:51 on modular  [Seed = 3416296378]
   -------------------------------------

Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1081   
        Rep (1, 13)(2, 21)(3, 40)(4, 18)(5, 19)(6, 36)(7, 46)(8, 11)(9, 43)(10, 
            23)(12, 35)(14, 45)(15, 41)(16, 31)(17, 47)(20, 30)(22, 28)(24, 
            44)(25, 34)(26, 39)(27, 48)(29, 37)(32, 42)(33, 38)

[3]     Order 3       Length 2162   
        Rep (1, 22, 18)(2, 47, 19)(3, 25, 17)(4, 26, 12)(5, 24, 9)(6, 38, 29)(7,
            21, 13)(8, 23, 28)(10, 30, 33)(11, 20, 31)(14, 34, 48)(15, 41, 
            42)(16, 35, 37)(27, 39, 46)(32, 36, 43)(40, 45, 44)

[4]     Order 4       Length 2162   
        Rep (1, 3, 13, 40)(2, 8, 21, 11)(4, 7, 18, 46)(5, 27, 19, 48)(6, 24, 36,
            44)(9, 33, 43, 38)(10, 17, 23, 47)(12, 34, 35, 25)(14, 31, 45, 
            16)(15, 42, 41, 32)(20, 39, 30, 26)(22, 29, 28, 37)

[5]     Order 6       Length 2162   
        Rep (1, 2, 46, 23, 3, 4)(5, 43, 48, 8, 38, 47)(6, 36, 14, 19, 10, 26)(7,
            18, 45, 25, 20, 41)(9, 33, 29, 34, 30, 24)(11, 13, 44, 31, 16, 
            35)(12, 27, 28, 15, 32, 17)(21, 22, 37, 42, 40, 39)

[6]     Order 8       Length 2162   
        Rep (1, 31, 40, 14, 13, 16, 3, 45)(2, 34, 11, 12, 21, 25, 8, 35)(4, 41, 
            46, 42, 18, 15, 7, 32)(5, 24, 48, 6, 19, 44, 27, 36)(9, 28, 38, 29, 
            43, 22, 33, 37)(10, 20, 47, 26, 23, 30, 17, 39)

[7]     Order 8       Length 2162   
        Rep (1, 14, 3, 31, 13, 45, 40, 16)(2, 12, 8, 34, 21, 35, 11, 25)(4, 42, 
            7, 41, 18, 32, 46, 15)(5, 6, 27, 24, 19, 36, 48, 44)(9, 29, 33, 28, 
            43, 37, 38, 22)(10, 26, 17, 20, 23, 39, 47, 30)

[8]     Order 12      Length 2162   
        Rep (1, 37, 2, 42, 46, 40, 23, 39, 3, 21, 4, 22)(5, 32, 43, 17, 48, 12, 
            8, 27, 38, 28, 47, 15)(6, 9, 36, 33, 14, 29, 19, 34, 10, 30, 26, 
            24)(7, 31, 18, 16, 45, 35, 25, 11, 20, 13, 41, 44)

[9]     Order 12      Length 2162   
        Rep (1, 40, 4, 42, 3, 37, 23, 22, 46, 21, 2, 39)(5, 12, 47, 17, 38, 32, 
            8, 15, 48, 28, 43, 27)(6, 29, 26, 33, 10, 9, 19, 24, 14, 30, 36, 
            34)(7, 35, 41, 16, 20, 31, 25, 44, 45, 13, 18, 11)

[10]    Order 23      Length 2256   
        Rep (1, 30, 44, 3, 29, 8, 48, 25, 23, 9, 41, 26, 40, 11, 16, 6, 39, 7, 
            46, 24, 45, 15, 28)(2, 13, 36, 18, 20, 42, 31, 33, 17, 27, 43, 14, 
            21, 22, 47, 35, 12, 19, 10, 37, 32, 38, 5)

[11]    Order 23      Length 2256   
        Rep (1, 41, 45, 25, 7, 29, 16, 30, 26, 15, 23, 46, 8, 6, 44, 40, 28, 9, 
            24, 48, 39, 3, 11)(2, 43, 32, 33, 19, 20, 47, 13, 14, 38, 17, 10, 
            42, 35, 36, 21, 5, 27, 37, 31, 12, 18, 22)

[12]    Order 23      Length 2256   
        Rep (1, 16, 8, 24, 41, 30, 6, 48, 45, 26, 44, 39, 25, 15, 40, 3, 7, 23, 
            28, 11, 29, 46, 9)(2, 47, 42, 37, 43, 13, 35, 31, 32, 14, 36, 12, 
            33, 38, 21, 18, 19, 17, 5, 22, 20, 10, 27)

[13]    Order 23      Length 2256   
        Rep (1, 6, 25, 28, 16, 48, 15, 11, 8, 45, 40, 29, 24, 26, 3, 46, 41, 44,
            7, 9, 30, 39, 23)(2, 35, 33, 5, 47, 31, 38, 22, 42, 32, 21, 20, 37, 
            14, 18, 10, 43, 36, 19, 27, 13, 12, 17)

[14]    Order 23      Length 2256   
        Rep (1, 48, 40, 46, 30, 25, 11, 24, 44, 23, 16, 45, 3, 9, 6, 15, 29, 41,
            39, 28, 8, 26, 7)(2, 31, 21, 10, 13, 33, 22, 37, 36, 17, 47, 32, 18,
            27, 35, 38, 20, 43, 12, 5, 42, 14, 19)

[15]    Order 23      Length 2256   
        Rep (1, 45, 7, 16, 26, 23, 8, 44, 28, 24, 39, 11, 41, 25, 29, 30, 15, 
            46, 6, 40, 9, 48, 3)(2, 32, 19, 47, 14, 17, 42, 36, 5, 37, 12, 22, 
            43, 33, 20, 13, 38, 10, 35, 21, 27, 31, 18)

[16]    Order 23      Length 2256   
        Rep (1, 26, 28, 41, 15, 9, 45, 23, 24, 25, 46, 48, 7, 8, 39, 29, 6, 3, 
            16, 44, 11, 30, 40)(2, 14, 5, 43, 38, 27, 32, 17, 37, 33, 10, 31, 
            19, 42, 12, 20, 35, 18, 47, 36, 22, 13, 21)

[17]    Order 23      Length 2256   
        Rep (1, 44, 29, 48, 23, 41, 40, 16, 39, 46, 45, 28, 30, 3, 8, 25, 9, 26,
            11, 6, 7, 24, 15)(2, 36, 20, 31, 17, 43, 21, 47, 12, 10, 32, 5, 13, 
            18, 42, 33, 27, 14, 22, 35, 19, 37, 38)

[18]    Order 23      Length 2256   
        Rep (1, 39, 9, 44, 46, 26, 29, 45, 11, 48, 28, 6, 23, 30, 7, 41, 3, 24, 
            40, 8, 15, 16, 25)(2, 12, 27, 36, 10, 14, 20, 32, 22, 31, 5, 35, 17,
            13, 19, 43, 18, 37, 21, 42, 38, 47, 33)

[19]    Order 23      Length 2256   
        Rep (1, 8, 41, 6, 45, 44, 25, 40, 7, 28, 29, 9, 16, 24, 30, 48, 26, 39, 
            15, 3, 23, 11, 46)(2, 42, 43, 35, 32, 36, 33, 21, 19, 5, 20, 27, 47,
            37, 13, 31, 14, 12, 38, 18, 17, 22, 10)

[20]    Order 23      Length 2256   
        Rep (1, 24, 6, 26, 25, 3, 28, 46, 16, 41, 48, 44, 15, 7, 11, 9, 8, 30, 
            45, 39, 40, 23, 29)(2, 37, 35, 14, 33, 18, 5, 10, 47, 43, 31, 36, 
            38, 19, 22, 27, 42, 13, 32, 12, 21, 17, 20)

[21]    Order 24      Length 2162   
        Rep (1, 6, 37, 9, 2, 36, 42, 33, 46, 14, 40, 29, 23, 19, 39, 34, 3, 10, 
            21, 30, 4, 26, 22, 24)(5, 45, 32, 35, 43, 25, 17, 11, 48, 20, 12, 
            13, 8, 41, 27, 44, 38, 7, 28, 31, 47, 18, 15, 16)

[22]    Order 24      Length 2162   
        Rep (1, 36, 40, 34, 4, 6, 42, 29, 3, 26, 37, 33, 23, 10, 22, 9, 46, 19, 
            21, 24, 2, 14, 39, 30)(5, 25, 12, 44, 47, 45, 17, 13, 38, 18, 32, 
            11, 8, 7, 15, 35, 48, 41, 28, 16, 43, 20, 27, 31)

[23]    Order 24      Length 2162   
        Rep (1, 33, 39, 26, 2, 29, 21, 6, 46, 34, 22, 36, 23, 30, 37, 14, 3, 24,
            42, 19, 4, 9, 40, 10)(5, 11, 27, 18, 43, 13, 28, 45, 48, 44, 15, 25,
            8, 31, 32, 20, 38, 16, 17, 41, 47, 35, 12, 7)

[24]    Order 24      Length 2162   
        Rep (1, 29, 22, 14, 4, 33, 21, 36, 3, 9, 39, 6, 23, 24, 40, 26, 46, 30, 
            42, 10, 2, 34, 37, 19)(5, 13, 15, 20, 47, 11, 28, 25, 38, 35, 27, 
            45, 8, 16, 12, 18, 48, 31, 17, 7, 43, 44, 32, 41)

[25]    Order 47      Length 1104   
        Rep (1, 16, 22, 30, 31, 48, 15, 4, 5, 34, 45, 40, 35, 7, 17, 29, 46, 32,
            42, 27, 44, 23, 3, 8, 36, 28, 2, 33, 20, 25, 10, 14, 43, 18, 26, 19,
            47, 38, 24, 37, 11, 6, 41, 39, 21, 12, 13)

[26]    Order 47      Length 1104   
        Rep (1, 48, 45, 29, 44, 28, 10, 19, 11, 12, 30, 5, 7, 42, 8, 20, 18, 24,
            39, 16, 15, 40, 46, 23, 2, 14, 47, 6, 13, 31, 34, 17, 27, 36, 25, 
            26, 37, 21, 22, 4, 35, 32, 3, 33, 43, 38, 41)



Total time: 0.630 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:41:31 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
WeightDistribution(C);

Output: Magma V2.11-2     Mon Aug 23 2004 10:41:29 on modular  [Seed = 3934366141]
   -------------------------------------

[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 2.010 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:42:14 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
<Length(G),Dimenstion(C)>;
WeightDistribution(C);

Output: Magma V2.11-2     Mon Aug 23 2004 10:42:12 on modular  [Seed = 3800670696]
   -------------------------------------


>> <Length(G),Dimenstion(C)>;
           ^
User error: Identifier 'G' has not been declared or assigned
[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 2.009 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:42:35 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
<Length(C),Dimenstion(C)>;
WeightDistribution(C);

Output: Magma V2.11-2     Mon Aug 23 2004 10:42:33 on modular  [Seed = 4203854317]
   -------------------------------------


>> <Length(C),Dimenstion(C)>;
              ^
User error: Identifier 'Dimenstion' has not been declared or assigned
[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 2.020 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:43:06 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimenstion(C);
WeightDistribution(C);

Output: Magma V2.11-2     Mon Aug 23 2004 10:43:04 on modular  [Seed = 4070158788]
   -------------------------------------


>> Dimenstion(C);
   ^
User error: Identifier 'Dimenstion' has not been declared or assigned
[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 1.990 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:43:36 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
WeightDistribution(C);

Output: Magma V2.11-2     Mon Aug 23 2004 10:43:34 on modular  [Seed = 2346764371]
   -------------------------------------

24
[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 1.990 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:44:43 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
WeightDistribution(C);
Order(e2);
Order(e3);


Output: Magma V2.11-2     Mon Aug 23 2004 10:44:40 on modular  [Seed = 2781799987]
   -------------------------------------

24
[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]
23
23

Total time: 1.990 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:45:30 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2]));
Dimension(C);
WeightDistribution(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:45:28 on modular  [Seed = 1479744001]
   -------------------------------------

23
[ <0, 1>, <12, 10672>, <16, 292215>, <20, 2011856>, <24, 3759120>, <28, 
2011856>, <32, 292215>, <36, 10672>, <48, 1> ]

Total time: 1.270 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:45:48 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M3]));
Dimension(C);
WeightDistribution(C);


Output: Magma V2.11-2     Mon Aug 23 2004 10:45:46 on modular  [Seed = 1177355277]
   -------------------------------------

23
[ <0, 1>, <12, 10672>, <16, 292215>, <20, 2011856>, <24, 3759120>, <28, 
2011856>, <32, 292215>, <36, 10672>, <48, 1> ]

Total time: 1.310 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:48:57 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1]>;
M0:=GeneratorMatrix(C0);
M1:=GeneratorMatrix(C0^e1);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
G:=sub<Sym(48)|e1,e2,e3>;
CompositionFactors(G);

Output: Magma V2.11-2     Mon Aug 23 2004 10:48:56 on modular  [Seed = 1761749984]
   -------------------------------------

    G
    |  A(1, 47)               = L(2, 47)
    1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:57:27 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
0^e3);

G:=sub<Sym(48)|e1,e2,e3> meet sub<Sym(48)| (1,2), (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)>;
G;
CompositionFactors(G);

Output: Magma V2.11-2     Mon Aug 23 2004 10:57:26 on modular  [Seed = 377311889]
   -------------------------------------


>> 0^e3);
       ^
User error: bad syntax
Permutation group G acting on a set of cardinality 48
Order = 1
    Empty

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:57:45 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);

G:=sub<Sym(48)|e1,e2,e3> meet sub<Sym(48)| (1,2), (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)>;
G;
CompositionFactors(G);

Output: Magma V2.11-2     Mon Aug 23 2004 10:57:45 on modular  [Seed = 511007398]
   -------------------------------------

Permutation group G acting on a set of cardinality 48
Order = 1
    Empty

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 10:59:22 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);

G:=sub<Sym(48)|e1,e2,e3> meet sub<Sym(48)| (1,2)(25,26), 
(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
G;
CompositionFactors(G);

Output: Magma V2.11-2     Mon Aug 23 2004 10:59:22 on modular  [Seed = 107823389]
   -------------------------------------

Permutation group G acting on a set of cardinality 48
Order = 1
    Empty

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:03:04 2004

Input: e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);

G:=sub<Sym(48)|e1,e2,e3>;
G2:=sub<Sym(48)| (1,2)(25,26), 
(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
G;
Order(G2);
CompositionFactors(G2);
Order(G meet G2);


Output: Magma V2.11-2     Mon Aug 23 2004 11:03:03 on modular  [Seed = 659317073]
   -------------------------------------

Permutation group G acting on a set of cardinality 48
    (1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14, 
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31, 
        39)(34, 46)(36, 41)(37, 47)(40, 44)
    (2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 30,
        35, 8, 20, 47, 41, 18, 16, 11)
    (3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37, 
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)
620448401733239439360000
    G
    |  Cyclic(2)
    *
    |  Alternating(24)
    1
1

Total time: 0.579 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:05:35 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);

G:=sub<Sym(48)|e1,e2,e3>;
G2:=sub<Sym(48)| e, (1,2)(25,26), 
(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
CompositionFactors(G2);
Order(G meet G2);


Output: Magma V2.11-2     Mon Aug 23 2004 11:05:34 on modular  [Seed = 776300737]
   -------------------------------------


>> G:=sub<Sym(48)|e1,e2,e3>;
                  ^
User error: Identifier 'e1' has not been declared or assigned
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Alternating(24)
    1

>> Order(G meet G2);
         ^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:06:17 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
G:=sub<Sym(48)|e1,e2,e3>;
G2:=sub<Sym(48)| e, (1,2)(25,26), 
(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
CompositionFactors(G2);
Order(G meet G2);


Output: Magma V2.11-2     Mon Aug 23 2004 11:06:16 on modular  [Seed = 3635650145]
   -------------------------------------

    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Alternating(24)
    1
2

Total time: 0.579 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:07:00 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
G:=sub<Sym(48)|e1,e2,e3>;
G2:=sub<Sym(48)| e1, (1,2)(25,26), 
(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
CompositionFactors(G2);
Order(G meet G2);


Output: Magma V2.11-2     Mon Aug 23 2004 11:06:59 on modular  [Seed = 3232467330]
   -------------------------------------

    G
    |  Alternating(48)
    1
51888

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:08:03 2004

Input: e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e1:=Sym(48)!(1, 2)(3, 5)(4, 16)(6, 29)(7, 8)(9, 21)(10, 23)(11, 26)(12, 38)(13, 32)(14,
        35)(15, 24)(17, 33)(18, 27)(19, 30)(20, 42)(22, 48)(25, 45)(28, 43)(31,
        39)(34, 46)(36, 41)(37, 47)(40, 44);
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16);
G:=sub<Sym(48)|e,e2,e3>;
G2:=sub<Sym(48)| e, (1,2)(25,26), 
(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
CompositionFactors(G2);
Order(G meet G2);


Output: Magma V2.11-2     Mon Aug 23 2004 11:08:03 on modular  [Seed = 3399582664]
   -------------------------------------

    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Alternating(24)
    1
2

Total time: 0.579 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:17:13 2004

Input: f :=Sym(48)!(11,12,13)(35,36,37)(13,37);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f eq C;
C0 eq C^f;


Output: Magma V2.11-2     Mon Aug 23 2004 11:17:12 on modular  [Seed = 3985024708]
   -------------------------------------

false
false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:17:38 2004

Input: f :=Sym(48)!(11,12,13)(35,36,37)(13,37);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f;



Output: Magma V2.11-2     Mon Aug 23 2004 11:17:37 on modular  [Seed = 2499796820]
   -------------------------------------

[48, 24] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1
    1 1 1 1 1 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0
    1 1 0 1 0 0 1 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1
    1 1 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1
    0 1 0 1 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1
    0 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1
    1 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1
    0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0
    1 1 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1
    1 0 0 1 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1
    1 1 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0
    0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1
    1 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1
    1 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1
    1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1
    1 1 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0
    1 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1
    0 0 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0
    0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0
    1 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1
    0 0 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0
    0 1 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1
    1 1 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0
    0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0
    1 0 1 1 0 1 0 1]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:19:06 2004

Input: f :=Sym(48)!(11,12,13)(35,36,37);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f eq C;
C0 eq C^f;


Output: Magma V2.11-2     Mon Aug 23 2004 11:19:05 on modular  [Seed = 2313339441]
   -------------------------------------

false
false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:21:03 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f eq C;
C0 eq C^f;


Output: Magma V2.11-2     Mon Aug 23 2004 11:21:02 on modular  [Seed = 2781802410]
   -------------------------------------

false
false

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:22:51 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(22,46);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f eq C;
C0 eq C^f;


Output: Magma V2.11-2     Mon Aug 23 2004 11:22:50 on modular  [Seed = 2898781750]
   -------------------------------------

false
false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:24:00 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f eq C;
C0 eq C^f;


Output: Magma V2.11-2     Mon Aug 23 2004 11:24:00 on modular  [Seed = 1479742744]
   -------------------------------------

false
false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:24:16 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
C0:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,1],
[0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1],
[0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0]>;
C:=LinearCode<GF(2), 48 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0]>;
C0^f eq C;
C0 eq C^f;


Output: Magma V2.11-2     Mon Aug 23 2004 11:24:16 on modular  [Seed = 1076563248]
   -------------------------------------

true
false

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:28:53 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
e2:=f^(-1)*Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11)*f;
e3:=f^(-1)*Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)*f;
D:=LenearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
M1:=GeneratorMatrix(C^e1);
M2:=GeneratorMatrix(C^e2);
M3:=GeneratorMatrix(C^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 11:28:53 on modular  [Seed = 1277624361]
   -------------------------------------


>> D:=LenearCode<GF(2), 24 |
                ^
User error: bad syntax

>> [0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
                                                    ^
User error: bad syntax

>> M:=GeneratorMatrix(D);
                      ^
User error: Identifier 'D' has not been declared or assigned

>> M0:=HorizontalJoin([M, M]);
                       ^
User error: Identifier 'M' has not been declared or assigned

>> M1:=GeneratorMatrix(C^e1);
                       ^
User error: Identifier 'C' has not been declared or assigned

>> M2:=GeneratorMatrix(C^e2);
                       ^
User error: Identifier 'C' has not been declared or assigned

>> M3:=GeneratorMatrix(C^e3);
                       ^
User error: Identifier 'C' has not been declared or assigned

>> C:=LinearCode(VerticalJoin([ M0, M2, M3]));
                                ^
User error: Identifier 'M0' has not been declared or assigned

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:29:13 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
e2:=f^(-1)*Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11)*f;
e3:=f^(-1)*Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)*f;
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
M1:=GeneratorMatrix(C^e1);
M2:=GeneratorMatrix(C^e2);
M3:=GeneratorMatrix(C^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 11:29:12 on modular  [Seed = 1948203116]
   -------------------------------------


>> M1:=GeneratorMatrix(C^e1);
                       ^
User error: Identifier 'C' has not been declared or assigned

>> M2:=GeneratorMatrix(C^e2);
                       ^
User error: Identifier 'C' has not been declared or assigned

>> M3:=GeneratorMatrix(C^e3);
                       ^
User error: Identifier 'C' has not been declared or assigned

>> C:=LinearCode(VerticalJoin([ M0, M2, M3]));
                                    ^
User error: Identifier 'M2' has not been declared or assigned

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:30:39 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
e2:=f^(-1)*Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11)*f;
e3:=f^(-1)*Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)*f;
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C:=LinearCode(M0);
M1:=GeneratorMatrix(C^e1);
M2:=GeneratorMatrix(C^e2);
M3:=GeneratorMatrix(C^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 11:30:38 on modular  [Seed = 2081894578]
   -------------------------------------


>> M1:=GeneratorMatrix(C^e1);
                         ^
User error: Identifier 'e1' has not been declared or assigned
24

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:31:52 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
e2:=f^(-1)*Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11)*f;
e3:=f^(-1)*Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)*f;
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
WeightDistribution(C);


Output: Magma V2.11-2     Mon Aug 23 2004 11:31:50 on modular  [Seed = 1712138960]
   -------------------------------------

24
[ <0, 1>, <12, 17296>, <16, 535095>, <20, 3995376>, <24, 7681680>, <28, 
3995376>, <32, 535095>, <36, 17296>, <48, 1> ]

Total time: 1.999 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:34:52 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=f^(-1)*Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11)*f;
e3:=f^(-1)*Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)*f;
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e, e2, e3>;
C eq C^G;
G;


Output: Magma V2.11-2     Mon Aug 23 2004 11:34:52 on modular  [Seed = 1862541475]
   -------------------------------------

24

>> C eq C^G;
     ^
Runtime error in 'eq': Bad argument types
Argument types given: CodeLinFld, GSetEnum
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:35:48 2004

Input: f :=Sym(48)!(13,12,11)(37,36,35)(24,23,22)(48,47,46)(24,48);
e:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=f^(-1)*Sym(48)!(2, 3, 4, 45, 32, 38, 46, 34, 40, 10, 43, 28, 31, 36, 14, 26, 27, 29, 33, 
        12, 21, 39, 17)(5, 13, 48, 7, 42, 25, 24, 23, 22, 15, 9, 19, 37, 44, 
        30, 35, 8, 20, 47, 41, 18, 16, 11)*f;
e3:=f^(-1)*Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 12, 6, 30, 27, 31, 13, 46, 23, 26, 15, 44, 37,
        48, 45, 33)(5, 17, 25, 22, 47, 40, 24, 11, 10, 34, 32, 39, 18, 19, 29, 
        38, 36, 21, 35, 42, 28, 7, 16)*f;
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e, e2, e3>;
CompositionFactors(G);
G;


Output: Magma V2.11-2     Mon Aug 23 2004 11:35:47 on modular  [Seed = 426923677]
   -------------------------------------

24
    G
    |  A(1, 47)               = L(2, 47)
    1
Permutation group G acting on a set of cardinality 48
Order = 51888 = 2^4 * 3 * 23 * 47
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:39:14 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;



Output: Magma V2.11-2     Mon Aug 23 2004 11:39:13 on modular  [Seed = 241516799]
   -------------------------------------

24

>> G:=sub<Sym(48)|e, e2, e3>;
                  ^
User error: Identifier 'e' has not been declared or assigned
true
true
true

>> G;
   ^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:39:54 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;


Output: Magma V2.11-2     Mon Aug 23 2004 11:39:53 on modular  [Seed = 912095407]
   -------------------------------------

24
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:43:48 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);



Output: Magma V2.11-2     Mon Aug 23 2004 11:43:47 on modular  [Seed = 3569321271]
   -------------------------------------

24
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:52:08 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48),e1>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 11:52:07 on modular  [Seed = 3232469815]
   -------------------------------------

24
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1

>> C2:=Fix(C,sub<Sym(48),e1>);
                           ^
User error: bad syntax

>> Dimension(C2);;
             ^
User error: Identifier 'C2' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:52:37 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e1>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 11:52:36 on modular  [Seed = 3366165341]
   -------------------------------------

24
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1
12

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:53:14 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e2>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 11:53:14 on modular  [Seed = 4070154568]
   -------------------------------------

24
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1
2

Total time: 0.579 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:53:56 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:=LinearCode(VerticalJoin([ M0, M2, M3]));
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e3>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 11:53:55 on modular  [Seed = 4237799103]
   -------------------------------------

24
true
true
true
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1
2

Total time: 0.590 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 11:59:08 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:= C0 cat C^e2 cat C^e3;
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e3>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 11:59:07 on modular  [Seed = 4001741813]
   -------------------------------------


>> C:= C0 cat C^e2 cat C^e3;
              ^
User error: Identifier 'C' has not been declared or assigned

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e1;
   ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e2;
   ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e3;
   ^
User error: Identifier 'C' has not been declared or assigned
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1

>> C2:=Fix(C,sub<Sym(48) | e3>);
           ^
User error: Identifier 'C' has not been declared or assigned

>> Dimension(C2);;
             ^
User error: Identifier 'C2' has not been declared or assigned

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:00:20 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:= &cat[C0, C0^e2, C0^e3];
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e3>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 12:00:19 on modular  [Seed = 2346769992]
   -------------------------------------


>> C:= &cat[C0, C0^e2, C0^e3];
       ^
Runtime error in '&cat': Bad argument types
Argument types given: SeqEnum[CodeLinFld]

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e1;
   ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e2;
   ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e3;
   ^
User error: Identifier 'C' has not been declared or assigned
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1

>> C2:=Fix(C,sub<Sym(48) | e3>);
           ^
User error: Identifier 'C' has not been declared or assigned

>> Dimension(C2);;
             ^
User error: Identifier 'C2' has not been declared or assigned

Total time: 0.580 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:00:52 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:= &cat{C0, C0^e2, C0^e3};
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e3>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 12:00:51 on modular  [Seed = 3017336400]
   -------------------------------------


>> C:= &cat{C0, C0^e2, C0^e3};
       ^
Runtime error in '&cat': Bad argument types
Argument types given: SetEnum[CodeLinFld]

>> Dimension(C);
             ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e1;
   ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e2;
   ^
User error: Identifier 'C' has not been declared or assigned

>> C eq C^e3;
   ^
User error: Identifier 'C' has not been declared or assigned
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1

>> C2:=Fix(C,sub<Sym(48) | e3>);
           ^
User error: Identifier 'C' has not been declared or assigned

>> Dimension(C2);;
             ^
User error: Identifier 'C2' has not been declared or assigned

Total time: 0.579 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:01:15 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
C:= C0 cat C0^e2 cat C0^e3;
Dimension(C);
G:=sub<Sym(48)|e1, e2, e3>;
C eq C^e1;
C eq C^e2;
C eq C^e3;
G;
S24:=sub<Sym(48)| (1,2)(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1)
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);

C2:=Fix(C,sub<Sym(48) | e3>);
Dimension(C2);

Output: Magma V2.11-2     Mon Aug 23 2004 12:01:14 on modular  [Seed = 3168266534]
   -------------------------------------

34

>> C eq C^e1;
         ^
Runtime error in '^': Cannot apply permutation to this object

>> C eq C^e2;
         ^
Runtime error in '^': Cannot apply permutation to this object

>> C eq C^e3;
         ^
Runtime error in '^': Cannot apply permutation to this object
Permutation group G acting on a set of cardinality 48
    (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 
        35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 
        44)(21, 45)(22, 46)(23, 47)(24, 48)
    (2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 
        11, 21, 39, 17)(5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30,
        37, 8, 20, 46, 41, 18, 16, 13)
    (3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 
        47, 45, 33)(5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 
        38, 35, 21, 37, 42, 28, 7, 16)
1

>> C2:=Fix(C,sub<Sym(48) | e3>);
          ^
Runtime error in 'Fix': Arguments 1 and 2 have incompatible degrees

>> Dimension(C2);;
             ^
User error: Identifier 'C2' has not been declared or assigned

Total time: 0.640 seconds, Total memory usage: 3.18MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:08:36 2004

Input: BCH(GF(2),24,1);
BCH(GF(2),24,2);
BCH(GF(2),24,3);


Output: Magma V2.11-2     Mon Aug 23 2004 12:08:36 on modular  [Seed = 2898787192]
   -------------------------------------


>> BCH(GF(2),24,1);
   ^
User error: Identifier 'BCH' has not been declared or assigned

>> BCH(GF(2),24,2);
   ^
User error: Identifier 'BCH' has not been declared or assigned

>> BCH(GF(2),24,3);
   ^
User error: Identifier 'BCH' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:08:56 2004

Input: BCHCode(GF(2),24,1);
BCHCode(GF(2),24,2);
BCHCode(GF(2),24,3);


Output: Magma V2.11-2     Mon Aug 23 2004 12:08:55 on modular  [Seed = 1463550099]
   -------------------------------------


>> BCHCode(GF(2),24,1);
          ^
Runtime error in 'BCHCode': Order of argument 1 (2) and argument 2 (24) are not 
coprime

>> BCHCode(GF(2),24,2);
          ^
Runtime error in 'BCHCode': Order of argument 1 (2) and argument 2 (24) are not 
coprime

>> BCHCode(GF(2),24,3);
          ^
Runtime error in 'BCHCode': Order of argument 1 (2) and argument 2 (24) are not 
coprime

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:10:57 2004

Input: BCHCode(GF(2),23,1);
BCHCode(GF(2),23,2);
BCHCode(GF(2),23,3);


Output: Magma V2.11-2     Mon Aug 23 2004 12:10:56 on modular  [Seed = 1126700288]
   -------------------------------------

[23, 23, 1] "BCH code (d = 1, b = 1)" Cyclic Linear Code over GF(2)
[23, 12, 7] "BCH code (d = 2, b = 1)" Cyclic Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1]
[23, 12, 7] "BCH code (d = 3, b = 1)" Cyclic Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1]

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:12:13 2004

Input: [ Dimension(BCHCode(GF(2),23,k)) : k in [1..10]];


Output: Magma V2.11-2     Mon Aug 23 2004 12:12:12 on modular  [Seed = 1327765824]
   -------------------------------------

[ 23, 12, 12, 12, 12, 1, 1, 1, 1, 1 ]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:12:39 2004

Input: [ MinimumWeight(BCHCode(GF(2),23,k)) : k in [2..5]];


Output: Magma V2.11-2     Mon Aug 23 2004 12:12:38 on modular  [Seed = 1998332242]
   -------------------------------------

[ 7, 7, 7, 7 ]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:13:00 2004

Input: [ WeightDistribution(BCHCode(GF(2),23,k)) : k in [2..5]];


Output: Magma V2.11-2     Mon Aug 23 2004 12:13:00 on modular  [Seed = 2132027808]
   -------------------------------------

[
    [ <0, 1>, <7, 253>, <8, 506>, <11, 1288>, <12, 1288>, <15, 506>, <16, 253>, 
    <23, 1> ],
    [ <0, 1>, <7, 253>, <8, 506>, <11, 1288>, <12, 1288>, <15, 506>, <16, 253>, 
    <23, 1> ],
    [ <0, 1>, <7, 253>, <8, 506>, <11, 1288>, <12, 1288>, <15, 506>, <16, 253>, 
    <23, 1> ],
    [ <0, 1>, <7, 253>, <8, 506>, <11, 1288>, <12, 1288>, <15, 506>, <16, 253>, 
    <23, 1> ]
]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:26:04 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
G:=sub<Sym(48)|e1, e2, e3>;
ConjugacyClasses(G);


Output: Magma V2.11-2     Mon Aug 23 2004 12:26:03 on modular  [Seed = 190861507]
   -------------------------------------

Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1081   
        Rep (1, 24)(2, 47)(3, 42)(4, 20)(5, 45)(6, 7)(8, 28)(9, 13)(10, 23)(11, 
            21)(12, 37)(14, 39)(15, 34)(16, 27)(17, 43)(18, 32)(19, 46)(22, 
            26)(25, 31)(29, 40)(30, 41)(33, 35)(36, 44)(38, 48)

[3]     Order 3       Length 2162   
        Rep (1, 20, 10)(2, 32, 41)(3, 43, 46)(4, 23, 24)(5, 26, 6)(7, 45, 22)(8,
            44, 37)(9, 38, 39)(11, 27, 29)(12, 28, 36)(13, 48, 14)(15, 35, 
            25)(16, 40, 21)(17, 19, 42)(18, 30, 47)(31, 34, 33)

[4]     Order 4       Length 2162   
        Rep (1, 27, 24, 16)(2, 42, 47, 3)(4, 40, 20, 29)(5, 36, 45, 44)(6, 28, 
            7, 8)(9, 25, 13, 31)(10, 11, 23, 21)(12, 22, 37, 26)(14, 33, 39, 
            35)(15, 48, 34, 38)(17, 18, 43, 32)(19, 30, 46, 41)

[5]     Order 6       Length 2162   
        Rep (1, 23, 20, 24, 10, 4)(2, 30, 32, 47, 41, 18)(3, 19, 43, 42, 46, 
            17)(5, 7, 26, 45, 6, 22)(8, 12, 44, 28, 37, 36)(9, 14, 38, 13, 39, 
            48)(11, 40, 27, 21, 29, 16)(15, 31, 35, 34, 25, 33)

[6]     Order 8       Length 2162   
        Rep (1, 42, 16, 2, 24, 3, 27, 47)(4, 43, 29, 18, 20, 17, 40, 32)(5, 33, 
            44, 14, 45, 35, 36, 39)(6, 34, 8, 48, 7, 15, 28, 38)(9, 26, 31, 37, 
            13, 22, 25, 12)(10, 19, 21, 41, 23, 46, 11, 30)

[7]     Order 8       Length 2162   
        Rep (1, 2, 27, 42, 24, 47, 16, 3)(4, 18, 40, 43, 20, 32, 29, 17)(5, 14, 
            36, 33, 45, 39, 44, 35)(6, 48, 28, 34, 7, 38, 8, 15)(9, 37, 25, 26, 
            13, 12, 31, 22)(10, 41, 11, 19, 23, 30, 21, 46)

[8]     Order 12      Length 2162   
        Rep (1, 40, 23, 27, 20, 21, 24, 29, 10, 16, 4, 11)(2, 43, 30, 42, 32, 
            46, 47, 17, 41, 3, 18, 19)(5, 37, 7, 36, 26, 8, 45, 12, 6, 44, 22, 
            28)(9, 34, 14, 25, 38, 33, 13, 15, 39, 31, 48, 35)

[9]     Order 12      Length 2162   
        Rep (1, 21, 4, 27, 10, 40, 24, 11, 20, 16, 23, 29)(2, 46, 18, 42, 41, 
            43, 47, 19, 32, 3, 30, 17)(5, 8, 22, 36, 6, 37, 45, 28, 26, 44, 7, 
            12)(9, 33, 48, 25, 39, 34, 13, 35, 38, 31, 14, 15)

[10]    Order 23      Length 2256   
        Rep (1, 27, 31, 34, 37, 36, 39, 41, 13, 29, 23, 7, 40, 45, 17, 6, 21, 
            48, 26, 15, 2, 9, 33)(4, 22, 8, 46, 25, 42, 16, 11, 18, 30, 44, 5, 
            47, 19, 35, 32, 10, 43, 12, 20, 38, 24, 28)

[11]    Order 23      Length 2256   
        Rep (1, 23, 2, 41, 48, 37, 17, 27, 7, 9, 13, 26, 36, 6, 31, 40, 33, 29, 
            15, 39, 21, 34, 45)(4, 44, 38, 11, 43, 25, 35, 22, 5, 24, 18, 12, 
            42, 32, 8, 47, 28, 30, 20, 16, 10, 46, 19)

[12]    Order 23      Length 2256   
        Rep (1, 17, 36, 15, 23, 27, 6, 39, 2, 7, 31, 21, 41, 9, 40, 34, 48, 13, 
            33, 45, 37, 26, 29)(4, 35, 42, 20, 44, 22, 32, 16, 38, 5, 8, 10, 11,
            24, 47, 46, 43, 18, 28, 19, 25, 12, 30)

[13]    Order 23      Length 2256   
        Rep (1, 6, 41, 33, 17, 39, 9, 45, 36, 2, 40, 37, 15, 7, 34, 26, 23, 31, 
            48, 29, 27, 21, 13)(4, 32, 11, 28, 35, 16, 24, 19, 42, 38, 47, 25, 
            20, 5, 46, 12, 44, 8, 43, 30, 22, 10, 18)

[14]    Order 23      Length 2256   
        Rep (1, 39, 40, 26, 27, 41, 45, 15, 31, 13, 17, 2, 34, 29, 6, 9, 37, 23,
            21, 33, 36, 7, 48)(4, 16, 47, 12, 22, 11, 19, 20, 8, 18, 35, 38, 46,
            30, 32, 24, 25, 44, 10, 28, 42, 5, 43)

[15]    Order 23      Length 2256   
        Rep (1, 2, 48, 17, 7, 13, 36, 31, 33, 15, 21, 45, 23, 41, 37, 27, 9, 26,
            6, 40, 29, 39, 34)(4, 38, 43, 35, 5, 18, 42, 8, 28, 20, 10, 19, 44, 
            11, 25, 22, 24, 12, 32, 47, 30, 16, 46)

[16]    Order 23      Length 2256   
        Rep (1, 7, 33, 23, 9, 29, 2, 13, 15, 41, 26, 39, 48, 36, 21, 37, 6, 34, 
            17, 31, 45, 27, 40)(4, 5, 28, 44, 24, 30, 38, 18, 20, 11, 12, 16, 
            43, 42, 10, 25, 32, 46, 35, 8, 19, 22, 47)

[17]    Order 23      Length 2256   
        Rep (1, 31, 37, 39, 13, 23, 40, 17, 21, 26, 2, 33, 27, 34, 36, 41, 29, 
            7, 45, 6, 48, 15, 9)(4, 8, 25, 16, 18, 44, 47, 35, 10, 12, 38, 28, 
            22, 46, 42, 11, 30, 5, 19, 32, 43, 20, 24)

[18]    Order 23      Length 2256   
        Rep (1, 21, 29, 31, 26, 7, 37, 2, 45, 39, 33, 6, 13, 27, 48, 23, 34, 15,
            40, 36, 9, 17, 41)(4, 10, 30, 8, 12, 5, 25, 38, 19, 16, 28, 32, 18, 
            22, 43, 44, 46, 20, 47, 42, 24, 35, 11)

[19]    Order 23      Length 2256   
        Rep (1, 36, 23, 6, 2, 31, 41, 40, 48, 33, 37, 29, 17, 15, 27, 39, 7, 21,
            9, 34, 13, 45, 26)(4, 42, 44, 32, 38, 8, 11, 47, 43, 28, 25, 30, 35,
            20, 22, 16, 5, 10, 24, 46, 18, 19, 12)

[20]    Order 23      Length 2256   
        Rep (1, 15, 6, 7, 41, 34, 33, 26, 17, 23, 39, 31, 9, 48, 45, 29, 36, 27,
            2, 21, 40, 13, 37)(4, 20, 32, 5, 11, 46, 28, 12, 35, 44, 16, 8, 24, 
            43, 19, 30, 42, 22, 38, 10, 47, 18, 25)

[21]    Order 24      Length 2162   
        Rep (1, 43, 21, 47, 4, 19, 27, 32, 10, 3, 40, 30, 24, 17, 11, 2, 20, 46,
            16, 18, 23, 42, 29, 41)(5, 25, 8, 39, 22, 34, 36, 13, 6, 35, 37, 38,
            45, 31, 28, 14, 26, 15, 44, 9, 7, 33, 12, 48)

[22]    Order 24      Length 2162   
        Rep (1, 30, 29, 3, 23, 32, 16, 19, 20, 47, 11, 43, 24, 41, 40, 42, 10, 
            18, 27, 46, 4, 2, 21, 17)(5, 38, 12, 35, 7, 13, 44, 34, 26, 39, 28, 
            25, 45, 48, 37, 33, 6, 9, 36, 15, 22, 14, 8, 31)

[23]    Order 24      Length 2162   
        Rep (1, 32, 11, 42, 4, 30, 16, 43, 10, 2, 29, 19, 24, 18, 21, 3, 20, 41,
            27, 17, 23, 47, 40, 46)(5, 13, 28, 33, 22, 38, 44, 25, 6, 14, 12, 
            34, 45, 9, 8, 35, 26, 48, 36, 31, 7, 39, 37, 15)

[24]    Order 24      Length 2162   
        Rep (1, 19, 40, 2, 23, 43, 27, 30, 20, 42, 21, 32, 24, 46, 29, 47, 10, 
            17, 16, 41, 4, 3, 11, 18)(5, 34, 37, 14, 7, 25, 36, 38, 26, 33, 8, 
            13, 45, 15, 12, 39, 6, 31, 44, 48, 22, 35, 28, 9)

[25]    Order 47      Length 1104   
        Rep (1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36)

[26]    Order 47      Length 1104   
        Rep (1, 18, 44, 24, 15, 10, 25, 16, 6, 28, 46, 22, 26, 29, 31, 47, 21, 
            43, 37, 27, 13, 9, 30, 35, 14, 40, 12, 23, 36, 20, 34, 3, 4, 42, 48,
            41, 17, 7, 38, 33, 8, 45, 39, 2, 19, 5, 32)



Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:28:44 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
G:=sub<Sym(48)|e1, e4>;
CompositionFactor(G);


Output: Magma V2.11-2     Mon Aug 23 2004 12:28:44 on modular  [Seed = 844720221]
   -------------------------------------


>> CompositionFactor(G);
   ^
User error: Identifier 'CompositionFactor' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:28:58 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
G:=sub<Sym(48)|e1, e4>;
CompositionFactors(G);


Output: Magma V2.11-2     Mon Aug 23 2004 12:28:58 on modular  [Seed = 978411555]
   -------------------------------------

    G
    |  A(1, 47)               = L(2, 47)
    1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:30:03 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e2:=Sym(48)!(2, 3, 4, 45, 32, 38, 24, 34, 40, 10, 43, 28, 31, 35, 14, 26, 27, 29, 33, 11, 21, 39, 17)
            (5, 12, 47, 7, 42, 25, 23, 22, 48, 15, 9, 19, 36, 44, 30, 37, 8, 20, 46, 41, 18, 16, 13);
e3:=Sym(48)!(3, 4, 8, 43, 20, 14, 9, 41, 11, 6, 30, 27, 31, 12, 24, 22, 26, 15, 44, 36, 47, 45, 33)
            (5, 17, 25, 48, 46, 40, 23, 13, 10, 34, 32, 39, 18, 19, 29, 38, 35, 21, 37, 42, 28, 7, 16);
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M2:=GeneratorMatrix(C0^e2);
M3:=GeneratorMatrix(C0^e3);
M4:=GeneratorMatrix(C0^e4);
C:=LinearCode(VerticalJoin([ M0, M4]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 12:30:02 on modular  [Seed = 575240443]
   -------------------------------------

22

Total time: 0.500 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host rigel2.cyberpass.net. (168.143.113.102)
Time: Mon Aug 23 12:37:59 2004

Input: 0022202323

Output: Magma V2.11-2     Mon Aug 23 2004 12:37:58 on modular  [Seed = 759591192]
   -------------------------------------

22202323

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 12:53:29 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
D:=LinearCode<GF(2), 24 |
[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1]>;
M:=GeneratorMatrix(D);
M0:=HorizontalJoin([M, M]);
C0:=LinearCode(M0);
M4:=GeneratorMatrix(C0^e4);
M5:=GeneratorMatrix(C0^(e4^2));
C:=LinearCode(VerticalJoin([ M0, M4, M5]));
Dimension(C);


Output: Magma V2.11-2     Mon Aug 23 2004 12:53:28 on modular  [Seed = 3900934323]
   -------------------------------------

24

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 19:20:30 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
G:=sub<Sym(48)|e1, e4>;
24:=sub<Sym(48)| (1,2),(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1),
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);


Output: Magma V2.11-2     Mon Aug 23 2004 19:20:25 on modular  [Seed = 3783973646]
   -------------------------------------


>> 24:=sub<Sym(48)| (1,2),(25,26), 
     ^
User error: Illegal left hand side of an assignment statement

>> Order(G meet S24);
                ^
User error: Identifier 'S24' has not been declared or assigned

Total time: 0.750 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 19:21:03 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
G:=sub<Sym(48)|e1, e4>;
Order(G);
S24:=sub<Sym(48)| (1,2),(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1),
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);


Output: Magma V2.11-2     Mon Aug 23 2004 19:21:02 on modular  [Seed = 3917665122]
   -------------------------------------

51888
1

Total time: 0.620 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 19:21:39 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
G:=sub<Sym(48)|e1, e4>;
CompositionFactors(G);
S24:=sub<Sym(48)| (1,2),(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1),
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(G meet S24);


Output: Magma V2.11-2     Mon Aug 23 2004 19:21:39 on modular  [Seed = 2449124551]
   -------------------------------------

    G
    |  A(1, 47)               = L(2, 47)
    1
1

Total time: 0.610 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host 29.41.44.61.ap.yournet.ne.jp. (61.44.41.29)
Time: Mon Aug 23 19:22:16 2004

Input: e1:=Sym(48)![25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 
             1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
e4:=Sym(48)!(1, 27, 38, 46, 20, 18, 13, 33, 22, 34, 44, 9, 8, 26, 3, 24, 30, 45,
            29, 4, 15, 35, 39, 31, 42, 10, 14, 2, 47, 48, 25, 40, 19, 21, 41, 
            16, 12, 5, 43, 17, 6, 23, 32, 37, 7, 28, 36);
G:=sub<Sym(48)|e1, e4>;
CompositionFactors(G);
S24:=sub<Sym(48)| (1,2),(25,26), 
                  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1),
                  (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,25)>;
Order(S24) eq Factorial(24)^2;
Order(G meet S24);


Output: Magma V2.11-2     Mon Aug 23 2004 19:22:15 on modular  [Seed = 2582815979]
   -------------------------------------

    G
    |  A(1, 47)               = L(2, 47)
    1
true
1

Total time: 0.610 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host gcy248128.columbus.rr.com. (204.210.248.128)
Time: Mon Aug 23 19:32:01 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Mon Aug 23 2004 19:32:00 on modular  [Seed = 2397417899]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ip68-99-240-48.ph.ph.cox.net. (68.99.240.48)
Time: Mon Aug 23 21:13:53 2004

Input: 20


Output: Magma V2.11-2     Mon Aug 23 2004 21:13:52 on modular  [Seed = 2549891219]
   -------------------------------------

20

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ip68-99-240-48.ph.ph.cox.net. (68.99.240.48)
Time: Mon Aug 23 21:14:09 2004

Input: (x+y)^2

Output: Magma V2.11-2     Mon Aug 23 2004 21:14:08 on modular  [Seed = 2683586731]
   -------------------------------------


>> (x+y)^2;
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Mon Aug 23 23:58:19 2004

Input: x^54 + x^48 + x^46 + x^41 + x^38 + x^33 + x^32


Output: Magma V2.11-2     Mon Aug 23 2004 23:58:18 on modular  [Seed = 1862570723]
   -------------------------------------


>> x^54 + x^48 + x^46 + x^41 + x^38 + x^33 + x^32
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Mon Aug 23 23:58:39 2004

Input: int x
x^54 + x^48 + x^46 + x^41 + x^38 + x^33 + x^32


Output: Magma V2.11-2     Mon Aug 23 2004 23:58:38 on modular  [Seed = 394062511]
   -------------------------------------


>> int x
       ^
User error: bad syntax

>> x^54 + x^48 + x^46 + x^41 + x^38 + x^33 + x^32
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host isiproxyb.isical.ac.in. (210.212.1.35)
Time: Tue Aug 24 00:56:28 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Tue Aug 24 2004 00:56:19 on modular  [Seed = 2499747761]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host isibrowse.isical.ac.in. (202.54.54.150)
Time: Tue Aug 24 00:57:43 2004

Input: //odd
l:=PolynomialRing(RationalField(),8);
R<f3,f2,Z1,Z2,u1,u0,v1,v0>:=FieldOfFractions(l);

h2:=0;
h1:=0;
h0:=0;
f4:=0;

U1:=u1*Z1^2;
U0:=u0*Z1^2;
V1:=v1*Z1^3*Z2;
V0:=v0*Z1^3*Z2;

z1:=Z1^2;
z2:=Z2^2;

v1t:=h1+2*v1-h2*u1;
v0t:=h0+2*v0-h2*u0;


wi0:=v1^2;
wi1:=u1^2;
wi2:=v1t^2;
wi3:=u1*v1t;
ri:=u0*wi2+v0t*(v0t-wi3);


invi1:=-v1t;
invi0:=v0t-wi3;






//begin new coord, declaration of variables

T1:=U0;
T2:=U1;
T3:=V0;
T4:=V1;
T5:=Z1;
T6:=Z2;
T7:=z1;
T8:=z2;

//G1 & G2
T9:=T4*T4;
T10:=T2*T4;
//
//
//
T10:=-T10;
//
//

//G3 & G4
T11:=T3*T7;
T12:=T9*T1;
T11:=T11+T10;
//
T4:=-T4;
//
//
//

//G5 & G6
T10:=T3*T11;
T13:=T1*T7;
T10:=T10+T12;
//
T9:=-T9;
T13:=-T13;
//
//



printf("r/ri= "); T10/ri;


// corresponding part from affine


wi3:=f3+wi1;
wi4:=2*u0;
ki1:=2*(wi1-f4*u1)+wi3-wi4-h2*v1;
ki0:=u1*(2*wi4-wi3+f4*u1+h2*v1)+f2-wi0-2*f4*u0-h1*v1-h2*v0;


//G7 & G8
T12:=T2*T2;
T15:=T7*T7;
T14:=T12+T13;
//
T13:=-T13;
//
T14:=T14+T14;
//

//G9 & G10
T16:=T15*f3;
T6:=T6*T10;
T16:=T16+T12;
//
//
//
T12:=T13+T13;
//

//G11 & G12
T15:=T15*T7;
T6:=T6*T7;
T14:=T14+T16;
//
T16:=-T16;
//
T12:=T12+T12;
//

//G13 & G14
T15:=T15*f2;
T14:=T8*T14;
T12:=T12+T16;
//
//
//
//
//

//G15 & G16
T12:=T12*T2;
T16:=T14*T4;
T12:=T12+T15;
T2:=T2+1;
//
T16:=-T16;
//
//

//G17 & G18
T8:=T8*T12;
T13:=T13*T16;
T8:=T8+T9;
//
//
//
//
//


printf("k1/ki1= ");T14/ki1;
printf("k0/ki0= ");T8/ki0;



//affine formulae
wi0:=ki0*invi0;
wi1:=ki1*invi1;
si1:=(invi0+invi1)*(ki0+ki1)-wi0-wi1*(1+u1);
si0:=wi0-u0*wi1;

//G19 & G20
T9:=T8*T11;
T16:=T16*T2;
T8:=T8+T14;
//
//
T2:=-T2;
T12:=T4+T11;
T2:=T2+1;

//G21 & G22
T12:=T12*T8;
T14:=T6*T5;
T12:=T12+T16;
T13:=T13+T9;
T4:=-T4;
T9:=-T9;
T14:=T14+T14; //should be T6


//G23 & G24
T11:=T13*T13;
T6:=T6*T6;
T12:=T12+T9;
//
//
T2:=-T2;
//
//


printf("s1/si1= "); T12/si1;
printf("s0/si0= "); T13/si0;

//affine:

wi1:=1/(ri*si1);
wi2:=ri*wi1;
wi3:=si1^2*wi1;
wi4:=ri*wi2;
wi5:=wi4^2;
si0:=si0*wi2;

//G25 & G26
T5:=T7*T12;
T9:=T12*T13;
//
//
//
//
//
//

//G27 & G28
T7:=T5*T5;
T6:=T6*T2;
//
T8:=T1+T2;
//
//T8:=-T8;// ???
//
T6:=T6+T6;

//G29 & G30
T1:=T1*T9;
T12:=T12*T5;
//
T15:=T12+T9;
T1:=-T1;
//
//
T6:=T6+T6;

//G31 & G32
T2:=T2*T12;
T15:=T8*T15;
//
T15:=T1+T15;
T2:=-T2;
T1:=-T1;
//
//

//G33 & G34
T13:=T5*T13;
T10:=T5*T10;
T15:=T15+T2;
T10:=T10+T10;
T13:=-T13;
//T10:=-T10;
T2:=T2+T13;
//

//G35 & G36
T4:=T4*T10;
T3:=T3*T10;
T6:=T4+T6;
T13:=T13+T13;
T4:=-T4;
T15:=-T15;
T6:=T6+T6;
T3:=T1+T3;

//G37 & G38
T3:=T3*T7;
T8:=T14*T14;
T1:=T6+T11;
T16:=T13+T8;
T3:=-T3;
T2:=-T2;
T4:=T1+T4;
T12:=T2+T16;

//G39 & G40
T11:=T12*T1;
T13:=T12*T16;
T3:=T3+T11;
T13:=-T13;
T2:=-T16;
T4:=T4+T15;
//

//G41 
T4:=T4*T7;
//
T4:=T4+T13;
//
T6:=T14;
//
//
//





li2:=u1+si0;
li1:=u1*si0+u0;
li0:=u0*si0;


u0s:=si0^2+wi4*(h2*(si0-u1)+2*v1+h1)+wi5*(2*u1-f4);
u1s:=2*si0+h2*wi4-wi5;


printf("U0S/(u0s*z1s)= "); T1/(u0s*T7);
printf("U1S/(u1s*z1s)= "); T2/(u1s*T7);

printf("Z1^2/(z1)= "); T5^2/T7;
printf("Z2^2/(z2)= "); T6^2/T8;

wi1:=li2-u1s;
wi2:=u1s*wi1+u0s-li1;
v1s:=wi2*wi3-v1-h1+h2*u1s;
wi2:=u0s*wi1-li0;
v0s:=wi2*wi3-v0-h0+h2*u0s;


printf("V1S/(v1s*r*Z1S^3)= ");T4/(v1s*T5*T6*T7);
printf("V0S/(v0s*r*Z1S^3)= ");T3/(v0s*T5*T6*T7);

printf("End of tests, the last four results should evaluate to 1");

Output: Magma V2.11-2     Tue Aug 24 2004 00:57:41 on modular  [Seed = 2633438991]
   -------------------------------------

r/ri= 1/4*Z1^8*Z2^2
k1/ki1= Z1^4*Z2^2
k0/ki0= Z1^6*Z2^2
s1/si1= 1/2*Z1^9*Z2^3
s0/si0= 1/2*Z1^11*Z2^3
U0S/(u0s*z1s)= 1
U1S/(u1s*z1s)= 1
Z1^2/(z1)= 1
Z2^2/(z2)= 1
V1S/(v1s*r*Z1S^3)= 1
V0S/(v0s*r*Z1S^3)= 1
End of tests, the last four results should evaluate to 1
Total time: 0.659 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host baana-pppoes-213-139-167-75.suomi.net. (213.139.167.75)
Time: Tue Aug 24 03:18:22 2004

Input: (x+y)^3

Output: Magma V2.11-2     Tue Aug 24 2004 03:18:21 on modular  [Seed = 4187116316]
   -------------------------------------


>> (x+y)^3;
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host bzq-80-39-126.red.bezeqint.net. (82.80.39.126)
Time: Tue Aug 24 07:48:56 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Tue Aug 24 2004 07:48:55 on modular  [Seed = 3399524602]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:12:57 2004

Input: R<x_0,x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]);
MonomialsOfWeightedDegree(R,1);

Output: Magma V2.11-2     Tue Aug 24 2004 09:12:57 on modular  [Seed = 575167963]
   -------------------------------------

{@
    x_0,
    x
@}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:13:54 2004

Input: R<x_0,x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]);
for i from 1 to 12 do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:13:53 on modular  [Seed = 995181834]
   -------------------------------------


>> for i from 1 to 12 do
         ^
User error: bad syntax

>> MonomialsOfWeightedDegree(R,i);
                               ^
User error: Identifier 'i' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:14:12 2004

Input: R<x_0,x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]);
for i in {1,..,12} do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:14:11 on modular  [Seed = 190936328]
   -------------------------------------


>> for i in {1,..,12} do
               ^
User error: bad syntax

>> MonomialsOfWeightedDegree(R,i);
                               ^
User error: Identifier 'i' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:14:23 2004

Input: R<x_0,x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]);
for i in [1..12] do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:14:22 on modular  [Seed = 343829018]
   -------------------------------------

{@
    x_0,
    x
@}
{@
    x_0^2,
    x_0*x,
    x^2,
    y
@}
{@
    x_0^3,
    x_0^2*x,
    x_0*x^2,
    x_0*y,
    x^3,
    x*y,
    z
@}
{@
    x_0^4,
    x_0^3*x,
    x_0^2*x^2,
    x_0^2*y,
    x_0*x^3,
    x_0*x*y,
    x_0*z,
    x^4,
    x^2*y,
    x*z,
    y^2,
    t,
    B
@}
{@
    x_0^5,
    x_0^4*x,
    x_0^3*x^2,
    x_0^3*y,
    x_0^2*x^3,
    x_0^2*x*y,
    x_0^2*z,
    x_0*x^4,
    x_0*x^2*y,
    x_0*x*z,
    x_0*y^2,
    x_0*t,
    x_0*B,
    x^5,
    x^3*y,
    x^2*z,
    x*y^2,
    x*t,
    x*B,
    y*z,
    u
@}
{@
    x_0^6,
    x_0^5*x,
    x_0^4*x^2,
    x_0^4*y,
    x_0^3*x^3,
    x_0^3*x*y,
    x_0^3*z,
    x_0^2*x^4,
    x_0^2*x^2*y,
    x_0^2*x*z,
    x_0^2*y^2,
    x_0^2*t,
    x_0^2*B,
    x_0*x^5,
    x_0*x^3*y,
    x_0*x^2*z,
    x_0*x*y^2,
    x_0*x*t,
    x_0*x*B,
    x_0*y*z,
    x_0*u,
    x^6,
    x^4*y,
    x^3*z,
    x^2*y^2,
    x^2*t,
    x^2*B,
    x*y*z,
    x*u,
    y^3,
    y*t,
    y*B,
    z^2,
    v
@}
{@
    x_0^7,
    x_0^6*x,
    x_0^5*x^2,
    x_0^5*y,
    x_0^4*x^3,
    x_0^4*x*y,
    x_0^4*z,
    x_0^3*x^4,
    x_0^3*x^2*y,
    x_0^3*x*z,
    x_0^3*y^2,
    x_0^3*t,
    x_0^3*B,
    x_0^2*x^5,
    x_0^2*x^3*y,
    x_0^2*x^2*z,
    x_0^2*x*y^2,
    x_0^2*x*t,
    x_0^2*x*B,
    x_0^2*y*z,
    x_0^2*u,
    x_0*x^6,
    x_0*x^4*y,
    x_0*x^3*z,
    x_0*x^2*y^2,
    x_0*x^2*t,
    x_0*x^2*B,
    x_0*x*y*z,
    x_0*x*u,
    x_0*y^3,
    x_0*y*t,
    x_0*y*B,
    x_0*z^2,
    x_0*v,
    x^7,
    x^5*y,
    x^4*z,
    x^3*y^2,
    x^3*t,
    x^3*B,
    x^2*y*z,
    x^2*u,
    x*y^3,
    x*y*t,
    x*y*B,
    x*z^2,
    x*v,
    y^2*z,
    y*u,
    z*t,
    z*B
@}
{@
    x_0^8,
    x_0^7*x,
    x_0^6*x^2,
    x_0^6*y,
    x_0^5*x^3,
    x_0^5*x*y,
    x_0^5*z,
    x_0^4*x^4,
    x_0^4*x^2*y,
    x_0^4*x*z,
    x_0^4*y^2,
    x_0^4*t,
    x_0^4*B,
    x_0^3*x^5,
    x_0^3*x^3*y,
    x_0^3*x^2*z,
    x_0^3*x*y^2,
    x_0^3*x*t,
    x_0^3*x*B,
    x_0^3*y*z,
    x_0^3*u,
    x_0^2*x^6,
    x_0^2*x^4*y,
    x_0^2*x^3*z,
    x_0^2*x^2*y^2,
    x_0^2*x^2*t,
    x_0^2*x^2*B,
    x_0^2*x*y*z,
    x_0^2*x*u,
    x_0^2*y^3,
    x_0^2*y*t,
    x_0^2*y*B,
    x_0^2*z^2,
    x_0^2*v,
    x_0*x^7,
    x_0*x^5*y,
    x_0*x^4*z,
    x_0*x^3*y^2,
    x_0*x^3*t,
    x_0*x^3*B,
    x_0*x^2*y*z,
    x_0*x^2*u,
    x_0*x*y^3,
    x_0*x*y*t,
    x_0*x*y*B,
    x_0*x*z^2,
    x_0*x*v,
    x_0*y^2*z,
    x_0*y*u,
    x_0*z*t,
    x_0*z*B,
    x^8,
    x^6*y,
    x^5*z,
    x^4*y^2,
    x^4*t,
    x^4*B,
    x^3*y*z,
    x^3*u,
    x^2*y^3,
    x^2*y*t,
    x^2*y*B,
    x^2*z^2,
    x^2*v,
    x*y^2*z,
    x*y*u,
    x*z*t,
    x*z*B,
    y^4,
    y^2*t,
    y^2*B,
    y*z^2,
    y*v,
    z*u,
    t^2,
    t*B,
    B^2
@}
{@
    x_0^9,
    x_0^8*x,
    x_0^7*x^2,
    x_0^7*y,
    x_0^6*x^3,
    x_0^6*x*y,
    x_0^6*z,
    x_0^5*x^4,
    x_0^5*x^2*y,
    x_0^5*x*z,
    x_0^5*y^2,
    x_0^5*t,
    x_0^5*B,
    x_0^4*x^5,
    x_0^4*x^3*y,
    x_0^4*x^2*z,
    x_0^4*x*y^2,
    x_0^4*x*t,
    x_0^4*x*B,
    x_0^4*y*z,
    x_0^4*u,
    x_0^3*x^6,
    x_0^3*x^4*y,
    x_0^3*x^3*z,
    x_0^3*x^2*y^2,
    x_0^3*x^2*t,
    x_0^3*x^2*B,
    x_0^3*x*y*z,
    x_0^3*x*u,
    x_0^3*y^3,
    x_0^3*y*t,
    x_0^3*y*B,
    x_0^3*z^2,
    x_0^3*v,
    x_0^2*x^7,
    x_0^2*x^5*y,
    x_0^2*x^4*z,
    x_0^2*x^3*y^2,
    x_0^2*x^3*t,
    x_0^2*x^3*B,
    x_0^2*x^2*y*z,
    x_0^2*x^2*u,
    x_0^2*x*y^3,
    x_0^2*x*y*t,
    x_0^2*x*y*B,
    x_0^2*x*z^2,
    x_0^2*x*v,
    x_0^2*y^2*z,
    x_0^2*y*u,
    x_0^2*z*t,
    x_0^2*z*B,
    x_0*x^8,
    x_0*x^6*y,
    x_0*x^5*z,
    x_0*x^4*y^2,
    x_0*x^4*t,
    x_0*x^4*B,
    x_0*x^3*y*z,
    x_0*x^3*u,
    x_0*x^2*y^3,
    x_0*x^2*y*t,
    x_0*x^2*y*B,
    x_0*x^2*z^2,
    x_0*x^2*v,
    x_0*x*y^2*z,
    x_0*x*y*u,
    x_0*x*z*t,
    x_0*x*z*B,
    x_0*y^4,
    x_0*y^2*t,
    x_0*y^2*B,
    x_0*y*z^2,
    x_0*y*v,
    x_0*z*u,
    x_0*t^2,
    x_0*t*B,
    x_0*B^2,
    x^9,
    x^7*y,
    x^6*z,
    x^5*y^2,
    x^5*t,
    x^5*B,
    x^4*y*z,
    x^4*u,
    x^3*y^3,
    x^3*y*t,
    x^3*y*B,
    x^3*z^2,
    x^3*v,
    x^2*y^2*z,
    x^2*y*u,
    x^2*z*t,
    x^2*z*B,
    x*y^4,
    x*y^2*t,
    x*y^2*B,
    x*y*z^2,
    x*y*v,
    x*z*u,
    x*t^2,
    x*t*B,
    x*B^2,
    y^3*z,
    y^2*u,
    y*z*t,
    y*z*B,
    z^3,
    z*v,
    t*u,
    u*B,
    A
@}
{@
    x_0^10,
    x_0^9*x,
    x_0^8*x^2,
    x_0^8*y,
    x_0^7*x^3,
    x_0^7*x*y,
    x_0^7*z,
    x_0^6*x^4,
    x_0^6*x^2*y,
    x_0^6*x*z,
    x_0^6*y^2,
    x_0^6*t,
    x_0^6*B,
    x_0^5*x^5,
    x_0^5*x^3*y,
    x_0^5*x^2*z,
    x_0^5*x*y^2,
    x_0^5*x*t,
    x_0^5*x*B,
    x_0^5*y*z,
    x_0^5*u,
    x_0^4*x^6,
    x_0^4*x^4*y,
    x_0^4*x^3*z,
    x_0^4*x^2*y^2,
    x_0^4*x^2*t,
    x_0^4*x^2*B,
    x_0^4*x*y*z,
    x_0^4*x*u,
    x_0^4*y^3,
    x_0^4*y*t,
    x_0^4*y*B,
    x_0^4*z^2,
    x_0^4*v,
    x_0^3*x^7,
    x_0^3*x^5*y,
    x_0^3*x^4*z,
    x_0^3*x^3*y^2,
    x_0^3*x^3*t,
    x_0^3*x^3*B,
    x_0^3*x^2*y*z,
    x_0^3*x^2*u,
    x_0^3*x*y^3,
    x_0^3*x*y*t,
    x_0^3*x*y*B,
    x_0^3*x*z^2,
    x_0^3*x*v,
    x_0^3*y^2*z,
    x_0^3*y*u,
    x_0^3*z*t,
    x_0^3*z*B,
    x_0^2*x^8,
    x_0^2*x^6*y,
    x_0^2*x^5*z,
    x_0^2*x^4*y^2,
    x_0^2*x^4*t,
    x_0^2*x^4*B,
    x_0^2*x^3*y*z,
    x_0^2*x^3*u,
    x_0^2*x^2*y^3,
    x_0^2*x^2*y*t,
    x_0^2*x^2*y*B,
    x_0^2*x^2*z^2,
    x_0^2*x^2*v,
    x_0^2*x*y^2*z,
    x_0^2*x*y*u,
    x_0^2*x*z*t,
    x_0^2*x*z*B,
    x_0^2*y^4,
    x_0^2*y^2*t,
    x_0^2*y^2*B,
    x_0^2*y*z^2,
    x_0^2*y*v,
    x_0^2*z*u,
    x_0^2*t^2,
    x_0^2*t*B,
    x_0^2*B^2,
    x_0*x^9,
    x_0*x^7*y,
    x_0*x^6*z,
    x_0*x^5*y^2,
    x_0*x^5*t,
    x_0*x^5*B,
    x_0*x^4*y*z,
    x_0*x^4*u,
    x_0*x^3*y^3,
    x_0*x^3*y*t,
    x_0*x^3*y*B,
    x_0*x^3*z^2,
    x_0*x^3*v,
    x_0*x^2*y^2*z,
    x_0*x^2*y*u,
    x_0*x^2*z*t,
    x_0*x^2*z*B,
    x_0*x*y^4,
    x_0*x*y^2*t,
    x_0*x*y^2*B,
    x_0*x*y*z^2,
    x_0*x*y*v,
    x_0*x*z*u,
    x_0*x*t^2,
    x_0*x*t*B,
    x_0*x*B^2,
    x_0*y^3*z,
    x_0*y^2*u,
    x_0*y*z*t,
    x_0*y*z*B,
    x_0*z^3,
    x_0*z*v,
    x_0*t*u,
    x_0*u*B,
    x_0*A,
    x^10,
    x^8*y,
    x^7*z,
    x^6*y^2,
    x^6*t,
    x^6*B,
    x^5*y*z,
    x^5*u,
    x^4*y^3,
    x^4*y*t,
    x^4*y*B,
    x^4*z^2,
    x^4*v,
    x^3*y^2*z,
    x^3*y*u,
    x^3*z*t,
    x^3*z*B,
    x^2*y^4,
    x^2*y^2*t,
    x^2*y^2*B,
    x^2*y*z^2,
    x^2*y*v,
    x^2*z*u,
    x^2*t^2,
    x^2*t*B,
    x^2*B^2,
    x*y^3*z,
    x*y^2*u,
    x*y*z*t,
    x*y*z*B,
    x*z^3,
    x*z*v,
    x*t*u,
    x*u*B,
    x*A,
    y^5,
    y^3*t,
    y^3*B,
    y^2*z^2,
    y^2*v,
    y*z*u,
    y*t^2,
    y*t*B,
    y*B^2,
    z^2*t,
    z^2*B,
    t*v,
    u^2,
    v*B
@}
{@
    x_0^11,
    x_0^10*x,
    x_0^9*x^2,
    x_0^9*y,
    x_0^8*x^3,
    x_0^8*x*y,
    x_0^8*z,
    x_0^7*x^4,
    x_0^7*x^2*y,
    x_0^7*x*z,
    x_0^7*y^2,
    x_0^7*t,
    x_0^7*B,
    x_0^6*x^5,
    x_0^6*x^3*y,
    x_0^6*x^2*z,
    x_0^6*x*y^2,
    x_0^6*x*t,
    x_0^6*x*B,
    x_0^6*y*z,
    x_0^6*u,
    x_0^5*x^6,
    x_0^5*x^4*y,
    x_0^5*x^3*z,
    x_0^5*x^2*y^2,
    x_0^5*x^2*t,
    x_0^5*x^2*B,
    x_0^5*x*y*z,
    x_0^5*x*u,
    x_0^5*y^3,
    x_0^5*y*t,
    x_0^5*y*B,
    x_0^5*z^2,
    x_0^5*v,
    x_0^4*x^7,
    x_0^4*x^5*y,
    x_0^4*x^4*z,
    x_0^4*x^3*y^2,
    x_0^4*x^3*t,
    x_0^4*x^3*B,
    x_0^4*x^2*y*z,
    x_0^4*x^2*u,
    x_0^4*x*y^3,
    x_0^4*x*y*t,
    x_0^4*x*y*B,
    x_0^4*x*z^2,
    x_0^4*x*v,
    x_0^4*y^2*z,
    x_0^4*y*u,
    x_0^4*z*t,
    x_0^4*z*B,
    x_0^3*x^8,
    x_0^3*x^6*y,
    x_0^3*x^5*z,
    x_0^3*x^4*y^2,
    x_0^3*x^4*t,
    x_0^3*x^4*B,
    x_0^3*x^3*y*z,
    x_0^3*x^3*u,
    x_0^3*x^2*y^3,
    x_0^3*x^2*y*t,
    x_0^3*x^2*y*B,
    x_0^3*x^2*z^2,
    x_0^3*x^2*v,
    x_0^3*x*y^2*z,
    x_0^3*x*y*u,
    x_0^3*x*z*t,
    x_0^3*x*z*B,
    x_0^3*y^4,
    x_0^3*y^2*t,
    x_0^3*y^2*B,
    x_0^3*y*z^2,
    x_0^3*y*v,
    x_0^3*z*u,
    x_0^3*t^2,
    x_0^3*t*B,
    x_0^3*B^2,
    x_0^2*x^9,
    x_0^2*x^7*y,
    x_0^2*x^6*z,
    x_0^2*x^5*y^2,
    x_0^2*x^5*t,
    x_0^2*x^5*B,
    x_0^2*x^4*y*z,
    x_0^2*x^4*u,
    x_0^2*x^3*y^3,
    x_0^2*x^3*y*t,
    x_0^2*x^3*y*B,
    x_0^2*x^3*z^2,
    x_0^2*x^3*v,
    x_0^2*x^2*y^2*z,
    x_0^2*x^2*y*u,
    x_0^2*x^2*z*t,
    x_0^2*x^2*z*B,
    x_0^2*x*y^4,
    x_0^2*x*y^2*t,
    x_0^2*x*y^2*B,
    x_0^2*x*y*z^2,
    x_0^2*x*y*v,
    x_0^2*x*z*u,
    x_0^2*x*t^2,
    x_0^2*x*t*B,
    x_0^2*x*B^2,
    x_0^2*y^3*z,
    x_0^2*y^2*u,
    x_0^2*y*z*t,
    x_0^2*y*z*B,
    x_0^2*z^3,
    x_0^2*z*v,
    x_0^2*t*u,
    x_0^2*u*B,
    x_0^2*A,
    x_0*x^10,
    x_0*x^8*y,
    x_0*x^7*z,
    x_0*x^6*y^2,
    x_0*x^6*t,
    x_0*x^6*B,
    x_0*x^5*y*z,
    x_0*x^5*u,
    x_0*x^4*y^3,
    x_0*x^4*y*t,
    x_0*x^4*y*B,
    x_0*x^4*z^2,
    x_0*x^4*v,
    x_0*x^3*y^2*z,
    x_0*x^3*y*u,
    x_0*x^3*z*t,
    x_0*x^3*z*B,
    x_0*x^2*y^4,
    x_0*x^2*y^2*t,
    x_0*x^2*y^2*B,
    x_0*x^2*y*z^2,
    x_0*x^2*y*v,
    x_0*x^2*z*u,
    x_0*x^2*t^2,
    x_0*x^2*t*B,
    x_0*x^2*B^2,
    x_0*x*y^3*z,
    x_0*x*y^2*u,
    x_0*x*y*z*t,
    x_0*x*y*z*B,
    x_0*x*z^3,
    x_0*x*z*v,
    x_0*x*t*u,
    x_0*x*u*B,
    x_0*x*A,
    x_0*y^5,
    x_0*y^3*t,
    x_0*y^3*B,
    x_0*y^2*z^2,
    x_0*y^2*v,
    x_0*y*z*u,
    x_0*y*t^2,
    x_0*y*t*B,
    x_0*y*B^2,
    x_0*z^2*t,
    x_0*z^2*B,
    x_0*t*v,
    x_0*u^2,
    x_0*v*B,
    x^11,
    x^9*y,
    x^8*z,
    x^7*y^2,
    x^7*t,
    x^7*B,
    x^6*y*z,
    x^6*u,
    x^5*y^3,
    x^5*y*t,
    x^5*y*B,
    x^5*z^2,
    x^5*v,
    x^4*y^2*z,
    x^4*y*u,
    x^4*z*t,
    x^4*z*B,
    x^3*y^4,
    x^3*y^2*t,
    x^3*y^2*B,
    x^3*y*z^2,
    x^3*y*v,
    x^3*z*u,
    x^3*t^2,
    x^3*t*B,
    x^3*B^2,
    x^2*y^3*z,
    x^2*y^2*u,
    x^2*y*z*t,
    x^2*y*z*B,
    x^2*z^3,
    x^2*z*v,
    x^2*t*u,
    x^2*u*B,
    x^2*A,
    x*y^5,
    x*y^3*t,
    x*y^3*B,
    x*y^2*z^2,
    x*y^2*v,
    x*y*z*u,
    x*y*t^2,
    x*y*t*B,
    x*y*B^2,
    x*z^2*t,
    x*z^2*B,
  
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:14:49 2004

Input: R<x_0,x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]);
for i in [1..12] do
x_0*MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:14:48 on modular  [Seed = 1678645772]
   -------------------------------------


>> x_0*MonomialsOfWeightedDegree(R,i);
      ^
Runtime error in '*': Bad argument types
Argument types given: RngMPolElt, SetIndx[RngMPolElt]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:15:01 2004

Input: R<x_0,x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]);
for i in [1..12] do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:15:01 on modular  [Seed = 1948125697]
   -------------------------------------

{@
    x_0,
    x
@}
{@
    x_0^2,
    x_0*x,
    x^2,
    y
@}
{@
    x_0^3,
    x_0^2*x,
    x_0*x^2,
    x_0*y,
    x^3,
    x*y,
    z
@}
{@
    x_0^4,
    x_0^3*x,
    x_0^2*x^2,
    x_0^2*y,
    x_0*x^3,
    x_0*x*y,
    x_0*z,
    x^4,
    x^2*y,
    x*z,
    y^2,
    t,
    B
@}
{@
    x_0^5,
    x_0^4*x,
    x_0^3*x^2,
    x_0^3*y,
    x_0^2*x^3,
    x_0^2*x*y,
    x_0^2*z,
    x_0*x^4,
    x_0*x^2*y,
    x_0*x*z,
    x_0*y^2,
    x_0*t,
    x_0*B,
    x^5,
    x^3*y,
    x^2*z,
    x*y^2,
    x*t,
    x*B,
    y*z,
    u
@}
{@
    x_0^6,
    x_0^5*x,
    x_0^4*x^2,
    x_0^4*y,
    x_0^3*x^3,
    x_0^3*x*y,
    x_0^3*z,
    x_0^2*x^4,
    x_0^2*x^2*y,
    x_0^2*x*z,
    x_0^2*y^2,
    x_0^2*t,
    x_0^2*B,
    x_0*x^5,
    x_0*x^3*y,
    x_0*x^2*z,
    x_0*x*y^2,
    x_0*x*t,
    x_0*x*B,
    x_0*y*z,
    x_0*u,
    x^6,
    x^4*y,
    x^3*z,
    x^2*y^2,
    x^2*t,
    x^2*B,
    x*y*z,
    x*u,
    y^3,
    y*t,
    y*B,
    z^2,
    v
@}
{@
    x_0^7,
    x_0^6*x,
    x_0^5*x^2,
    x_0^5*y,
    x_0^4*x^3,
    x_0^4*x*y,
    x_0^4*z,
    x_0^3*x^4,
    x_0^3*x^2*y,
    x_0^3*x*z,
    x_0^3*y^2,
    x_0^3*t,
    x_0^3*B,
    x_0^2*x^5,
    x_0^2*x^3*y,
    x_0^2*x^2*z,
    x_0^2*x*y^2,
    x_0^2*x*t,
    x_0^2*x*B,
    x_0^2*y*z,
    x_0^2*u,
    x_0*x^6,
    x_0*x^4*y,
    x_0*x^3*z,
    x_0*x^2*y^2,
    x_0*x^2*t,
    x_0*x^2*B,
    x_0*x*y*z,
    x_0*x*u,
    x_0*y^3,
    x_0*y*t,
    x_0*y*B,
    x_0*z^2,
    x_0*v,
    x^7,
    x^5*y,
    x^4*z,
    x^3*y^2,
    x^3*t,
    x^3*B,
    x^2*y*z,
    x^2*u,
    x*y^3,
    x*y*t,
    x*y*B,
    x*z^2,
    x*v,
    y^2*z,
    y*u,
    z*t,
    z*B
@}
{@
    x_0^8,
    x_0^7*x,
    x_0^6*x^2,
    x_0^6*y,
    x_0^5*x^3,
    x_0^5*x*y,
    x_0^5*z,
    x_0^4*x^4,
    x_0^4*x^2*y,
    x_0^4*x*z,
    x_0^4*y^2,
    x_0^4*t,
    x_0^4*B,
    x_0^3*x^5,
    x_0^3*x^3*y,
    x_0^3*x^2*z,
    x_0^3*x*y^2,
    x_0^3*x*t,
    x_0^3*x*B,
    x_0^3*y*z,
    x_0^3*u,
    x_0^2*x^6,
    x_0^2*x^4*y,
    x_0^2*x^3*z,
    x_0^2*x^2*y^2,
    x_0^2*x^2*t,
    x_0^2*x^2*B,
    x_0^2*x*y*z,
    x_0^2*x*u,
    x_0^2*y^3,
    x_0^2*y*t,
    x_0^2*y*B,
    x_0^2*z^2,
    x_0^2*v,
    x_0*x^7,
    x_0*x^5*y,
    x_0*x^4*z,
    x_0*x^3*y^2,
    x_0*x^3*t,
    x_0*x^3*B,
    x_0*x^2*y*z,
    x_0*x^2*u,
    x_0*x*y^3,
    x_0*x*y*t,
    x_0*x*y*B,
    x_0*x*z^2,
    x_0*x*v,
    x_0*y^2*z,
    x_0*y*u,
    x_0*z*t,
    x_0*z*B,
    x^8,
    x^6*y,
    x^5*z,
    x^4*y^2,
    x^4*t,
    x^4*B,
    x^3*y*z,
    x^3*u,
    x^2*y^3,
    x^2*y*t,
    x^2*y*B,
    x^2*z^2,
    x^2*v,
    x*y^2*z,
    x*y*u,
    x*z*t,
    x*z*B,
    y^4,
    y^2*t,
    y^2*B,
    y*z^2,
    y*v,
    z*u,
    t^2,
    t*B,
    B^2
@}
{@
    x_0^9,
    x_0^8*x,
    x_0^7*x^2,
    x_0^7*y,
    x_0^6*x^3,
    x_0^6*x*y,
    x_0^6*z,
    x_0^5*x^4,
    x_0^5*x^2*y,
    x_0^5*x*z,
    x_0^5*y^2,
    x_0^5*t,
    x_0^5*B,
    x_0^4*x^5,
    x_0^4*x^3*y,
    x_0^4*x^2*z,
    x_0^4*x*y^2,
    x_0^4*x*t,
    x_0^4*x*B,
    x_0^4*y*z,
    x_0^4*u,
    x_0^3*x^6,
    x_0^3*x^4*y,
    x_0^3*x^3*z,
    x_0^3*x^2*y^2,
    x_0^3*x^2*t,
    x_0^3*x^2*B,
    x_0^3*x*y*z,
    x_0^3*x*u,
    x_0^3*y^3,
    x_0^3*y*t,
    x_0^3*y*B,
    x_0^3*z^2,
    x_0^3*v,
    x_0^2*x^7,
    x_0^2*x^5*y,
    x_0^2*x^4*z,
    x_0^2*x^3*y^2,
    x_0^2*x^3*t,
    x_0^2*x^3*B,
    x_0^2*x^2*y*z,
    x_0^2*x^2*u,
    x_0^2*x*y^3,
    x_0^2*x*y*t,
    x_0^2*x*y*B,
    x_0^2*x*z^2,
    x_0^2*x*v,
    x_0^2*y^2*z,
    x_0^2*y*u,
    x_0^2*z*t,
    x_0^2*z*B,
    x_0*x^8,
    x_0*x^6*y,
    x_0*x^5*z,
    x_0*x^4*y^2,
    x_0*x^4*t,
    x_0*x^4*B,
    x_0*x^3*y*z,
    x_0*x^3*u,
    x_0*x^2*y^3,
    x_0*x^2*y*t,
    x_0*x^2*y*B,
    x_0*x^2*z^2,
    x_0*x^2*v,
    x_0*x*y^2*z,
    x_0*x*y*u,
    x_0*x*z*t,
    x_0*x*z*B,
    x_0*y^4,
    x_0*y^2*t,
    x_0*y^2*B,
    x_0*y*z^2,
    x_0*y*v,
    x_0*z*u,
    x_0*t^2,
    x_0*t*B,
    x_0*B^2,
    x^9,
    x^7*y,
    x^6*z,
    x^5*y^2,
    x^5*t,
    x^5*B,
    x^4*y*z,
    x^4*u,
    x^3*y^3,
    x^3*y*t,
    x^3*y*B,
    x^3*z^2,
    x^3*v,
    x^2*y^2*z,
    x^2*y*u,
    x^2*z*t,
    x^2*z*B,
    x*y^4,
    x*y^2*t,
    x*y^2*B,
    x*y*z^2,
    x*y*v,
    x*z*u,
    x*t^2,
    x*t*B,
    x*B^2,
    y^3*z,
    y^2*u,
    y*z*t,
    y*z*B,
    z^3,
    z*v,
    t*u,
    u*B,
    A
@}
{@
    x_0^10,
    x_0^9*x,
    x_0^8*x^2,
    x_0^8*y,
    x_0^7*x^3,
    x_0^7*x*y,
    x_0^7*z,
    x_0^6*x^4,
    x_0^6*x^2*y,
    x_0^6*x*z,
    x_0^6*y^2,
    x_0^6*t,
    x_0^6*B,
    x_0^5*x^5,
    x_0^5*x^3*y,
    x_0^5*x^2*z,
    x_0^5*x*y^2,
    x_0^5*x*t,
    x_0^5*x*B,
    x_0^5*y*z,
    x_0^5*u,
    x_0^4*x^6,
    x_0^4*x^4*y,
    x_0^4*x^3*z,
    x_0^4*x^2*y^2,
    x_0^4*x^2*t,
    x_0^4*x^2*B,
    x_0^4*x*y*z,
    x_0^4*x*u,
    x_0^4*y^3,
    x_0^4*y*t,
    x_0^4*y*B,
    x_0^4*z^2,
    x_0^4*v,
    x_0^3*x^7,
    x_0^3*x^5*y,
    x_0^3*x^4*z,
    x_0^3*x^3*y^2,
    x_0^3*x^3*t,
    x_0^3*x^3*B,
    x_0^3*x^2*y*z,
    x_0^3*x^2*u,
    x_0^3*x*y^3,
    x_0^3*x*y*t,
    x_0^3*x*y*B,
    x_0^3*x*z^2,
    x_0^3*x*v,
    x_0^3*y^2*z,
    x_0^3*y*u,
    x_0^3*z*t,
    x_0^3*z*B,
    x_0^2*x^8,
    x_0^2*x^6*y,
    x_0^2*x^5*z,
    x_0^2*x^4*y^2,
    x_0^2*x^4*t,
    x_0^2*x^4*B,
    x_0^2*x^3*y*z,
    x_0^2*x^3*u,
    x_0^2*x^2*y^3,
    x_0^2*x^2*y*t,
    x_0^2*x^2*y*B,
    x_0^2*x^2*z^2,
    x_0^2*x^2*v,
    x_0^2*x*y^2*z,
    x_0^2*x*y*u,
    x_0^2*x*z*t,
    x_0^2*x*z*B,
    x_0^2*y^4,
    x_0^2*y^2*t,
    x_0^2*y^2*B,
    x_0^2*y*z^2,
    x_0^2*y*v,
    x_0^2*z*u,
    x_0^2*t^2,
    x_0^2*t*B,
    x_0^2*B^2,
    x_0*x^9,
    x_0*x^7*y,
    x_0*x^6*z,
    x_0*x^5*y^2,
    x_0*x^5*t,
    x_0*x^5*B,
    x_0*x^4*y*z,
    x_0*x^4*u,
    x_0*x^3*y^3,
    x_0*x^3*y*t,
    x_0*x^3*y*B,
    x_0*x^3*z^2,
    x_0*x^3*v,
    x_0*x^2*y^2*z,
    x_0*x^2*y*u,
    x_0*x^2*z*t,
    x_0*x^2*z*B,
    x_0*x*y^4,
    x_0*x*y^2*t,
    x_0*x*y^2*B,
    x_0*x*y*z^2,
    x_0*x*y*v,
    x_0*x*z*u,
    x_0*x*t^2,
    x_0*x*t*B,
    x_0*x*B^2,
    x_0*y^3*z,
    x_0*y^2*u,
    x_0*y*z*t,
    x_0*y*z*B,
    x_0*z^3,
    x_0*z*v,
    x_0*t*u,
    x_0*u*B,
    x_0*A,
    x^10,
    x^8*y,
    x^7*z,
    x^6*y^2,
    x^6*t,
    x^6*B,
    x^5*y*z,
    x^5*u,
    x^4*y^3,
    x^4*y*t,
    x^4*y*B,
    x^4*z^2,
    x^4*v,
    x^3*y^2*z,
    x^3*y*u,
    x^3*z*t,
    x^3*z*B,
    x^2*y^4,
    x^2*y^2*t,
    x^2*y^2*B,
    x^2*y*z^2,
    x^2*y*v,
    x^2*z*u,
    x^2*t^2,
    x^2*t*B,
    x^2*B^2,
    x*y^3*z,
    x*y^2*u,
    x*y*z*t,
    x*y*z*B,
    x*z^3,
    x*z*v,
    x*t*u,
    x*u*B,
    x*A,
    y^5,
    y^3*t,
    y^3*B,
    y^2*z^2,
    y^2*v,
    y*z*u,
    y*t^2,
    y*t*B,
    y*B^2,
    z^2*t,
    z^2*B,
    t*v,
    u^2,
    v*B
@}
{@
    x_0^11,
    x_0^10*x,
    x_0^9*x^2,
    x_0^9*y,
    x_0^8*x^3,
    x_0^8*x*y,
    x_0^8*z,
    x_0^7*x^4,
    x_0^7*x^2*y,
    x_0^7*x*z,
    x_0^7*y^2,
    x_0^7*t,
    x_0^7*B,
    x_0^6*x^5,
    x_0^6*x^3*y,
    x_0^6*x^2*z,
    x_0^6*x*y^2,
    x_0^6*x*t,
    x_0^6*x*B,
    x_0^6*y*z,
    x_0^6*u,
    x_0^5*x^6,
    x_0^5*x^4*y,
    x_0^5*x^3*z,
    x_0^5*x^2*y^2,
    x_0^5*x^2*t,
    x_0^5*x^2*B,
    x_0^5*x*y*z,
    x_0^5*x*u,
    x_0^5*y^3,
    x_0^5*y*t,
    x_0^5*y*B,
    x_0^5*z^2,
    x_0^5*v,
    x_0^4*x^7,
    x_0^4*x^5*y,
    x_0^4*x^4*z,
    x_0^4*x^3*y^2,
    x_0^4*x^3*t,
    x_0^4*x^3*B,
    x_0^4*x^2*y*z,
    x_0^4*x^2*u,
    x_0^4*x*y^3,
    x_0^4*x*y*t,
    x_0^4*x*y*B,
    x_0^4*x*z^2,
    x_0^4*x*v,
    x_0^4*y^2*z,
    x_0^4*y*u,
    x_0^4*z*t,
    x_0^4*z*B,
    x_0^3*x^8,
    x_0^3*x^6*y,
    x_0^3*x^5*z,
    x_0^3*x^4*y^2,
    x_0^3*x^4*t,
    x_0^3*x^4*B,
    x_0^3*x^3*y*z,
    x_0^3*x^3*u,
    x_0^3*x^2*y^3,
    x_0^3*x^2*y*t,
    x_0^3*x^2*y*B,
    x_0^3*x^2*z^2,
    x_0^3*x^2*v,
    x_0^3*x*y^2*z,
    x_0^3*x*y*u,
    x_0^3*x*z*t,
    x_0^3*x*z*B,
    x_0^3*y^4,
    x_0^3*y^2*t,
    x_0^3*y^2*B,
    x_0^3*y*z^2,
    x_0^3*y*v,
    x_0^3*z*u,
    x_0^3*t^2,
    x_0^3*t*B,
    x_0^3*B^2,
    x_0^2*x^9,
    x_0^2*x^7*y,
    x_0^2*x^6*z,
    x_0^2*x^5*y^2,
    x_0^2*x^5*t,
    x_0^2*x^5*B,
    x_0^2*x^4*y*z,
    x_0^2*x^4*u,
    x_0^2*x^3*y^3,
    x_0^2*x^3*y*t,
    x_0^2*x^3*y*B,
    x_0^2*x^3*z^2,
    x_0^2*x^3*v,
    x_0^2*x^2*y^2*z,
    x_0^2*x^2*y*u,
    x_0^2*x^2*z*t,
    x_0^2*x^2*z*B,
    x_0^2*x*y^4,
    x_0^2*x*y^2*t,
    x_0^2*x*y^2*B,
    x_0^2*x*y*z^2,
    x_0^2*x*y*v,
    x_0^2*x*z*u,
    x_0^2*x*t^2,
    x_0^2*x*t*B,
    x_0^2*x*B^2,
    x_0^2*y^3*z,
    x_0^2*y^2*u,
    x_0^2*y*z*t,
    x_0^2*y*z*B,
    x_0^2*z^3,
    x_0^2*z*v,
    x_0^2*t*u,
    x_0^2*u*B,
    x_0^2*A,
    x_0*x^10,
    x_0*x^8*y,
    x_0*x^7*z,
    x_0*x^6*y^2,
    x_0*x^6*t,
    x_0*x^6*B,
    x_0*x^5*y*z,
    x_0*x^5*u,
    x_0*x^4*y^3,
    x_0*x^4*y*t,
    x_0*x^4*y*B,
    x_0*x^4*z^2,
    x_0*x^4*v,
    x_0*x^3*y^2*z,
    x_0*x^3*y*u,
    x_0*x^3*z*t,
    x_0*x^3*z*B,
    x_0*x^2*y^4,
    x_0*x^2*y^2*t,
    x_0*x^2*y^2*B,
    x_0*x^2*y*z^2,
    x_0*x^2*y*v,
    x_0*x^2*z*u,
    x_0*x^2*t^2,
    x_0*x^2*t*B,
    x_0*x^2*B^2,
    x_0*x*y^3*z,
    x_0*x*y^2*u,
    x_0*x*y*z*t,
    x_0*x*y*z*B,
    x_0*x*z^3,
    x_0*x*z*v,
    x_0*x*t*u,
    x_0*x*u*B,
    x_0*x*A,
    x_0*y^5,
    x_0*y^3*t,
    x_0*y^3*B,
    x_0*y^2*z^2,
    x_0*y^2*v,
    x_0*y*z*u,
    x_0*y*t^2,
    x_0*y*t*B,
    x_0*y*B^2,
    x_0*z^2*t,
    x_0*z^2*B,
    x_0*t*v,
    x_0*u^2,
    x_0*v*B,
    x^11,
    x^9*y,
    x^8*z,
    x^7*y^2,
    x^7*t,
    x^7*B,
    x^6*y*z,
    x^6*u,
    x^5*y^3,
    x^5*y*t,
    x^5*y*B,
    x^5*z^2,
    x^5*v,
    x^4*y^2*z,
    x^4*y*u,
    x^4*z*t,
    x^4*z*B,
    x^3*y^4,
    x^3*y^2*t,
    x^3*y^2*B,
    x^3*y*z^2,
    x^3*y*v,
    x^3*z*u,
    x^3*t^2,
    x^3*t*B,
    x^3*B^2,
    x^2*y^3*z,
    x^2*y^2*u,
    x^2*y*z*t,
    x^2*y*z*B,
    x^2*z^3,
    x^2*z*v,
    x^2*t*u,
    x^2*u*B,
    x^2*A,
    x*y^5,
    x*y^3*t,
    x*y^3*B,
    x*y^2*z^2,
    x*y^2*v,
    x*y*z*u,
    x*y*t^2,
    x*y*t*B,
    x*y*B^2,
    x*z^2*t,
    x*z^2*B,
 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:15:28 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
for i in [1..12] do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:15:27 on modular  [Seed = 1143880203]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    z
@}
{@
    x^4,
    x^2*y,
    x*z,
    y^2,
    t,
    B
@}
{@
    x^5,
    x^3*y,
    x^2*z,
    x*y^2,
    x*t,
    x*B,
    y*z,
    u
@}
{@
    x^6,
    x^4*y,
    x^3*z,
    x^2*y^2,
    x^2*t,
    x^2*B,
    x*y*z,
    x*u,
    y^3,
    y*t,
    y*B,
    z^2,
    v
@}
{@
    x^7,
    x^5*y,
    x^4*z,
    x^3*y^2,
    x^3*t,
    x^3*B,
    x^2*y*z,
    x^2*u,
    x*y^3,
    x*y*t,
    x*y*B,
    x*z^2,
    x*v,
    y^2*z,
    y*u,
    z*t,
    z*B
@}
{@
    x^8,
    x^6*y,
    x^5*z,
    x^4*y^2,
    x^4*t,
    x^4*B,
    x^3*y*z,
    x^3*u,
    x^2*y^3,
    x^2*y*t,
    x^2*y*B,
    x^2*z^2,
    x^2*v,
    x*y^2*z,
    x*y*u,
    x*z*t,
    x*z*B,
    y^4,
    y^2*t,
    y^2*B,
    y*z^2,
    y*v,
    z*u,
    t^2,
    t*B,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^6*z,
    x^5*y^2,
    x^5*t,
    x^5*B,
    x^4*y*z,
    x^4*u,
    x^3*y^3,
    x^3*y*t,
    x^3*y*B,
    x^3*z^2,
    x^3*v,
    x^2*y^2*z,
    x^2*y*u,
    x^2*z*t,
    x^2*z*B,
    x*y^4,
    x*y^2*t,
    x*y^2*B,
    x*y*z^2,
    x*y*v,
    x*z*u,
    x*t^2,
    x*t*B,
    x*B^2,
    y^3*z,
    y^2*u,
    y*z*t,
    y*z*B,
    z^3,
    z*v,
    t*u,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    x^7*z,
    x^6*y^2,
    x^6*t,
    x^6*B,
    x^5*y*z,
    x^5*u,
    x^4*y^3,
    x^4*y*t,
    x^4*y*B,
    x^4*z^2,
    x^4*v,
    x^3*y^2*z,
    x^3*y*u,
    x^3*z*t,
    x^3*z*B,
    x^2*y^4,
    x^2*y^2*t,
    x^2*y^2*B,
    x^2*y*z^2,
    x^2*y*v,
    x^2*z*u,
    x^2*t^2,
    x^2*t*B,
    x^2*B^2,
    x*y^3*z,
    x*y^2*u,
    x*y*z*t,
    x*y*z*B,
    x*z^3,
    x*z*v,
    x*t*u,
    x*u*B,
    x*A,
    y^5,
    y^3*t,
    y^3*B,
    y^2*z^2,
    y^2*v,
    y*z*u,
    y*t^2,
    y*t*B,
    y*B^2,
    z^2*t,
    z^2*B,
    t*v,
    u^2,
    v*B
@}
{@
    x^11,
    x^9*y,
    x^8*z,
    x^7*y^2,
    x^7*t,
    x^7*B,
    x^6*y*z,
    x^6*u,
    x^5*y^3,
    x^5*y*t,
    x^5*y*B,
    x^5*z^2,
    x^5*v,
    x^4*y^2*z,
    x^4*y*u,
    x^4*z*t,
    x^4*z*B,
    x^3*y^4,
    x^3*y^2*t,
    x^3*y^2*B,
    x^3*y*z^2,
    x^3*y*v,
    x^3*z*u,
    x^3*t^2,
    x^3*t*B,
    x^3*B^2,
    x^2*y^3*z,
    x^2*y^2*u,
    x^2*y*z*t,
    x^2*y*z*B,
    x^2*z^3,
    x^2*z*v,
    x^2*t*u,
    x^2*u*B,
    x^2*A,
    x*y^5,
    x*y^3*t,
    x*y^3*B,
    x*y^2*z^2,
    x*y^2*v,
    x*y*z*u,
    x*y*t^2,
    x*y*t*B,
    x*y*B^2,
    x*z^2*t,
    x*z^2*B,
    x*t*v,
    x*u^2,
    x*v*B,
    y^4*z,
    y^3*u,
    y^2*z*t,
    y^2*z*B,
    y*z^3,
    y*z*v,
    y*t*u,
    y*u*B,
    y*A,
    z^2*u,
    z*t^2,
    z*t*B,
    z*B^2,
    u*v
@}
{@
    x^12,
    x^10*y,
    x^9*z,
    x^8*y^2,
    x^8*t,
    x^8*B,
    x^7*y*z,
    x^7*u,
    x^6*y^3,
    x^6*y*t,
    x^6*y*B,
    x^6*z^2,
    x^6*v,
    x^5*y^2*z,
    x^5*y*u,
    x^5*z*t,
    x^5*z*B,
    x^4*y^4,
    x^4*y^2*t,
    x^4*y^2*B,
    x^4*y*z^2,
    x^4*y*v,
    x^4*z*u,
    x^4*t^2,
    x^4*t*B,
    x^4*B^2,
    x^3*y^3*z,
    x^3*y^2*u,
    x^3*y*z*t,
    x^3*y*z*B,
    x^3*z^3,
    x^3*z*v,
    x^3*t*u,
    x^3*u*B,
    x^3*A,
    x^2*y^5,
    x^2*y^3*t,
    x^2*y^3*B,
    x^2*y^2*z^2,
    x^2*y^2*v,
    x^2*y*z*u,
    x^2*y*t^2,
    x^2*y*t*B,
    x^2*y*B^2,
    x^2*z^2*t,
    x^2*z^2*B,
    x^2*t*v,
    x^2*u^2,
    x^2*v*B,
    x*y^4*z,
    x*y^3*u,
    x*y^2*z*t,
    x*y^2*z*B,
    x*y*z^3,
    x*y*z*v,
    x*y*t*u,
    x*y*u*B,
    x*y*A,
    x*z^2*u,
    x*z*t^2,
    x*z*t*B,
    x*z*B^2,
    x*u*v,
    y^6,
    y^4*t,
    y^4*B,
    y^3*z^2,
    y^3*v,
    y^2*z*u,
    y^2*t^2,
    y^2*t*B,
    y^2*B^2,
    y*z^2*t,
    y*z^2*B,
    y*t*v,
    y*u^2,
    y*v*B,
    z^4,
    z^2*v,
    z*t*u,
    z*u*B,
    z*A,
    t^3,
    t^2*B,
    t*B^2,
    v^2,
    B^3
@}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:22:39 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
for i in [1..12] do
PrintFile(i,MonomialsOfWeightedDegree(R,i));
end for;


Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed.

************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:31:51 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R_>S|x+1,y,z,t,u,v,A,B>;
for i in [1..12] do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:31:50 on modular  [Seed = 4154324370]
   -------------------------------------


>> subs:=hom<R_>S|x+1,y,z,t,u,v,A,B>;
               ^
User error: bad syntax
{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    z
@}
{@
    x^4,
    x^2*y,
    x*z,
    y^2,
    t,
    B
@}
{@
    x^5,
    x^3*y,
    x^2*z,
    x*y^2,
    x*t,
    x*B,
    y*z,
    u
@}
{@
    x^6,
    x^4*y,
    x^3*z,
    x^2*y^2,
    x^2*t,
    x^2*B,
    x*y*z,
    x*u,
    y^3,
    y*t,
    y*B,
    z^2,
    v
@}
{@
    x^7,
    x^5*y,
    x^4*z,
    x^3*y^2,
    x^3*t,
    x^3*B,
    x^2*y*z,
    x^2*u,
    x*y^3,
    x*y*t,
    x*y*B,
    x*z^2,
    x*v,
    y^2*z,
    y*u,
    z*t,
    z*B
@}
{@
    x^8,
    x^6*y,
    x^5*z,
    x^4*y^2,
    x^4*t,
    x^4*B,
    x^3*y*z,
    x^3*u,
    x^2*y^3,
    x^2*y*t,
    x^2*y*B,
    x^2*z^2,
    x^2*v,
    x*y^2*z,
    x*y*u,
    x*z*t,
    x*z*B,
    y^4,
    y^2*t,
    y^2*B,
    y*z^2,
    y*v,
    z*u,
    t^2,
    t*B,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^6*z,
    x^5*y^2,
    x^5*t,
    x^5*B,
    x^4*y*z,
    x^4*u,
    x^3*y^3,
    x^3*y*t,
    x^3*y*B,
    x^3*z^2,
    x^3*v,
    x^2*y^2*z,
    x^2*y*u,
    x^2*z*t,
    x^2*z*B,
    x*y^4,
    x*y^2*t,
    x*y^2*B,
    x*y*z^2,
    x*y*v,
    x*z*u,
    x*t^2,
    x*t*B,
    x*B^2,
    y^3*z,
    y^2*u,
    y*z*t,
    y*z*B,
    z^3,
    z*v,
    t*u,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    x^7*z,
    x^6*y^2,
    x^6*t,
    x^6*B,
    x^5*y*z,
    x^5*u,
    x^4*y^3,
    x^4*y*t,
    x^4*y*B,
    x^4*z^2,
    x^4*v,
    x^3*y^2*z,
    x^3*y*u,
    x^3*z*t,
    x^3*z*B,
    x^2*y^4,
    x^2*y^2*t,
    x^2*y^2*B,
    x^2*y*z^2,
    x^2*y*v,
    x^2*z*u,
    x^2*t^2,
    x^2*t*B,
    x^2*B^2,
    x*y^3*z,
    x*y^2*u,
    x*y*z*t,
    x*y*z*B,
    x*z^3,
    x*z*v,
    x*t*u,
    x*u*B,
    x*A,
    y^5,
    y^3*t,
    y^3*B,
    y^2*z^2,
    y^2*v,
    y*z*u,
    y*t^2,
    y*t*B,
    y*B^2,
    z^2*t,
    z^2*B,
    t*v,
    u^2,
    v*B
@}
{@
    x^11,
    x^9*y,
    x^8*z,
    x^7*y^2,
    x^7*t,
    x^7*B,
    x^6*y*z,
    x^6*u,
    x^5*y^3,
    x^5*y*t,
    x^5*y*B,
    x^5*z^2,
    x^5*v,
    x^4*y^2*z,
    x^4*y*u,
    x^4*z*t,
    x^4*z*B,
    x^3*y^4,
    x^3*y^2*t,
    x^3*y^2*B,
    x^3*y*z^2,
    x^3*y*v,
    x^3*z*u,
    x^3*t^2,
    x^3*t*B,
    x^3*B^2,
    x^2*y^3*z,
    x^2*y^2*u,
    x^2*y*z*t,
    x^2*y*z*B,
    x^2*z^3,
    x^2*z*v,
    x^2*t*u,
    x^2*u*B,
    x^2*A,
    x*y^5,
    x*y^3*t,
    x*y^3*B,
    x*y^2*z^2,
    x*y^2*v,
    x*y*z*u,
    x*y*t^2,
    x*y*t*B,
    x*y*B^2,
    x*z^2*t,
    x*z^2*B,
    x*t*v,
    x*u^2,
    x*v*B,
    y^4*z,
    y^3*u,
    y^2*z*t,
    y^2*z*B,
    y*z^3,
    y*z*v,
    y*t*u,
    y*u*B,
    y*A,
    z^2*u,
    z*t^2,
    z*t*B,
    z*B^2,
    u*v
@}
{@
    x^12,
    x^10*y,
    x^9*z,
    x^8*y^2,
    x^8*t,
    x^8*B,
    x^7*y*z,
    x^7*u,
    x^6*y^3,
    x^6*y*t,
    x^6*y*B,
    x^6*z^2,
    x^6*v,
    x^5*y^2*z,
    x^5*y*u,
    x^5*z*t,
    x^5*z*B,
    x^4*y^4,
    x^4*y^2*t,
    x^4*y^2*B,
    x^4*y*z^2,
    x^4*y*v,
    x^4*z*u,
    x^4*t^2,
    x^4*t*B,
    x^4*B^2,
    x^3*y^3*z,
    x^3*y^2*u,
    x^3*y*z*t,
    x^3*y*z*B,
    x^3*z^3,
    x^3*z*v,
    x^3*t*u,
    x^3*u*B,
    x^3*A,
    x^2*y^5,
    x^2*y^3*t,
    x^2*y^3*B,
    x^2*y^2*z^2,
    x^2*y^2*v,
    x^2*y*z*u,
    x^2*y*t^2,
    x^2*y*t*B,
    x^2*y*B^2,
    x^2*z^2*t,
    x^2*z^2*B,
    x^2*t*v,
    x^2*u^2,
    x^2*v*B,
    x*y^4*z,
    x*y^3*u,
    x*y^2*z*t,
    x*y^2*z*B,
    x*y*z^3,
    x*y*z*v,
    x*y*t*u,
    x*y*u*B,
    x*y*A,
    x*z^2*u,
    x*z*t^2,
    x*z*t*B,
    x*z*B^2,
    x*u*v,
    y^6,
    y^4*t,
    y^4*B,
    y^3*z^2,
    y^3*v,
    y^2*z*u,
    y^2*t^2,
    y^2*t*B,
    y^2*B^2,
    y*z^2*t,
    y*z^2*B,
    y*t*v,
    y*u^2,
    y*v*B,
    z^4,
    z^2*v,
    z*t*u,
    z*u*B,
    z*A,
    t^3,
    t^2*B,
    t*B^2,
    v^2,
    B^3
@}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:32:02 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R->S|x+1,y,z,t,u,v,A,B>;
for i in [1..12] do
MonomialsOfWeightedDegree(R,i);
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:32:01 on modular  [Seed = 3350054325]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    z
@}
{@
    x^4,
    x^2*y,
    x*z,
    y^2,
    t,
    B
@}
{@
    x^5,
    x^3*y,
    x^2*z,
    x*y^2,
    x*t,
    x*B,
    y*z,
    u
@}
{@
    x^6,
    x^4*y,
    x^3*z,
    x^2*y^2,
    x^2*t,
    x^2*B,
    x*y*z,
    x*u,
    y^3,
    y*t,
    y*B,
    z^2,
    v
@}
{@
    x^7,
    x^5*y,
    x^4*z,
    x^3*y^2,
    x^3*t,
    x^3*B,
    x^2*y*z,
    x^2*u,
    x*y^3,
    x*y*t,
    x*y*B,
    x*z^2,
    x*v,
    y^2*z,
    y*u,
    z*t,
    z*B
@}
{@
    x^8,
    x^6*y,
    x^5*z,
    x^4*y^2,
    x^4*t,
    x^4*B,
    x^3*y*z,
    x^3*u,
    x^2*y^3,
    x^2*y*t,
    x^2*y*B,
    x^2*z^2,
    x^2*v,
    x*y^2*z,
    x*y*u,
    x*z*t,
    x*z*B,
    y^4,
    y^2*t,
    y^2*B,
    y*z^2,
    y*v,
    z*u,
    t^2,
    t*B,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^6*z,
    x^5*y^2,
    x^5*t,
    x^5*B,
    x^4*y*z,
    x^4*u,
    x^3*y^3,
    x^3*y*t,
    x^3*y*B,
    x^3*z^2,
    x^3*v,
    x^2*y^2*z,
    x^2*y*u,
    x^2*z*t,
    x^2*z*B,
    x*y^4,
    x*y^2*t,
    x*y^2*B,
    x*y*z^2,
    x*y*v,
    x*z*u,
    x*t^2,
    x*t*B,
    x*B^2,
    y^3*z,
    y^2*u,
    y*z*t,
    y*z*B,
    z^3,
    z*v,
    t*u,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    x^7*z,
    x^6*y^2,
    x^6*t,
    x^6*B,
    x^5*y*z,
    x^5*u,
    x^4*y^3,
    x^4*y*t,
    x^4*y*B,
    x^4*z^2,
    x^4*v,
    x^3*y^2*z,
    x^3*y*u,
    x^3*z*t,
    x^3*z*B,
    x^2*y^4,
    x^2*y^2*t,
    x^2*y^2*B,
    x^2*y*z^2,
    x^2*y*v,
    x^2*z*u,
    x^2*t^2,
    x^2*t*B,
    x^2*B^2,
    x*y^3*z,
    x*y^2*u,
    x*y*z*t,
    x*y*z*B,
    x*z^3,
    x*z*v,
    x*t*u,
    x*u*B,
    x*A,
    y^5,
    y^3*t,
    y^3*B,
    y^2*z^2,
    y^2*v,
    y*z*u,
    y*t^2,
    y*t*B,
    y*B^2,
    z^2*t,
    z^2*B,
    t*v,
    u^2,
    v*B
@}
{@
    x^11,
    x^9*y,
    x^8*z,
    x^7*y^2,
    x^7*t,
    x^7*B,
    x^6*y*z,
    x^6*u,
    x^5*y^3,
    x^5*y*t,
    x^5*y*B,
    x^5*z^2,
    x^5*v,
    x^4*y^2*z,
    x^4*y*u,
    x^4*z*t,
    x^4*z*B,
    x^3*y^4,
    x^3*y^2*t,
    x^3*y^2*B,
    x^3*y*z^2,
    x^3*y*v,
    x^3*z*u,
    x^3*t^2,
    x^3*t*B,
    x^3*B^2,
    x^2*y^3*z,
    x^2*y^2*u,
    x^2*y*z*t,
    x^2*y*z*B,
    x^2*z^3,
    x^2*z*v,
    x^2*t*u,
    x^2*u*B,
    x^2*A,
    x*y^5,
    x*y^3*t,
    x*y^3*B,
    x*y^2*z^2,
    x*y^2*v,
    x*y*z*u,
    x*y*t^2,
    x*y*t*B,
    x*y*B^2,
    x*z^2*t,
    x*z^2*B,
    x*t*v,
    x*u^2,
    x*v*B,
    y^4*z,
    y^3*u,
    y^2*z*t,
    y^2*z*B,
    y*z^3,
    y*z*v,
    y*t*u,
    y*u*B,
    y*A,
    z^2*u,
    z*t^2,
    z*t*B,
    z*B^2,
    u*v
@}
{@
    x^12,
    x^10*y,
    x^9*z,
    x^8*y^2,
    x^8*t,
    x^8*B,
    x^7*y*z,
    x^7*u,
    x^6*y^3,
    x^6*y*t,
    x^6*y*B,
    x^6*z^2,
    x^6*v,
    x^5*y^2*z,
    x^5*y*u,
    x^5*z*t,
    x^5*z*B,
    x^4*y^4,
    x^4*y^2*t,
    x^4*y^2*B,
    x^4*y*z^2,
    x^4*y*v,
    x^4*z*u,
    x^4*t^2,
    x^4*t*B,
    x^4*B^2,
    x^3*y^3*z,
    x^3*y^2*u,
    x^3*y*z*t,
    x^3*y*z*B,
    x^3*z^3,
    x^3*z*v,
    x^3*t*u,
    x^3*u*B,
    x^3*A,
    x^2*y^5,
    x^2*y^3*t,
    x^2*y^3*B,
    x^2*y^2*z^2,
    x^2*y^2*v,
    x^2*y*z*u,
    x^2*y*t^2,
    x^2*y*t*B,
    x^2*y*B^2,
    x^2*z^2*t,
    x^2*z^2*B,
    x^2*t*v,
    x^2*u^2,
    x^2*v*B,
    x*y^4*z,
    x*y^3*u,
    x*y^2*z*t,
    x*y^2*z*B,
    x*y*z^3,
    x*y*z*v,
    x*y*t*u,
    x*y*u*B,
    x*y*A,
    x*z^2*u,
    x*z*t^2,
    x*z*t*B,
    x*z*B^2,
    x*u*v,
    y^6,
    y^4*t,
    y^4*B,
    y^3*z^2,
    y^3*v,
    y^2*z*u,
    y^2*t^2,
    y^2*t*B,
    y^2*B^2,
    y*z^2*t,
    y*z^2*B,
    y*t*v,
    y*u^2,
    y*v*B,
    z^4,
    z^2*v,
    z*t*u,
    z*u*B,
    z*A,
    t^3,
    t^2*B,
    t*B^2,
    v^2,
    B^3
@}

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:32:21 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R->S|x+1,y,z,t,u,v,A,B>;
for i in [1..12] do
hom(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:32:20 on modular  [Seed = 3569276563]
   -------------------------------------


>> hom(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'hom' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:32:30 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R->S|x+1,y,z,t,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:32:29 on modular  [Seed = 625944426]
   -------------------------------------

{@
    x + 1
@}
{@
    x^2 + 2*x + 1,
    y
@}
{@
    x^3 + 3*x^2 + 3*x + 1,
    x*y + y,
    z
@}
{@
    x^4 + 4*x^3 + 6*x^2 + 4*x + 1,
    x^2*y + 2*x*y + y,
    x*z + z,
    y^2,
    t,
    B
@}
{@
    x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,
    x^3*y + 3*x^2*y + 3*x*y + y,
    x^2*z + 2*x*z + z,
    x*y^2 + y^2,
    x*t + t,
    x*B + B,
    y*z,
    u
@}
{@
    x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,
    x^4*y + 4*x^3*y + 6*x^2*y + 4*x*y + y,
    x^3*z + 3*x^2*z + 3*x*z + z,
    x^2*y^2 + 2*x*y^2 + y^2,
    x^2*t + 2*x*t + t,
    x^2*B + 2*x*B + B,
    x*y*z + y*z,
    x*u + u,
    y^3,
    y*t,
    y*B,
    z^2,
    v
@}
{@
    x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,
    x^5*y + 5*x^4*y + 10*x^3*y + 10*x^2*y + 5*x*y + y,
    x^4*z + 4*x^3*z + 6*x^2*z + 4*x*z + z,
    x^3*y^2 + 3*x^2*y^2 + 3*x*y^2 + y^2,
    x^3*t + 3*x^2*t + 3*x*t + t,
    x^3*B + 3*x^2*B + 3*x*B + B,
    x^2*y*z + 2*x*y*z + y*z,
    x^2*u + 2*x*u + u,
    x*y^3 + y^3,
    x*y*t + y*t,
    x*y*B + y*B,
    x*z^2 + z^2,
    x*v + v,
    y^2*z,
    y*u,
    z*t,
    z*B
@}
{@
    x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,
    x^6*y + 6*x^5*y + 15*x^4*y + 20*x^3*y + 15*x^2*y + 6*x*y + y,
    x^5*z + 5*x^4*z + 10*x^3*z + 10*x^2*z + 5*x*z + z,
    x^4*y^2 + 4*x^3*y^2 + 6*x^2*y^2 + 4*x*y^2 + y^2,
    x^4*t + 4*x^3*t + 6*x^2*t + 4*x*t + t,
    x^4*B + 4*x^3*B + 6*x^2*B + 4*x*B + B,
    x^3*y*z + 3*x^2*y*z + 3*x*y*z + y*z,
    x^3*u + 3*x^2*u + 3*x*u + u,
    x^2*y^3 + 2*x*y^3 + y^3,
    x^2*y*t + 2*x*y*t + y*t,
    x^2*y*B + 2*x*y*B + y*B,
    x^2*z^2 + 2*x*z^2 + z^2,
    x^2*v + 2*x*v + v,
    x*y^2*z + y^2*z,
    x*y*u + y*u,
    x*z*t + z*t,
    x*z*B + z*B,
    y^4,
    y^2*t,
    y^2*B,
    y*z^2,
    y*v,
    z*u,
    t^2,
    t*B,
    B^2
@}
{@
    x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 
        1,
    x^7*y + 7*x^6*y + 21*x^5*y + 35*x^4*y + 35*x^3*y + 21*x^2*y + 7*x*y + y,
    x^6*z + 6*x^5*z + 15*x^4*z + 20*x^3*z + 15*x^2*z + 6*x*z + z,
    x^5*y^2 + 5*x^4*y^2 + 10*x^3*y^2 + 10*x^2*y^2 + 5*x*y^2 + y^2,
    x^5*t + 5*x^4*t + 10*x^3*t + 10*x^2*t + 5*x*t + t,
    x^5*B + 5*x^4*B + 10*x^3*B + 10*x^2*B + 5*x*B + B,
    x^4*y*z + 4*x^3*y*z + 6*x^2*y*z + 4*x*y*z + y*z,
    x^4*u + 4*x^3*u + 6*x^2*u + 4*x*u + u,
    x^3*y^3 + 3*x^2*y^3 + 3*x*y^3 + y^3,
    x^3*y*t + 3*x^2*y*t + 3*x*y*t + y*t,
    x^3*y*B + 3*x^2*y*B + 3*x*y*B + y*B,
    x^3*z^2 + 3*x^2*z^2 + 3*x*z^2 + z^2,
    x^3*v + 3*x^2*v + 3*x*v + v,
    x^2*y^2*z + 2*x*y^2*z + y^2*z,
    x^2*y*u + 2*x*y*u + y*u,
    x^2*z*t + 2*x*z*t + z*t,
    x^2*z*B + 2*x*z*B + z*B,
    x*y^4 + y^4,
    x*y^2*t + y^2*t,
    x*y^2*B + y^2*B,
    x*y*z^2 + y*z^2,
    x*y*v + y*v,
    x*z*u + z*u,
    x*t^2 + t^2,
    x*t*B + t*B,
    x*B^2 + B^2,
    y^3*z,
    y^2*u,
    y*z*t,
    y*z*B,
    z^3,
    z*v,
    t*u,
    u*B,
    A
@}
{@
    x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 
        45*x^2 + 10*x + 1,
    x^8*y + 8*x^7*y + 28*x^6*y + 56*x^5*y + 70*x^4*y + 56*x^3*y + 28*x^2*y + 
        8*x*y + y,
    x^7*z + 7*x^6*z + 21*x^5*z + 35*x^4*z + 35*x^3*z + 21*x^2*z + 7*x*z + z,
    x^6*y^2 + 6*x^5*y^2 + 15*x^4*y^2 + 20*x^3*y^2 + 15*x^2*y^2 + 6*x*y^2 + y^2,
    x^6*t + 6*x^5*t + 15*x^4*t + 20*x^3*t + 15*x^2*t + 6*x*t + t,
    x^6*B + 6*x^5*B + 15*x^4*B + 20*x^3*B + 15*x^2*B + 6*x*B + B,
    x^5*y*z + 5*x^4*y*z + 10*x^3*y*z + 10*x^2*y*z + 5*x*y*z + y*z,
    x^5*u + 5*x^4*u + 10*x^3*u + 10*x^2*u + 5*x*u + u,
    x^4*y^3 + 4*x^3*y^3 + 6*x^2*y^3 + 4*x*y^3 + y^3,
    x^4*y*t + 4*x^3*y*t + 6*x^2*y*t + 4*x*y*t + y*t,
    x^4*y*B + 4*x^3*y*B + 6*x^2*y*B + 4*x*y*B + y*B,
    x^4*z^2 + 4*x^3*z^2 + 6*x^2*z^2 + 4*x*z^2 + z^2,
    x^4*v + 4*x^3*v + 6*x^2*v + 4*x*v + v,
    x^3*y^2*z + 3*x^2*y^2*z + 3*x*y^2*z + y^2*z,
    x^3*y*u + 3*x^2*y*u + 3*x*y*u + y*u,
    x^3*z*t + 3*x^2*z*t + 3*x*z*t + z*t,
    x^3*z*B + 3*x^2*z*B + 3*x*z*B + z*B,
    x^2*y^4 + 2*x*y^4 + y^4,
    x^2*y^2*t + 2*x*y^2*t + y^2*t,
    x^2*y^2*B + 2*x*y^2*B + y^2*B,
    x^2*y*z^2 + 2*x*y*z^2 + y*z^2,
    x^2*y*v + 2*x*y*v + y*v,
    x^2*z*u + 2*x*z*u + z*u,
    x^2*t^2 + 2*x*t^2 + t^2,
    x^2*t*B + 2*x*t*B + t*B,
    x^2*B^2 + 2*x*B^2 + B^2,
    x*y^3*z + y^3*z,
    x*y^2*u + y^2*u,
    x*y*z*t + y*z*t,
    x*y*z*B + y*z*B,
    x*z^3 + z^3,
    x*z*v + z*v,
    x*t*u + t*u,
    x*u*B + u*B,
    x*A + A,
    y^5,
    y^3*t,
    y^3*B,
    y^2*z^2,
    y^2*v,
    y*z*u,
    y*t^2,
    y*t*B,
    y*B^2,
    z^2*t,
    z^2*B,
    t*v,
    u^2,
    v*B
@}
{@
    x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 
        165*x^3 + 55*x^2 + 11*x + 1,
    x^9*y + 9*x^8*y + 36*x^7*y + 84*x^6*y + 126*x^5*y + 126*x^4*y + 84*x^3*y + 
        36*x^2*y + 9*x*y + y,
    x^8*z + 8*x^7*z + 28*x^6*z + 56*x^5*z + 70*x^4*z + 56*x^3*z + 28*x^2*z + 
        8*x*z + z,
    x^7*y^2 + 7*x^6*y^2 + 21*x^5*y^2 + 35*x^4*y^2 + 35*x^3*y^2 + 21*x^2*y^2 + 
        7*x*y^2 + y^2,
    x^7*t + 7*x^6*t + 21*x^5*t + 35*x^4*t + 35*x^3*t + 21*x^2*t + 7*x*t + t,
    x^7*B + 7*x^6*B + 21*x^5*B + 35*x^4*B + 35*x^3*B + 21*x^2*B + 7*x*B + B,
    x^6*y*z + 6*x^5*y*z + 15*x^4*y*z + 20*x^3*y*z + 15*x^2*y*z + 6*x*y*z + y*z,
    x^6*u + 6*x^5*u + 15*x^4*u + 20*x^3*u + 15*x^2*u + 6*x*u + u,
    x^5*y^3 + 5*x^4*y^3 + 10*x^3*y^3 + 10*x^2*y^3 + 5*x*y^3 + y^3,
    x^5*y*t + 5*x^4*y*t + 10*x^3*y*t + 10*x^2*y*t + 5*x*y*t + y*t,
    x^5*y*B + 5*x^4*y*B + 10*x^3*y*B + 10*x^2*y*B + 5*x*y*B + y*B,
    x^5*z^2 + 5*x^4*z^2 + 10*x^3*z^2 + 10*x^2*z^2 + 5*x*z^2 + z^2,
    x^5*v + 5*x^4*v + 10*x^3*v + 10*x^2*v + 5*x*v + v,
    x^4*y^2*z + 4*x^3*y^2*z + 6*x^2*y^2*z + 4*x*y^2*z + y^2*z,
    x^4*y*u + 4*x^3*y*u + 6*x^2*y*u + 4*x*y*u + y*u,
    x^4*z*t + 4*x^3*z*t + 6*x^2*z*t + 4*x*z*t + z*t,
    x^4*z*B + 4*x^3*z*B + 6*x^2*z*B + 4*x*z*B + z*B,
    x^3*y^4 + 3*x^2*y^4 + 3*x*y^4 + y^4,
    x^3*y^2*t + 3*x^2*y^2*t + 3*x*y^2*t + y^2*t,
    x^3*y^2*B + 3*x^2*y^2*B + 3*x*y^2*B + y^2*B,
    x^3*y*z^2 + 3*x^2*y*z^2 + 3*x*y*z^2 + y*z^2,
    x^3*y*v + 3*x^2*y*v + 3*x*y*v + y*v,
    x^3*z*u + 3*x^2*z*u + 3*x*z*u + z*u,
    x^3*t^2 + 3*x^2*t^2 + 3*x*t^2 + t^2,
    x^3*t*B + 3*x^2*t*B + 3*x*t*B + t*B,
    x^3*B^2 + 3*x^2*B^2 + 3*x*B^2 + B^2,
    x^2*y^3*z + 2*x*y^3*z + y^3*z,
    x^2*y^2*u + 2*x*y^2*u + y^2*u,
    x^2*y*z*t + 2*x*y*z*t + y*z*t,
    x^2*y*z*B + 2*x*y*z*B + y*z*B,
    x^2*z^3 + 2*x*z^3 + z^3,
    x^2*z*v + 2*x*z*v + z*v,
    x^2*t*u + 2*x*t*u + t*u,
    x^2*u*B + 2*x*u*B + u*B,
    x^2*A + 2*x*A + A,
    x*y^5 + y^5,
    x*y^3*t + y^3*t,
    x*y^3*B + y^3*B,
    x*y^2*z^2 + y^2*z^2,
    x*y^2*v + y^2*v,
    x*y*z*u + y*z*u,
    x*y*t^2 + y*t^2,
    x*y*t*B + y*t*B,
    x*y*B^2 + y*B^2,
    x*z^2*t + z^2*t,
    x*z^2*B + z^2*B,
    x*t*v + t*v,
    x*u^2 + u^2,
    x*v*B + v*B,
    y^4*z,
    y^3*u,
    y^2*z*t,
    y^2*z*B,
    y*z^3,
    y*z*v,
    y*t*u,
    y*u*B,
    y*A,
    z^2*u,
    z*t^2,
    z*t*B,
    z*B^2,
    u*v
@}
{@
    x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 +
        495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1,
    x^10*y + 10*x^9*y + 45*x^8*y + 120*x^7*y + 210*x^6*y + 252*x^5*y + 210*x^4*y
        + 120*x^3*y + 45*x^2*y + 10*x*y + y,
    x^9*z + 9*x^8*z + 36*x^7*z + 84*x^6*z + 126*x^5*z + 126*x^4*z + 84*x^3*z + 
        36*x^2*z + 9*x*z + z,
    x^8*y^2 + 8*x^7*y^2 + 28*x^6*y^2 + 56*x^5*y^2 + 70*x^4*y^2 + 56*x^3*y^2 + 
        28*x^2*y^2 + 8*x*y^2 + y^2,
    x^8*t + 8*x^7*t + 28*x^6*t + 56*x^5*t + 70*x^4*t + 56*x^3*t + 28*x^2*t + 
        8*x*t + t,
    x^8*B + 8*x^7*B + 28*x^6*B + 56*x^5*B + 70*x^4*B + 56*x^3*B + 28*x^2*B + 
        8*x*B + B,
    x^7*y*z + 7*x^6*y*z + 21*x^5*y*z + 35*x^4*y*z + 35*x^3*y*z + 21*x^2*y*z + 
        7*x*y*z + y*z,
    x^7*u + 7*x^6*u + 21*x^5*u + 35*x^4*u + 35*x^3*u + 21*x^2*u + 7*x*u + u,
    x^6*y^3 + 6*x^5*y^3 + 15*x^4*y^3 + 20*x^3*y^3 + 15*x^2*y^3 + 6*x*y^3 + y^3,
    x^6*y*t + 6*x^5*y*t + 15*x^4*y*t + 20*x^3*y*t + 15*x^2*y*t + 6*x*y*t + y*t,
    x^6*y*B + 6*x^5*y*B + 15*x^4*y*B + 20*x^3*y*B + 15*x^2*y*B + 6*x*y*B + y*B,
    x^6*z^2 + 6*x^5*z^2 + 15*x^4*z^2 + 20*x^3*z^2 + 15*x^2*z^2 + 6*x*z^2 + z^2,
    x^6*v + 6*x^5*v + 15*x^4*v + 20*x^3*v + 15*x^2*v + 6*x*v + v,
    x^5*y^2*z + 5*x^4*y^2*z + 10*x^3*y^2*z + 10*x^2*y^2*z + 5*x*y^2*z + y^2*z,
    x^5*y*u + 5*x^4*y*u + 10*x^3*y*u + 10*x^2*y*u + 5*x*y*u + y*u,
    x^5*z*t + 5*x^4*z*t + 10*x^3*z*t + 10*x^2*z*t + 5*x*z*t + z*t,
    x^5*z*B + 5*x^4*z*B + 10*x^3*z*B + 10*x^2*z*B + 5*x*z*B + z*B,
    x^4*y^4 + 4*x^3*y^4 + 6*x^2*y^4 + 4*x*y^4 + y^4,
    x^4*y^2*t + 4*x^3*y^2*t + 6*x^2*y^2*t + 4*x*y^2*t + y^2*t,
    x^4*y^2*B + 4*x^3*y^2*B + 6*x^2*y^2*B + 4*x*y^2*B + y^2*B,
    x^4*y*z^2 + 4*x^3*y*z^2 + 6*x^2*y*z^2 + 4*x*y*z^2 + y*z^2,
    x^4*y*v + 4*x^3*y*v + 6*x^2*y*v + 4*x*y*v + y*v,
    x^4*z*u + 4*x^3*z*u + 6*x^2*z*u + 4*x*z*u + z*u,
    x^4*t^2 + 4*x^3*t^2 + 6*x^2*t^2 + 4*x*t^2 + t^2,
    x^4*t*B + 4*x^3*t*B + 6*x^2*t*B + 4*x*t*B + t*B,
    x^4*B^2 + 4*x^3*B^2 + 6*x^2*B^2 + 4*x*B^2 + B^2,
    x^3*y^3*z + 3*x^2*y^3*z + 3*x*y^3*z + y^3*z,
    x^3*y^2*u + 3*x^2*y^2*u + 3*x*y^2*u + y^2*u,
    x^3*y*z*t + 3*x^2*y*z*t + 3*x*y*z*t + y*z*t,
    x^3*y*z*B + 3*x^2*y*z*B + 3*x*y*z*B + y*z*B,
    x^3*z^3 + 3*x^2*z^3 + 3*x*z^3 + z^3,
    x^3*z*v + 3*x^2*z*v + 3*x*z*v + z*v,
    x^3*t*u + 3*x^2*t*u + 3*x*t*u + t*u,
    x^3*u*B + 3*x^2*u*B + 3*x*u*B + u*B,
    x^3*A + 3*x^2*A + 3*x*A + A,
    x^2*y^5 + 2*x*y^5 + y^5,
    x^2*y^3*t + 2*x*y^3*t + y^3*t,
    x^2*y^3*B + 2*x*y^3*B + y^3*B,
    x^2*y^2*z^2 + 2*x*y^2*z^2 + y^2*z^2,
    x^2*y^2*v + 2*x*y^2*v + y^2*v,
    x^2*y*z*u + 2*x*y*z*u + y*z*u,
    x^2*y*t^2 + 2*x*y*t^2 + y*t^2,
    x^2*y*t*B + 2*x*y*t*B + y*t*B,
    x^2*y*B^2 + 2*x*y*B^2 + y*B^2,
    x^2*z^2*t + 2*x*z^2*t + z^2*t,
    x^2*z^2*B + 2*x*z^2*B + z^2*B,
    x^2*t*v + 2*x*t*v + t*v,
    x^2*u^2 + 2*x*u^2 + u^2,
    x^2*v*B + 2*x*v*B + v*B,
    x*y^4*z + y^4*z,
    x*y^3*u + y^3*u,
    x*y^2*z*t + y^2*z*t,
    x*y^2*z*B + y
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:33:46 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:33:45 on modular  [Seed = 91162526]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
            ^
Runtime error in hom< ... >: Argument 3 does not describe an image

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:34:05 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R->S|x,y,y^2x^(-1),y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:34:04 on modular  [Seed = 360650747]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2x^(-1),y^3/x^2,u,v,A,B>;
                         ^
User error: Invalid hexadecimal integer

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:34:14 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
subs:=hom<R->S|x,y,y^2*x^(-1),y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:34:13 on modular  [Seed = 1695508370]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2*x^(-1),y^3/x^2,u,v,A,B>;
                           ^
Runtime error in '^': Argument 2 (-1) should be >= 0

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB07a.cache.pol.co.uk. (195.92.168.169)
Time: Tue Aug 24 09:35:35 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 09:35:34 on modular  [Seed = 1327843915]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    y^2/x
@}
{@
    x^4,
    x^2*y,
    y^2,
    y^3/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    x*y^2,
    y^3/x,
    x*B,
    u
@}
{@
    x^6,
    x^4*y,
    x^2*y^2,
    y^3,
    x^2*B,
    x*u,
    y^4/x^2,
    y*B,
    v
@}
{@
    x^7,
    x^5*y,
    x^3*y^2,
    x*y^3,
    x^3*B,
    x^2*u,
    y^4/x,
    x*y*B,
    x*v,
    y*u,
    y^5/x^3,
    y^2*B/x
@}
{@
    x^8,
    x^6*y,
    x^4*y^2,
    x^2*y^3,
    x^4*B,
    x^3*u,
    y^4,
    x^2*y*B,
    x^2*v,
    x*y*u,
    y^5/x^2,
    y^2*B,
    y*v,
    y^2*u/x,
    y^6/x^4,
    y^3*B/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^5*y^2,
    x^3*y^3,
    x^5*B,
    x^4*u,
    x*y^4,
    x^3*y*B,
    x^3*v,
    x^2*y*u,
    y^5/x,
    x*y^2*B,
    x*y*v,
    y^2*u,
    y^6/x^3,
    y^3*B/x,
    x*B^2,
    y^2*v/x,
    y^3*u/x^2,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    x^6*y^2,
    x^4*y^3,
    x^6*B,
    x^5*u,
    x^2*y^4,
    x^4*y*B,
    x^4*v,
    x^3*y*u,
    y^5,
    x^2*y^2*B,
    x^2*y*v,
    x*y^2*u,
    y^6/x^2,
    y^3*B,
    x^2*B^2,
    y^2*v,
    y^3*u/x,
    x*u*B,
    x*A,
    y^7/x^4,
    y^4*B/x^2,
    y*B^2,
    y^3*v/x^2,
    u^2,
    v*B
@}
{@
    x^11,
    x^9*y,
    x^7*y^2,
    x^5*y^3,
    x^7*B,
    x^6*u,
    x^3*y^4,
    x^5*y*B,
    x^5*v,
    x^4*y*u,
    x*y^5,
    x^3*y^2*B,
    x^3*y*v,
    x^2*y^2*u,
    y^6/x,
    x*y^3*B,
    x^3*B^2,
    x*y^2*v,
    y^3*u,
    x^2*u*B,
    x^2*A,
    y^7/x^3,
    y^4*B/x,
    x*y*B^2,
    y^3*v/x,
    x*u^2,
    x*v*B,
    y^4*u/x^2,
    y*u*B,
    y*A,
    y^8/x^5,
    y^5*B/x^3,
    y^2*B^2/x,
    u*v
@}
{@
    x^12,
    x^10*y,
    x^8*y^2,
    x^6*y^3,
    x^8*B,
    x^7*u,
    x^4*y^4,
    x^6*y*B,
    x^6*v,
    x^5*y*u,
    x^2*y^5,
    x^4*y^2*B,
    x^4*y*v,
    x^3*y^2*u,
    y^6,
    x^2*y^3*B,
    x^4*B^2,
    x^2*y^2*v,
    x*y^3*u,
    x^3*u*B,
    x^3*A,
    y^7/x^2,
    y^4*B,
    x^2*y*B^2,
    y^3*v,
    x^2*u^2,
    x^2*v*B,
    y^4*u/x,
    x*y*u*B,
    x*y*A,
    y^8/x^4,
    y^5*B/x^2,
    y^2*B^2,
    x*u*v,
    y^4*v/x^2,
    y*u^2,
    y*v*B,
    y^5*u/x^3,
    y^2*u*B/x,
    y^2*A/x,
    y^9/x^6,
    y^6*B/x^4,
    y^3*B^2/x^2,
    v^2,
    B^3
@}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:25:19 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-(a_1),y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:25:19 on modular  [Seed = 2115268761]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x-(a_1),y^3/x^2,u,v,A,B>;
                             ^
User error: Identifier 'a_1' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:25:30 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-(a_1)*x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:25:30 on modular  [Seed = 1998420357]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x-(a_1)*x,y^3/x^2,u,v,A,B>;
                             ^
User error: Identifier 'a_1' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:25:44 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-a_1*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:25:43 on modular  [Seed = 1479693975]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x-a_1*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a_1' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:27:45 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:27:45 on modular  [Seed = 2683670230]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:28:03 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
a_1!Rationals();
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:28:02 on modular  [Seed = 3867998140]
   -------------------------------------


>> a_1!Rationals();
   ^
User error: Identifier 'a_1' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:28:11 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
a!Rationals();
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:28:11 on modular  [Seed = 4154320548]
   -------------------------------------


>> a!Rationals();
   ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:31:25 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
R!a;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:31:24 on modular  [Seed = 2031315310]
   -------------------------------------


>> R!a;
     ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:32:27 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
elt<R|a>;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:32:27 on modular  [Seed = 1413366788]
   -------------------------------------


>> elt<R|a>;
         ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:34:30 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
elt<R|a>;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:34:29 on modular  [Seed = 4203801124]
   -------------------------------------


>> elt<R|a>;
         ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:36:31 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
elt<RationalField()|a>;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:36:30 on modular  [Seed = 1045704058]
   -------------------------------------


>> elt<RationalField()|a>;
                       ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:36:42 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
RationalField()!a;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:36:41 on modular  [Seed = 912008549]
   -------------------------------------


>> RationalField()!a;
                   ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:36:51 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
RationalField() ! a;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:36:50 on modular  [Seed = 241442214]
   -------------------------------------


>> RationalField() ! a;
                     ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:39:02 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
a:=elt<R>;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:39:02 on modular  [Seed = 2014472788]
   -------------------------------------


>> a:=elt<R>;
           ^
User error: bad syntax

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:39:20 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
a:=elt<RationalField()>;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:39:20 on modular  [Seed = 1210210938]
   -------------------------------------


>> a:=elt<RationalField()>;
                         ^
User error: bad syntax

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:40:03 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
a:=elt(RationalField());
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:40:03 on modular  [Seed = 2967118553]
   -------------------------------------


>> a:=elt(RationalField());
      ^
User error: Identifier 'elt' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:40:17 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
RationalField()!a;
subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:40:16 on modular  [Seed = 2179699707]
   -------------------------------------


>> RationalField()!a;
                   ^
User error: Identifier 'a' has not been declared or assigned

>> subs:=hom<R->S|x,y,y^2/x-a*x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'a' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.590 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:47:21 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-x_0,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:47:20 on modular  [Seed = 2666826570]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x-x_0,y^3/x^2,u,v,A,B>;
                            ^
User error: Identifier 'x_0' has not been declared or assigned

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:51:10 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-x[0],y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:51:09 on modular  [Seed = 377225959]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x-x[0],y^3/x^2,u,v,A,B>;
                             ^
Runtime error in '[]': Bad argument types

>> subs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'subs' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Tue Aug 24 10:54:19 2004

Input: R<x,y,z,t,u,v,C,D>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,8]);
S<x,y,z,t,u,v,C,D>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,C,D>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 10:54:18 on modular  [Seed = 2247070259]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    y^2/x
@}
{@
    x^4,
    x^2*y,
    y^2,
    y^3/x^2
@}
{@
    x^5,
    x^3*y,
    x*y^2,
    y^3/x,
    u
@}
{@
    x^6,
    x^4*y,
    x^2*y^2,
    y^3,
    x*u,
    y^4/x^2,
    v
@}
{@
    x^7,
    x^5*y,
    x^3*y^2,
    x*y^3,
    x^2*u,
    y^4/x,
    x*v,
    y*u,
    y^5/x^3
@}
{@
    x^8,
    x^6*y,
    x^4*y^2,
    x^2*y^3,
    x^3*u,
    y^4,
    x^2*v,
    x*y*u,
    y^5/x^2,
    y*v,
    y^2*u/x,
    y^6/x^4,
    D
@}
{@
    x^9,
    x^7*y,
    x^5*y^2,
    x^3*y^3,
    x^4*u,
    x*y^4,
    x^3*v,
    x^2*y*u,
    y^5/x,
    x*y*v,
    y^2*u,
    y^6/x^3,
    x*D,
    y^2*v/x,
    y^3*u/x^2,
    C
@}
{@
    x^10,
    x^8*y,
    x^6*y^2,
    x^4*y^3,
    x^5*u,
    x^2*y^4,
    x^4*v,
    x^3*y*u,
    y^5,
    x^2*y*v,
    x*y^2*u,
    y^6/x^2,
    x^2*D,
    y^2*v,
    y^3*u/x,
    x*C,
    y^7/x^4,
    y*D,
    y^3*v/x^2,
    u^2
@}
{@
    x^11,
    x^9*y,
    x^7*y^2,
    x^5*y^3,
    x^6*u,
    x^3*y^4,
    x^5*v,
    x^4*y*u,
    x*y^5,
    x^3*y*v,
    x^2*y^2*u,
    y^6/x,
    x^3*D,
    x*y^2*v,
    y^3*u,
    x^2*C,
    y^7/x^3,
    x*y*D,
    y^3*v/x,
    x*u^2,
    y^4*u/x^2,
    y*C,
    y^8/x^5,
    y^2*D/x,
    u*v
@}
{@
    x^12,
    x^10*y,
    x^8*y^2,
    x^6*y^3,
    x^7*u,
    x^4*y^4,
    x^6*v,
    x^5*y*u,
    x^2*y^5,
    x^4*y*v,
    x^3*y^2*u,
    y^6,
    x^4*D,
    x^2*y^2*v,
    x*y^3*u,
    x^3*C,
    y^7/x^2,
    x^2*y*D,
    y^3*v,
    x^2*u^2,
    y^4*u/x,
    x*y*C,
    y^8/x^4,
    y^2*D,
    x*u*v,
    y^4*v/x^2,
    y*u^2,
    y^5*u/x^3,
    y^2*C/x,
    y^9/x^6,
    y^3*D/x^2,
    v^2
@}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB04a.cache.pol.co.uk. (195.92.168.166)
Time: Tue Aug 24 12:29:20 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
T<x_0,y,z,t,u,v,A,B>:=FieldOfFractions(PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]));
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
newsubs:=hom<R->T|x,y,y^2/x+x^2*x_0+2*y*x_0+3*x*x_0^2+4*x_0^3,y^3/x^2-x*y*x_0-2*y^2*x_0/x-3*y*x_0^2-4*y*x_0^3/x,u,v,A,B>;
for i in [1..12] do
newsubs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 12:29:19 on modular  [Seed = 3501915443]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
                         ^
Runtime error in '/': Arguments are not compatible
Argument types given: FldFunRatMElt, FldFunRatMElt

>> newsubs:=hom<R->T|x,y,y^2/x+x^2*x_0+2*y*x_0+3*x*x_0^2+4*x_0^3,y^3/x^2-x*y*x
                            ^
Runtime error in '/': Arguments are not compatible
Argument types given: FldFunRatMElt, FldFunRatMElt

>> newsubs(MonomialsOfWeightedDegree(R,i));
   ^
User error: Identifier 'newsubs' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB04a.cache.pol.co.uk. (195.92.168.166)
Time: Tue Aug 24 12:29:46 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
T<x_0,x,y,z,t,u,v,A,B>:=FieldOfFractions(PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]));
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
newsubs:=hom<R->T|x,y,y^2/x+x^2*x_0+2*y*x_0+3*x*x_0^2+4*x_0^3,y^3/x^2-x*y*x_0-2*y^2*x_0/x-3*y*x_0^2-4*y*x_0^3/x,u,v,A,B>;
for i in [1..12] do
newsubs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 12:29:45 on modular  [Seed = 1045697528]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
            ^
Runtime error in hom< ... >: RHS has arity 8 but should have length 8
{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (4*x_0^3*x + 3*x_0^2*x^2 + x_0*x^3 + 2*x_0*x*y + y^2)/x
@}
{@
    x^4,
    x^2*y,
    4*x_0^3*x + 3*x_0^2*x^2 + x_0*x^3 + 2*x_0*x*y + y^2,
    y^2,
    (-4*x_0^3*x*y - 3*x_0^2*x^2*y - x_0*x^3*y - 2*x_0*x*y^2 + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    4*x_0^3*x^2 + 3*x_0^2*x^3 + x_0*x^4 + 2*x_0*x^2*y + x*y^2,
    x*y^2,
    (-4*x_0^3*x*y - 3*x_0^2*x^2*y - x_0*x^3*y - 2*x_0*x*y^2 + y^3)/x,
    x*B,
    (4*x_0^3*x*y + 3*x_0^2*x^2*y + x_0*x^3*y + 2*x_0*x*y^2 + y^3)/x,
    u
@}
{@
    x^6,
    x^4*y,
    4*x_0^3*x^3 + 3*x_0^2*x^4 + x_0*x^5 + 2*x_0*x^3*y + x^2*y^2,
    x^2*y^2,
    -4*x_0^3*x*y - 3*x_0^2*x^2*y - x_0*x^3*y - 2*x_0*x*y^2 + y^3,
    x^2*B,
    4*x_0^3*x*y + 3*x_0^2*x^2*y + x_0*x^3*y + 2*x_0*x*y^2 + y^3,
    x*u,
    y^3,
    (-4*x_0^3*x*y^2 - 3*x_0^2*x^2*y^2 - x_0*x^3*y^2 - 2*x_0*x*y^3 + y^4)/x^2,
    y*B,
    (16*x_0^6*x^2 + 24*x_0^5*x^3 + 17*x_0^4*x^4 + 16*x_0^4*x^2*y + 6*x_0^3*x^5 +
        12*x_0^3*x^3*y + 8*x_0^3*x*y^2 + x_0^2*x^6 + 4*x_0^2*x^4*y + 
        10*x_0^2*x^2*y^2 + 2*x_0*x^3*y^2 + 4*x_0*x*y^3 + y^4)/x^2,
    v
@}
{@
    x^7,
    x^5*y,
    4*x_0^3*x^4 + 3*x_0^2*x^5 + x_0*x^6 + 2*x_0*x^4*y + x^3*y^2,
    x^3*y^2,
    -4*x_0^3*x^2*y - 3*x_0^2*x^3*y - x_0*x^4*y - 2*x_0*x^2*y^2 + x*y^3,
    x^3*B,
    4*x_0^3*x^2*y + 3*x_0^2*x^3*y + x_0*x^4*y + 2*x_0*x^2*y^2 + x*y^3,
    x^2*u,
    x*y^3,
    (-4*x_0^3*x*y^2 - 3*x_0^2*x^2*y^2 - x_0*x^3*y^2 - 2*x_0*x*y^3 + y^4)/x,
    x*y*B,
    (16*x_0^6*x^2 + 24*x_0^5*x^3 + 17*x_0^4*x^4 + 16*x_0^4*x^2*y + 6*x_0^3*x^5 +
        12*x_0^3*x^3*y + 8*x_0^3*x*y^2 + x_0^2*x^6 + 4*x_0^2*x^4*y + 
        10*x_0^2*x^2*y^2 + 2*x_0*x^3*y^2 + 4*x_0*x*y^3 + y^4)/x,
    x*v,
    (4*x_0^3*x*y^2 + 3*x_0^2*x^2*y^2 + x_0*x^3*y^2 + 2*x_0*x*y^3 + y^4)/x,
    y*u,
    (-16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5)/x^3,
    (4*x_0^3*x*B + 3*x_0^2*x^2*B + x_0*x^3*B + 2*x_0*x*y*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    4*x_0^3*x^5 + 3*x_0^2*x^6 + x_0*x^7 + 2*x_0*x^5*y + x^4*y^2,
    x^4*y^2,
    -4*x_0^3*x^3*y - 3*x_0^2*x^4*y - x_0*x^5*y - 2*x_0*x^3*y^2 + x^2*y^3,
    x^4*B,
    4*x_0^3*x^3*y + 3*x_0^2*x^4*y + x_0*x^5*y + 2*x_0*x^3*y^2 + x^2*y^3,
    x^3*u,
    x^2*y^3,
    -4*x_0^3*x*y^2 - 3*x_0^2*x^2*y^2 - x_0*x^3*y^2 - 2*x_0*x*y^3 + y^4,
    x^2*y*B,
    16*x_0^6*x^2 + 24*x_0^5*x^3 + 17*x_0^4*x^4 + 16*x_0^4*x^2*y + 6*x_0^3*x^5 + 
        12*x_0^3*x^3*y + 8*x_0^3*x*y^2 + x_0^2*x^6 + 4*x_0^2*x^4*y + 
        10*x_0^2*x^2*y^2 + 2*x_0*x^3*y^2 + 4*x_0*x*y^3 + y^4,
    x^2*v,
    4*x_0^3*x*y^2 + 3*x_0^2*x^2*y^2 + x_0*x^3*y^2 + 2*x_0*x*y^3 + y^4,
    x*y*u,
    (-16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5)/x^2,
    4*x_0^3*x*B + 3*x_0^2*x^2*B + x_0*x^3*B + 2*x_0*x*y*B + y^2*B,
    y^4,
    (-4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5)/x^2,
    y^2*B,
    (16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + 
        y^5)/x^2,
    y*v,
    (4*x_0^3*x*u + 3*x_0^2*x^2*u + x_0*x^3*u + 2*x_0*x*y*u + y^2*u)/x,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^4,
    (-4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + 
        y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    4*x_0^3*x^6 + 3*x_0^2*x^7 + x_0*x^8 + 2*x_0*x^6*y + x^5*y^2,
    x^5*y^2,
    -4*x_0^3*x^4*y - 3*x_0^2*x^5*y - x_0*x^6*y - 2*x_0*x^4*y^2 + x^3*y^3,
    x^5*B,
    4*x_0^3*x^4*y + 3*x_0^2*x^5*y + x_0*x^6*y + 2*x_0*x^4*y^2 + x^3*y^3,
    x^4*u,
    x^3*y^3,
    -4*x_0^3*x^2*y^2 - 3*x_0^2*x^3*y^2 - x_0*x^4*y^2 - 2*x_0*x^2*y^3 + x*y^4,
    x^3*y*B,
    16*x_0^6*x^3 + 24*x_0^5*x^4 + 17*x_0^4*x^5 + 16*x_0^4*x^3*y + 6*x_0^3*x^6 + 
        12*x_0^3*x^4*y + 8*x_0^3*x^2*y^2 + x_0^2*x^7 + 4*x_0^2*x^5*y + 
        10*x_0^2*x^3*y^2 + 2*x_0*x^4*y^2 + 4*x_0*x^2*y^3 + x*y^4,
    x^3*v,
    4*x_0^3*x^2*y^2 + 3*x_0^2*x^3*y^2 + x_0*x^4*y^2 + 2*x_0*x^2*y^3 + x*y^4,
    x^2*y*u,
    (-16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5)/x,
    4*x_0^3*x^2*B + 3*x_0^2*x^3*B + x_0*x^4*B + 2*x_0*x^2*y*B + x*y^2*B,
    x*y^4,
    (-4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5)/x,
    x*y^2*B,
    (16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + 
        y^5)/x,
    x*y*v,
    4*x_0^3*x*u + 3*x_0^2*x^2*u + x_0*x^3*u + 2*x_0*x*y*u + y^2*u,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^3,
    (-4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + y^3*B)/x,
    x*B^2,
    (4*x_0^3*x*y^3 + 3*x_0^2*x^2*y^3 + x_0*x^3*y^3 + 2*x_0*x*y^4 + y^5)/x,
    y^2*u,
    (-16*x_0^6*x^2*y^2 - 24*x_0^5*x^3*y^2 - 17*x_0^4*x^4*y^2 - 16*x_0^4*x^2*y^3 
        - 6*x_0^3*x^5*y^2 - 12*x_0^3*x^3*y^3 - x_0^2*x^6*y^2 - 4*x_0^2*x^4*y^3 -
        4*x_0^2*x^2*y^4 + y^6)/x^3,
    (4*x_0^3*x*y*B + 3*x_0^2*x^2*y*B + x_0*x^3*y*B + 2*x_0*x*y^2*B + y^3*B)/x,
    (64*x_0^9*x^3 + 144*x_0^8*x^4 + 156*x_0^7*x^5 + 96*x_0^7*x^3*y + 
        99*x_0^6*x^6 + 144*x_0^6*x^4*y + 48*x_0^6*x^2*y^2 + 39*x_0^5*x^7 + 
        102*x_0^5*x^5*y + 120*x_0^5*x^3*y^2 + 9*x_0^4*x^8 + 36*x_0^4*x^6*y + 
        87*x_0^4*x^4*y^2 + 48*x_0^4*x^2*y^3 + x_0^3*x^9 + 6*x_0^3*x^7*y + 
        30*x_0^3*x^5*y^2 + 44*x_0^3*x^3*y^3 + 12*x_0^3*x*y^4 + 3*x_0^2*x^6*y^2 +
        12*x_0^2*x^4*y^3 + 21*x_0^2*x^2*y^4 + 3*x_0*x^3*y^4 + 6*x_0*x*y^5 + 
        y^6)/x^3,
    (4*x_0^3*x*v + 3*x_0^2*x^2*v + x_0*x^3*v + 2*x_0*x*y*v + y^2*v)/x,
    (-4*x_0^3*x*y*u - 3*x_0^2*x^2*y*u - x_0*x^3*y*u - 2*x_0*x*y^2*u + 
        y^3*u)/x^2,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    4*x_0^3*x^7 + 3*x_0^2*x^8 + x_0*x^9 + 2*x_0*x^7*y + x^6*y^2,
    x^6*y^2,
    -4*x_0^3*x^5*y - 3*x_0^2*x^6*y - x_0*x^7*y - 2*x_0*x^5*y^2 + x^4*y^3,
    x^6*B,
    4*x_0^3*x^5*y + 3*x_0^2*x^6*y + x_0*x^7*y + 2*x_0*x^5*y^2 + x^4*y^3,
    x^5*u,
    x^4*y^3,
    -4*x_0^3*x^3*y^2 - 3*x_0^2*x^4*y^2 - x_0*x^5*y^2 - 2*x_0*x^3*y^3 + x^2*y^4,
    x^4*y*B,
    16*x_0^6*x^4 + 24*x_0^5*x^5 + 17*x_0^4*x^6 + 16*x_0^4*x^4*y + 6*x_0^3*x^7 + 
        12*x_0^3*x^5*y + 8*x_0^3*x^3*y^2 + x_0^2*x^8 + 4*x_0^2*x^6*y + 
        10*x_0^2*x^4*y^2 + 2*x_0*x^5*y^2 + 4*x_0*x^3*y^3 + x^2*y^4,
    x^4*v,
    4*x_0^3*x^3*y^2 + 3*x_0^2*x^4*y^2 + x_0*x^5*y^2 + 2*x_0*x^3*y^3 + x^2*y^4,
    x^3*y*u,
    -16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5,
    4*x_0^3*x^3*B + 3*x_0^2*x^4*B + x_0*x^5*B + 2*x_0*x^3*y*B + x^2*y^2*B,
    x^2*y^4,
    -4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5,
    x^2*y^2*B,
    16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + y^5,
    x^2*y*v,
    4*x_0^3*x^2*u + 3*x_0^2*x^3*u + x_0*x^4*u + 2*x_0*x^2*y*u + x*y^2*u,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^2,
    -4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + y^3*B,
    x^2*B^2,
    4*x_0^3*x*y^3 + 3*x_0^2*x^2*y^3 + x_0*x^3*y^3 + 2*x_0*x*y^4 + y^5,
    x*y^2*u,
    (-16*x_0^6*x^2*y^2 - 24*x_0^5*x^3*y^2 - 17*x_0^4*x^4*y^2 - 16*x_0^4*x^2*y^3 
        - 6*x_0^3*x^5*y^2 - 12*x_0^3*x^3*y^3 - x_0^2*x^6*y^2 - 4*x_0^2*x^4*y^3 -
        4*x_0^2*x^2*y^4 + y^6)/x^2,
    4*x_0^3*x*y*B + 3*x_0^2*x^2*y*B + x_0*x^3*y*B + 2*x_0*x*y^2*B + y^3*B,
    (64*x_0^9*x^3 + 144*x_0^8*x^4 + 156*x_0^7*x^5 + 96*x_0^7*x^3*y + 
        99*x_0^6*x^6 + 144*x_0^6*x^4*y + 48*x_0^6*x^2*y^2 + 39*x_0^5*x^7 + 
        102*x_0^5*x^5*y + 120*x_0^5*x^3*y^2 + 9*x_0^4*x^8 + 36*x_0^4*x^6*y + 
        87*x_0^4*x^4*y^2 + 48*x_0^4*x^2*y^3 + x_0^3*x^9 + 6*x_0^3*x^7*y + 
        30*x_0^3*x^5*y^2 + 44*x_0^3*x^3*y^3 + 12*x_0^3*x*y^4 + 3*x_0^2*x^6*y^2 +
        12*x_0^2*x^4*y^3 + 21*x_0^2*x^2*y^4 + 3*x_0*x^3*y^4 + 6*x_0*x*y^5 + 
        y^6)/x^2,
    4*x_0^3*x*v + 3*x_0^2*x^2*v + x_0*x^3*v + 2*x_0*x*y*v + y^2*v,
    (-4*x_0^3*x*y*u - 3*x_0^2*x^2*y*u - x_0*x^3*y*u - 2*x_0*x*y^2*u + y^3*u)/x,
    x*u*B,
    x*A,
    y^5,
    (-4*x_0^3*x*y^4 - 3*x_0^2*x^2*y^4 - x_0*x^3*y^4 - 2*x_0*x*y^5 + y^6)/x^2,
    y^3*B,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 + 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 + 10*x_0^2*x^2*y^4 + 2*x_0*x^3*y^4 + 4*x_0*x*y^5 + 
        y^6)/x^2,
    y^2*v,
    (4*x_0^3*x*y*u + 3*x_0^2*x^2*y*u + x_0*x^3*y*u + 2*x_0*x*y^2*u + y^3*u)/x,
    (16*x_0^6*x^2*y^3 + 24*x_0^5*x^3*y^3 + 17*x_0^4*x^4*y^3 + 16*x_0^4*x^2*y^4 +
        6*x_0^3*x^5*y^3 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB04a.cache.pol.co.uk. (195.92.168.166)
Time: Tue Aug 24 12:34:02 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
T<x_0,x,y,z,t,u,v,A,B>:=FieldOfFractions(PolynomialRing(RationalField(),[1,1,2,3,4,5,6,9,4]));
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
newsubs:=hom<R->T|x,y,y^2/x+x^2*x_0+2*y*x_0+3*x*x_0^2+4*x_0^3,y^3/x^2-x*y*x_0-2*y^2*x_0/x-3*y*x_0^2-4*y*x_0^3/x,u,v,A,B>;
for i in [10..10] do
newsubs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 12:34:02 on modular  [Seed = 3951150894]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
            ^
Runtime error in hom< ... >: RHS has arity 8 but should have length 8
{@
    x^10,
    x^8*y,
    4*x_0^3*x^7 + 3*x_0^2*x^8 + x_0*x^9 + 2*x_0*x^7*y + x^6*y^2,
    x^6*y^2,
    -4*x_0^3*x^5*y - 3*x_0^2*x^6*y - x_0*x^7*y - 2*x_0*x^5*y^2 + x^4*y^3,
    x^6*B,
    4*x_0^3*x^5*y + 3*x_0^2*x^6*y + x_0*x^7*y + 2*x_0*x^5*y^2 + x^4*y^3,
    x^5*u,
    x^4*y^3,
    -4*x_0^3*x^3*y^2 - 3*x_0^2*x^4*y^2 - x_0*x^5*y^2 - 2*x_0*x^3*y^3 + x^2*y^4,
    x^4*y*B,
    16*x_0^6*x^4 + 24*x_0^5*x^5 + 17*x_0^4*x^6 + 16*x_0^4*x^4*y + 6*x_0^3*x^7 + 
        12*x_0^3*x^5*y + 8*x_0^3*x^3*y^2 + x_0^2*x^8 + 4*x_0^2*x^6*y + 
        10*x_0^2*x^4*y^2 + 2*x_0*x^5*y^2 + 4*x_0*x^3*y^3 + x^2*y^4,
    x^4*v,
    4*x_0^3*x^3*y^2 + 3*x_0^2*x^4*y^2 + x_0*x^5*y^2 + 2*x_0*x^3*y^3 + x^2*y^4,
    x^3*y*u,
    -16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5,
    4*x_0^3*x^3*B + 3*x_0^2*x^4*B + x_0*x^5*B + 2*x_0*x^3*y*B + x^2*y^2*B,
    x^2*y^4,
    -4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5,
    x^2*y^2*B,
    16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + y^5,
    x^2*y*v,
    4*x_0^3*x^2*u + 3*x_0^2*x^3*u + x_0*x^4*u + 2*x_0*x^2*y*u + x*y^2*u,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^2,
    -4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + y^3*B,
    x^2*B^2,
    4*x_0^3*x*y^3 + 3*x_0^2*x^2*y^3 + x_0*x^3*y^3 + 2*x_0*x*y^4 + y^5,
    x*y^2*u,
    (-16*x_0^6*x^2*y^2 - 24*x_0^5*x^3*y^2 - 17*x_0^4*x^4*y^2 - 16*x_0^4*x^2*y^3 
        - 6*x_0^3*x^5*y^2 - 12*x_0^3*x^3*y^3 - x_0^2*x^6*y^2 - 4*x_0^2*x^4*y^3 -
        4*x_0^2*x^2*y^4 + y^6)/x^2,
    4*x_0^3*x*y*B + 3*x_0^2*x^2*y*B + x_0*x^3*y*B + 2*x_0*x*y^2*B + y^3*B,
    (64*x_0^9*x^3 + 144*x_0^8*x^4 + 156*x_0^7*x^5 + 96*x_0^7*x^3*y + 
        99*x_0^6*x^6 + 144*x_0^6*x^4*y + 48*x_0^6*x^2*y^2 + 39*x_0^5*x^7 + 
        102*x_0^5*x^5*y + 120*x_0^5*x^3*y^2 + 9*x_0^4*x^8 + 36*x_0^4*x^6*y + 
        87*x_0^4*x^4*y^2 + 48*x_0^4*x^2*y^3 + x_0^3*x^9 + 6*x_0^3*x^7*y + 
        30*x_0^3*x^5*y^2 + 44*x_0^3*x^3*y^3 + 12*x_0^3*x*y^4 + 3*x_0^2*x^6*y^2 +
        12*x_0^2*x^4*y^3 + 21*x_0^2*x^2*y^4 + 3*x_0*x^3*y^4 + 6*x_0*x*y^5 + 
        y^6)/x^2,
    4*x_0^3*x*v + 3*x_0^2*x^2*v + x_0*x^3*v + 2*x_0*x*y*v + y^2*v,
    (-4*x_0^3*x*y*u - 3*x_0^2*x^2*y*u - x_0*x^3*y*u - 2*x_0*x*y^2*u + y^3*u)/x,
    x*u*B,
    x*A,
    y^5,
    (-4*x_0^3*x*y^4 - 3*x_0^2*x^2*y^4 - x_0*x^3*y^4 - 2*x_0*x*y^5 + y^6)/x^2,
    y^3*B,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 + 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 + 10*x_0^2*x^2*y^4 + 2*x_0*x^3*y^4 + 4*x_0*x*y^5 + 
        y^6)/x^2,
    y^2*v,
    (4*x_0^3*x*y*u + 3*x_0^2*x^2*y*u + x_0*x^3*y*u + 2*x_0*x*y^2*u + y^3*u)/x,
    (16*x_0^6*x^2*y^3 + 24*x_0^5*x^3*y^3 + 17*x_0^4*x^4*y^3 + 16*x_0^4*x^2*y^4 +
        6*x_0^3*x^5*y^3 + 12*x_0^3*x^3*y^4 - 8*x_0^3*x*y^5 + x_0^2*x^6*y^3 + 
        4*x_0^2*x^4*y^4 - 2*x_0^2*x^2*y^5 - 2*x_0*x^3*y^5 - 4*x_0*x*y^6 + 
        y^7)/x^4,
    (-4*x_0^3*x*y^2*B - 3*x_0^2*x^2*y^2*B - x_0*x^3*y^2*B - 2*x_0*x*y^3*B + 
        y^4*B)/x^2,
    y*B^2,
    (-64*x_0^9*x^3*y - 144*x_0^8*x^4*y - 156*x_0^7*x^5*y - 96*x_0^7*x^3*y^2 - 
        99*x_0^6*x^6*y - 144*x_0^6*x^4*y^2 - 16*x_0^6*x^2*y^3 - 39*x_0^5*x^7*y -
        102*x_0^5*x^5*y^2 - 72*x_0^5*x^3*y^3 - 9*x_0^4*x^8*y - 36*x_0^4*x^6*y^2 
        - 53*x_0^4*x^4*y^3 - 16*x_0^4*x^2*y^4 - x_0^3*x^9*y - 6*x_0^3*x^7*y^2 - 
        18*x_0^3*x^5*y^3 - 20*x_0^3*x^3*y^4 + 4*x_0^3*x*y^5 - x_0^2*x^6*y^3 - 
        4*x_0^2*x^4*y^4 - x_0^2*x^2*y^5 + x_0*x^3*y^5 + 2*x_0*x*y^6 + y^7)/x^4,
    (16*x_0^6*x^2*B + 24*x_0^5*x^3*B + 17*x_0^4*x^4*B + 16*x_0^4*x^2*y*B + 
        6*x_0^3*x^5*B + 12*x_0^3*x^3*y*B + 8*x_0^3*x*y^2*B + x_0^2*x^6*B + 
        4*x_0^2*x^4*y*B + 10*x_0^2*x^2*y^2*B + 2*x_0*x^3*y^2*B + 4*x_0*x*y^3*B +
        y^4*B)/x^2,
    (-4*x_0^3*x*y*v - 3*x_0^2*x^2*y*v - x_0*x^3*y*v - 2*x_0*x*y^2*v + 
        y^3*v)/x^2,
    u^2,
    v*B
@}

Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB04a.cache.pol.co.uk. (195.92.168.166)
Time: Tue Aug 24 12:35:51 2004

Input: R<x,y,z,t,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,9,4]);
S<x,y,z,t,A,B>:=FieldOfFractions(R);
T<x_0,x,y,z,t,A,B>:=FieldOfFractions(PolynomialRing(RationalField(),[1,1,2,3,4,9,4]));
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,A,B>;
newsubs:=hom<R->T|x,y,y^2/x+x^2*x_0+2*y*x_0+3*x*x_0^2+4*x_0^3,y^3/x^2-x*y*x_0-2*y^2*x_0/x-3*y*x_0^2-4*y*x_0^3/x,A,B>;
for i in [1..10] do
newsubs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 12:35:51 on modular  [Seed = 426980928]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x,y^3/x^2,A,B>;
            ^
Runtime error in hom< ... >: RHS has arity 6 but should have length 6
{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (4*x_0^3*x + 3*x_0^2*x^2 + x_0*x^3 + 2*x_0*x*y + y^2)/x
@}
{@
    x^4,
    x^2*y,
    4*x_0^3*x + 3*x_0^2*x^2 + x_0*x^3 + 2*x_0*x*y + y^2,
    y^2,
    (-4*x_0^3*x*y - 3*x_0^2*x^2*y - x_0*x^3*y - 2*x_0*x*y^2 + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    4*x_0^3*x^2 + 3*x_0^2*x^3 + x_0*x^4 + 2*x_0*x^2*y + x*y^2,
    x*y^2,
    (-4*x_0^3*x*y - 3*x_0^2*x^2*y - x_0*x^3*y - 2*x_0*x*y^2 + y^3)/x,
    x*B,
    (4*x_0^3*x*y + 3*x_0^2*x^2*y + x_0*x^3*y + 2*x_0*x*y^2 + y^3)/x
@}
{@
    x^6,
    x^4*y,
    4*x_0^3*x^3 + 3*x_0^2*x^4 + x_0*x^5 + 2*x_0*x^3*y + x^2*y^2,
    x^2*y^2,
    -4*x_0^3*x*y - 3*x_0^2*x^2*y - x_0*x^3*y - 2*x_0*x*y^2 + y^3,
    x^2*B,
    4*x_0^3*x*y + 3*x_0^2*x^2*y + x_0*x^3*y + 2*x_0*x*y^2 + y^3,
    y^3,
    (-4*x_0^3*x*y^2 - 3*x_0^2*x^2*y^2 - x_0*x^3*y^2 - 2*x_0*x*y^3 + y^4)/x^2,
    y*B,
    (16*x_0^6*x^2 + 24*x_0^5*x^3 + 17*x_0^4*x^4 + 16*x_0^4*x^2*y + 6*x_0^3*x^5 +
        12*x_0^3*x^3*y + 8*x_0^3*x*y^2 + x_0^2*x^6 + 4*x_0^2*x^4*y + 
        10*x_0^2*x^2*y^2 + 2*x_0*x^3*y^2 + 4*x_0*x*y^3 + y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    4*x_0^3*x^4 + 3*x_0^2*x^5 + x_0*x^6 + 2*x_0*x^4*y + x^3*y^2,
    x^3*y^2,
    -4*x_0^3*x^2*y - 3*x_0^2*x^3*y - x_0*x^4*y - 2*x_0*x^2*y^2 + x*y^3,
    x^3*B,
    4*x_0^3*x^2*y + 3*x_0^2*x^3*y + x_0*x^4*y + 2*x_0*x^2*y^2 + x*y^3,
    x*y^3,
    (-4*x_0^3*x*y^2 - 3*x_0^2*x^2*y^2 - x_0*x^3*y^2 - 2*x_0*x*y^3 + y^4)/x,
    x*y*B,
    (16*x_0^6*x^2 + 24*x_0^5*x^3 + 17*x_0^4*x^4 + 16*x_0^4*x^2*y + 6*x_0^3*x^5 +
        12*x_0^3*x^3*y + 8*x_0^3*x*y^2 + x_0^2*x^6 + 4*x_0^2*x^4*y + 
        10*x_0^2*x^2*y^2 + 2*x_0*x^3*y^2 + 4*x_0*x*y^3 + y^4)/x,
    (4*x_0^3*x*y^2 + 3*x_0^2*x^2*y^2 + x_0*x^3*y^2 + 2*x_0*x*y^3 + y^4)/x,
    (-16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5)/x^3,
    (4*x_0^3*x*B + 3*x_0^2*x^2*B + x_0*x^3*B + 2*x_0*x*y*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    4*x_0^3*x^5 + 3*x_0^2*x^6 + x_0*x^7 + 2*x_0*x^5*y + x^4*y^2,
    x^4*y^2,
    -4*x_0^3*x^3*y - 3*x_0^2*x^4*y - x_0*x^5*y - 2*x_0*x^3*y^2 + x^2*y^3,
    x^4*B,
    4*x_0^3*x^3*y + 3*x_0^2*x^4*y + x_0*x^5*y + 2*x_0*x^3*y^2 + x^2*y^3,
    x^2*y^3,
    -4*x_0^3*x*y^2 - 3*x_0^2*x^2*y^2 - x_0*x^3*y^2 - 2*x_0*x*y^3 + y^4,
    x^2*y*B,
    16*x_0^6*x^2 + 24*x_0^5*x^3 + 17*x_0^4*x^4 + 16*x_0^4*x^2*y + 6*x_0^3*x^5 + 
        12*x_0^3*x^3*y + 8*x_0^3*x*y^2 + x_0^2*x^6 + 4*x_0^2*x^4*y + 
        10*x_0^2*x^2*y^2 + 2*x_0*x^3*y^2 + 4*x_0*x*y^3 + y^4,
    4*x_0^3*x*y^2 + 3*x_0^2*x^2*y^2 + x_0*x^3*y^2 + 2*x_0*x*y^3 + y^4,
    (-16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5)/x^2,
    4*x_0^3*x*B + 3*x_0^2*x^2*B + x_0*x^3*B + 2*x_0*x*y*B + y^2*B,
    y^4,
    (-4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5)/x^2,
    y^2*B,
    (16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + 
        y^5)/x^2,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^4,
    (-4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + 
        y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    4*x_0^3*x^6 + 3*x_0^2*x^7 + x_0*x^8 + 2*x_0*x^6*y + x^5*y^2,
    x^5*y^2,
    -4*x_0^3*x^4*y - 3*x_0^2*x^5*y - x_0*x^6*y - 2*x_0*x^4*y^2 + x^3*y^3,
    x^5*B,
    4*x_0^3*x^4*y + 3*x_0^2*x^5*y + x_0*x^6*y + 2*x_0*x^4*y^2 + x^3*y^3,
    x^3*y^3,
    -4*x_0^3*x^2*y^2 - 3*x_0^2*x^3*y^2 - x_0*x^4*y^2 - 2*x_0*x^2*y^3 + x*y^4,
    x^3*y*B,
    16*x_0^6*x^3 + 24*x_0^5*x^4 + 17*x_0^4*x^5 + 16*x_0^4*x^3*y + 6*x_0^3*x^6 + 
        12*x_0^3*x^4*y + 8*x_0^3*x^2*y^2 + x_0^2*x^7 + 4*x_0^2*x^5*y + 
        10*x_0^2*x^3*y^2 + 2*x_0*x^4*y^2 + 4*x_0*x^2*y^3 + x*y^4,
    4*x_0^3*x^2*y^2 + 3*x_0^2*x^3*y^2 + x_0*x^4*y^2 + 2*x_0*x^2*y^3 + x*y^4,
    (-16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5)/x,
    4*x_0^3*x^2*B + 3*x_0^2*x^3*B + x_0*x^4*B + 2*x_0*x^2*y*B + x*y^2*B,
    x*y^4,
    (-4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5)/x,
    x*y^2*B,
    (16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + 
        y^5)/x,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^3,
    (-4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + y^3*B)/x,
    x*B^2,
    (4*x_0^3*x*y^3 + 3*x_0^2*x^2*y^3 + x_0*x^3*y^3 + 2*x_0*x*y^4 + y^5)/x,
    (-16*x_0^6*x^2*y^2 - 24*x_0^5*x^3*y^2 - 17*x_0^4*x^4*y^2 - 16*x_0^4*x^2*y^3 
        - 6*x_0^3*x^5*y^2 - 12*x_0^3*x^3*y^3 - x_0^2*x^6*y^2 - 4*x_0^2*x^4*y^3 -
        4*x_0^2*x^2*y^4 + y^6)/x^3,
    (4*x_0^3*x*y*B + 3*x_0^2*x^2*y*B + x_0*x^3*y*B + 2*x_0*x*y^2*B + y^3*B)/x,
    (64*x_0^9*x^3 + 144*x_0^8*x^4 + 156*x_0^7*x^5 + 96*x_0^7*x^3*y + 
        99*x_0^6*x^6 + 144*x_0^6*x^4*y + 48*x_0^6*x^2*y^2 + 39*x_0^5*x^7 + 
        102*x_0^5*x^5*y + 120*x_0^5*x^3*y^2 + 9*x_0^4*x^8 + 36*x_0^4*x^6*y + 
        87*x_0^4*x^4*y^2 + 48*x_0^4*x^2*y^3 + x_0^3*x^9 + 6*x_0^3*x^7*y + 
        30*x_0^3*x^5*y^2 + 44*x_0^3*x^3*y^3 + 12*x_0^3*x*y^4 + 3*x_0^2*x^6*y^2 +
        12*x_0^2*x^4*y^3 + 21*x_0^2*x^2*y^4 + 3*x_0*x^3*y^4 + 6*x_0*x*y^5 + 
        y^6)/x^3,
    A
@}
{@
    x^10,
    x^8*y,
    4*x_0^3*x^7 + 3*x_0^2*x^8 + x_0*x^9 + 2*x_0*x^7*y + x^6*y^2,
    x^6*y^2,
    -4*x_0^3*x^5*y - 3*x_0^2*x^6*y - x_0*x^7*y - 2*x_0*x^5*y^2 + x^4*y^3,
    x^6*B,
    4*x_0^3*x^5*y + 3*x_0^2*x^6*y + x_0*x^7*y + 2*x_0*x^5*y^2 + x^4*y^3,
    x^4*y^3,
    -4*x_0^3*x^3*y^2 - 3*x_0^2*x^4*y^2 - x_0*x^5*y^2 - 2*x_0*x^3*y^3 + x^2*y^4,
    x^4*y*B,
    16*x_0^6*x^4 + 24*x_0^5*x^5 + 17*x_0^4*x^6 + 16*x_0^4*x^4*y + 6*x_0^3*x^7 + 
        12*x_0^3*x^5*y + 8*x_0^3*x^3*y^2 + x_0^2*x^8 + 4*x_0^2*x^6*y + 
        10*x_0^2*x^4*y^2 + 2*x_0*x^5*y^2 + 4*x_0*x^3*y^3 + x^2*y^4,
    4*x_0^3*x^3*y^2 + 3*x_0^2*x^4*y^2 + x_0*x^5*y^2 + 2*x_0*x^3*y^3 + x^2*y^4,
    -16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5,
    4*x_0^3*x^3*B + 3*x_0^2*x^4*B + x_0*x^5*B + 2*x_0*x^3*y*B + x^2*y^2*B,
    x^2*y^4,
    -4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5,
    x^2*y^2*B,
    16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + y^5,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^2,
    -4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + y^3*B,
    x^2*B^2,
    4*x_0^3*x*y^3 + 3*x_0^2*x^2*y^3 + x_0*x^3*y^3 + 2*x_0*x*y^4 + y^5,
    (-16*x_0^6*x^2*y^2 - 24*x_0^5*x^3*y^2 - 17*x_0^4*x^4*y^2 - 16*x_0^4*x^2*y^3 
        - 6*x_0^3*x^5*y^2 - 12*x_0^3*x^3*y^3 - x_0^2*x^6*y^2 - 4*x_0^2*x^4*y^3 -
        4*x_0^2*x^2*y^4 + y^6)/x^2,
    4*x_0^3*x*y*B + 3*x_0^2*x^2*y*B + x_0*x^3*y*B + 2*x_0*x*y^2*B + y^3*B,
    (64*x_0^9*x^3 + 144*x_0^8*x^4 + 156*x_0^7*x^5 + 96*x_0^7*x^3*y + 
        99*x_0^6*x^6 + 144*x_0^6*x^4*y + 48*x_0^6*x^2*y^2 + 39*x_0^5*x^7 + 
        102*x_0^5*x^5*y + 120*x_0^5*x^3*y^2 + 9*x_0^4*x^8 + 36*x_0^4*x^6*y + 
        87*x_0^4*x^4*y^2 + 48*x_0^4*x^2*y^3 + x_0^3*x^9 + 6*x_0^3*x^7*y + 
        30*x_0^3*x^5*y^2 + 44*x_0^3*x^3*y^3 + 12*x_0^3*x*y^4 + 3*x_0^2*x^6*y^2 +
        12*x_0^2*x^4*y^3 + 21*x_0^2*x^2*y^4 + 3*x_0*x^3*y^4 + 6*x_0*x*y^5 + 
        y^6)/x^2,
    x*A,
    y^5,
    (-4*x_0^3*x*y^4 - 3*x_0^2*x^2*y^4 - x_0*x^3*y^4 - 2*x_0*x*y^5 + y^6)/x^2,
    y^3*B,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 + 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 + 10*x_0^2*x^2*y^4 + 2*x_0*x^3*y^4 + 4*x_0*x*y^5 + 
        y^6)/x^2,
    (16*x_0^6*x^2*y^3 + 24*x_0^5*x^3*y^3 + 17*x_0^4*x^4*y^3 + 16*x_0^4*x^2*y^4 +
        6*x_0^3*x^5*y^3 + 12*x_0^3*x^3*y^4 - 8*x_0^3*x*y^5 + x_0^2*x^6*y^3 + 
        4*x_0^2*x^4*y^4 - 2*x_0^2*x^2*y^5 - 2*x_0*x^3*y^5 - 4*x_0*x*y^6 + 
        y^7)/x^4,
    (-4*x_0^3*x*y^2*B - 3*x_0^2*x^2*y^2*B - x_0*x^3*y^2*B - 2*x_0*x*y^3*B + 
        y^4*B)/x^2,
    y*B^2,
    (-64*x_0^9*x^3*y - 144*x_0^8*x^4*y - 156*x_0^7*x^5*y - 96*x_0^7*x^3*y^2 - 
        99*x_0^6*x^6*y - 144*x_0^6*x^4*y^2 - 16*x_0^6*x^2*y^3 - 39*x_0^5*x^7*y -
        102*x_0^5*x^5*y^2 - 72*x_0^5*x^3*y^3 - 9*x_0^4*x^8*y - 36*x_0^4*x^6*y^2 
        - 53*x_0^4*x^4*y^3 - 16*x_0^4*x^2*y^4 - x_0^3*x^9*y - 6*x_0^3*x^7*y^2 - 
        18*x_0^3*x^5*y^3 - 20*x_0^3*x^3*y^4 + 4*x_0^3*x*y^5 - x_0^2*x^6*y^3 - 
        4*x_0^2*x^4*y^4 - x_0^2*x^2*y^5 + x_0*x^3*y^5 + 2*x_0*x*y^6 + y^7)/x^4,
    (16*x_0^6*x^2*B + 24*x_0^5*x^3*B + 17*x_0^4*x^4*B + 16*x_0^4*x^2*y*B + 
        6*x_0^3*x^5*B + 12*x_0^3*x^
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB04a.cache.pol.co.uk. (195.92.168.166)
Time: Tue Aug 24 12:36:52 2004

Input: R<x,y,z,t,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,9,4]);
S<x,y,z,t,A,B>:=FieldOfFractions(R);
T<x_0,x,y,z,t,A,B>:=FieldOfFractions(PolynomialRing(RationalField(),[1,1,2,3,4,9,4]));
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,A,B>;
newsubs:=hom<R->T|x,y,y^2/x+x^2*x_0+2*y*x_0+3*x*x_0^2+4*x_0^3,y^3/x^2-x*y*x_0-2*y^2*x_0/x-3*y*x_0^2-4*y*x_0^3/x,A,B>;
for i in [10..10] do
newsubs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Tue Aug 24 2004 12:36:51 on modular  [Seed = 1597337794]
   -------------------------------------


>> subs:=hom<R->S|x,y,y^2/x,y^3/x^2,A,B>;
            ^
Runtime error in hom< ... >: RHS has arity 6 but should have length 6
{@
    x^10,
    x^8*y,
    4*x_0^3*x^7 + 3*x_0^2*x^8 + x_0*x^9 + 2*x_0*x^7*y + x^6*y^2,
    x^6*y^2,
    -4*x_0^3*x^5*y - 3*x_0^2*x^6*y - x_0*x^7*y - 2*x_0*x^5*y^2 + x^4*y^3,
    x^6*B,
    4*x_0^3*x^5*y + 3*x_0^2*x^6*y + x_0*x^7*y + 2*x_0*x^5*y^2 + x^4*y^3,
    x^4*y^3,
    -4*x_0^3*x^3*y^2 - 3*x_0^2*x^4*y^2 - x_0*x^5*y^2 - 2*x_0*x^3*y^3 + x^2*y^4,
    x^4*y*B,
    16*x_0^6*x^4 + 24*x_0^5*x^5 + 17*x_0^4*x^6 + 16*x_0^4*x^4*y + 6*x_0^3*x^7 + 
        12*x_0^3*x^5*y + 8*x_0^3*x^3*y^2 + x_0^2*x^8 + 4*x_0^2*x^6*y + 
        10*x_0^2*x^4*y^2 + 2*x_0*x^5*y^2 + 4*x_0*x^3*y^3 + x^2*y^4,
    4*x_0^3*x^3*y^2 + 3*x_0^2*x^4*y^2 + x_0*x^5*y^2 + 2*x_0*x^3*y^3 + x^2*y^4,
    -16*x_0^6*x^2*y - 24*x_0^5*x^3*y - 17*x_0^4*x^4*y - 16*x_0^4*x^2*y^2 - 
        6*x_0^3*x^5*y - 12*x_0^3*x^3*y^2 - x_0^2*x^6*y - 4*x_0^2*x^4*y^2 - 
        4*x_0^2*x^2*y^3 + y^5,
    4*x_0^3*x^3*B + 3*x_0^2*x^4*B + x_0*x^5*B + 2*x_0*x^3*y*B + x^2*y^2*B,
    x^2*y^4,
    -4*x_0^3*x*y^3 - 3*x_0^2*x^2*y^3 - x_0*x^3*y^3 - 2*x_0*x*y^4 + y^5,
    x^2*y^2*B,
    16*x_0^6*x^2*y + 24*x_0^5*x^3*y + 17*x_0^4*x^4*y + 16*x_0^4*x^2*y^2 + 
        6*x_0^3*x^5*y + 12*x_0^3*x^3*y^2 + 8*x_0^3*x*y^3 + x_0^2*x^6*y + 
        4*x_0^2*x^4*y^2 + 10*x_0^2*x^2*y^3 + 2*x_0*x^3*y^3 + 4*x_0*x*y^4 + y^5,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 - 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 - 2*x_0^2*x^2*y^4 - 2*x_0*x^3*y^4 - 4*x_0*x*y^5 + 
        y^6)/x^2,
    -4*x_0^3*x*y*B - 3*x_0^2*x^2*y*B - x_0*x^3*y*B - 2*x_0*x*y^2*B + y^3*B,
    x^2*B^2,
    4*x_0^3*x*y^3 + 3*x_0^2*x^2*y^3 + x_0*x^3*y^3 + 2*x_0*x*y^4 + y^5,
    (-16*x_0^6*x^2*y^2 - 24*x_0^5*x^3*y^2 - 17*x_0^4*x^4*y^2 - 16*x_0^4*x^2*y^3 
        - 6*x_0^3*x^5*y^2 - 12*x_0^3*x^3*y^3 - x_0^2*x^6*y^2 - 4*x_0^2*x^4*y^3 -
        4*x_0^2*x^2*y^4 + y^6)/x^2,
    4*x_0^3*x*y*B + 3*x_0^2*x^2*y*B + x_0*x^3*y*B + 2*x_0*x*y^2*B + y^3*B,
    (64*x_0^9*x^3 + 144*x_0^8*x^4 + 156*x_0^7*x^5 + 96*x_0^7*x^3*y + 
        99*x_0^6*x^6 + 144*x_0^6*x^4*y + 48*x_0^6*x^2*y^2 + 39*x_0^5*x^7 + 
        102*x_0^5*x^5*y + 120*x_0^5*x^3*y^2 + 9*x_0^4*x^8 + 36*x_0^4*x^6*y + 
        87*x_0^4*x^4*y^2 + 48*x_0^4*x^2*y^3 + x_0^3*x^9 + 6*x_0^3*x^7*y + 
        30*x_0^3*x^5*y^2 + 44*x_0^3*x^3*y^3 + 12*x_0^3*x*y^4 + 3*x_0^2*x^6*y^2 +
        12*x_0^2*x^4*y^3 + 21*x_0^2*x^2*y^4 + 3*x_0*x^3*y^4 + 6*x_0*x*y^5 + 
        y^6)/x^2,
    x*A,
    y^5,
    (-4*x_0^3*x*y^4 - 3*x_0^2*x^2*y^4 - x_0*x^3*y^4 - 2*x_0*x*y^5 + y^6)/x^2,
    y^3*B,
    (16*x_0^6*x^2*y^2 + 24*x_0^5*x^3*y^2 + 17*x_0^4*x^4*y^2 + 16*x_0^4*x^2*y^3 +
        6*x_0^3*x^5*y^2 + 12*x_0^3*x^3*y^3 + 8*x_0^3*x*y^4 + x_0^2*x^6*y^2 + 
        4*x_0^2*x^4*y^3 + 10*x_0^2*x^2*y^4 + 2*x_0*x^3*y^4 + 4*x_0*x*y^5 + 
        y^6)/x^2,
    (16*x_0^6*x^2*y^3 + 24*x_0^5*x^3*y^3 + 17*x_0^4*x^4*y^3 + 16*x_0^4*x^2*y^4 +
        6*x_0^3*x^5*y^3 + 12*x_0^3*x^3*y^4 - 8*x_0^3*x*y^5 + x_0^2*x^6*y^3 + 
        4*x_0^2*x^4*y^4 - 2*x_0^2*x^2*y^5 - 2*x_0*x^3*y^5 - 4*x_0*x*y^6 + 
        y^7)/x^4,
    (-4*x_0^3*x*y^2*B - 3*x_0^2*x^2*y^2*B - x_0*x^3*y^2*B - 2*x_0*x*y^3*B + 
        y^4*B)/x^2,
    y*B^2,
    (-64*x_0^9*x^3*y - 144*x_0^8*x^4*y - 156*x_0^7*x^5*y - 96*x_0^7*x^3*y^2 - 
        99*x_0^6*x^6*y - 144*x_0^6*x^4*y^2 - 16*x_0^6*x^2*y^3 - 39*x_0^5*x^7*y -
        102*x_0^5*x^5*y^2 - 72*x_0^5*x^3*y^3 - 9*x_0^4*x^8*y - 36*x_0^4*x^6*y^2 
        - 53*x_0^4*x^4*y^3 - 16*x_0^4*x^2*y^4 - x_0^3*x^9*y - 6*x_0^3*x^7*y^2 - 
        18*x_0^3*x^5*y^3 - 20*x_0^3*x^3*y^4 + 4*x_0^3*x*y^5 - x_0^2*x^6*y^3 - 
        4*x_0^2*x^4*y^4 - x_0^2*x^2*y^5 + x_0*x^3*y^5 + 2*x_0*x*y^6 + y^7)/x^4,
    (16*x_0^6*x^2*B + 24*x_0^5*x^3*B + 17*x_0^4*x^4*B + 16*x_0^4*x^2*y*B + 
        6*x_0^3*x^5*B + 12*x_0^3*x^3*y*B + 8*x_0^3*x*y^2*B + x_0^2*x^6*B + 
        4*x_0^2*x^4*y*B + 10*x_0^2*x^2*y^2*B + 2*x_0*x^3*y^2*B + 4*x_0*x*y^3*B +
        y^4*B)/x^2
@}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Tue Aug 24 14:22:17 2004

Input: function count3(p,e,r)
  sum:=-1-p^r;
  F:=FiniteField(p^r);   for t in F do
         if (t^(5*e)*(t^(2*e)-11*t^e-1) ne 0) then
       E:=EllipticCurve(
               [FiniteField(p^r)|(1-t^e),-t^e, -t^e,0,0]);
               sum:=sum-p^r+#E;
            end if;
  end for;
return sum;
 end function;
count3(29,7,1);


Output: Magma V2.11-2     Tue Aug 24 2004 14:22:16 on modular  [Seed = 912060470]
   -------------------------------------

-2

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Tue Aug 24 14:22:31 2004

Input: function count3(p,e,r)
  sum:=-1-p^r;
  F:=FiniteField(p^r);   for t in F do
         if (t^(5*e)*(t^(2*e)-11*t^e-1) ne 0) then
       E:=EllipticCurve(
               [FiniteField(p^r)|(1-t^e),-t^e, -t^e,0,0]);
               sum:=sum-p^r+#E;
            end if;
  end for;
return sum;
 end function;
count3(29,7,2);


Output: Magma V2.11-2     Tue Aug 24 2004 14:22:26 on modular  [Seed = 659415325]
   -------------------------------------

-8262

Total time: 4.320 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Tue Aug 24 14:23:54 2004

Input: function count3(p,e,r)
  sum:=-1-p^r;
  F:=FiniteField(p^r);   for t in F do
         if (t^(5*e)*(t^(2*e)-11*t^e-1) ne 0) then
       E:=EllipticCurve(
               [FiniteField(p^r)|(1-t^e),-t^e, -t^e,0,0]);
               sum:=sum-p^r+#E;
            end if;
  end for;
return sum;
 end function;
count3(29,7,3);


Output: Magma V2.11-2     Tue Aug 24 2004 14:23:33 on modular  [Seed = 2432325229]
   -------------------------------------



************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Tue Aug 24 14:27:13 2004

Input: function count3(p,e,r)
  sum:=-1-p^r;
  F:=FiniteField(p^r);   for t in F do
         if (t^(5*e)*(t^(2*e)-11*t^e-1) ne 0) then
       E:=EllipticCurve(
               [FiniteField(p^r)|(1-t^e),-t^e, -t^e,0,0]);
               sum:=sum-p^r+#E;
            end if;
  end for;
return sum;
 end function;
count3(29,43,2);


Output: Magma V2.11-2     Tue Aug 24 2004 14:27:09 on modular  [Seed = 3900842446]
   -------------------------------------

0

Total time: 4.280 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (129.186.63.116)
Time: Tue Aug 24 14:29:42 2004

Input: function count3(p,e,r)
  sum:=-1-p^r;
  F:=FiniteField(p^r);   for t in F do
         if (t^(5*e)*(t^(2*e)-11*t^e-1) ne 0) then
       E:=EllipticCurve(
               [FiniteField(p^r)|(1-t^e),-t^e, -t^e,0,0]);
               sum:=sum-p^r+#E;
            end if;
  end for;
return sum;
 end function;
count3(43,7,2);


Output: Magma V2.11-2     Tue Aug 24 2004 14:29:25 on modular  [Seed = 1761845558]
   -------------------------------------

-8766

Total time: 17.489 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Wed Aug 25 06:44:24 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Wed Aug 25 2004 06:44:20 on modular  [Seed = 675611851]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.659 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Wed Aug 25 06:44:33 2004

Input: ABC

Output: Magma V2.11-2     Wed Aug 25 2004 06:44:33 on modular  [Seed = 377174752]
   -------------------------------------


>> ABC;
   ^
User error: Identifier 'ABC' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 10:54:33 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;
Dimension(I);
V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];
S;

Output: Magma V2.11-2     Wed Aug 25 2004 10:54:32 on modular  [Seed = 2533064581]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    y^10,
    y^11,
    y^12,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12
]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:16:12 2004

Input: 
K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);
S:=[
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
    
]

L := [ x^3*y^11];
L;
B, V := HomogeneousModuleTest(P, S, L);
B;

Output: Magma V2.11-2     Wed Aug 25 2004 11:16:12 on modular  [Seed = 2848212395]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72

>> L := [ x^3*y^11];
   ^
User error: bad syntax

>> L;
   ^
User error: Identifier 'L' has not been declared or assigned

>> B, V := HomogeneousModuleTest(P, S, L);
                                    ^
User error: Identifier 'S' has not been declared or assigned

>> B;;
   ^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:20:47 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);
S:=[
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
    
]
T := {R | y^11, x^12*y^3 };
T;

L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;

Output: Magma V2.11-2     Wed Aug 25 2004 11:20:46 on modular  [Seed = 1597157458]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72

>> T := {R | y^11, x^12*y^3 };
   ^
User error: bad syntax

>> T;
   ^
User error: Identifier 'T' has not been declared or assigned

>> HomogeneousModuleTestBasis(P, S, L ) ;;
                                 ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:21:13 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);
S:=[1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
    
]
T := {R | y^11, x^12*y^3 };
T;

L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;

Output: Magma V2.11-2     Wed Aug 25 2004 11:21:13 on modular  [Seed = 2048365904]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72

>> T := {R | y^11, x^12*y^3 };
   ^
User error: bad syntax

>> T;
   ^
User error: Identifier 'T' has not been declared or assigned

>> HomogeneousModuleTestBasis(P, S, L ) ;;
                                 ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:22:08 2004

Input: K<w> := GF(2);
R<x, y, z, w, u > := PolynomialRing(K, [2, 3, 16, 24, 28]);
R;
P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, 
x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ;
S :=[  x^5*y^9,
        x^7*y^7,
        x^10*y^4,
        x^9*y^2,
        x^5*y^4,
        x^12*y^6,
        x^3*y,
        x^12*y^3,
        x^14,
        x^9*y^3,
        x^2*y^4,
        y^8,
        x*y^2,
        x^3,
        x*y^9,
        x^3*y^10,
        x^4,
        x^9*y^4,
        x*y^6,
        x^9*y^8,
        x^6*y^4,
        x^12*y^10,
        x^6*y^9,
        x^7,
        x^3*y^7,
        x^10*y^9,
        y^5,
        x^6*y,
        x^7*y^8,
        x^4*y^7,
        x^13*y^4,
        y^9,
        x^13,
        x^6,
        x^13*y^8,
        x^4*y^2,
        y^4,
        x^5*y,
        x*y^8,
        y^7,
        x^2*y,
        x^9*y^10,
        x^13*y^3,
        x^10*y^7,
        x^7*y^10,
        x^8*y,
        x^2*y^8,
        x^11*y^7,
        x^3*y^2,
        x^8*y^10,
        x^13*y^9,
        x^12*y^5,
        y^10,
        x^9*y^6,
        x^8*y^4,
        x^4*y^6,
        x*y,
        x^10*y^2,
        x^3*y^5,
        x^7*y^3,
        x^4*y^10,
        x^12*y^9,
        x^2*y^7,
        x^6*y^7,
        y^6,
        x^7*y^2,
        x^10*y^8,
        x^2*y^3,
        x^11*y^10,
        x^12,
        x*y^10,
        x^10*y^10,
        x^11*y^6,
        x^6*y^6,
        x^7*y^5,
        x^12*y^8,
        x^6*y^3,
        x^8*y^9,
        x^12*y^2,
        x^5*y^2,
        x^10*y^5,
        x^6*y^2,
        x^12*y^7,
        y,
        x^8*y^3,
        x*y^5,
        x^2*y^9,
        x^4*y,
        x^9*y,
        x^6*y^5,
        x^5*y^5,
        x^2*y^2,
        x^9*y^5,
        x^13*y^2,
        x^8*y^7,
        x^2*y^10,
        x^5*y^3,
        x^9*y^7,
        x^7*y^4,
        x^2*y^5,
        x^4*y^9,
        x*y^4,
        x^12*y,
        x^9*y^9,
        x^11*y^8,
        x^12*y^4,
        x^10*y^3,
        x^4*y^8,
        x^7*y^9,
        x^5*y^8,
        x^5*y^7,
        x^8*y^8,
        x^8*y^6,
        x^10*y^6,
        x,
        x^11*y^3,
        x^5,
        1,
        x^4*y^5,
        x^3*y^4,
        x^4*y^4,
        x^10,
        x^7*y^6,
        x^11*y^4,
        x^2*y^6,
        x^11*y^2,
        x^13*y^10,
        x^5*y^10,
        x*y^3,
        x^3*y^6,
        x^8,
        x^11,
        x^6*y^8,
        x^11*y^5,
        x^10*y,
        x^9,
        x^2,
        x^3*y^9,
        y^2,
        x^5*y^6,
        x^13*y^6,
        x^13*y^5,
        x^8*y^2,
        x^4*y^3,
        y^3,
        x*y^7,
        x^7*y,
        x^3*y^8,
        x^6*y^10,
        x^3*y^3,
        x^11*y^9,
        x^8*y^5,
        x^13*y^7,
        x^11*y,
        x^13*y ] ;
[IsHomogeneous(f): f in S];
I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:22:07 on modular  [Seed = 759218929]
   -------------------------------------

Graded Polynomial ring of rank 5 over GF(2)
Lexicographical Order
Variables: x, y, z, w, u
Variable weights: 2 3 16 24 28
[ true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true ]
0 []
[ 1 ]

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:27:46 2004

Input: 
p=3 2-4

K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


K<w> := GF(2);
R<x, y, z, w, u > := PolynomialRing(K, [2, 3, 16, 24, 28]);
R;
P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, 
x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ;
S :=[  
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
     ] ;
[IsHomogeneous(f): f in S];
I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:27:46 on modular  [Seed = 2499377700]
   -------------------------------------


>> p=3 2-4
       ^
User error: bad syntax
Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
Graded Polynomial ring of rank 5 over GF(2)
Lexicographical Order
Variables: x, y, z, w, u
Variable weights: 2 3 16 24 28
[ true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true ]
0 []
[ 1 ]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:27:55 2004

Input: 

K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


K<w> := GF(2);
R<x, y, z, w, u > := PolynomialRing(K, [2, 3, 16, 24, 28]);
R;
P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, 
x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ;
S :=[  
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
     ] ;
[IsHomogeneous(f): f in S];
I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:27:55 on modular  [Seed = 2714521368]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
Graded Polynomial ring of rank 5 over GF(2)
Lexicographical Order
Variables: x, y, z, w, u
Variable weights: 2 3 16 24 28
[ true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true ]
0 []
[ 1 ]

Total time: 0.600 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:28:40 2004

Input: 
K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


K<w> := GF(2);
R<x, y, z, w, u > := PolynomialRing(K, [2, 3, 16, 24, 28]);
R;
P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, 
x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ;
S :=[  
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
     ] ;
[IsHomogeneous(f): f in S];
I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^5];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:28:40 on modular  [Seed = 1563470896]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
Graded Polynomial ring of rank 5 over GF(2)
Lexicographical Order
Variables: x, y, z, w, u
Variable weights: 2 3 16 24 28
[ true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true, 
true, true, true, true, true, true, true, true, true, true, true, true, true ]
0 []
[]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:31:03 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[  
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
     ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^5];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:31:02 on modular  [Seed = 3901036827]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:32:28 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[  
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9
     ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:32:28 on modular  [Seed = 3218231286]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:34:07 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[  
 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    y^10,
    y^11,
    y^12,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12    ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:34:07 on modular  [Seed = 1011993623]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:45:41 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^0 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:45:41 on modular  [Seed = 140901732]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:46:04 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^0 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:46:03 on modular  [Seed = 7206258]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:46:15 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^0 *y^12];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:46:14 on modular  [Seed = 410381591]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:46:47 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^1 *y^12];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:46:46 on modular  [Seed = 276686143]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:47:08 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^1 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:47:08 on modular  [Seed = 675667229]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:47:24 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^1 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:47:24 on modular  [Seed = 541971941]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:47:44 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^1 *y^9];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:47:43 on modular  [Seed = 945147374]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:52:49 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^2 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:52:48 on modular  [Seed = 3867873918]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:53:52 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^3 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:53:52 on modular  [Seed = 1177268509]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.600 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:54:55 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^4 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:54:54 on modular  [Seed = 792909866]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:55:41 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^5 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:55:40 on modular  [Seed = 4001569241]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.600 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:56:20 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^6 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:56:19 on modular  [Seed = 2881903683]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:57:29 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^7 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:57:29 on modular  [Seed = 241433005]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:58:25 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^8 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:58:24 on modular  [Seed = 3568902846]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.610 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:59:06 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:59:05 on modular  [Seed = 2449237906]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.639 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:59:27 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^10 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:59:27 on modular  [Seed = 1310963804]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:59:36 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^11 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:59:35 on modular  [Seed = 1580443764]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 11:59:46 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^12 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 11:59:46 on modular  [Seed = 1845729361]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:00:17 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^10];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:00:16 on modular  [Seed = 327083470]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.620 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:00:26 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^11];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:00:25 on modular  [Seed = 1045678314]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.639 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:00:35 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^12];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:00:35 on modular  [Seed = 861849053]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.559 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:00:45 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^9*y^9,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^13];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:00:44 on modular  [Seed = 3282973986]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.580 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:01:27 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^9*y^8,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^9];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:01:26 on modular  [Seed = 4120380270]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.590 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:03:05 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^9*y^7,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^8];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:03:04 on modular  [Seed = 40893302]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.559 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:03:37 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^9*y^6,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^7];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:03:36 on modular  [Seed = 3449828568]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.630 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:03:58 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^9*y^5,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^6];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:03:57 on modular  [Seed = 3784054976]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:04:20 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^9*y^4,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^5];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:04:19 on modular  [Seed = 2179758158]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:04:46 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^4];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:04:45 on modular  [Seed = 2848215160]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:05:19 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^9 *y^3];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:05:18 on modular  [Seed = 1379904419]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:06:15 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^10*y^9,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^8 *y^12];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:06:15 on modular  [Seed = 642506654]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:06:51 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^4,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^10 *y^9];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:06:50 on modular  [Seed = 3719308680]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.610 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:07:41 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^10*y^5,
    x^10*y^6,
    x^10*y^7,
    x^10*y^8,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^11*y^4,
    x^11*y^5,
    x^11*y^6,
    x^11*y^7,
    x^11*y^8,
    x^11*y^9,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^10 *y^4];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:07:41 on modular  [Seed = 3000978096]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:09:25 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^11 *y^4];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:09:24 on modular  [Seed = 3635748898]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.559 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:09:36 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^11 *y^5];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:09:36 on modular  [Seed = 3901034598]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:09:46 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^11 *y^6];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:09:46 on modular  [Seed = 4170514556]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:09:56 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
    x^12*y^4,
    x^12*y^5,
    x^12*y^6,
    x^12*y^7,
    x^12*y^8,
    x^12*y^9 
] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^11 *y^16];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:09:56 on modular  [Seed = 2313449747]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.580 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:10:26 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3,
   ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^12 *y^6];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:10:25 on modular  [Seed = 3184542978]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72

>>    ] ;
      ^
User error: bad syntax
0 []

>> HomogeneousModuleTestBasis(P, S, L ) ;
                                 ^
User error: Identifier 'S' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:10:51 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2,
    x^12*y^3
   ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^12 *y^6];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:10:50 on modular  [Seed = 1210430227]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[]

Total time: 0.610 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:11:16 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12
       ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^12 *y^1];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:11:16 on modular  [Seed = 343535457]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.569 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Wed Aug 25 12:11:58 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);


S :=[ 
    1,
    y,
    y^2,
    y^3,
    y^4,
    y^5,
    y^6,
    y^7,
    y^8,
    y^9,
    x,
    x*y,
    x*y^2,
    x*y^3,
    x*y^4,
    x*y^5,
    x*y^6,
    x*y^7,
    x*y^8,
    x*y^9,
    x*y^10,
    x*y^11,
    x*y^12,
    x^2,
    x^2*y,
    x^2*y^2,
    x^2*y^3,
    x^2*y^4,
    x^2*y^5,
    x^2*y^6,
    x^2*y^7,
    x^2*y^8,
    x^2*y^9,
    x^2*y^10,
    x^2*y^11,
    x^2*y^12,
    x^3,
    x^3*y,
    x^3*y^2,
    x^3*y^3,
    x^3*y^4,
    x^3*y^5,
    x^3*y^6,
    x^3*y^7,
    x^3*y^8,
    x^3*y^9,
    x^3*y^10,
    x^3*y^11,
    x^3*y^12,
    x^4,
    x^4*y,
    x^4*y^2,
    x^4*y^3,
    x^4*y^4,
    x^4*y^5,
    x^4*y^6,
    x^4*y^7,
    x^4*y^8,
    x^4*y^9,
    x^4*y^10,
    x^4*y^11,
    x^4*y^12,
    x^5,
    x^5*y,
    x^5*y^2,
    x^5*y^3,
    x^5*y^4,
    x^5*y^5,
    x^5*y^6,
    x^5*y^7,
    x^5*y^8,
    x^5*y^9,
    x^5*y^10,
    x^5*y^11,
    x^5*y^12,
    x^6,
    x^6*y,
    x^6*y^2,
    x^6*y^3,
    x^6*y^4,
    x^6*y^5,
    x^6*y^6,
    x^6*y^7,
    x^6*y^8,
    x^6*y^9,
    x^6*y^10,
    x^6*y^11,
    x^6*y^12,
    x^7,
    x^7*y,
    x^7*y^2,
    x^7*y^3,
    x^7*y^4,
    x^7*y^5,
    x^7*y^6,
    x^7*y^7,
    x^7*y^8,
    x^7*y^9,
    x^7*y^10,
    x^7*y^11,
    x^7*y^12,
    x^8,
    x^8*y,
    x^8*y^2,
    x^8*y^3,
    x^8*y^4,
    x^8*y^5,
    x^8*y^6,
    x^8*y^7,
    x^8*y^8,
    x^8*y^9,
    x^8*y^10,
    x^8*y^11,
    x^8*y^12,
    x^9,
    x^9*y,
    x^9*y^2,
    x^9*y^3,
    x^10,
    x^10*y,
    x^10*y^2,
    x^10*y^3,
    x^11,
    x^11*y,
    x^11*y^2,
    x^11*y^3,
    x^12,
    x^12*y,
    x^12*y^2
       ] ;

I:=ideal<R | P>;
Dimension(I);
L := [x^12 *y^3];
HomogeneousModuleTestBasis(P, S, L ) ;


Output: Magma V2.11-2     Wed Aug 25 2004 12:11:57 on modular  [Seed = 726061111]
   -------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
0 []
[ 1 ]

Total time: 0.630 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host IP-213157001027.dialin.heagmedianet.de. (213.157.1.27)
Time: Wed Aug 25 16:41:59 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Wed Aug 25 2004 16:41:58 on modular  [Seed = 510895764]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157001027.dialin.heagmedianet.de. (213.157.1.27)
Time: Wed Aug 25 16:42:18 2004

Input: (x^2+x) * x

Output: Magma V2.11-2     Wed Aug 25 2004 16:42:18 on modular  [Seed = 107724465]
   -------------------------------------


>> (x^2+x) * x;
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157001027.dialin.heagmedianet.de. (213.157.1.27)
Time: Wed Aug 25 17:04:23 2004

Input: FiniteField(3,97)


Output: Magma V2.11-2     Wed Aug 25 2004 17:04:22 on modular  [Seed = 527605994]
   -------------------------------------

Finite field of size 3^97

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:35:16 2004

Input: isIrreducible(x^6 + x + 2)

Output: Magma V2.11-2     Wed Aug 25 2004 18:35:16 on modular  [Seed = 811361582]
   -------------------------------------


>> isIrreducible(x^6 + x + 2);
                 ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:37:05 2004

Input: PQ<x> := PowerSeriesRing(RationalField());
isIrreducible(x^6 + x + 2);

Output: Magma V2.11-2     Wed Aug 25 2004 18:37:05 on modular  [Seed = 2848324610]
   -------------------------------------


>> isIrreducible(x^6 + x + 2);;
   ^
User error: Identifier 'isIrreducible' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:37:54 2004

Input: PQ<x> := PolynomialRing(RationalField());
isIrreducible(x^6 + x + 2);

Output: Magma V2.11-2     Wed Aug 25 2004 18:37:53 on modular  [Seed = 4018387476]
   -------------------------------------


>> isIrreducible(x^6 + x + 2);;
   ^
User error: Identifier 'isIrreducible' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:38:02 2004

Input: PQ<x> := PolynomialRing(RationalField());
IsIrreducible(x^6 + x + 2);

Output: Magma V2.11-2     Wed Aug 25 2004 18:38:02 on modular  [Seed = 3552544291]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:38:10 2004

Input: PQ<x> := PolynomialRing(RationalField());
IsIrreducible(x^6 + x + 1);

Output: Magma V2.11-2     Wed Aug 25 2004 18:38:10 on modular  [Seed = 3283064363]
   -------------------------------------

true

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:38:18 2004

Input: PQ<x> := PolynomialRing(RationalField());
IsIrreducible(x^6 + x + 2);

Output: Magma V2.11-2     Wed Aug 25 2004 18:38:17 on modular  [Seed = 928735955]
   -------------------------------------

true

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:39:18 2004

Input: PQ<x> := PolynomialRing(RationalField());
(x^6+x+1)*(x+1);

Output: Magma V2.11-2     Wed Aug 25 2004 18:39:18 on modular  [Seed = 1880892507]
   -------------------------------------

x^7 + x^6 + x^2 + 2*x + 1

Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:39:41 2004

Input: PQ<x> := PolynomialRing(RationalField());
(x^6+x+1)*(x+1) % (x^6+x+2),  

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:39:52 2004

Input: PQ<x> := PolynomialRing(RationalField());
(x^6+x+1)*(x+1) % (x^6+x+2);

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:40:06 2004

Input: PQ<x> := PolynomialRing(RationalField());
Mod((x^6+x+1)*(x+1), (x^6+x+2));

Output: Magma V2.11-2     Wed Aug 25 2004 18:40:06 on modular  [Seed = 2179847674]
   -------------------------------------


>> Mod((x^6+x+1)*(x+1), (x^6+x+2));;
      ^
Runtime error in procedure call: Attempting to call something that is not 
callable

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:43:49 2004

Input: PQ<x> := PolynomialRing(RationalField());
(x^6+x+1)*(x+1);

Output: Magma V2.11-2     Wed Aug 25 2004 18:43:48 on modular  [Seed = 2414074007]
   -------------------------------------

x^7 + x^6 + x^2 + 2*x + 1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:51:58 2004

Input: nextprime(3412342342423412341234231412341234123421^10)

Output: Magma V2.11-2     Wed Aug 25 2004 18:51:57 on modular  [Seed = 1880893757]
   -------------------------------------


>> nextprime(3412342342423412341234231412341234123421^10);
   ^
User error: Identifier 'nextprime' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:52:41 2004

Input: 3412342342423412341234231412341234123421^20

Output: Magma V2.11-2     Wed Aug 25 2004 18:52:40 on modular  [Seed = 726102611]
   -------------------------------------

4581966434479685358009727214635544513188983254351524053544953348012394917988035\
4401410961677271688096982505270641776949434366036372031398096612513957706012217\
6531861267289870995453440663459923748803655306986189995374194899456182132758571\
4898222782106487910210489333992189784554362334231244103593283906672279383609668\
4982897830641844444850972576012042452893015007851850628096114299594757683956881\
6542267961967234622520522964085406803496415020599144017128468525022413144499436\
9838754268504275632978754274110990670068005006045395522663703406536962352461763\
5595406261038763887289968067070470800769583817225919676263442704575299211355895\
0856132537475316557691638553305378450151420933886892068989097581437271840689990\
7687018378547435721983142677355634303457460592509081723045079920563246726510440\
1

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 18:54:23 2004

Input: 93412342342423412341234231412341234123421^204

Output: Magma V2.11-2     Wed Aug 25 2004 18:54:22 on modular  [Seed = 3067801448]
   -------------------------------------

9172115293072811078255248433033150428347307653618571099616051834565331618677875\
3405837252902637100357479774230606334574942029970027510286699094333213093131273\
9730116072421882276211546796097139799830291707175811276589070735009713009988866\
2021631877938207146698772841525876889656817994096464055264685425749053234392667\
0043557912144225922114062917603290710642429884772695909910193903437097360521869\
8616347322617724187870642294475619959825205921722447779095822476063966807715897\
2848803962609509030822879992615051093916250443231306600175103027006652124279723\
2429412820147489905139537184412078755972931704346524667927180560538663591798039\
8067039500034735877974419093914677394220897815209730274020465364900870983483951\
7337291178304437779007675231909392642124613357177402776058462289375532851630288\
3731137125693463442804732528798408233465749724272128345484971794781220111805143\
1206472734620242259325590369394316900140407063025102670719516993200100194091244\
0561111144475174398676230669177980620436304246367600985325796987363249589055677\
6471396104108245388353439044700522695846780519994891743599030060039770423834760\
4179892903806652249596000607751857285643031401851074849540094725515502611707275\
0608436739553294819608003602861609630038941610594981557989305917860843959862479\
6312758704336584847303413248153357919752692689094924736292811824954862228038518\
2696309092610010293127757843713935538999223113343513230979491578857349106946383\
5061101955747567462637861786107842727471045387361815369123241118535570785440274\
3309805730653653934938241258662538312076238782436254070456842005762680082278186\
8327833011299142587006236166368493250353933895690279451159647546160771879802495\
1672162881244206922730085439632744871213194006938033326167494702893854182907671\
4348535895446907029612971935841707832657502700824540508456526649324344588294689\
4559732612108569384166736718163299930656772273177140007924868218593657303055028\
9996871219988672281341720215614245150083658059904807949437953259483976832839941\
2639972856435976317688223794954106893396653367449008371383245141465948733399363\
1655315708162287669161698326476369988596299629446277741861869905741713270467893\
1577157396673653767149027026903058486228377041662026537915761635219811610280378\
2771243994670349715259580275272450723880104466632433915746977033734308519417911\
7886674137195076113815810864518914210396889774805810747384574034429201941744885\
2147550207610237266416843121766655180226837877908242941966370662507895283361247\
6024566016673028599184193479770242561373093115757398683236499972236966357345999\
6103854119394043281277708523485005285975396324298257439013799622399310757932870\
7156550692593784625217292177793672326911191602694493699907951831310291248548974\
0942976393600862077649725745470381724327911953528644224002692163092406836068975\
4359651504794719876459705947526822214386890721049399529219269157931392715138479\
2889920294329672820224301481675095025178540739563637192018562602665653079444540\
9497596555143004399740135316527921489064456002250820360536597458917210502440564\
5997021630070958352739662168755502755384647214982574410516512145002004308378107\
3698555122000387367482416557264589954468472207150140062875706393696930611865936\
1774738781214714868879326357978533210285605152537743592075113438658657183268705\
4242506400286354147183974888153856229128822416989268679784859604590552696316726\
5975440206998177435759074783334881339557563845495751322279771367549961550169496\
5345503857168095443544019366333043004533929520245347366781464592541847109307153\
2513276035790711125010638064761967843305811328079667702887259501761684157256904\
5745833954431090864794331171819601475959647911277748113023838231730359388159106\
6461847713835157078127512593660070625716356302572747627987759423908470620036737\
6835271171502525700594620194792649072561190886057894238661218985470918188653779\
4147299036424625916133975546874560844826567461069537439526390384604290036808648\
7395961521439445381786240534817769723859710957050674083290445709195831621869928\
3436732276754228135212281643693710837901289715489245540852090969696202387570597\
2201871414548579171667691459231378294196627071624484904862669762596465720286459\
1853517443474239229329667219203272052798958138233046711439856330244283038468980\
7305234731147918701430877534927684142562429077269823826991839920242821993101768\
7116418119952360807378990765830703730753815766783455583800502310381249545340749\
8387979927187092298098258395959858600968805151473150911620014988291507033317810\
7373961385744542069798782326881791799467829187196504210793824996667940612221246\
4511743150344279751915159058429963086484432327533615941550596254178524713682945\
0273710327117363111556965030542443883468427771118333668726086683507687992165745\
9945034752489014770316233009588795151404820037590522940660257395761415138377542\
1154231560362533782086838523249178063696303700861734190054748340798589809905737\
7920544643047556938387463919205690044664657748948676308617556166431370770898910\
8855703416176076273551436647201600772947314599580877467693893555312844289577376\
3138539473739061319172400463699473638702137823933765939217625788237944636004908\
4339940437523546729614337614538929620950683695513828092802064401978847924904353\
9327070924349697340423876503314444062926507451204711833968647575444388827782732\
7636360722745646830266164651554816750251677117818200849641802155374276468965090\
7615451700370667118382910535597767217830909206315569680836381634892876141779999\
0270132139362480958305243094279004653514178317957562349982943629258482489389463\
2240167630579494459655834163762032655425853954167202860075904150412364695746987\
7190116524888258647121197218361649368010601673626773648399618483504627151294329\
6973762829076896211142379313771512327089678535499646509317697058337559202495769\
7467078083129601790387141188403861797338151188899493783413460423257251445443301\
7221337825753674308778429555097095260705491591278977666147415389924865917736110\
6401785883586758001474030567611288177074368677191111049195063704669909158726978\
3433516684383254938808012349864289233770585882342160235590807215125972063894988\
3747624981387333286154022690707918208928321014998923563670072123657285485498052\
7159703785634229481326117303559093971521230844564706935709921605346795541377100\
3400320058995250772476658714274697222275834972324643396287663926382222076478741\
1995851339093197839753813709612520948424754100776024468258586307175156838456729\
2987760911006085292647068565632095056583830713451447548702597122424649135480946\
3236601382769345013657501977518341184106931078850835946601191975986970109766237\
5813390287486966813124345789703854569417329044890862998649517088998686014687476\
0988006278881116064694403089138804373131428292494918724408538357592261539880290\
1690721949976279600166905772890228913198504979807123038672580153877407857198795\
7052349840442641277896161758622092454865220396404022079244902320751537712788888\
1967378395606334696633888418762053355276678892575850773655603465804144964966133\
0780831424102996341658528678522103281055012401755487191499308464918919993039863\
1976197508248536014592317240417029614469386816885130196640209561012697937175816\
5588728468147467806162049213230088805379813575579334541717350277223192405589012\
4289779370161887908212101447478314980856672350829845014082107243424704195406729\
0715480503073342789177303033991175184123881038716728137723213617922826001750616\
4791202951998316542961987492151323983471807429367713103274515605132117953135218\
3527213857684284303794497918985522559339695268870085884818591551877567193451704\
0355728412310788634824118215735770063491104190736887055592786667480138340786720\
4791542542442198266315114086442546469740234423607991068889149593292431732810161\
4427660798106775997069509256664058441877447343840364808449217877881715982102678\
0178545945276835370594922171774525073065121087635090139084566156544291454175843\
2348978117275560640799766709887775549194484604500254893985786143982895654966529\
2882312132554423215737144695264238430328811069926503446494187848534892334190698\
3134868233133885046374218795182702004217258174809013575106781332855068520014091\
6013200765627677963633864267914648505622920366007970501025840949752441717439811\
8734196854094979741690168752805056107976232986756727972230746676880201511112869\
1504591111723266244224938370760342787960642439815165796890714146689737198747941\
4683643666536294383020207448115988995379172160408312860519960861531063035665400\
667984563511858626203611793435224825200779668364888752004948081

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:03:37 2004

Input: Factor(3^(2*97)+1)

Output: Magma V2.11-2     Wed Aug 25 2004 19:03:36 on modular  [Seed = 1695104744]
   -------------------------------------


>> Factor(3^(2*97)+1);
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:05:38 2004

Input: Factor(3^97+1)

Output: Magma V2.11-2     Wed Aug 25 2004 19:05:37 on modular  [Seed = 3232537284]
   -------------------------------------


>> Factor(3^97+1);
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngIntElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:06:56 2004

Input: Factor(1513452345214123412341234231423423412342342341234123412341234123412341234123421341234123412341)

Output: Magma V2.11-2     Wed Aug 25 2004 19:06:56 on modular  [Seed = 2549861698]
   -------------------------------------


>> Factor(15134523452141234123412342314234234123423423412341234123412341234123
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: RngIntElt

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:08:10 2004

Input: RandomPrime(3^10)

Output: Magma V2.11-2     Wed Aug 25 2004 19:07:49 on modular  [Seed = 1429802964]
   -------------------------------------



************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:08:44 2004

Input: RandomPrime(3^10)

Output: Magma V2.11-2     Wed Aug 25 2004 19:08:24 on modular  [Seed = 2014585556]
   -------------------------------------



************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:08:49 2004

Input: RandomPrime(3^10);

Output: Magma V2.11-2     Wed Aug 25 2004 19:08:28 on modular  [Seed = 2065113555]
   -------------------------------------



************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:09:04 2004

Input: RandomPrime(300);

Output: Magma V2.11-2     Wed Aug 25 2004 19:09:01 on modular  [Seed = 911895423]
   -------------------------------------

8850827930679283872035184938399760623690827125079421653012629880297506072755489\
0061810083

Total time: 2.129 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:09:41 2004

Input: RandomPrime(3000);

Output: Magma V2.11-2     Wed Aug 25 2004 19:09:20 on modular  [Seed = 3719397560]
   -------------------------------------



************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:10:10 2004

Input: RandomPrime(500);

Output: Magma V2.11-2     Wed Aug 25 2004 19:09:50 on modular  [Seed = 4237336966]
   -------------------------------------



************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:10:36 2004

Input: RandomPrime(400);

Output: Magma V2.11-2     Wed Aug 25 2004 19:10:21 on modular  [Seed = 2781477052]
   -------------------------------------

9773919966695295065144139713407763196654985513153388985242738674305430218344478\
93012943610937966712740630032556390729409

Total time: 14.299 seconds, Total memory usage: 4.06MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:10:56 2004

Input: RandomPrime(460);

Output: Magma V2.11-2     Wed Aug 25 2004 19:10:45 on modular  [Seed = 3117802632]
   -------------------------------------

7857309272804078717474867428398664717210366182053666753163955813671475765854724\
40946741876695223179199310684175319757957844217461686321537

Total time: 11.360 seconds, Total memory usage: 3.96MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:12:04 2004

Input: K<w> := GF(3^(97*2));
P<x> := PolynomialRing (K);

Output: Magma V2.11-2     Wed Aug 25 2004 19:12:03 on modular  [Seed = 2031428861]
   -------------------------------------


Total time: 0.829 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:12:18 2004

Input: K<w> := GF(3^(97*2));
P<x> := PolynomialRing(K);

Output: Magma V2.11-2     Wed Aug 25 2004 19:12:17 on modular  [Seed = 527647369]
   -------------------------------------


Total time: 0.870 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:12:27 2004

Input: K<w> := GF(3^97);
P<x> := PolynomialRing(K);

Output: Magma V2.11-2     Wed Aug 25 2004 19:12:26 on modular  [Seed = 726103735]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:12:58 2004

Input: K<w> := GF(3^97);


Output: Magma V2.11-2     Wed Aug 25 2004 19:12:58 on modular  [Seed = 3686237798]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:15:20 2004

Input: K<w> := GF(3^97);
P<x> := PolynomialRing(K);
f := x^5 + 2;

Factorisation (f);

Output: Magma V2.11-2     Wed Aug 25 2004 19:15:20 on modular  [Seed = 1661943725]
   -------------------------------------

[
    <x + 2, 1>,
    <x^4 + x^3 + x^2 + x + 1, 1>
]

Total time: 0.610 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:15:41 2004

Input: K<w> := GF(3^97);
P<x> := PolynomialRing(K);
f := x^5 + 2 + x^85;

Factorisation (f);

Output: Magma V2.11-2     Wed Aug 25 2004 19:15:41 on modular  [Seed = 124476380]
   -------------------------------------

[
    <x + 1, 2>,
    <x^3 + 2*x + 1, 1>,
    <x^4 + 2*x^3 + x^2 + 2*x + 1, 2>,
    <x^5 + x^3 + 2*x^2 + 2*x + 1, 1>,
    <x^7 + 2*x^6 + 2*x^5 + x^4 + x^2 + x + 2, 1>,
    <x^12 + x^10 + 2*x^9 + x^8 + 2*x^6 + 2*x^5 + 2*x^4 + x^2 + x + 1, 1>,
    <x^20 + 2*x^18 + x^17 + 2*x^16 + x^15 + x^14 + x^12 + 2*x^10 + 2*x^8 + x^7 +
        2*x^3 + 2*x^2 + x + 1, 1>,
    <x^28 + x^27 + 2*x^26 + 2*x^25 + 2*x^22 + 2*x^20 + x^18 + 2*x^16 + x^15 + 
        x^14 + 2*x^12 + 2*x^10 + x^6 + x^5 + 2*x^2 + x + 1, 1>
]

Total time: 0.600 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:16:20 2004

Input: K<w> := GF(3^(97*2));
P<x> := PolynomialRing(K);
f := x^5 + 2 + x^85;

(x^5)^100;

Output: Magma V2.11-2     Wed Aug 25 2004 19:16:19 on modular  [Seed = 928738226]
   -------------------------------------

x^500

Total time: 0.779 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:21:51 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(x^97+x^12+2);
d;



Output: Magma V2.11-2     Wed Aug 25 2004 19:21:50 on modular  [Seed = 2483015124]
   -------------------------------------


>> d<x> := DefiningPolynomial(x^97+x^12+2);
                              ^
User error: Identifier 'x' has not been declared or assigned

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:22:18 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(w3^97+w3^12+2);
d;



Output: Magma V2.11-2     Wed Aug 25 2004 19:22:18 on modular  [Seed = 1127161121]
   -------------------------------------


>> d<x> := DefiningPolynomial(w3^97+w3^12+2);
                             ^
Runtime error in 'DefiningPolynomial': Bad argument types
Argument types given: FldFinElt

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:22:44 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(F3^97+F3^12+2);
d;



Output: Magma V2.11-2     Wed Aug 25 2004 19:22:43 on modular  [Seed = 1695103854]
   -------------------------------------


>> d<x> := DefiningPolynomial(F3^97+F3^12+2);
                                ^
Runtime error in '^': Bad argument types
Argument types given: FldFin, RngIntElt

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:22:59 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(F3);
d;



Output: Magma V2.11-2     Wed Aug 25 2004 19:22:59 on modular  [Seed = 157636370]
   -------------------------------------

x^97 + 2*x^3 + 2*x^2 + 2*x + 1

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:23:58 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(F3);
d;
d<x> := x^97+x^12+2;
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:23:57 on modular  [Seed = 3349911810]
   -------------------------------------

x^97 + 2*x^3 + 2*x^2 + 2*x + 1
x^97 + x^12 + 2

Total time: 0.620 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:24:36 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(F3);
d;
d<x> := x^97+x^12+2;
d;
MinimalPolynomial(d,F3);

Output: Magma V2.11-2     Wed Aug 25 2004 19:24:35 on modular  [Seed = 2363544183]
   -------------------------------------

x^97 + 2*x^3 + 2*x^2 + 2*x + 1
x^97 + x^12 + 2

>> MinimalPolynomial(d,F3);;
                    ^
Runtime error in 'MinimalPolynomial': Bad argument types
Argument types given: RngUPolElt[FldFin], FldFin

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:25:01 2004

Input: F3<w3> := FiniteField(3,97);
d<x> := DefiningPolynomial(F3);
d;
MinimalPolynomial(d,F3);

Output: Magma V2.11-2     Wed Aug 25 2004 19:25:01 on modular  [Seed = 2898326057]
   -------------------------------------

x^97 + 2*x^3 + 2*x^2 + 2*x + 1

>> MinimalPolynomial(d,F3);;
                    ^
Runtime error in 'MinimalPolynomial': Bad argument types
Argument types given: RngUPolElt[FldFin], FldFin

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:25:44 2004

Input: F3<w3> := FiniteField(3,97);
d<w3> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:25:43 on modular  [Seed = 1379798241]
   -------------------------------------

w3^97 + 2*w3^3 + 2*w3^2 + 2*w3 + 1

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:26:35 2004

Input: F3<w3> := FiniteField(3,97*2);
d<x> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:26:34 on modular  [Seed = 726092363]
   -------------------------------------

x^194 + x^193 + 2*x^192 + x^191 + x^189 + x^188 + 2*x^187 + x^185 + x^184 + 
    2*x^183 + 2*x^182 + x^179 + x^178 + x^176 + x^175 + 2*x^174 + 2*x^173 + 
    x^172 + x^171 + 2*x^170 + x^168 + 2*x^167 + x^166 + x^165 + x^164 + 2*x^162 
    + x^161 + x^160 + 2*x^159 + x^157 + 2*x^155 + 2*x^154 + x^153 + x^151 + 
    x^150 + x^149 + x^148 + x^147 + x^146 + 2*x^144 + 2*x^142 + x^141 + x^140 + 
    x^138 + x^137 + x^136 + 2*x^135 + 2*x^133 + x^131 + 2*x^130 + 2*x^125 + 
    x^124 + 2*x^123 + 2*x^121 + x^120 + x^119 + 2*x^118 + 2*x^116 + x^115 + 
    2*x^114 + 2*x^113 + 2*x^112 + x^111 + 2*x^110 + x^108 + 2*x^107 + x^106 + 
    2*x^104 + x^103 + x^100 + 2*x^99 + x^97 + 2*x^96 + x^95 + x^94 + 2*x^93 + 
    x^92 + x^91 + x^90 + 2*x^89 + 2*x^86 + x^85 + 2*x^84 + 2*x^83 + x^80 + x^79 
    + 2*x^77 + 2*x^75 + 2*x^74 + x^73 + x^72 + x^70 + x^69 + 2*x^68 + x^66 + 
    2*x^65 + 2*x^64 + 2*x^62 + x^61 + x^59 + x^58 + x^57 + x^51 + 2*x^50 + 
    2*x^49 + 2*x^48 + 2*x^46 + 2*x^45 + 2*x^44 + x^43 + x^42 + x^40 + 2*x^39 + 
    x^38 + 2*x^37 + 2*x^36 + 2*x^35 + x^34 + 2*x^33 + x^32 + 2*x^29 + x^28 + 
    2*x^27 + 2*x^26 + 2*x^25 + x^24 + 2*x^22 + 2*x^21 + 2*x^20 + 2*x^19 + 2*x^17
    + 2*x^16 + x^13 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^4 + 2*x^3 + 2*x^2 + 
    2*x + 1

Total time: 0.789 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:26:41 2004

Input: F3<w3> := FiniteField(3,97^2);
d<x> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:26:20 on modular  [Seed = 73950547]
   -------------------------------------



************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:28:00 2004

Input: F3<w3> := FiniteField(3,97);
F32<x> := FiniteField(F3,2);
FF<x> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:27:59 on modular  [Seed = 4254178505]
   -------------------------------------


>> F32<x> := FiniteField(F3,2);
                        ^
Runtime error in 'FiniteField': Bad argument types
Argument types given: FldFin, RngIntElt

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:28:13 2004

Input: F3<w3> := FiniteField(3,97);
F32<x> := FiniteField(w3,2);
FF<x> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:28:12 on modular  [Seed = 2246698050]
   -------------------------------------


>> F32<x> := FiniteField(w3,2);
                        ^
Runtime error in 'FiniteField': Bad argument types
Argument types given: FldFinElt, RngIntElt

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:28:45 2004

Input: F3<w3> := FiniteField(3,97);
F32<x> := FiniteField(3^97,2);
FF<x> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:28:44 on modular  [Seed = 3167804763]
   -------------------------------------


>> F32<x> := FiniteField(3^97,2);
                        ^
Runtime error in 'FiniteField': Argument 1 
(19088056323407827075424486287615602692670648963) should be prime

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host IP-213157024042.dialin.heagmedianet.de. (213.157.24.42)
Time: Wed Aug 25 19:29:05 2004

Input: F3<w3> := FiniteField(3,97);
F32<x> := FiniteField((3^97),2);
FF<x> := DefiningPolynomial(F3);
d;


Output: Magma V2.11-2     Wed Aug 25 2004 19:29:04 on modular  [Seed = 1110320072]
   -------------------------------------


>> F32<x> := FiniteField((3^97),2);
                        ^
Runtime error in 'FiniteField': Argument 1 
(19088056323407827075424486287615602692670648963) should be prime

>> d;
   ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host squid.prod1.dngr.net. (63.241.65.90)
Time: Wed Aug 25 23:43:22 2004

Input: (1 - x) * (1 + 2 * x)


Output: Magma V2.11-2     Wed Aug 25 2004 23:43:21 on modular  [Seed = 360253543]
   -------------------------------------


>> (1 - x) * (1 + 2 * x)
        ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.620 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ppp-66-63-133-93.sndg-pm4-1.dialup.nethere.net. (66.63.133.93)
Time: Thu Aug 26 00:43:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([23,0,224741094914,0,519535132904052734375]);
f;
S := FourDescent(f);
#S;
F := S[1];
pts := Points(F,100);
pts;
X,m := Scheme(F);
X;
m(pts[1]);
Height($1)


Output: Magma V2.11-2     Thu Aug 26 2004 00:43:22 on modular  [Seed = 1011881759]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 
54326190625369714087362857318400 over Rational Field
23*x^4 + 224741094914*x^2 + 519535132904052734375


************** MAGMA *****************
Host ppp-66-63-133-93.sndg-pm4-1.dialup.nethere.net. (66.63.133.93)
Time: Thu Aug 26 00:44:50 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([23,0,224741094914,0,519535132904052734375]);
f;
S := FourDescent(f);
#S;
F := S[1];
pts := Points(F,100);
pts;
X,m := Scheme(F);
X;
m(pts[1]);
Height($1)

Output: Magma V2.11-2     Thu Aug 26 2004 00:44:30 on modular  [Seed = 1346141110]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 
54326190625369714087362857318400 over Rational Field
23*x^4 + 224741094914*x^2 + 519535132904052734375


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Thu Aug 26 01:34:04 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug 26 2004 01:34:03 on modular  [Seed = 742398724]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.590 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Thu Aug 26 01:34:12 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Thu Aug 26 2004 01:34:11 on modular  [Seed = 327099428]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Thu Aug 26 01:34:36 2004

Input: "10110000/1011"

Output: Magma V2.11-2     Thu Aug 26 2004 01:34:36 on modular  [Seed = 3753109712]
   -------------------------------------

10110000/1011

Total time: 0.639 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:35:02 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y]
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;



Output: Magma V2.11-2     Thu Aug 26 2004 02:35:00 on modular  [Seed = 427154571]
   -------------------------------------


>> for f in S do
   ^
User error: bad syntax

>> f := brumer(b, c, d);
               ^
User error: Identifier 'b' has not been declared or assigned

>> if not IsIrreducible(f) then 
                        ^
User error: Identifier 'f' has not been declared or assigned

>> G, R:= GaloisGroup(f);
                      ^
User error: Identifier 'f' has not been declared or assigned

>> if isA5(G) then
           ^
User error: Identifier 'G' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 0.789 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:35:33 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 02:35:32 on modular  [Seed = 1795665624]
   -------------------------------------


>> S := [ P |
        ^
Runtime error in [ ... ]: Coerce failed for sequence element

>> for f in S do
            ^
User error: Identifier 'S' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:36:01 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:36:00 on modular  [Seed = 2831445375]
   -------------------------------------


>> S := [ P | 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
        ^
Runtime error in [ ... ]: Coerce failed for sequence element

>> for f in S do
            ^
User error: Identifier 'S' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.760 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:37:46 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y);
Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y);
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:37:45 on modular  [Seed = 2865131157]
   -------------------------------------


>> Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y);
         ^
Runtime error in 'Append': Could not lift element into sequence

>> Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y);
         ^
Runtime error in 'Append': Could not lift element into sequence

>> 1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
                                        ^
User error: bad syntax

>> f := brumer(b, c, d);
               ^
User error: Identifier 'b' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:38:26 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*t);
Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*t);
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:38:25 on modular  [Seed = 276616312]
   -------------------------------------


>> Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*t);
         ^
Runtime error in 'Append': Could not lift element into sequence

>> Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*t);
         ^
Runtime error in 'Append': Could not lift element into sequence

>> 1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
                                        ^
User error: bad syntax

>> f := brumer(b, c, d);
               ^
User error: Identifier 'b' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.779 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:38:52 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + (2*y)*x^3);
Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*t);
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:38:51 on modular  [Seed = 1628284179]
   -------------------------------------


>> Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + (2*y)*x^3);
         ^
Runtime error in 'Append': Could not lift element into sequence

>> Append(~S, 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*t);
                                                    ^
User error: Identifier 't' has not been declared or assigned

>> 1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
                                        ^
User error: bad syntax

>> f := brumer(b, c, d);
               ^
User error: Identifier 'b' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:39:58 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + (2*x^3*y
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:39:57 on modular  [Seed = 207669433]
   -------------------------------------


>> 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
   ^
User error: bad syntax

>> 1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
                                        ^
User error: bad syntax

>> for f in S do
            ^
User error: Identifier 'S' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.750 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:40:09 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:40:08 on modular  [Seed = 895087093]
   -------------------------------------


>> 1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
   ^
User error: bad syntax

>> 1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
                                        ^
User error: bad syntax

>> for f in S do
            ^
User error: Identifier 'S' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.759 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:40:21 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:40:20 on modular  [Seed = 1862511539]
   -------------------------------------


>> f := brumer(b, c, d);
               ^
User error: Identifier 'b' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 0.769 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:40:59 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:40:56 on modular  [Seed = 3333030454]
   -------------------------------------

x^6 + 2*x^5 + (2*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + 2*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*y*x^3 + 3*x + 1
x^6 + 2*x^5 + y*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 1)*x^3 + 3*x + 1

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 2.370 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:41:35 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 02:41:32 on modular  [Seed = 792979512]
   -------------------------------------

x^6 + (3*y + 2)*x^5 + 3*x + 2*y + 1
x^6 + (2*y + 2)*x^5 + 3*x + 3*y + 1
x^6 + (y + 2)*x^5 + 3*x + 4*y + 1
x^6 + (4*y + 2)*x^5 + 3*x + y + 1

>> end for;
   ^
User error: bad syntax

>> end for;;
   ^
User error: bad syntax

Total time: 2.369 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:41:56 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:41:53 on modular  [Seed = 2115156292]
   -------------------------------------

x^6 + (3*y + 2)*x^5 + 3*x + 2*y + 1
x^6 + (2*y + 2)*x^5 + 3*x + 3*y + 1
x^6 + (y + 2)*x^5 + 3*x + 4*y + 1
x^6 + (4*y + 2)*x^5 + 3*x + y + 1
Finished

Total time: 2.289 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:42:31 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:42:28 on modular  [Seed = 3201464801]
   -------------------------------------

x^6 + (3*y + 2)*x^5 + 3*x + 2*y + 1
x^6 + (2*y + 2)*x^5 + 3*x + 3*y + 1
x^6 + (y + 2)*x^5 + 3*x + 4*y + 1
x^6 + (4*y + 2)*x^5 + 3*x + y + 1
Finished

Total time: 2.250 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:43:20 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and isSS(f) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:43:19 on modular  [Seed = 1210355653]
   -------------------------------------


>> if isA5(G) and isSS(f) then
                      ^
Runtime error: Number of arguments (1) does not equal expected number of 
arguments (2)
Finished

Total time: 1.109 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:43:28 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) && isSS(f) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:43:27 on modular  [Seed = 1346148309]
   -------------------------------------


>> if isA5(G) && isSS(f) then
              ^
User error: Bad reduction operator

>>         print f;
                 ^
User error: Identifier 'f' has not been declared or assigned

>> end if;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
Finished

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:43:52 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:43:49 on modular  [Seed = 2246656554]
   -------------------------------------

x^6 + 2*x^5 + (2*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + 2*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*y*x^3 + 3*x + 1
x^6 + 2*x^5 + y*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 1)*x^3 + 3*x + 1
Finished

Total time: 2.310 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:44:57 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if (isA5(G) && isSS(f, p)) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:44:56 on modular  [Seed = 1160348320]
   -------------------------------------


>> if (isA5(G) && isSS(f, p)) then
               ^
User error: Bad reduction operator

>>         print f;
                 ^
User error: Identifier 'f' has not been declared or assigned

>> end if;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
Finished

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:45:20 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and isSS(f, p) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:45:18 on modular  [Seed = 2131998860]
   -------------------------------------

x^6 + 2*x^5 + (2*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + 2*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*y*x^3 + 3*x + 1
x^6 + 2*x^5 + y*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 1)*x^3 + 3*x + 1
Finished

Total time: 2.240 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:45:52 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if not isSS(f, p) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:45:50 on modular  [Seed = 3366194907]
   -------------------------------------

Finished

Total time: 2.289 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:46:10 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and isSS(f, p) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:46:08 on modular  [Seed = 4103615177]
   -------------------------------------

x^6 + 2*x^5 + (2*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + 2*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*y*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*y*x^3 + 3*x + 1
x^6 + 2*x^5 + y*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (y + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*y + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*y + 1)*x^3 + 3*x + 1
Finished

Total time: 2.280 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:58:56 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:58:54 on modular  [Seed = 558754333]
   -------------------------------------

x^6 + (3*y + 2)*x^5 + 3*x + 2*y + 1
x^6 + (2*y + 2)*x^5 + 3*x + 3*y + 1
x^6 + (y + 2)*x^5 + 3*x + 4*y + 1
x^6 + (4*y + 2)*x^5 + 3*x + y + 1
Finished

Total time: 2.229 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 02:59:55 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 2*y + 3*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 3*y + 2*x^5*y,
1 + 3*x + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 2*x^5 + x^6 + 4*y + x^5*y,
1 + 3*x + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 2*x^5 + x^6 + y + 4*x^5*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 3*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 3*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + 4*x^3*y,
1 + 3*x + 4*x^3 + 2*x^5 + x^6 + x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 2*x^3*y,
1 + 3*x + x^3 + 2*x^5 + x^6 + 3*x^3*y];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 02:59:53 on modular  [Seed = 759293526]
   -------------------------------------

Not A5  x^6 + (3*y + 2)*x^5 + 3*x + 2*y + 1
Not A5  x^6 + (2*y + 2)*x^5 + 3*x + 3*y + 1
Not A5  x^6 + (y + 2)*x^5 + 3*x + 4*y + 1
Not A5  x^6 + (4*y + 2)*x^5 + 3*x + y + 1
Finished

Total time: 2.240 seconds, Total memory usage: 7.61MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:02:44 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:02:42 on modular  [Seed = 1310884942]
   -------------------------------------

Finished

Total time: 2.110 seconds, Total memory usage: 7.59MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:04:26 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,
x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,
x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,
x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:04:20 on modular  [Seed = 2666681593]
   -------------------------------------

Not SS  x^6 + 2*x^4 + (t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 2*t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 3*t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 4*t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1
Not SS  x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 5.089 seconds, Total memory usage: 7.92MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:17:03 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:16:58 on modular  [Seed = 1678289691]
   -------------------------------------

Not SS  x^6 + 2*x^4 + t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 2*t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 3*t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 4*t*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
Not SS  x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 5.110 seconds, Total memory usage: 7.92MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:22:27 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t : = y^2;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:22:26 on modular  [Seed = 443995324]
   -------------------------------------


>> t : = y^2;
       ^
User error: bad syntax

>> x^6 + 2*x^4 + t*x^3 + x + 1,
                 ^
User error: Identifier 't' has not been declared or assigned

>> for f in S do
            ^
User error: Identifier 'S' has not been declared or assigned
Finished

Total time: 0.740 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:22:43 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^2;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:22:37 on modular  [Seed = 57658794]
   -------------------------------------

Not SS  x^6 + 2*x^4 + y^2*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 2*y^2*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 3*y^2*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 4*y^2*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + 4)*x^3 + x + 1
Not SS  x^6 + 4*x^5 + y^2*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 2*y^2*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 3*y^2*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 4*y^2*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + x^5 + 2*x^4 + y^2*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 2*y^2*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 3*y^2*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 4*y^2*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + 3*x^5 + x^4 + y^2*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 2*y^2*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 3*y^2*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 4*y^2*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + 4)*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 5.860 seconds, Total memory usage: 8.42MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:23:06 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^2 - y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:23:01 on modular  [Seed = 845085939]
   -------------------------------------

Not SS  x^6 + 2*x^4 + (y^2 + 4*y)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 4*y + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 4*y + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 4*y + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^2 + 4*y + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 3*y)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 3*y + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 3*y + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 3*y + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^2 + 3*y + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 2*y)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 2*y + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 2*y + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 2*y + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^2 + 2*y + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + y)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + y + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + y + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + y + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^2 + y + 4)*x^3 + x + 1
Not SS  x^6 + 4*x^5 + (y^2 + 4*y)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 4*y + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 4*y + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 4*y + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^2 + 4*y + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 3*y)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 3*y + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 3*y + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 3*y + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^2 + 3*y + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 2*y)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 2*y + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 2*y + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 2*y + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^2 + 2*y + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + y)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + y + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + y + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + y + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^2 + y + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 4*y)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 4*y + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 4*y + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 4*y + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^2 + 4*y + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 3*y)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 3*y + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 3*y + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 3*y + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^2 + 3*y + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 2*y)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 2*y + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 2*y + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 2*y + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^2 + 2*y + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + y)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + y + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + y + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + y + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^2 + y + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 4*y)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 4*y + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 4*y + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 4*y + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^2 + 4*y + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 3*y)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 3*y + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 3*y + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 3*y + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^2 + 3*y + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 2*y)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 2*y + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 2*y + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 2*y + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^2 + 2*y + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + y)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + y + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + y + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + y + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^2 + y + 4)*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 5.709 seconds, Total memory usage: 8.42MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:24:40 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := 1;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:24:39 on modular  [Seed = 1227200618]
   -------------------------------------

Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 0.789 seconds, Total memory usage: 3.34MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:24:48 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := 2;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:24:47 on modular  [Seed = 1897767002]
   -------------------------------------

Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + 3*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 4*x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + x + 1
Not irreducible  x^6 + 2*x^4 + x^3 + x + 1
Not irreducible  x^6 + 2*x^4 + 2*x^3 + x + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + 2*x^2 + 1
Not irreducible  x^6 + 4*x^5 + x^3 + 2*x^2 + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
Not irreducible  x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 0.799 seconds, Total memory usage: 3.34MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:24:56 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := t^3;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:24:55 on modular  [Seed = 2031462437]
   -------------------------------------


>> t := t^3;
        ^
User error: Identifier 't' has not been declared or assigned

>> x^6 + 2*x^4 + t*x^3 + x + 1,
                 ^
User error: Identifier 't' has not been declared or assigned

>> for f in S do
            ^
User error: Identifier 'S' has not been declared or assigned
Finished

Total time: 0.789 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:25:08 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^3;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^4 + t*x^3 + x + 1,
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 2*t*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 3*t*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,

x^6 + 2*x^4 + 4*t*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,

x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,

x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,

x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,

x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,

x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:25:02 on modular  [Seed = 1761982515]
   -------------------------------------

Not SS  x^6 + 2*x^4 + y^3*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^3 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^3 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^3 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (y^3 + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 2*y^3*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^3 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^3 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^3 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (2*y^3 + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 3*y^3*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^3 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^3 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^3 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (3*y^3 + 4)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + 4*y^3*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^3 + 1)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^3 + 2)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^3 + 3)*x^3 + x + 1
Not SS  x^6 + 2*x^4 + (4*y^3 + 4)*x^3 + x + 1
Not SS  x^6 + 4*x^5 + y^3*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^3 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^3 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^3 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (y^3 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 2*y^3*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^3 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^3 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^3 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (2*y^3 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 3*y^3*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^3 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^3 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^3 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (3*y^3 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + 4*y^3*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^3 + 4)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^3 + 1)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^3 + 2)*x^3 + 2*x^2 + 1
Not SS  x^6 + 4*x^5 + (4*y^3 + 3)*x^3 + 2*x^2 + 1
Not SS  x^6 + x^5 + 2*x^4 + y^3*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^3 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^3 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^3 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (y^3 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 2*y^3*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^3 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^3 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^3 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (2*y^3 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 3*y^3*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^3 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^3 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^3 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (3*y^3 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + 4*y^3*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^3 + 1)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^3 + 2)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^3 + 3)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + x^5 + 2*x^4 + (4*y^3 + 4)*x^3 + x^2 + 2*x + 1
Not SS  x^6 + 3*x^5 + x^4 + y^3*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^3 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^3 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^3 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (y^3 + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 2*y^3*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^3 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^3 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^3 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (2*y^3 + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 3*y^3*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^3 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^3 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^3 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (3*y^3 + 4)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + 4*y^3*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^3 + 1)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^3 + 2)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^3 + 3)*x^3 + 2*x^2 + 4*x + 1
Not SS  x^6 + 3*x^5 + x^4 + (4*y^3 + 4)*x^3 + 2*x^2 + 4*x + 1
Finished

Total time: 5.499 seconds, Total memory usage: 8.32MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:26:36 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^3;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1]
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:26:36 on modular  [Seed = 3134614274]
   -------------------------------------


>> for f in S do
   ^
User error: bad syntax

>> if not IsIrreducible(f) then
                        ^
User error: Identifier 'f' has not been declared or assigned

>> G, R:= GaloisGroup(f);
                      ^
User error: Identifier 'f' has not been declared or assigned

>> if not isA5(G) then
               ^
User error: Identifier 'G' has not been declared or assigned

>> if not isSS(f, p) then
               ^
User error: Identifier 'f' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
Finished

Total time: 0.760 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:26:48 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^3;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:26:46 on modular  [Seed = 2948824589]
   -------------------------------------

Finished

Total time: 2.220 seconds, Total memory usage: 8.19MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:26:56 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:26:54 on modular  [Seed = 3619358333]
   -------------------------------------

Finished

Total time: 2.229 seconds, Total memory usage: 7.59MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:27:02 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y-1;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:27:00 on modular  [Seed = 3232502032]
   -------------------------------------

Finished

Total time: 2.090 seconds, Total memory usage: 7.59MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:27:08 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^2-1;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:27:06 on modular  [Seed = 3366197526]
   -------------------------------------

Finished

Total time: 2.239 seconds, Total memory usage: 8.19MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:27:21 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^3-y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ Q |
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1];
 
for f in S do

if not IsIrreducible(f) then
	print "Not irreducible ", f;
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print "Not A5 ", f;
end if;

if not isSS(f, p) then
	print "Not SS ", f;
end if;

end for;

print "Finished";

Output: Magma V2.11-2     Thu Aug 26 2004 03:27:19 on modular  [Seed = 4036763955]
   -------------------------------------

Finished

Total time: 2.269 seconds, Total memory usage: 7.59MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:49:10 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^3-y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

        print(n*m);
	return n*m eq zeromat;
end function;

f := x^6+2*x^5+t*x^3+3*x+1;
isSS(f, p);

Output: Magma V2.11-2     Thu Aug 26 2004 03:49:09 on modular  [Seed = 157670885]
   -------------------------------------

[0 0]
[0 0]
true

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:49:53 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y^3-y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

        print(n*m);
	return n*m eq zeromat;
end function;

f := x^6 + 2*x^4 + t*x^3 + x + 1;
isSS(f, p);

Output: Magma V2.11-2     Thu Aug 26 2004 03:49:52 on modular  [Seed = 675610385]
   -------------------------------------

[3*y^18 + 2*y^16 + 3*y^15 + 2*y^8 + 3*y^6 + 2*y^5 + 3*y^3 + 2*y + 1   4*y^18 + 
    y^16 + 3*y^15 + y^8 + 4*y^6 + 2*y^5 + 3*y^3 + 2*y]
[4*y^18 + y^16 + 3*y^15 + y^8 + 4*y^6 + 2*y^5 + 3*y^3 + 2*y   4*y^18 + y^16 + 
    y^8 + 4*y^6 + 1]
false

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:50:30 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

        print(n*m);
	return n*m eq zeromat;
end function;

f := x^6 + 2*x^4 + t*x^3 + x + 1;
isSS(f, p);

Output: Magma V2.11-2     Thu Aug 26 2004 03:50:30 on modular  [Seed = 659288184]
   -------------------------------------

[3*y^6 + 3*y^5 + 3*y + 1     4*y^6 + 3*y^5 + 3*y]
[    4*y^6 + 3*y^5 + 3*y               4*y^6 + 1]
false

Total time: 0.769 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:52:19 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

        print(n*m);
	return n*m eq zeromat;
end function;

f := x^6 + 4*x^5 + t*x^3 + 2*x + 1;
isSS(f, p);

Output: Magma V2.11-2     Thu Aug 26 2004 03:52:18 on modular  [Seed = 1761984194]
   -------------------------------------

[    0 4*y^6]
[4*y^6 3*y^6]
false

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:53:49 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

        print(n*m);
	return n*m eq zeromat;
end function;

f := x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1;
isSS(f, p);

Output: Magma V2.11-2     Thu Aug 26 2004 03:53:48 on modular  [Seed = 2380356504]
   -------------------------------------

[        3*y^5 + 3*y + 1 2*y^6 + 3*y^5 + 3*y + 4]
[2*y^6 + 3*y^5 + 3*y + 4               3*y^6 + 2]
false

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 03:54:10 2004

Input: Z := Integers();
p:=Z ! 5;
P<y>:= FunctionField(GF(p));
t := y;
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

        print(n*m);
	return n*m eq zeromat;
end function;

f := x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1;
isSS(f, p);

Output: Magma V2.11-2     Thu Aug 26 2004 03:54:09 on modular  [Seed = 3184618373]
   -------------------------------------

[              3*y^6 + 2 3*y^6 + 3*y^5 + 3*y + 1]
[3*y^6 + 3*y^5 + 3*y + 1         2*y^5 + 2*y + 1]
false

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:03:40 2004

Input: Z := Integers();
p:=Z ! 5;
P<b>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;
 
for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;
end for;
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 04:03:39 on modular  [Seed = 3232503939]
   -------------------------------------


>>                 Append(~S, r*t+s);
                                ^
User error: Identifier 't' has not been declared or assigned

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:04:12 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;
 
for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 04:03:51 on modular  [Seed = 3967825043]
   -------------------------------------

x^6 + 2*x^4 + (t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1
x^6 + 2*x^4 + t*x^3 + x + 1
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1
x^6 + 2*x^4 + 2*t*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1
x^6 + 2*x^4 + 3*t*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
x^6 + 2*x^4 + 4*t*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 4*t)*x^2 + (2*t
    + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 4*t)*x^2 + (2*t
    + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 4*t)*x^2 + (2*t
    + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + 2*t^2*x^3 + (t^2 + 4*t)*x^2 + (2*t + 1)*x 
    + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + t)*x^2 + (2*t
    + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + t)*x^2 + (2*t
    + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + t)*x^2 + (2*t
    + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + 2*t^2*x^3 + (t^2 + t)*x^2 + (2*t + 3)*x 
    + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + 3*t + 
    2)*x^2 + 2*t*x + 1
x^6 + (2*t + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:05:09 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;
 
for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

if isSS(f, p) then
	print f;
end if;

end for;
end for;
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 04:04:48 on modular  [Seed = 1028777350]
   -------------------------------------

x^6 + 2*x^4 + x^3 + x + 1
x^6 + 2*x^5 + x^3 + 3*x + 1
x^6 + 2*x^5 + 2*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*x + 1
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + t*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1
x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x
x^6 + 2*x^5 + 3*x^4 + 4*x^3
x^6 + 4*x^5 + 3*x^3 + 4*x^2 + 2*x
x^6 + 4*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x
x^6 + 2*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4
x^6 + 2*x^5 + 4*x^4 + 4*x^3 + 3*x^2 + 2*x + 4
x^6 + 4*x^5 + 2*x^3 + x^2 + 4*x + 4
x^6 + 4*x^5 + 4*x^4 + 2*x^3 + 4*x + 4
x^6 + 3*x^5 + 3*x + 4
x^6 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3
x^6 + 4*x^5 + x^3 + 3*x^2 + x + 3
x^6 + 4*x^5 + 3*x^4 + 3*x^3 + x^2 + x + 3
x^6 + x^5 + 3*x + 3
x^6 + 4*x^5 + 3*x + 2
x^6 + x^5 + 2*x^4 + 2*x^3 + 4*x^2 + 2
x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x + 2
x^6 + 3*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2
x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1
x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1
x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 
    4)*x + 4*t + 1
x^6 + (3*t + 2)*x^5 + 3*x + 4*t + 1
x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1
x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t
x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t
x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t
x^6 + 3*t*x^5 + 3*x + 4*t
x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t
x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4
x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 
    2)*x + 4*t + 4
x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4
x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4
x^6 + (3*t + 3)*x^5 + 3*x + 4*t + 4
x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3
x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 
    1)*x + 4*t + 3
x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3
x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3
x^6 + (3*t + 1)*x^5 + 3*x + 4*t + 3
x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2
x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 
    4*t + 2
x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2
x^6 + (3*t + 4)*x^5 + 3*x + 4*t + 2
x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2
x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1
x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1
x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x 
    + 3*t + 1
x^6 + (t + 2)*x^5 + 3*x + 3*t + 1
x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1
x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t
x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t
x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t
x^6 + t*x^5 + 3*x + 3*t
x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t
x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4
x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x 
    + 3*t + 4
x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4
x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4
x^6 + (t + 3)*x^5 + 3*x + 3*t + 4
x^6 + 4*x^5 + (3*t + 1)*x^3 + (4*t + 3)*x^2 + (4*t + 1)*x + 3*t + 3
x^6 + (4*t + 4)*x^5 + (3*t + 3)*x^4 + (3*t + 3)*x^3 + (t + 1)*x^2 + (3*t + 1)*x 
    + 3*t + 3
x^6 + (4*t + 1)*x^5 + 2*t*x^4 + t*x^3 + (3*t + 3)*x + 3*t + 3
x^6 + t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 3
x^6 + (t + 1)*x^5 + 3*x + 3*t + 3
x^6 + 4*x^5 + 3*t*x^3 + 4*t*x^2 + (4*t + 3)*x + 3*t + 2
x^6 + (4*t + 1)*x^5 + (3*t + 2)*x^4 + (3*t + 2)*x^3 + (t + 4)*x^2 + 3*t*x + 3*t 
    + 2
x^6 + (4*t + 3)*x^5 + (2*t + 1)*x^4 + (t + 3)*x^3 + (3*t + 2)*x + 3*t + 2
x^6 + (t + 4)*x^5 + 3*x + 3*t + 2
x^6 + (t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 2
x^6 + 4*x^5 + (2*t + 4)*x^3 + (t + 2)*x^2 + t*x + 2*t + 1
x^6 + (4*t + 2)*x^5 + 3*x + 2*t + 1
x^6 + (4*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t + 1
x^6 + t*x^5 + (3*t + 2)*x^4 + (4*t + 1)*x^3 + (2*t + 1)*x + 2*t + 1
x^6 + (t + 3)*x^5 + (2*t + 1)*x^4 + (2*t + 1)*x^3 + (4*t + 2)*x^2 + (2*t + 4)*x 
    + 2*t + 1
x^6 + 4*x^5 + (2*t + 3)*x^3 + (t + 4)*x^2 + (t + 2)*x + 2*t
x^6 + 4*t*x^5 + 3*x + 2*t
x^6 + (4*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t
x^6 + t*x^5 + 2*t*x^4 + 2*t*x^3 + 4*t*x^2 + (2*t + 3)*x + 2*t
x^6 + (t + 2)*x^5 + (3*t + 3)*x^4 + (4*t + 4)*x^3 + 2*t*x + 2*t
x^6 + 4*x^5 + (2*t + 2)*x^3 + (t + 1)*x^2 + (t + 4)*x + 2*t + 4


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:10:25 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;
 
for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

if isSS(f, p) then
	print f;
end if;

end for;
end for;
end for;

print "Done."

Output: Magma V2.11-2     Thu Aug 26 2004 04:10:04 on modular  [Seed = 3034083187]
   -------------------------------------

x^6 + 2*x^4 + x^3 + x + 1
x^6 + 2*x^5 + x^3 + 3*x + 1
x^6 + 2*x^5 + 2*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*x + 1
x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + t*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1
x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1
x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1
x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1
x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x
x^6 + 2*x^5 + 3*x^4 + 4*x^3
x^6 + 4*x^5 + 3*x^3 + 4*x^2 + 2*x
x^6 + 4*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x
x^6 + 2*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4
x^6 + 2*x^5 + 4*x^4 + 4*x^3 + 3*x^2 + 2*x + 4
x^6 + 4*x^5 + 2*x^3 + x^2 + 4*x + 4
x^6 + 4*x^5 + 4*x^4 + 2*x^3 + 4*x + 4
x^6 + 3*x^5 + 3*x + 4
x^6 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3
x^6 + 4*x^5 + x^3 + 3*x^2 + x + 3
x^6 + 4*x^5 + 3*x^4 + 3*x^3 + x^2 + x + 3
x^6 + x^5 + 3*x + 3
x^6 + 4*x^5 + 3*x + 2
x^6 + x^5 + 2*x^4 + 2*x^3 + 4*x^2 + 2
x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x + 2
x^6 + 3*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2
x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1
x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1
x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 
    4)*x + 4*t + 1
x^6 + (3*t + 2)*x^5 + 3*x + 4*t + 1
x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1
x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t
x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t
x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t
x^6 + 3*t*x^5 + 3*x + 4*t
x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t
x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4
x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 
    2)*x + 4*t + 4
x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4
x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4
x^6 + (3*t + 3)*x^5 + 3*x + 4*t + 4
x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3
x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 
    1)*x + 4*t + 3
x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3
x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3
x^6 + (3*t + 1)*x^5 + 3*x + 4*t + 3
x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2
x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 
    4*t + 2
x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2
x^6 + (3*t + 4)*x^5 + 3*x + 4*t + 2
x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2
x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1
x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1
x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x 
    + 3*t + 1
x^6 + (t + 2)*x^5 + 3*x + 3*t + 1
x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1
x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t
x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t
x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t
x^6 + t*x^5 + 3*x + 3*t
x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t
x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4
x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x 
    + 3*t + 4
x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4
x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4
x^6 + (t + 3)*x^5 + 3*x + 3*t + 4
x^6 + 4*x^5 + (3*t + 1)*x^3 + (4*t + 3)*x^2 + (4*t + 1)*x + 3*t + 3
x^6 + (4*t + 4)*x^5 + (3*t + 3)*x^4 + (3*t + 3)*x^3 + (t + 1)*x^2 + (3*t + 1)*x 
    + 3*t + 3
x^6 + (4*t + 1)*x^5 + 2*t*x^4 + t*x^3 + (3*t + 3)*x + 3*t + 3
x^6 + t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 3
x^6 + (t + 1)*x^5 + 3*x + 3*t + 3
x^6 + 4*x^5 + 3*t*x^3 + 4*t*x^2 + (4*t + 3)*x + 3*t + 2
x^6 + (4*t + 1)*x^5 + (3*t + 2)*x^4 + (3*t + 2)*x^3 + (t + 4)*x^2 + 3*t*x + 3*t 
    + 2
x^6 + (4*t + 3)*x^5 + (2*t + 1)*x^4 + (t + 3)*x^3 + (3*t + 2)*x + 3*t + 2
x^6 + (t + 4)*x^5 + 3*x + 3*t + 2
x^6 + (t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 2
x^6 + 4*x^5 + (2*t + 4)*x^3 + (t + 2)*x^2 + t*x + 2*t + 1
x^6 + (4*t + 2)*x^5 + 3*x + 2*t + 1
x^6 + (4*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t + 1
x^6 + t*x^5 + (3*t + 2)*x^4 + (4*t + 1)*x^3 + (2*t + 1)*x + 2*t + 1
x^6 + (t + 3)*x^5 + (2*t + 1)*x^4 + (2*t + 1)*x^3 + (4*t + 2)*x^2 + (2*t + 4)*x 
    + 2*t + 1
x^6 + 4*x^5 + (2*t + 3)*x^3 + (t + 4)*x^2 + (t + 2)*x + 2*t
x^6 + 4*t*x^5 + 3*x + 2*t
x^6 + (4*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t
x^6 + t*x^5 + 2*t*x^4 + 2*t*x^3 + 4*t*x^2 + (2*t + 3)*x + 2*t
x^6 + (t + 2)*x^5 + (3*t + 3)*x^4 + (4*t + 4)*x^3 + 2*t*x + 2*t
x^6 + 4*x^5 + (2*t + 2)*x^3 + (t + 1)*x^2 + (t + 4)*x + 2*t + 4


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:11:48 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(GF(p));
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;
 
for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then
	print f;
end if;

end for;
end for;
end for;

print "Done."

Output: Magma V2.11-2     Thu Aug 26 2004 04:11:27 on modular  [Seed = 4204142798]
   -------------------------------------

x^6 + 2*x^4 + 2*x^3 + x + 1
x^6 + 2*x^4 + 3*x^3 + x + 1
x^6 + 2*x^4 + 4*x^3 + x + 1
x^6 + 2*x^4 + x + 1
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1
x^6 + 2*x^4 + t*x^3 + x + 1
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1
x^6 + 2*x^4 + 2*t*x^3 + x + 1
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1
x^6 + 2*x^4 + 3*t*x^3 + x + 1
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
x^6 + 2*x^4 + 4*t*x^3 + x + 1
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1
x^6 + 4*x^5 + 2*x^2 + 1
x^6 + 4*x^5 + x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1
x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1
x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1
x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1
x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1
x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 4*t)*x^2 + (2*t
    + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 4*t)*x^2 + (2*t
    + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 4*t)*x^2 + (2*t
    + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + 2*t^2*x^3 + (t^2 + 4*t)*x^2 + (2*t + 1)*x 
    + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
    1)*x + 1
x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + 4*t)*x^2 + 
    (2*t + 1)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + t)*x^2 + (2*t
    + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + t)*x^2 + (2*t
    + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 1)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 2)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + t)*x^2 + 
    (2*t + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + t)*x^2 + (2*t
    + 3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + t)*x^2 + (2*t +
    3)*x + 1
x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + 2*t^2*x^3 + (t^2 + t)*x^2 + (2*t + 3)*x 
    + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + 2*t^2*x^3 + (t^2 + 3*t + 2)*x^2 + 2*t*x + 
    1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 3*t + 2)*x^2 + 
    2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 3*t + 2)*x^2 
    + 2*t*x + 1
x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 4)*x^3 +
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:23:19 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

print brumer(0, 1, t);

Output: Magma V2.11-2     Thu Aug 26 2004 04:23:18 on modular  [Seed = 224514534]
   -------------------------------------

x^6 + 2*x^5 + 5*x^4 + (-4*t + 6)*x^3 + 10*x^2 + 8*x + 1

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:27:09 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 1, t);
print f;
print isIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:27:08 on modular  [Seed = 1110351235]
   -------------------------------------

x^6 + 2*x^5 + 5*x^4 + (-4*t + 6)*x^3 + 10*x^2 + 8*x + 1

>> print isIrreducible(f);;
         ^
User error: Identifier 'isIrreducible' has not been declared or assigned

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:27:30 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 1, t);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:27:29 on modular  [Seed = 1845670274]
   -------------------------------------

x^6 + 2*x^5 + 5*x^4 + (-4*t + 6)*x^3 + 10*x^2 + 8*x + 1
true

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:28:27 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 0, t);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:28:26 on modular  [Seed = 2449297318]
   -------------------------------------

x^6 + 2*x^4 + (-4*t + 2)*x^3 + 5*x^2 + 6*x + 1
true

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:32:11 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 2, t);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:32:10 on modular  [Seed = 3316196562]
   -------------------------------------

x^6 + 4*x^5 + 10*x^4 + (-4*t + 14)*x^3 + 17*x^2 + 10*x + 1
true

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:39:24 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 2, t^2);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:39:23 on modular  [Seed = 3984657739]
   -------------------------------------

x^6 + 4*x^5 + 10*x^4 + (-4*t^2 + 14)*x^3 + 17*x^2 + 10*x + 1
true

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:39:42 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 2, t^2-t);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:39:42 on modular  [Seed = 3850962230]
   -------------------------------------

x^6 + 4*x^5 + 10*x^4 + (-4*t^2 + 4*t + 14)*x^3 + 17*x^2 + 10*x + 1
true

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:39:50 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 2, t^2-t+1);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:39:49 on modular  [Seed = 477166805]
   -------------------------------------

x^6 + 4*x^5 + 10*x^4 + (-4*t^2 + 4*t + 10)*x^3 + 17*x^2 + 10*x + 1
true

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:52:58 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 3, t);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:52:57 on modular  [Seed = 410320366]
   -------------------------------------

x^6 + 6*x^5 + 17*x^4 + (-4*t + 26)*x^3 + 26*x^2 + 12*x + 1
true

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Thu Aug 26 04:53:29 2004

Input: Z := Integers();
p:=Z ! 5;
P<t>:= FunctionField(RationalField());
Q<x>:= PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

f := brumer(0, 0, t);
print f;
print IsIrreducible(f);
f := brumer(0, 1, t);
print f;
print IsIrreducible(f);
f := brumer(0, 2, t);
print f;
print IsIrreducible(f);
f := brumer(0, 3, t);
print f;
print IsIrreducible(f);
f := brumer(0, 4, t);
print f;
print IsIrreducible(f);

Output: Magma V2.11-2     Thu Aug 26 2004 04:53:28 on modular  [Seed = 107667985]
   -------------------------------------

x^6 + 2*x^4 + (-4*t + 2)*x^3 + 5*x^2 + 6*x + 1
true
x^6 + 2*x^5 + 5*x^4 + (-4*t + 6)*x^3 + 10*x^2 + 8*x + 1
true
x^6 + 4*x^5 + 10*x^4 + (-4*t + 14)*x^3 + 17*x^2 + 10*x + 1
true
x^6 + 6*x^5 + 17*x^4 + (-4*t + 26)*x^3 + 26*x^2 + 12*x + 1
true
x^6 + 8*x^5 + 26*x^4 + (-4*t + 42)*x^3 + 37*x^2 + 14*x + 1
true

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 05:07:04 2004

Input: 
K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2)-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2))) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);
I:=ideal<R | P>;
Dimension(I);

V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];



Output: Magma V2.11-2     Thu Aug 26 2004 05:07:04 on modular  [Seed = 2499313074]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension
2 [ 1, 2 ]

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> S:=[R!(v@@phi ): v in Basis(V)];
                               ^
User error: Identifier 'V' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 05:14:45 2004

Input: K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2)-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2))) ] ;

I:=ideal<R | P>;
Dimension(I);
V,phi:=VectorSpace(quo<R | I>);
I:=ideal<R | P>;
Dimension(I);

V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];



Output: Magma V2.11-2     Thu Aug 26 2004 05:14:45 on modular  [Seed = 1981455698]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128
2 [ 1, 2 ]

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension
2 [ 1, 2 ]

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> S:=[R!(v@@phi ): v in Basis(V)];
                               ^
User error: Identifier 'V' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 05:19:27 2004

Input: K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2))-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2)) ] ;

I:=ideal<R | P>;
Dimension(I);
V,phi:=VectorSpace(quo<R | I>);

V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];


Output: Magma V2.11-2     Thu Aug 26 2004 05:19:26 on modular  [Seed = 4270986433]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128
1 [ 2 ]

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> S:=[R!(v@@phi ): v in Basis(V)];
                               ^
User error: Identifier 'V' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 05:30:07 2004

Input: K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2)-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2))) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);
I:=ideal<R | P>;
Dimension(I);

V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];



Output: Magma V2.11-2     Thu Aug 26 2004 05:30:06 on modular  [Seed = 1711966931]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension
2 [ 1, 2 ]

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> S:=[R!(v@@phi ): v in Basis(V)];
                               ^
User error: Identifier 'V' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 05:31:48 2004

Input: K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2)+
-y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2)) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2)-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2))) ] ;

I:=ideal<R | P>;
Dimension(I);
V,phi:=VectorSpace(quo<R | I>);
I:=ideal<R | P>;


V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];



Output: Magma V2.11-2     Thu Aug 26 2004 05:31:48 on modular  [Seed = 258203686]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128
2 [ 1, 2 ]

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> V,phi:=VectorSpace(quo<R | I>);
                     ^
Runtime error in 'VectorSpace': Quotient does not have finite dimension

>> S:=[R!(v@@phi ): v in Basis(V)];
                               ^
User error: Identifier 'V' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 05:36:37 2004

Input: K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2))-
y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2))-
y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2))-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2)) ] ;

I:=ideal<R | P>;
Dimension(I);
V,phi:=VectorSpace(quo<R | I>);



V,phi:=VectorSpace(quo<R | I>);
S:=[R!(v@@phi ): v in Basis(V)];



Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-2     Thu Aug 26 2004 05:36:33 on modular  [Seed = 174515227]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128
0 []

Current total memory usage: 95.3MB, failed memory request: 0.1MB
System Error: User memory limit has been reached

Total time: 3.360 seconds, Total memory usage: 99.98MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 06:48:31 2004

Input: K<w> := GF(p);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [p^2 -p, p^2 -1, p^8 -p^2, p^8 -p^3, p^8 -p^4, p^8 -p^5, p^8 -p^6, p^8 -p^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^p+f*(-y^(p^2)+x^(p^2 +p))+g*(x^(p^3)*y^p +y^(p^3)*x^p -x^(p^3 +p^2 +p)) +
z*(y^(p^4 +p^2 )-y^(p^4)*x^(p^2 +p)- y^(p^2)*x^(p^4 +p^3)-y^(p^3)*x^(p^4 +p)+ x^(p^4+p^3 +p^2 +p))+ 
w*(y^(p^5 +p^3 )*x ^p -x^(p^3)*y^(p^5 +p^2)- x^(p^5)*y^(p^4 +p^2)+y^(p^5)*x^(p^3 +p^2 +p)+ y^(p^4)*x^(p^5 +p^2 +p)+
y^(p^3)*x^(p^5 +p^4 +p)+y^(p^2)*x^(p^5 +p^4 +p^3)-x^(p^5+p^4 +p^3 +p^2 +p))-
y^(p^6 +p^4 +p^2)+y^(p^6 +p^4 )*x^(p^2 +p)+y^(p^6 +p^3 )*x^(p^4 +p)+y^(p^6 +p^2)*x^(p^4 +p^3)+
y^(p^5 +p^3 )*x^(p^6 +p)+y^(p^5 +p^2 )*x^(p^6 +p^3)+y^(p^2+p^4 )*x^(p^6 +p^5)-y^(p^6)*x^(p^4+p^3+p^2+p)-
y^(p^5)*x^(p^6+p^3+p^2+p)-y^(p^4)*x^(p^6+p^5+p^2+p)-y^(p^3)*x^(p^6+p^5+p^4+p)-y^(p^2)*x^(p^6+p^5+p^4+p^3)+
x^(p^6+p^5+p^4+p^3+p^2+p) ), 
x*(d-e*x^p+f*(-y^(p^2)+x^(p^2 +p))+g*(x^(p^3)*y^p +y^(p^3)*x^p -x^(p^3 +p^2 +p)) +
z*(y^(p^4 +p^2 )-y^(p^4)*x^(p^2 +p)- y^(p^2)*x^(p^4 +p^3)-y^(p^3)*x^(p^4 +p)+ x^(p^4+p^3 +p^2 +p))+ 
w*(y^(p^5 +p^3 )*x ^p -x^(p^3)*y^(p^5 +p^2)- x^(p^5)*y^(p^4 +p^2)+y^(p^5)*x^(p^3 +p^2 +p)+ y^(p^4)*x^(p^5 +p^2 +p)+
y^(p^3)*x^(p^5 +p^4 +p)+y^(p^2)*x^(p^5 +p^4 +p^3)-x^(p^5+p^4 +p^3 +p^2 +p))-
y^(p^6 +p^4 +p^2)+y^(p^6 +p^4 )*x^(p^2 +p)+y^(p^6 +p^3 )*x^(p^4 +p)+y^(p^6 +p^2)*x^(p^4 +p^3)+
y^(p^5 +p^3 )*x^(p^6 +p)+y^(p^5 +p^2 )*x^(p^6 +p^3)+y^(p^2+p^4 )*x^(p^6 +p^5)-y^(p^6)*x^(p^4+p^3+p^2+p)-
y^(p^5)*x^(p^6+p^3+p^2+p)-y^(p^4)*x^(p^6+p^5+p^2+p)-y^(p^3)*x^(p^6+p^5+p^4+p)-y^(p^2)*x^(p^6+p^5+p^4+p^3)+
x^(p^6+p^5+p^4+p^3+p^2+p) ) +
y^p *(e-f*x^(p^2)+g*(-y^(p^3)+x^(p^3 +p^2))+z*(y^(p^4)*x^(p^2)+y^(p^3)*x^(p^4)-x^(p^4+p^3+p^2))+
w*(y^(p^5+p^3)-y^(p^5)*x^(p^2+p^3)-y^(p^4)*x^(p^2+p^5)-y^(p^3)*x^(p^5+p^4)+x^(p^5+p^4+p^3+p^2))-
x^(p^2)*y^(p^6+p^4)-x^(p^4)*y^(p^6+p^3)-x^(p^6)*y^(p^5+p^3)+y^(p^6)*x^(p^4+p^3+p^2)+y^(p^5)*x^(p^6+p^3+p^2)+
y^(p^4)*x^(p^6+p^5+p^2)+y^(p^3)*x^(p^6+p^5+p^4)-x^(p^6+p^5+p^4+p^3+p^2)) ] ;






L :=[y*(x*(d-e*x^p+f*(-y^(p^2)+x^(p^2 +p))+g*(x^(p^3)*y^p +y^(p^3)*x^p -x^(p^3 +p^2 +p)) +
z*(y^(p^4 +p^2 )-y^(p^4)*x^(p^2 +p)- y^(p^2)*x^(p^4 +p^3)-y^(p^3)*x^(p^4 +p)+ x^(p^4+p^3 +p^2 +p))+ 
w*(y^(p^5 +p^3 )*x ^p -x^(p^3)*y^(p^5 +p^2)- x^(p^5)*y^(p^4 +p^2)+y^(p^5)*x^(p^3 +p^2 +p)+ y^(p^4)*x^(p^5 +p^2 +p)+
y^(p^3)*x^(p^5 +p^4 +p)+y^(p^2)*x^(p^5 +p^4 +p^3)-x^(p^5+p^4 +p^3 +p^2 +p))-
y^(p^6 +p^4 +p^2)+y^(p^6 +p^4 )*x^(p^2 +p)+y^(p^6 +p^3 )*x^(p^4 +p)+y^(p^6 +p^2)*x^(p^4 +p^3)+
y^(p^5 +p^3 )*x^(p^6 +p)+y^(p^5 +p^2 )*x^(p^6 +p^3)+y^(p^2+p^4 )*x^(p^6 +p^5)-y^(p^6)*x^(p^4+p^3+p^2+p)-
y^(p^5)*x^(p^6+p^3+p^2+p)-y^(p^4)*x^(p^6+p^5+p^2+p)-y^(p^3)*x^(p^6+p^5+p^4+p)-y^(p^2)*x^(p^6+p^5+p^4+p^3)+
x^(p^6+p^5+p^4+p^3+p^2+p) )+ y^p *(e-f*x^(p^2)+g*(-y^(p^3)+x^(p^3 +p^2))+z*(y^(p^4)*x^(p^2)+y^(p^3)*x^(p^4)-x^(p^4+p^3+p^2))+
w*(y^(p^5+p^3)-y^(p^5)*x^(p^2+p^3)-y^(p^4)*x^(p^2+p^5)-y^(p^3)*x^(p^5+p^4)+x^(p^5+p^4+p^3+p^2))-
x^(p^2)*y^(p^6+p^4)-x^(p^4)*y^(p^6+p^3)-x^(p^6)*y^(p^5+p^3)+y^(p^6)*x^(p^4+p^3+p^2)+y^(p^5)*x^(p^6+p^3+p^2)+
y^(p^4)*x^(p^6+p^5+p^2)+y^(p^3)*x^(p^6+p^5+p^4)-x^(p^6+p^5+p^4+p^3+p^2)))-x*( y*(d-e*x^p+f*(-y^(p^2)+x^(p^2 +p))+g*(x^(p^3)*y^p +y^(p^3)*x^p -x^(p^3 +p^2 +p)) +
z*(y^(p^4 +p^2 )-y^(p^4)*x^(p^2 +p)- y^(p^2)*x^(p^4 +p^3)-y^(p^3)*x^(p^4 +p)+ x^(p^4+p^3 +p^2 +p))+ 
w*(y^(p^5 +p^3 )*x ^p -x^(p^3)*y^(p^5 +p^2)- x^(p^5)*y^(p^4 +p^2)+y^(p^5)*x^(p^3 +p^2 +p)+ y^(p^4)*x^(p^5 +p^2 +p)+
y^(p^3)*x^(p^5 +p^4 +p)+y^(p^2)*x^(p^5 +p^4 +p^3)-x^(p^5+p^4 +p^3 +p^2 +p))-
y^(p^6 +p^4 +p^2)+y^(p^6 +p^4 )*x^(p^2 +p)+y^(p^6 +p^3 )*x^(p^4 +p)+y^(p^6 +p^2)*x^(p^4 +p^3)+
y^(p^5 +p^3 )*x^(p^6 +p)+y^(p^5 +p^2 )*x^(p^6 +p^3)+y^(p^2+p^4 )*x^(p^6 +p^5)-y^(p^6)*x^(p^4+p^3+p^2+p)-
y^(p^5)*x^(p^6+p^3+p^2+p)-y^(p^4)*x^(p^6+p^5+p^2+p)-y^(p^3)*x^(p^6+p^5+p^4+p)-y^(p^2)*x^(p^6+p^5+p^4+p^3)+
x^(p^6+p^5+p^4+p^3+p^2+p) ) ) ];

L;

Output: Magma V2.11-2     Thu Aug 26 2004 06:48:28 on modular  [Seed = 1277211371]
   -------------------------------------


>> K<w> := GF(p);
              ^
User error: Identifier 'p' has not been declared or assigned

>> R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [p^2 -p, p^2 -1, p^8 -p^2, 
                                                ^
User error: Identifier 'K' has not been declared or assigned

>> R;
   ^
User error: Identifier 'R' has not been declared or assigned

>> P := [ d, e, f, g, z, w, y*(d-e*x^p+f*(-y^(p^2)+x^(p^2 +p))+g*(x^(p^3)*y^p 
          ^
User error: Identifier 'd' has not been declared or assigned

>> L :=[y*(x*(d-e*x^p+f*(-y^(p^2)+x^(p^2 +p))+g*(x^(p^3)*y^p +y^(p^3)*x^p -x^(
        ^
User error: Identifier 'y' has not been declared or assigned

>> L;;
   ^
User error: Identifier 'L' has not been declared or assigned

Total time: 0.679 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host pc43.math.uoi.gr. (195.130.112.43)
Time: Thu Aug 26 06:54:08 2004

Input: K<w> := GF(2);
R<x, y, d, e, f, g, z, w > := PolynomialRing(K, [2^2 -2, 2^2 -1, 2^8 -2^2, 2^8 -2^3, 2^8 -2^4, 2^8 -2^5, 2^8 -2^6, 2^8 -2^7 ]);
R;
P := [ d, e, f, g, z, w, y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2))-
y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2) ), 
x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2))-
y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2) ) +
y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2))-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2)) ] ;

L := [y*(x*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2))-
y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2) )+ y^2 *(e-f*x^(2^2)+g*(-y^(2^3)+x^(2^3 +2^2))+z*(y^(2^4)*x^(2^2)+y^(2^3)*x^(2^4)-x^(2^4+2^3+2^2))+
w*(y^(2^5+2^3)-y^(2^5)*x^(2^2+2^3)-y^(2^4)*x^(2^2+2^5)-y^(2^3)*x^(2^5+2^4)+x^(2^5+2^4+2^3+2^2))-
x^(2^2)*y^(2^6+2^4)-x^(2^4)*y^(2^6+2^3)-x^(2^6)*y^(2^5+2^3)+y^(2^6)*x^(2^4+2^3+2^2)+y^(2^5)*x^(2^6+2^3+2^2)+
y^(2^4)*x^(2^6+2^5+2^2)+y^(2^3)*x^(2^6+2^5+2^4)-x^(2^6+2^5+2^4+2^3+2^2)))-x*( y*(d-e*x^2+f*(-y^(2^2)+x^(2^2 +2))+g*(x^(2^3)*y^2 +y^(2^3)*x^2 -x^(2^3 +2^2 +2)) +
z*(y^(2^4 +2^2 )-y^(2^4)*x^(2^2 +2)- y^(2^2)*x^(2^4 +2^3)-y^(2^3)*x^(2^4 +2)+ x^(2^4+2^3 +2^2 +2))+ 
w*(y^(2^5 +2^3 )*x ^2 -x^(2^3)*y^(2^5 +2^2)- x^(2^5)*y^(2^4 +2^2)+y^(2^5)*x^(2^3 +2^2 +2)+ y^(2^4)*x^(2^5 +2^2 +2)+
y^(2^3)*x^(2^5 +2^4 +2)+y^(2^2)*x^(2^5 +2^4 +2^3)-x^(2^5+2^4 +2^3 +2^2 +2))-
y^(2^6 +2^4 +2^2)+y^(2^6 +2^4 )*x^(2^2 +2)+y^(2^6 +2^3 )*x^(2^4 +2)+y^(2^6 +2^2)*x^(2^4 +2^3)+
y^(2^5 +2^3 )*x^(2^6 +2)+y^(2^5 +2^2 )*x^(2^6 +2^3)+y^(2^2+2^4 )*x^(2^6 +2^5)-y^(2^6)*x^(2^4+2^3+2^2+2)-
y^(2^5)*x^(2^6+2^3+2^2+2)-y^(2^4)*x^(2^6+2^5+2^2+2)-y^(2^3)*x^(2^6+2^5+2^4+2)-y^(2^2)*x^(2^6+2^5+2^4+2^3)+
x^(2^6+2^5+2^4+2^3+2^2+2) ) )
 ];
L;

Output: Magma V2.11-2     Thu Aug 26 2004 06:54:08 on modular  [Seed = 73958410]
   -------------------------------------

Graded Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: x, y, d, e, f, g, z, w
Variable weights: 2 3 252 248 240 224 192 128
[
    x^124*y^3 + x^112*y^11 + x^100*y^19 + x^76*y^35 + x^64*y^43 + x^60*y^3*w + 
        x^48*y^11*w + x^36*y^19*w + x^28*y^67 + x^28*y^3*z + x^16*y^75 + 
        x^16*y^11*z + x^12*y^35*w + x^12*y^3*g + x^4*y^83 + x^4*y^19*z + 
        x^4*y^3*f + y^43*w + y^11*g + y^3*e
]

Total time: 0.580 seconds, Total memory usage: 3.05MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Thu Aug 26 08:56:44 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 08:56:44 on modular  [Seed = 23961127]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    y^2/x
@}
{@
    x^4,
    x^2*y,
    y^2,
    y^3/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    x*y^2,
    y^3/x,
    x*B,
    u
@}
{@
    x^6,
    x^4*y,
    x^2*y^2,
    y^3,
    x^2*B,
    x*u,
    y^4/x^2,
    y*B,
    v
@}
{@
    x^7,
    x^5*y,
    x^3*y^2,
    x*y^3,
    x^3*B,
    x^2*u,
    y^4/x,
    x*y*B,
    x*v,
    y*u,
    y^5/x^3,
    y^2*B/x
@}
{@
    x^8,
    x^6*y,
    x^4*y^2,
    x^2*y^3,
    x^4*B,
    x^3*u,
    y^4,
    x^2*y*B,
    x^2*v,
    x*y*u,
    y^5/x^2,
    y^2*B,
    y*v,
    y^2*u/x,
    y^6/x^4,
    y^3*B/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^5*y^2,
    x^3*y^3,
    x^5*B,
    x^4*u,
    x*y^4,
    x^3*y*B,
    x^3*v,
    x^2*y*u,
    y^5/x,
    x*y^2*B,
    x*y*v,
    y^2*u,
    y^6/x^3,
    y^3*B/x,
    x*B^2,
    y^2*v/x,
    y^3*u/x^2,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    x^6*y^2,
    x^4*y^3,
    x^6*B,
    x^5*u,
    x^2*y^4,
    x^4*y*B,
    x^4*v,
    x^3*y*u,
    y^5,
    x^2*y^2*B,
    x^2*y*v,
    x*y^2*u,
    y^6/x^2,
    y^3*B,
    x^2*B^2,
    y^2*v,
    y^3*u/x,
    x*u*B,
    x*A,
    y^7/x^4,
    y^4*B/x^2,
    y*B^2,
    y^3*v/x^2,
    u^2,
    v*B
@}
{@
    x^11,
    x^9*y,
    x^7*y^2,
    x^5*y^3,
    x^7*B,
    x^6*u,
    x^3*y^4,
    x^5*y*B,
    x^5*v,
    x^4*y*u,
    x*y^5,
    x^3*y^2*B,
    x^3*y*v,
    x^2*y^2*u,
    y^6/x,
    x*y^3*B,
    x^3*B^2,
    x*y^2*v,
    y^3*u,
    x^2*u*B,
    x^2*A,
    y^7/x^3,
    y^4*B/x,
    x*y*B^2,
    y^3*v/x,
    x*u^2,
    x*v*B,
    y^4*u/x^2,
    y*u*B,
    y*A,
    y^8/x^5,
    y^5*B/x^3,
    y^2*B^2/x,
    u*v
@}
{@
    x^12,
    x^10*y,
    x^8*y^2,
    x^6*y^3,
    x^8*B,
    x^7*u,
    x^4*y^4,
    x^6*y*B,
    x^6*v,
    x^5*y*u,
    x^2*y^5,
    x^4*y^2*B,
    x^4*y*v,
    x^3*y^2*u,
    y^6,
    x^2*y^3*B,
    x^4*B^2,
    x^2*y^2*v,
    x*y^3*u,
    x^3*u*B,
    x^3*A,
    y^7/x^2,
    y^4*B,
    x^2*y*B^2,
    y^3*v,
    x^2*u^2,
    x^2*v*B,
    y^4*u/x,
    x*y*u*B,
    x*y*A,
    y^8/x^4,
    y^5*B/x^2,
    y^2*B^2,
    x*u*v,
    y^4*v/x^2,
    y*u^2,
    y*v*B,
    y^5*u/x^3,
    y^2*u*B/x,
    y^2*A/x,
    y^9/x^6,
    y^6*B/x^4,
    y^3*B^2/x^2,
    v^2,
    B^3
@}

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Thu Aug 26 08:59:12 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x+x^2+y+x+4,y^3/x^2-(x^2+y+x+4),u,v,A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 08:59:11 on modular  [Seed = 343444391]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (x^3 + x^2 + x*y + 4*x + y^2)/x
@}
{@
    x^4,
    x^2*y,
    x^3 + x^2 + x*y + 4*x + y^2,
    y^2,
    (-x^4 - x^3 - x^2*y - 4*x^2 + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    x^4 + x^3 + x^2*y + 4*x^2 + x*y^2,
    x*y^2,
    (-x^4 - x^3 - x^2*y - 4*x^2 + y^3)/x,
    x*B,
    (x^3*y + x^2*y + x*y^2 + 4*x*y + y^3)/x,
    u
@}
{@
    x^6,
    x^4*y,
    x^5 + x^4 + x^3*y + 4*x^3 + x^2*y^2,
    x^2*y^2,
    -x^4 - x^3 - x^2*y - 4*x^2 + y^3,
    x^2*B,
    x^3*y + x^2*y + x*y^2 + 4*x*y + y^3,
    x*u,
    y^3,
    (-x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4)/x^2,
    y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4)/x^2,
    v
@}
{@
    x^7,
    x^5*y,
    x^6 + x^5 + x^4*y + 4*x^4 + x^3*y^2,
    x^3*y^2,
    -x^5 - x^4 - x^3*y - 4*x^3 + x*y^3,
    x^3*B,
    x^4*y + x^3*y + x^2*y^2 + 4*x^2*y + x*y^3,
    x^2*u,
    x*y^3,
    (-x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4)/x,
    x*y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4)/x,
    x*v,
    (x^3*y^2 + x^2*y^2 + x*y^3 + 4*x*y^2 + y^4)/x,
    y*u,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x^3,
    (x^3*B + x^2*B + x*y*B + 4*x*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    x^7 + x^6 + x^5*y + 4*x^5 + x^4*y^2,
    x^4*y^2,
    -x^6 - x^5 - x^4*y - 4*x^4 + x^2*y^3,
    x^4*B,
    x^5*y + x^4*y + x^3*y^2 + 4*x^3*y + x^2*y^3,
    x^3*u,
    x^2*y^3,
    -x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4,
    x^2*y*B,
    x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4,
    x^2*v,
    x^3*y^2 + x^2*y^2 + x*y^3 + 4*x*y^2 + y^4,
    x*y*u,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x^2,
    x^3*B + x^2*B + x*y*B + 4*x*B + y^2*B,
    y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5)/x^2,
    y^2*B,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5)/x^2,
    y*v,
    (x^3*u + x^2*u + x*y*u + 4*x*u + y^2*u)/x,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^4,
    (-x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^8 + x^7 + x^6*y + 4*x^6 + x^5*y^2,
    x^5*y^2,
    -x^7 - x^6 - x^5*y - 4*x^5 + x^3*y^3,
    x^5*B,
    x^6*y + x^5*y + x^4*y^2 + 4*x^4*y + x^3*y^3,
    x^4*u,
    x^3*y^3,
    -x^5*y - x^4*y - x^3*y^2 - 4*x^3*y + x*y^4,
    x^3*y*B,
    x^7 + 2*x^6 + 2*x^5*y + 9*x^5 + 2*x^4*y^2 + 2*x^4*y + 8*x^4 + 3*x^3*y^2 + 
        8*x^3*y + 16*x^3 + 2*x^2*y^3 + 8*x^2*y^2 + x*y^4,
    x^3*v,
    x^4*y^2 + x^3*y^2 + x^2*y^3 + 4*x^2*y^2 + x*y^4,
    x^2*y*u,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x,
    x^4*B + x^3*B + x^2*y*B + 4*x^2*B + x*y^2*B,
    x*y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5)/x,
    x*y^2*B,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5)/x,
    x*y*v,
    x^3*u + x^2*u + x*y*u + 4*x*u + y^2*u,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^3,
    (-x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B)/x,
    x*B^2,
    (x^3*y^3 + x^2*y^3 + x*y^4 + 4*x*y^3 + y^5)/x,
    y^2*u,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x^3,
    (x^3*y*B + x^2*y*B + x*y^2*B + 4*x*y*B + y^3*B)/x,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x^3,
    (x^3*v + x^2*v + x*y*v + 4*x*v + y^2*v)/x,
    (-x^4*u - x^3*u - x^2*y*u - 4*x^2*u + y^3*u)/x^2,
    u*B,
    A
@}
{@
    x^10,
    x^8*y,
    x^9 + x^8 + x^7*y + 4*x^7 + x^6*y^2,
    x^6*y^2,
    -x^8 - x^7 - x^6*y - 4*x^6 + x^4*y^3,
    x^6*B,
    x^7*y + x^6*y + x^5*y^2 + 4*x^5*y + x^4*y^3,
    x^5*u,
    x^4*y^3,
    -x^6*y - x^5*y - x^4*y^2 - 4*x^4*y + x^2*y^4,
    x^4*y*B,
    x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y^2 + 2*x^5*y + 8*x^5 + 3*x^4*y^2 + 
        8*x^4*y + 16*x^4 + 2*x^3*y^3 + 8*x^3*y^2 + x^2*y^4,
    x^4*v,
    x^5*y^2 + x^4*y^2 + x^3*y^3 + 4*x^3*y^2 + x^2*y^4,
    x^3*y*u,
    -x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5,
    x^5*B + x^4*B + x^3*y*B + 4*x^3*B + x^2*y^2*B,
    x^2*y^4,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5,
    x^2*y^2*B,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5,
    x^2*y*v,
    x^4*u + x^3*u + x^2*y*u + 4*x^2*u + x*y^2*u,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^2,
    -x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B,
    x^2*B^2,
    x^3*y^3 + x^2*y^3 + x*y^4 + 4*x*y^3 + y^5,
    x*y^2*u,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x^2,
    x^3*y*B + x^2*y*B + x*y^2*B + 4*x*y*B + y^3*B,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x^2,
    x^3*v + x^2*v + x*y*v + 4*x*v + y^2*v,
    (-x^4*u - x^3*u - x^2*y*u - 4*x^2*u + y^3*u)/x,
    x*u*B,
    x*A,
    y^5,
    (-x^4*y^3 - x^3*y^3 - x^2*y^4 - 4*x^2*y^3 + y^6)/x^2,
    y^3*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 + 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 + 3*x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 + 2*x*y^5 + 8*x*y^4 + 
        y^6)/x^2,
    y^2*v,
    (x^3*y*u + x^2*y*u + x*y^2*u + 4*x*y*u + y^3*u)/x,
    (x^8*y + 2*x^7*y + 2*x^6*y^2 + 9*x^6*y + 2*x^5*y^2 + 8*x^5*y - 2*x^4*y^4 + 
        x^4*y^3 + 8*x^4*y^2 + 16*x^4*y - 2*x^3*y^4 - 2*x^2*y^5 - 8*x^2*y^4 + 
        y^7)/x^4,
    (-x^4*y*B - x^3*y*B - x^2*y^2*B - 4*x^2*y*B + y^4*B)/x^2,
    y*B^2,
    (-x^10 - 3*x^9 - 3*x^8*y - 15*x^8 - 2*x^7*y^2 - 6*x^7*y - 25*x^7 + x^6*y^3 -
        7*x^6*y^2 - 27*x^6*y - 60*x^6 - 2*x^5*y^3 - 21*x^5*y^2 - 24*x^5*y - 
        48*x^5 + x^4*y^4 + 4*x^4*y^3 - 28*x^4*y^2 - 48*x^4*y - 64*x^4 + 
        2*x^3*y^5 - x^3*y^4 - 8*x^3*y^3 - 32*x^3*y^2 + 2*x^2*y^5 + 4*x^2*y^4 + 
        16*x^2*y^3 + 2*x*y^6 + 8*x*y^5 + y^7)/x^4,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B + 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B +
        3*x^2*y^2*B + 8*x^2*y*B + 16*x^2*B + 2*x*y^3*B + 8*x*y^2*B + y^4*B)/x^2,
    (-x^4*v - x^3*v - x^2*y*v - 4*x^2*v + y^3*v)/x^2,
    u^2,
    v*B
@}
{@
    x^11,
    x^9*y,
    x^10 + x^9 + x^8*y + 4*x^8 + x^7*y^2,
    x^7*y^2,
    -x^9 - x^8 - x^7*y - 4*x^7 + x^5*y^3,
    x^7*B,
    x^8*y + x^7*y + x^6*y^2 + 4*x^6*y + x^5*y^3,
    x^6*u,
    x^5*y^3,
    -x^7*y - x^6*y - x^5*y^2 - 4*x^5*y + x^3*y^4,
    x^5*y*B,
    x^9 + 2*x^8 + 2*x^7*y + 9*x^7 + 2*x^6*y^2 + 2*x^6*y + 8*x^6 + 3*x^5*y^2 + 
        8*x^5*y + 16*x^5 + 2*x^4*y^3 + 8*x^4*y^2 + x^3*y^4,
    x^5*v,
    x^6*y^2 + x^5*y^2 + x^4*y^3 + 4*x^4*y^2 + x^3*y^4,
    x^4*y*u,
    -x^8 - 2*x^7 - 2*x^6*y - 9*x^6 - x^5*y^2 - 2*x^5*y - 8*x^5 + x^4*y^3 - 
        2*x^4*y^2 - 8*x^4*y - 16*x^4 - 4*x^3*y^2 + x^2*y^4 + 4*x^2*y^3 + x*y^5,
    x^6*B + x^5*B + x^4*y*B + 4*x^4*B + x^3*y^2*B,
    x^3*y^4,
    -x^5*y^2 - x^4*y^2 - x^3*y^3 - 4*x^3*y^2 + x*y^5,
    x^3*y^2*B,
    x^7*y + 2*x^6*y + 2*x^5*y^2 + 9*x^5*y + 2*x^4*y^3 + 2*x^4*y^2 + 8*x^4*y + 
        3*x^3*y^3 + 8*x^3*y^2 + 16*x^3*y + 2*x^2*y^4 + 8*x^2*y^3 + x*y^5,
    x^3*y*v,
    x^5*u + x^4*u + x^3*y*u + 4*x^3*u + x^2*y^2*u,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x,
    -x^5*B - x^4*B - x^3*y*B - 4*x^3*B + x*y^3*B,
    x^3*B^2,
    x^4*y^3 + x^3*y^3 + x^2*y^4 + 4*x^2*y^3 + x*y^5,
    x^2*y^2*u,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x,
    x^4*y*B + x^3*y*B + x^2*y^2*B + 4*x^2*y*B + x*y^3*B,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x,
    x^4*v + x^3*v + x^2*y*v + 4*x^2*v + x*y^2*v,
    -x^4*u - x^3*u - x^2*y*u - 4*x^2*u + y^3*u,
    x^2*u*B,
    x^2*A,
    x*y^5,
    (-x^4*y^3 - x^3*y^3 - x^2*y^4 - 4*x^2*y^3 + y^6)/x,
    x*y^3*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 + 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 + 3*x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 + 2*x*y^5 + 8*x*y^4 + 
        y^6)/x,
    x*y^2*v,
    x^3*y*u + x^2*y*u + x*y^2*u + 4*x*y*u + y^3*u,
    (x^8*y + 2*x^7*y + 2*x^6*y^2 + 9*x^6*y + 2*x^5*y^2 + 8*x^5*y - 2*x^4*y^4 + 
      
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Thu Aug 26 08:59:42 2004

Input: R<x,y,z,t,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,9,4]);
S<x,y,z,t,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x+x^2+y+x+4,y^3/x^2-(x^2+y+x+4),A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 08:59:41 on modular  [Seed = 2649817612]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (x^3 + x^2 + x*y + 4*x + y^2)/x
@}
{@
    x^4,
    x^2*y,
    x^3 + x^2 + x*y + 4*x + y^2,
    y^2,
    (-x^4 - x^3 - x^2*y - 4*x^2 + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    x^4 + x^3 + x^2*y + 4*x^2 + x*y^2,
    x*y^2,
    (-x^4 - x^3 - x^2*y - 4*x^2 + y^3)/x,
    x*B,
    (x^3*y + x^2*y + x*y^2 + 4*x*y + y^3)/x
@}
{@
    x^6,
    x^4*y,
    x^5 + x^4 + x^3*y + 4*x^3 + x^2*y^2,
    x^2*y^2,
    -x^4 - x^3 - x^2*y - 4*x^2 + y^3,
    x^2*B,
    x^3*y + x^2*y + x*y^2 + 4*x*y + y^3,
    y^3,
    (-x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4)/x^2,
    y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    x^6 + x^5 + x^4*y + 4*x^4 + x^3*y^2,
    x^3*y^2,
    -x^5 - x^4 - x^3*y - 4*x^3 + x*y^3,
    x^3*B,
    x^4*y + x^3*y + x^2*y^2 + 4*x^2*y + x*y^3,
    x*y^3,
    (-x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4)/x,
    x*y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4)/x,
    (x^3*y^2 + x^2*y^2 + x*y^3 + 4*x*y^2 + y^4)/x,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x^3,
    (x^3*B + x^2*B + x*y*B + 4*x*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    x^7 + x^6 + x^5*y + 4*x^5 + x^4*y^2,
    x^4*y^2,
    -x^6 - x^5 - x^4*y - 4*x^4 + x^2*y^3,
    x^4*B,
    x^5*y + x^4*y + x^3*y^2 + 4*x^3*y + x^2*y^3,
    x^2*y^3,
    -x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4,
    x^2*y*B,
    x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4,
    x^3*y^2 + x^2*y^2 + x*y^3 + 4*x*y^2 + y^4,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x^2,
    x^3*B + x^2*B + x*y*B + 4*x*B + y^2*B,
    y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5)/x^2,
    y^2*B,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5)/x^2,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^4,
    (-x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^8 + x^7 + x^6*y + 4*x^6 + x^5*y^2,
    x^5*y^2,
    -x^7 - x^6 - x^5*y - 4*x^5 + x^3*y^3,
    x^5*B,
    x^6*y + x^5*y + x^4*y^2 + 4*x^4*y + x^3*y^3,
    x^3*y^3,
    -x^5*y - x^4*y - x^3*y^2 - 4*x^3*y + x*y^4,
    x^3*y*B,
    x^7 + 2*x^6 + 2*x^5*y + 9*x^5 + 2*x^4*y^2 + 2*x^4*y + 8*x^4 + 3*x^3*y^2 + 
        8*x^3*y + 16*x^3 + 2*x^2*y^3 + 8*x^2*y^2 + x*y^4,
    x^4*y^2 + x^3*y^2 + x^2*y^3 + 4*x^2*y^2 + x*y^4,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x,
    x^4*B + x^3*B + x^2*y*B + 4*x^2*B + x*y^2*B,
    x*y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5)/x,
    x*y^2*B,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5)/x,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^3,
    (-x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B)/x,
    x*B^2,
    (x^3*y^3 + x^2*y^3 + x*y^4 + 4*x*y^3 + y^5)/x,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x^3,
    (x^3*y*B + x^2*y*B + x*y^2*B + 4*x*y*B + y^3*B)/x,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x^3,
    A
@}
{@
    x^10,
    x^8*y,
    x^9 + x^8 + x^7*y + 4*x^7 + x^6*y^2,
    x^6*y^2,
    -x^8 - x^7 - x^6*y - 4*x^6 + x^4*y^3,
    x^6*B,
    x^7*y + x^6*y + x^5*y^2 + 4*x^5*y + x^4*y^3,
    x^4*y^3,
    -x^6*y - x^5*y - x^4*y^2 - 4*x^4*y + x^2*y^4,
    x^4*y*B,
    x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y^2 + 2*x^5*y + 8*x^5 + 3*x^4*y^2 + 
        8*x^4*y + 16*x^4 + 2*x^3*y^3 + 8*x^3*y^2 + x^2*y^4,
    x^5*y^2 + x^4*y^2 + x^3*y^3 + 4*x^3*y^2 + x^2*y^4,
    -x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5,
    x^5*B + x^4*B + x^3*y*B + 4*x^3*B + x^2*y^2*B,
    x^2*y^4,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5,
    x^2*y^2*B,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^2,
    -x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B,
    x^2*B^2,
    x^3*y^3 + x^2*y^3 + x*y^4 + 4*x*y^3 + y^5,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x^2,
    x^3*y*B + x^2*y*B + x*y^2*B + 4*x*y*B + y^3*B,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x^2,
    x*A,
    y^5,
    (-x^4*y^3 - x^3*y^3 - x^2*y^4 - 4*x^2*y^3 + y^6)/x^2,
    y^3*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 + 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 + 3*x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 + 2*x*y^5 + 8*x*y^4 + 
        y^6)/x^2,
    (x^8*y + 2*x^7*y + 2*x^6*y^2 + 9*x^6*y + 2*x^5*y^2 + 8*x^5*y - 2*x^4*y^4 + 
        x^4*y^3 + 8*x^4*y^2 + 16*x^4*y - 2*x^3*y^4 - 2*x^2*y^5 - 8*x^2*y^4 + 
        y^7)/x^4,
    (-x^4*y*B - x^3*y*B - x^2*y^2*B - 4*x^2*y*B + y^4*B)/x^2,
    y*B^2,
    (-x^10 - 3*x^9 - 3*x^8*y - 15*x^8 - 2*x^7*y^2 - 6*x^7*y - 25*x^7 + x^6*y^3 -
        7*x^6*y^2 - 27*x^6*y - 60*x^6 - 2*x^5*y^3 - 21*x^5*y^2 - 24*x^5*y - 
        48*x^5 + x^4*y^4 + 4*x^4*y^3 - 28*x^4*y^2 - 48*x^4*y - 64*x^4 + 
        2*x^3*y^5 - x^3*y^4 - 8*x^3*y^3 - 32*x^3*y^2 + 2*x^2*y^5 + 4*x^2*y^4 + 
        16*x^2*y^3 + 2*x*y^6 + 8*x*y^5 + y^7)/x^4,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B + 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B +
        3*x^2*y^2*B + 8*x^2*y*B + 16*x^2*B + 2*x*y^3*B + 8*x*y^2*B + y^4*B)/x^2
@}
{@
    x^11,
    x^9*y,
    x^10 + x^9 + x^8*y + 4*x^8 + x^7*y^2,
    x^7*y^2,
    -x^9 - x^8 - x^7*y - 4*x^7 + x^5*y^3,
    x^7*B,
    x^8*y + x^7*y + x^6*y^2 + 4*x^6*y + x^5*y^3,
    x^5*y^3,
    -x^7*y - x^6*y - x^5*y^2 - 4*x^5*y + x^3*y^4,
    x^5*y*B,
    x^9 + 2*x^8 + 2*x^7*y + 9*x^7 + 2*x^6*y^2 + 2*x^6*y + 8*x^6 + 3*x^5*y^2 + 
        8*x^5*y + 16*x^5 + 2*x^4*y^3 + 8*x^4*y^2 + x^3*y^4,
    x^6*y^2 + x^5*y^2 + x^4*y^3 + 4*x^4*y^2 + x^3*y^4,
    -x^8 - 2*x^7 - 2*x^6*y - 9*x^6 - x^5*y^2 - 2*x^5*y - 8*x^5 + x^4*y^3 - 
        2*x^4*y^2 - 8*x^4*y - 16*x^4 - 4*x^3*y^2 + x^2*y^4 + 4*x^2*y^3 + x*y^5,
    x^6*B + x^5*B + x^4*y*B + 4*x^4*B + x^3*y^2*B,
    x^3*y^4,
    -x^5*y^2 - x^4*y^2 - x^3*y^3 - 4*x^3*y^2 + x*y^5,
    x^3*y^2*B,
    x^7*y + 2*x^6*y + 2*x^5*y^2 + 9*x^5*y + 2*x^4*y^3 + 2*x^4*y^2 + 8*x^4*y + 
        3*x^3*y^3 + 8*x^3*y^2 + 16*x^3*y + 2*x^2*y^4 + 8*x^2*y^3 + x*y^5,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x,
    -x^5*B - x^4*B - x^3*y*B - 4*x^3*B + x*y^3*B,
    x^3*B^2,
    x^4*y^3 + x^3*y^3 + x^2*y^4 + 4*x^2*y^3 + x*y^5,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x,
    x^4*y*B + x^3*y*B + x^2*y^2*B + 4*x^2*y*B + x*y^3*B,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x,
    x^2*A,
    x*y^5,
    (-x^4*y^3 - x^3*y^3 - x^2*y^4 - 4*x^2*y^3 + y^6)/x,
    x*y^3*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 + 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 + 3*x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 + 2*x*y^5 + 8*x*y^4 + 
        y^6)/x,
    (x^8*y + 2*x^7*y + 2*x^6*y^2 + 9*x^6*y + 2*x^5*y^2 + 8*x^5*y - 2*x^4*y^4 + 
        x^4*y^3 + 8*x^4*y^2 + 16*x^4*y - 2*x^3*y^4 - 2*x^2*y^5 - 8*x^2*y^4 + 
        y^7)/x^3,
    (-x^4*y*B - x^3*y*B - x^2*y^2*B - 4*x^2*y*B + y^4*B)/x,
    x*y*B^2,
    (-x^10 - 3*x^9 - 3*x^8*y - 15*x^8 - 2*x^7*y^2 - 6*x^7*y - 25*x^7 + x^6*y^3 -
        7*x^6*y^2 - 27*x^6*y - 60*x^6 - 2*x^5*y^3 - 21*x^5*y^2 - 24*x^5*y - 
        48*x^5 + x^4*y^4 + 4*x^4*y^3 - 28*x^4*y^2 - 48*x^4*y - 64*x^4 + 
        2*x^3*y^5 - x^3*y^4 - 8*x^3*y^3 - 32*x^3*y^2 + 2*x^2*y^5 + 4*x^2*y^4 + 
        16*x^2*y^3 + 2*x*y^6 + 8*x*y^5 + y^7)/x^3,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B + 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B +
        3*x^2*y^2*B + 8*x^2*y*B + 16*x^2*B + 2*x*y^3*B + 8*x*y^2*B + y^4*B)/x,
    (x^3*y^4 + x^2*y^4 + x*y^5 + 4*x*y^4 + y^6)/x,
    (-x^7*y^2 - 2*x^6*y^2 - 2*x^5*y^3 - 9*x^5*y^2 - x^4*y^4 - 2*x^4*y^3 - 
        8*x^4*y^2 + x^3*y^5 - 2*x^3*y^4 - 8*x^3*y^3 - 16*x^3*y^2 - 4*x^2*y^4 + 
        x*y^6 + 4*x*y^5 + y^7)/x^3,
    (x^3*y^2*B + x^2*y^2*B + x*y^3*B + 4*x*y^2*B + y^4*B)/x,
    
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Thu Aug 26 09:00:49 2004

Input: R<x,y,z,t,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,9,4]);
S<x,y,z,t,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x+x^2+y+x+4,y^3/x^2-(x^2+y+x+4),A,B>;
for i in [1..10] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 09:00:48 on modular  [Seed = 3967840963]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (x^3 + x^2 + x*y + 4*x + y^2)/x
@}
{@
    x^4,
    x^2*y,
    x^3 + x^2 + x*y + 4*x + y^2,
    y^2,
    (-x^4 - x^3 - x^2*y - 4*x^2 + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    x^4 + x^3 + x^2*y + 4*x^2 + x*y^2,
    x*y^2,
    (-x^4 - x^3 - x^2*y - 4*x^2 + y^3)/x,
    x*B,
    (x^3*y + x^2*y + x*y^2 + 4*x*y + y^3)/x
@}
{@
    x^6,
    x^4*y,
    x^5 + x^4 + x^3*y + 4*x^3 + x^2*y^2,
    x^2*y^2,
    -x^4 - x^3 - x^2*y - 4*x^2 + y^3,
    x^2*B,
    x^3*y + x^2*y + x*y^2 + 4*x*y + y^3,
    y^3,
    (-x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4)/x^2,
    y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    x^6 + x^5 + x^4*y + 4*x^4 + x^3*y^2,
    x^3*y^2,
    -x^5 - x^4 - x^3*y - 4*x^3 + x*y^3,
    x^3*B,
    x^4*y + x^3*y + x^2*y^2 + 4*x^2*y + x*y^3,
    x*y^3,
    (-x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4)/x,
    x*y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4)/x,
    (x^3*y^2 + x^2*y^2 + x*y^3 + 4*x*y^2 + y^4)/x,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x^3,
    (x^3*B + x^2*B + x*y*B + 4*x*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    x^7 + x^6 + x^5*y + 4*x^5 + x^4*y^2,
    x^4*y^2,
    -x^6 - x^5 - x^4*y - 4*x^4 + x^2*y^3,
    x^4*B,
    x^5*y + x^4*y + x^3*y^2 + 4*x^3*y + x^2*y^3,
    x^2*y^3,
    -x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + y^4,
    x^2*y*B,
    x^6 + 2*x^5 + 2*x^4*y + 9*x^4 + 2*x^3*y^2 + 2*x^3*y + 8*x^3 + 3*x^2*y^2 + 
        8*x^2*y + 16*x^2 + 2*x*y^3 + 8*x*y^2 + y^4,
    x^3*y^2 + x^2*y^2 + x*y^3 + 4*x*y^2 + y^4,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x^2,
    x^3*B + x^2*B + x*y*B + 4*x*B + y^2*B,
    y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5)/x^2,
    y^2*B,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5)/x^2,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^4,
    (-x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    x^8 + x^7 + x^6*y + 4*x^6 + x^5*y^2,
    x^5*y^2,
    -x^7 - x^6 - x^5*y - 4*x^5 + x^3*y^3,
    x^5*B,
    x^6*y + x^5*y + x^4*y^2 + 4*x^4*y + x^3*y^3,
    x^3*y^3,
    -x^5*y - x^4*y - x^3*y^2 - 4*x^3*y + x*y^4,
    x^3*y*B,
    x^7 + 2*x^6 + 2*x^5*y + 9*x^5 + 2*x^4*y^2 + 2*x^4*y + 8*x^4 + 3*x^3*y^2 + 
        8*x^3*y + 16*x^3 + 2*x^2*y^3 + 8*x^2*y^2 + x*y^4,
    x^4*y^2 + x^3*y^2 + x^2*y^3 + 4*x^2*y^2 + x*y^4,
    (-x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5)/x,
    x^4*B + x^3*B + x^2*y*B + 4*x^2*B + x*y^2*B,
    x*y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5)/x,
    x*y^2*B,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5)/x,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^3,
    (-x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B)/x,
    x*B^2,
    (x^3*y^3 + x^2*y^3 + x*y^4 + 4*x*y^3 + y^5)/x,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x^3,
    (x^3*y*B + x^2*y*B + x*y^2*B + 4*x*y*B + y^3*B)/x,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x^3,
    A
@}
{@
    x^10,
    x^8*y,
    x^9 + x^8 + x^7*y + 4*x^7 + x^6*y^2,
    x^6*y^2,
    -x^8 - x^7 - x^6*y - 4*x^6 + x^4*y^3,
    x^6*B,
    x^7*y + x^6*y + x^5*y^2 + 4*x^5*y + x^4*y^3,
    x^4*y^3,
    -x^6*y - x^5*y - x^4*y^2 - 4*x^4*y + x^2*y^4,
    x^4*y*B,
    x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y^2 + 2*x^5*y + 8*x^5 + 3*x^4*y^2 + 
        8*x^4*y + 16*x^4 + 2*x^3*y^3 + 8*x^3*y^2 + x^2*y^4,
    x^5*y^2 + x^4*y^2 + x^3*y^3 + 4*x^3*y^2 + x^2*y^4,
    -x^7 - 2*x^6 - 2*x^5*y - 9*x^5 - x^4*y^2 - 2*x^4*y - 8*x^4 + x^3*y^3 - 
        2*x^3*y^2 - 8*x^3*y - 16*x^3 - 4*x^2*y^2 + x*y^4 + 4*x*y^3 + y^5,
    x^5*B + x^4*B + x^3*y*B + 4*x^3*B + x^2*y^2*B,
    x^2*y^4,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + y^5,
    x^2*y^2*B,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y + 
        3*x^2*y^3 + 8*x^2*y^2 + 16*x^2*y + 2*x*y^4 + 8*x*y^3 + y^5,
    (x^8 + 2*x^7 + 2*x^6*y + 9*x^6 + 2*x^5*y + 8*x^5 - 2*x^4*y^3 + x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 2*x^2*y^4 - 8*x^2*y^3 + y^6)/x^2,
    -x^4*B - x^3*B - x^2*y*B - 4*x^2*B + y^3*B,
    x^2*B^2,
    x^3*y^3 + x^2*y^3 + x*y^4 + 4*x*y^3 + y^5,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - 9*x^5*y - x^4*y^3 - 2*x^4*y^2 - 8*x^4*y + 
        x^3*y^4 - 2*x^3*y^3 - 8*x^3*y^2 - 16*x^3*y - 4*x^2*y^3 + x*y^5 + 4*x*y^4
        + y^6)/x^2,
    x^3*y*B + x^2*y*B + x*y^2*B + 4*x*y*B + y^3*B,
    (x^9 + 3*x^8 + 3*x^7*y + 15*x^7 + 3*x^6*y^2 + 6*x^6*y + 25*x^6 + 9*x^5*y^2 +
        27*x^5*y + 60*x^5 + 6*x^4*y^3 + 30*x^4*y^2 + 24*x^4*y + 48*x^4 + 
        3*x^3*y^4 + 7*x^3*y^3 + 36*x^3*y^2 + 48*x^3*y + 64*x^3 + 6*x^2*y^4 + 
        24*x^2*y^3 + 48*x^2*y^2 + 3*x*y^5 + 12*x*y^4 + y^6)/x^2,
    x*A,
    y^5,
    (-x^4*y^3 - x^3*y^3 - x^2*y^4 - 4*x^2*y^3 + y^6)/x^2,
    y^3*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 + 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 + 3*x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 + 2*x*y^5 + 8*x*y^4 + 
        y^6)/x^2,
    (x^8*y + 2*x^7*y + 2*x^6*y^2 + 9*x^6*y + 2*x^5*y^2 + 8*x^5*y - 2*x^4*y^4 + 
        x^4*y^3 + 8*x^4*y^2 + 16*x^4*y - 2*x^3*y^4 - 2*x^2*y^5 - 8*x^2*y^4 + 
        y^7)/x^4,
    (-x^4*y*B - x^3*y*B - x^2*y^2*B - 4*x^2*y*B + y^4*B)/x^2,
    y*B^2,
    (-x^10 - 3*x^9 - 3*x^8*y - 15*x^8 - 2*x^7*y^2 - 6*x^7*y - 25*x^7 + x^6*y^3 -
        7*x^6*y^2 - 27*x^6*y - 60*x^6 - 2*x^5*y^3 - 21*x^5*y^2 - 24*x^5*y - 
        48*x^5 + x^4*y^4 + 4*x^4*y^3 - 28*x^4*y^2 - 48*x^4*y - 64*x^4 + 
        2*x^3*y^5 - x^3*y^4 - 8*x^3*y^3 - 32*x^3*y^2 + 2*x^2*y^5 + 4*x^2*y^4 + 
        16*x^2*y^3 + 2*x*y^6 + 8*x*y^5 + y^7)/x^4,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B + 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B +
        3*x^2*y^2*B + 8*x^2*y*B + 16*x^2*B + 2*x*y^3*B + 8*x*y^2*B + y^4*B)/x^2
@}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB16a.cache.pol.co.uk. (195.92.168.178)
Time: Thu Aug 26 09:02:55 2004

Input: R<x,y,z,t,C,D>:=PolynomialRing(RationalField(),[1,2,3,4,9,8]);
S<x,y,z,t,C,D>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x+x^2+y+x,y^3/x^2-(x^2+y+x),C,D>;
for i in [1..10] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 09:02:55 on modular  [Seed = 3900995238]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (x^3 + x^2 + x*y + y^2)/x
@}
{@
    x^4,
    x^2*y,
    x^3 + x^2 + x*y + y^2,
    y^2,
    (-x^4 - x^3 - x^2*y + y^3)/x^2
@}
{@
    x^5,
    x^3*y,
    x^4 + x^3 + x^2*y + x*y^2,
    x*y^2,
    (-x^4 - x^3 - x^2*y + y^3)/x,
    (x^3*y + x^2*y + x*y^2 + y^3)/x
@}
{@
    x^6,
    x^4*y,
    x^5 + x^4 + x^3*y + x^2*y^2,
    x^2*y^2,
    -x^4 - x^3 - x^2*y + y^3,
    x^3*y + x^2*y + x*y^2 + y^3,
    y^3,
    (-x^4*y - x^3*y - x^2*y^2 + y^4)/x^2,
    (x^6 + 2*x^5 + 2*x^4*y + x^4 + 2*x^3*y^2 + 2*x^3*y + 3*x^2*y^2 + 2*x*y^3 + 
        y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    x^6 + x^5 + x^4*y + x^3*y^2,
    x^3*y^2,
    -x^5 - x^4 - x^3*y + x*y^3,
    x^4*y + x^3*y + x^2*y^2 + x*y^3,
    x*y^3,
    (-x^4*y - x^3*y - x^2*y^2 + y^4)/x,
    (x^6 + 2*x^5 + 2*x^4*y + x^4 + 2*x^3*y^2 + 2*x^3*y + 3*x^2*y^2 + 2*x*y^3 + 
        y^4)/x,
    (x^3*y^2 + x^2*y^2 + x*y^3 + y^4)/x,
    (-x^7 - 2*x^6 - 2*x^5*y - x^5 - x^4*y^2 - 2*x^4*y + x^3*y^3 - 2*x^3*y^2 + 
        x*y^4 + y^5)/x^3
@}
{@
    x^8,
    x^6*y,
    x^7 + x^6 + x^5*y + x^4*y^2,
    x^4*y^2,
    -x^6 - x^5 - x^4*y + x^2*y^3,
    x^5*y + x^4*y + x^3*y^2 + x^2*y^3,
    x^2*y^3,
    -x^4*y - x^3*y - x^2*y^2 + y^4,
    x^6 + 2*x^5 + 2*x^4*y + x^4 + 2*x^3*y^2 + 2*x^3*y + 3*x^2*y^2 + 2*x*y^3 + 
        y^4,
    x^3*y^2 + x^2*y^2 + x*y^3 + y^4,
    (-x^7 - 2*x^6 - 2*x^5*y - x^5 - x^4*y^2 - 2*x^4*y + x^3*y^3 - 2*x^3*y^2 + 
        x*y^4 + y^5)/x^2,
    y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 + y^5)/x^2,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 3*x^2*y^3 + 
        2*x*y^4 + y^5)/x^2,
    (x^8 + 2*x^7 + 2*x^6*y + x^6 + 2*x^5*y - 2*x^4*y^3 + x^4*y^2 - 2*x^3*y^3 - 
        2*x^2*y^4 + y^6)/x^4,
    D
@}
{@
    x^9,
    x^7*y,
    x^8 + x^7 + x^6*y + x^5*y^2,
    x^5*y^2,
    -x^7 - x^6 - x^5*y + x^3*y^3,
    x^6*y + x^5*y + x^4*y^2 + x^3*y^3,
    x^3*y^3,
    -x^5*y - x^4*y - x^3*y^2 + x*y^4,
    x^7 + 2*x^6 + 2*x^5*y + x^5 + 2*x^4*y^2 + 2*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 + 
        x*y^4,
    x^4*y^2 + x^3*y^2 + x^2*y^3 + x*y^4,
    (-x^7 - 2*x^6 - 2*x^5*y - x^5 - x^4*y^2 - 2*x^4*y + x^3*y^3 - 2*x^3*y^2 + 
        x*y^4 + y^5)/x,
    x*y^4,
    (-x^4*y^2 - x^3*y^2 - x^2*y^3 + y^5)/x,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 3*x^2*y^3 + 
        2*x*y^4 + y^5)/x,
    (x^8 + 2*x^7 + 2*x^6*y + x^6 + 2*x^5*y - 2*x^4*y^3 + x^4*y^2 - 2*x^3*y^3 - 
        2*x^2*y^4 + y^6)/x^3,
    x*D,
    (x^3*y^3 + x^2*y^3 + x*y^4 + y^5)/x,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - x^5*y - x^4*y^3 - 2*x^4*y^2 + x^3*y^4 - 
        2*x^3*y^3 + x*y^5 + y^6)/x^3,
    (x^9 + 3*x^8 + 3*x^7*y + 3*x^7 + 3*x^6*y^2 + 6*x^6*y + x^6 + 9*x^5*y^2 + 
        3*x^5*y + 6*x^4*y^3 + 6*x^4*y^2 + 3*x^3*y^4 + 7*x^3*y^3 + 6*x^2*y^4 + 
        3*x*y^5 + y^6)/x^3,
    C
@}
{@
    x^10,
    x^8*y,
    x^9 + x^8 + x^7*y + x^6*y^2,
    x^6*y^2,
    -x^8 - x^7 - x^6*y + x^4*y^3,
    x^7*y + x^6*y + x^5*y^2 + x^4*y^3,
    x^4*y^3,
    -x^6*y - x^5*y - x^4*y^2 + x^2*y^4,
    x^8 + 2*x^7 + 2*x^6*y + x^6 + 2*x^5*y^2 + 2*x^5*y + 3*x^4*y^2 + 2*x^3*y^3 + 
        x^2*y^4,
    x^5*y^2 + x^4*y^2 + x^3*y^3 + x^2*y^4,
    -x^7 - 2*x^6 - 2*x^5*y - x^5 - x^4*y^2 - 2*x^4*y + x^3*y^3 - 2*x^3*y^2 + 
        x*y^4 + y^5,
    x^2*y^4,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 + y^5,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y + 2*x^3*y^3 + 2*x^3*y^2 + 3*x^2*y^3 + 
        2*x*y^4 + y^5,
    (x^8 + 2*x^7 + 2*x^6*y + x^6 + 2*x^5*y - 2*x^4*y^3 + x^4*y^2 - 2*x^3*y^3 - 
        2*x^2*y^4 + y^6)/x^2,
    x^2*D,
    x^3*y^3 + x^2*y^3 + x*y^4 + y^5,
    (-x^7*y - 2*x^6*y - 2*x^5*y^2 - x^5*y - x^4*y^3 - 2*x^4*y^2 + x^3*y^4 - 
        2*x^3*y^3 + x*y^5 + y^6)/x^2,
    (x^9 + 3*x^8 + 3*x^7*y + 3*x^7 + 3*x^6*y^2 + 6*x^6*y + x^6 + 9*x^5*y^2 + 
        3*x^5*y + 6*x^4*y^3 + 6*x^4*y^2 + 3*x^3*y^4 + 7*x^3*y^3 + 6*x^2*y^4 + 
        3*x*y^5 + y^6)/x^2,
    x*C,
    y^5,
    (-x^4*y^3 - x^3*y^3 - x^2*y^4 + y^6)/x^2,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + x^4*y^2 + 2*x^3*y^4 + 2*x^3*y^3 + 
        3*x^2*y^4 + 2*x*y^5 + y^6)/x^2,
    (x^8*y + 2*x^7*y + 2*x^6*y^2 + x^6*y + 2*x^5*y^2 - 2*x^4*y^4 + x^4*y^3 - 
        2*x^3*y^4 - 2*x^2*y^5 + y^7)/x^4,
    y*D,
    (-x^10 - 3*x^9 - 3*x^8*y - 3*x^8 - 2*x^7*y^2 - 6*x^7*y - x^7 + x^6*y^3 - 
        7*x^6*y^2 - 3*x^6*y - 2*x^5*y^3 - 5*x^5*y^2 + x^4*y^4 - 4*x^4*y^3 + 
        2*x^3*y^5 - x^3*y^4 + 2*x^2*y^5 + 2*x*y^6 + y^7)/x^4
@}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 064.b.012.mel.iprimus.net.au. (210.50.249.64)
Time: Thu Aug 26 09:05:16 2004

Input: ABC

Output: Magma V2.11-2     Thu Aug 26 2004 09:05:07 on modular  [Seed = 2714566801]
   -------------------------------------


>> ABC;
   ^
User error: Identifier 'ABC' has not been declared or assigned

Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 064.b.012.mel.iprimus.net.au. (210.50.249.64)
Time: Thu Aug 26 09:05:40 2004

Input: "ABC"

Output: Magma V2.11-2     Thu Aug 26 2004 09:05:40 on modular  [Seed = 1062444585]
   -------------------------------------

ABC

Total time: 0.620 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 064.b.012.mel.iprimus.net.au. (210.50.249.64)
Time: Thu Aug 26 09:06:49 2004

Input: 0x414243

Output: Magma V2.11-2     Thu Aug 26 2004 09:06:49 on modular  [Seed = 541884796]
   -------------------------------------

4276803

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB03a.cache.pol.co.uk. (195.92.168.165)
Time: Thu Aug 26 09:20:24 2004

Input: R<x,y,z,t,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,9,4]);
S<x,y,z,t,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-(x^2+y+x+4),y^3/x^2-(x*y+y^2/x+y+4*y/x),A,B>;
for i in [1..12] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 09:20:23 on modular  [Seed = 2081480405]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (-x^3 - x^2 - x*y - 4*x + y^2)/x
@}
{@
    x^4,
    x^2*y,
    -x^3 - x^2 - x*y - 4*x + y^2,
    y^2,
    (-x^3*y - x^2*y - x*y^2 - 4*x*y + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    -x^4 - x^3 - x^2*y - 4*x^2 + x*y^2,
    x*y^2,
    (-x^3*y - x^2*y - x*y^2 - 4*x*y + y^3)/x,
    x*B
@}
{@
    x^6,
    x^4*y,
    -x^5 - x^4 - x^3*y - 4*x^3 + x^2*y^2,
    x^2*y^2,
    -x^3*y - x^2*y - x*y^2 - 4*x*y + y^3,
    x^2*B,
    y^3,
    (-x^3*y^2 - x^2*y^2 - x*y^3 - 4*x*y^2 + y^4)/x^2,
    y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 - 2*x^3*y^2 + 2*x^3*y + 8*x^3 - x^2*y^2 + 
        8*x^2*y + 16*x^2 - 2*x*y^3 - 8*x*y^2 + y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    -x^6 - x^5 - x^4*y - 4*x^4 + x^3*y^2,
    x^3*y^2,
    -x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + x*y^3,
    x^3*B,
    x*y^3,
    (-x^3*y^2 - x^2*y^2 - x*y^3 - 4*x*y^2 + y^4)/x,
    x*y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 - 2*x^3*y^2 + 2*x^3*y + 8*x^3 - x^2*y^2 + 
        8*x^2*y + 16*x^2 - 2*x*y^3 - 8*x*y^2 + y^4)/x,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5)/x^3,
    (-x^3*B - x^2*B - x*y*B - 4*x*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    -x^7 - x^6 - x^5*y - 4*x^5 + x^4*y^2,
    x^4*y^2,
    -x^5*y - x^4*y - x^3*y^2 - 4*x^3*y + x^2*y^3,
    x^4*B,
    x^2*y^3,
    -x^3*y^2 - x^2*y^2 - x*y^3 - 4*x*y^2 + y^4,
    x^2*y*B,
    x^6 + 2*x^5 + 2*x^4*y + 9*x^4 - 2*x^3*y^2 + 2*x^3*y + 8*x^3 - x^2*y^2 + 
        8*x^2*y + 16*x^2 - 2*x*y^3 - 8*x*y^2 + y^4,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5)/x^2,
    -x^3*B - x^2*B - x*y*B - 4*x*B + y^2*B,
    y^4,
    (-x^3*y^3 - x^2*y^3 - x*y^4 - 4*x*y^3 + y^5)/x^2,
    y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x^4,
    (-x^3*y*B - x^2*y*B - x*y^2*B - 4*x*y*B + y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    -x^8 - x^7 - x^6*y - 4*x^6 + x^5*y^2,
    x^5*y^2,
    -x^6*y - x^5*y - x^4*y^2 - 4*x^4*y + x^3*y^3,
    x^5*B,
    x^3*y^3,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + x*y^4,
    x^3*y*B,
    x^7 + 2*x^6 + 2*x^5*y + 9*x^5 - 2*x^4*y^2 + 2*x^4*y + 8*x^4 - x^3*y^2 + 
        8*x^3*y + 16*x^3 - 2*x^2*y^3 - 8*x^2*y^2 + x*y^4,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5)/x,
    -x^4*B - x^3*B - x^2*y*B - 4*x^2*B + x*y^2*B,
    x*y^4,
    (-x^3*y^3 - x^2*y^3 - x*y^4 - 4*x*y^3 + y^5)/x,
    x*y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x^3,
    (-x^3*y*B - x^2*y*B - x*y^2*B - 4*x*y*B + y^3*B)/x,
    x*B^2,
    (-x^9 - 3*x^8 - 3*x^7*y - 15*x^7 + 3*x^6*y^2 - 6*x^6*y - 25*x^6 + 3*x^5*y^2 
        - 27*x^5*y - 60*x^5 + 6*x^4*y^3 + 24*x^4*y^2 - 24*x^4*y - 48*x^4 - 
        3*x^3*y^4 + 5*x^3*y^3 + 12*x^3*y^2 - 48*x^3*y - 64*x^3 + 24*x^2*y^3 + 
        48*x^2*y^2 - 3*x*y^5 - 12*x*y^4 + y^6)/x^3,
    A
@}
{@
    x^10,
    x^8*y,
    -x^9 - x^8 - x^7*y - 4*x^7 + x^6*y^2,
    x^6*y^2,
    -x^7*y - x^6*y - x^5*y^2 - 4*x^5*y + x^4*y^3,
    x^6*B,
    x^4*y^3,
    -x^5*y^2 - x^4*y^2 - x^3*y^3 - 4*x^3*y^2 + x^2*y^4,
    x^4*y*B,
    x^8 + 2*x^7 + 2*x^6*y + 9*x^6 - 2*x^5*y^2 + 2*x^5*y + 8*x^5 - x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 8*x^3*y^2 + x^2*y^4,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5,
    -x^5*B - x^4*B - x^3*y*B - 4*x^3*B + x^2*y^2*B,
    x^2*y^4,
    -x^3*y^3 - x^2*y^3 - x*y^4 - 4*x*y^3 + y^5,
    x^2*y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x^2,
    -x^3*y*B - x^2*y*B - x*y^2*B - 4*x*y*B + y^3*B,
    x^2*B^2,
    (-x^9 - 3*x^8 - 3*x^7*y - 15*x^7 + 3*x^6*y^2 - 6*x^6*y - 25*x^6 + 3*x^5*y^2 
        - 27*x^5*y - 60*x^5 + 6*x^4*y^3 + 24*x^4*y^2 - 24*x^4*y - 48*x^4 - 
        3*x^3*y^4 + 5*x^3*y^3 + 12*x^3*y^2 - 48*x^3*y - 64*x^3 + 24*x^2*y^3 + 
        48*x^2*y^2 - 3*x*y^5 - 12*x*y^4 + y^6)/x^2,
    x*A,
    y^5,
    (-x^3*y^4 - x^2*y^4 - x*y^5 - 4*x*y^4 + y^6)/x^2,
    y^3*B,
    (x^6*y^3 + 2*x^5*y^3 + 2*x^4*y^4 + 9*x^4*y^3 - 2*x^3*y^5 + 2*x^3*y^4 + 
        8*x^3*y^3 - x^2*y^5 + 8*x^2*y^4 + 16*x^2*y^3 - 2*x*y^6 - 8*x*y^5 + 
        y^7)/x^4,
    (-x^3*y^2*B - x^2*y^2*B - x*y^3*B - 4*x*y^2*B + y^4*B)/x^2,
    y*B^2,
    (-x^9*y - 3*x^8*y - 3*x^7*y^2 - 15*x^7*y + 3*x^6*y^3 - 6*x^6*y^2 - 25*x^6*y 
        + 3*x^5*y^3 - 27*x^5*y^2 - 60*x^5*y + 6*x^4*y^4 + 24*x^4*y^3 - 
        24*x^4*y^2 - 48*x^4*y - 3*x^3*y^5 + 5*x^3*y^4 + 12*x^3*y^3 - 48*x^3*y^2 
        - 64*x^3*y + 24*x^2*y^4 + 48*x^2*y^3 - 3*x*y^6 - 12*x*y^5 + y^7)/x^4,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B - 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B -
        x^2*y^2*B + 8*x^2*y*B + 16*x^2*B - 2*x*y^3*B - 8*x*y^2*B + y^4*B)/x^2
@}
{@
    x^11,
    x^9*y,
    -x^10 - x^9 - x^8*y - 4*x^8 + x^7*y^2,
    x^7*y^2,
    -x^8*y - x^7*y - x^6*y^2 - 4*x^6*y + x^5*y^3,
    x^7*B,
    x^5*y^3,
    -x^6*y^2 - x^5*y^2 - x^4*y^3 - 4*x^4*y^2 + x^3*y^4,
    x^5*y*B,
    x^9 + 2*x^8 + 2*x^7*y + 9*x^7 - 2*x^6*y^2 + 2*x^6*y + 8*x^6 - x^5*y^2 + 
        8*x^5*y + 16*x^5 - 2*x^4*y^3 - 8*x^4*y^2 + x^3*y^4,
    x^7*y + 2*x^6*y + 2*x^5*y^2 + 9*x^5*y - 2*x^4*y^3 + 2*x^4*y^2 + 8*x^4*y - 
        x^3*y^3 + 8*x^3*y^2 + 16*x^3*y - 2*x^2*y^4 - 8*x^2*y^3 + x*y^5,
    -x^6*B - x^5*B - x^4*y*B - 4*x^4*B + x^3*y^2*B,
    x^3*y^4,
    -x^4*y^3 - x^3*y^3 - x^2*y^4 - 4*x^2*y^3 + x*y^5,
    x^3*y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x,
    -x^4*y*B - x^3*y*B - x^2*y^2*B - 4*x^2*y*B + x*y^3*B,
    x^3*B^2,
    (-x^9 - 3*x^8 - 3*x^7*y - 15*x^7 + 3*x^6*y^2 - 6*x^6*y - 25*x^6 + 3*x^5*y^2 
        - 27*x^5*y - 60*x^5 + 6*x^4*y^3 + 24*x^4*y^2 - 24*x^4*y - 48*x^4 - 
        3*x^3*y^4 + 5*x^3*y^3 + 12*x^3*y^2 - 48*x^3*y - 64*x^3 + 24*x^2*y^3 + 
        48*x^2*y^2 - 3*x*y^5 - 12*x*y^4 + y^6)/x,
    x^2*A,
    x*y^5,
    (-x^3*y^4 - x^2*y^4 - x*y^5 - 4*x*y^4 + y^6)/x,
    x*y^3*B,
    (x^6*y^3 + 2*x^5*y^3 + 2*x^4*y^4 + 9*x^4*y^3 - 2*x^3*y^5 + 2*x^3*y^4 + 
        8*x^3*y^3 - x^2*y^5 + 8*x^2*y^4 + 16*x^2*y^3 - 2*x*y^6 - 8*x*y^5 + 
        y^7)/x^3,
    (-x^3*y^2*B - x^2*y^2*B - x*y^3*B - 4*x*y^2*B + y^4*B)/x,
    x*y*B^2,
    (-x^9*y - 3*x^8*y - 3*x^7*y^2 - 15*x^7*y + 3*x^6*y^3 - 6*x^6*y^2 - 25*x^6*y 
        + 3*x^5*y^3 - 27*x^5*y^2 - 60*x^5*y + 6*x^4*y^4 + 24*x^4*y^3 - 
        24*x^4*y^2 - 48*x^4*y - 3*x^3*y^5 + 5*x^3*y^4 + 12*x^3*y^3 - 48*x^3*y^2 
        - 64*x^3*y + 24*x^2*y^4 + 48*x^2*y^3 - 3*x*y^6 - 12*x*y^5 + y^7)/x^3,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B - 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B -
        x^2*y^2*B + 8*x^2*y*B + 16*x^2*B - 2*x*y^3*B - 8*x*y^2*B + y^4*B)/x,
    y*A,
    (-x^9*y^2 - 3*x^8*y^2 - 3*x^7*y^3 - 15*x^7*y^2 + 3*x^6*y^4 - 6*x^6*y^3 - 
        25*x^6*y^2 + 3*x^5*y^4 - 27*x^5*y^3 - 60*x^5*y^2 + 6*x^4*y^5 + 
        24*x^4*y^4 - 24*x^4*y^3 - 48*x^4*y^2 - 3*x^3*y^6 + 5*x^3*y^5 + 
        12*x^3*y^4 - 48*x^3*y^3 - 64*x^3*y^2 + 24*x^2*y^5 + 48*x^2*y^4 - 3*x*y^7
        - 12*x*y^6 + y^8)/x^5,
    (x^6*y*B + 2*x^5*y*B + 2*x^4*y^2*B + 9*x^4*y*B - 2*x^3*y^3*B + 2*x^3*y^2*B +
        8*x^3*y*B - x^2*y^3*B + 8*x^2*y^2*B + 16*x^2*y*B - 2*x*y^4*B - 8*x*y^3*B
        + y^5*B)/x^3,
    (-x^3*B^2 - x^2*B^2 - x*y*B^2 - 4*x*B^2 + y^2*B^2)/x
@}
{@
    x^12,
    x^10*y,
    -x^11 - x^10 - x^9*y - 4*x^9 + x^8*y^2,
    x^8*y^2,
    -x^9*y - x^8*y - x^7*y^2 - 4*x^7*y + x^6*y^3,
    x^8*B,
    x^6*y^3,
    -x^7*y^2 - x^6*y^2 - x^5*y^3 - 4*x^5*y^2 + x^4*y^4,
    x^6*y*B,
    x^10 + 2*x^9 + 2*x^8*y + 9*x^8 - 2*x^7*y^2 + 2*x^7*y + 8*x^7 - x^6*y^2 + 
        8*x^6*y + 16*x^6 - 2*x^5*y^3 - 8*x^5*y^2 + x^4*y^4,
    x^8*y + 2*x^7*y + 2*x^6*y^2 + 9*x^6*y - 2*x^5*y^3 + 2*x^5*y^2 + 8*x^5*y - 
        x^4*y^3 + 8*x^4*y^2 + 16*x^4*y - 2*x^3*y^4 - 8*x^3*y^3 + x^2*y^5,
    -x^7*B - x^6*B - x^5*y*B - 4*x^5*B + x^4*y^2*B,
    x^4*y^4,
    -x^5*y^3 - x^4*y^3 - x^3*y^4 - 4*x^3*y^3 + x^2*y^5,
    x^4*y^2*B,
    x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + y^6,
    -x^5*y*B - x^4*y*B - x^3*y^2*B - 4*x^3*y*B + x^2*y^3*B,
    x^4*B^2,
    -x^9 - 3*x^8 - 3*x^7*y - 15*x^7 + 3*x^6*y^2 - 6*x^6*y - 25*x^6 + 3*x^5*y^2 -
        27*x^5*y - 60*x^5 + 6*x^4*y^3 + 24*x^4*y^2 - 24*x^4*y - 48*x^4 - 
        3*x^3*y^4 + 5*x^3*y^3 + 12*x^3*y^2 - 48*x^3*y - 64*x^3 + 24*x^2*y^3 + 
        48*x^2*y^2 - 3*x*y^5 - 12*x*y^4 + y^6,
    x^3*A,
    x^2*y^5,
    -x^3*y^4 - x^2*y^4 - x*y^5 - 4*x*y^4 + y^6,
    x^2*y^3*B,
    (x^6*y^3 + 2*x^5*y^3 + 2*x^4*y^4 + 9*x^4*y^3 - 2*x^3*y^5 + 2*x^3*y^4 + 
        8*x^3*y^3 - x^2*y^5 + 8*x^2*y^4 + 16*x^2*y^3 - 2*x*y^6 - 8*x*y^5 + 
        y^7)/x^2,
    -x^3*y^2*B - x^2*y^2*B - x*y^3*B - 4*x*y^2*B + y^4*B,
    x^2*y*B^2,
    (-x^9*y - 3*x^8*y - 3*x^7*y^2 - 15*x^7*y + 3*x^6*y^3 - 6*x^6*y^2 - 25*x^6*y 
        + 3*x^5*y^3 - 27*x^5*y^2 - 60*x^5*y + 6*x^4*y^4 + 24*x^4*y^3 - 
        24*x^4*y^2 - 48*x^4*y - 3*x^3*y^5 + 5*x^3*y^4 + 12*x^3*y^3 - 48*x^3*y^2 
        - 64*x^3*y + 24*x^2*y^4 + 48*x^2*y^3 - 3*x*y^6 - 12*x*y^5 + y^7)/x^2,
    x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B - 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B - 
        x^2*y^2*B + 8*x^2*y*B + 16*x^2*B - 2*x*y^3*B - 8*x*y^2*B + y^4*B,
    x*y*A,
    (-x^9*y^2 - 3*x^8*y^2 - 3*x^7*y^3 - 15*x^7*y^2 + 3*x^6*y^4 - 6*x^6*y^3 - 
        25*x^6*y^2 + 3*x^5*y^4 - 27*x^5*y^3 - 60*x^5*y^2 + 6*x^4*y^5 + 
  
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB03a.cache.pol.co.uk. (195.92.168.165)
Time: Thu Aug 26 09:20:33 2004

Input: R<x,y,z,t,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,9,4]);
S<x,y,z,t,A,B>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-(x^2+y+x+4),y^3/x^2-(x*y+y^2/x+y+4*y/x),A,B>;
for i in [1..10] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 09:20:33 on modular  [Seed = 1396699596]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (-x^3 - x^2 - x*y - 4*x + y^2)/x
@}
{@
    x^4,
    x^2*y,
    -x^3 - x^2 - x*y - 4*x + y^2,
    y^2,
    (-x^3*y - x^2*y - x*y^2 - 4*x*y + y^3)/x^2,
    B
@}
{@
    x^5,
    x^3*y,
    -x^4 - x^3 - x^2*y - 4*x^2 + x*y^2,
    x*y^2,
    (-x^3*y - x^2*y - x*y^2 - 4*x*y + y^3)/x,
    x*B
@}
{@
    x^6,
    x^4*y,
    -x^5 - x^4 - x^3*y - 4*x^3 + x^2*y^2,
    x^2*y^2,
    -x^3*y - x^2*y - x*y^2 - 4*x*y + y^3,
    x^2*B,
    y^3,
    (-x^3*y^2 - x^2*y^2 - x*y^3 - 4*x*y^2 + y^4)/x^2,
    y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 - 2*x^3*y^2 + 2*x^3*y + 8*x^3 - x^2*y^2 + 
        8*x^2*y + 16*x^2 - 2*x*y^3 - 8*x*y^2 + y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    -x^6 - x^5 - x^4*y - 4*x^4 + x^3*y^2,
    x^3*y^2,
    -x^4*y - x^3*y - x^2*y^2 - 4*x^2*y + x*y^3,
    x^3*B,
    x*y^3,
    (-x^3*y^2 - x^2*y^2 - x*y^3 - 4*x*y^2 + y^4)/x,
    x*y*B,
    (x^6 + 2*x^5 + 2*x^4*y + 9*x^4 - 2*x^3*y^2 + 2*x^3*y + 8*x^3 - x^2*y^2 + 
        8*x^2*y + 16*x^2 - 2*x*y^3 - 8*x*y^2 + y^4)/x,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5)/x^3,
    (-x^3*B - x^2*B - x*y*B - 4*x*B + y^2*B)/x
@}
{@
    x^8,
    x^6*y,
    -x^7 - x^6 - x^5*y - 4*x^5 + x^4*y^2,
    x^4*y^2,
    -x^5*y - x^4*y - x^3*y^2 - 4*x^3*y + x^2*y^3,
    x^4*B,
    x^2*y^3,
    -x^3*y^2 - x^2*y^2 - x*y^3 - 4*x*y^2 + y^4,
    x^2*y*B,
    x^6 + 2*x^5 + 2*x^4*y + 9*x^4 - 2*x^3*y^2 + 2*x^3*y + 8*x^3 - x^2*y^2 + 
        8*x^2*y + 16*x^2 - 2*x*y^3 - 8*x*y^2 + y^4,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5)/x^2,
    -x^3*B - x^2*B - x*y*B - 4*x*B + y^2*B,
    y^4,
    (-x^3*y^3 - x^2*y^3 - x*y^4 - 4*x*y^3 + y^5)/x^2,
    y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x^4,
    (-x^3*y*B - x^2*y*B - x*y^2*B - 4*x*y*B + y^3*B)/x^2,
    B^2
@}
{@
    x^9,
    x^7*y,
    -x^8 - x^7 - x^6*y - 4*x^6 + x^5*y^2,
    x^5*y^2,
    -x^6*y - x^5*y - x^4*y^2 - 4*x^4*y + x^3*y^3,
    x^5*B,
    x^3*y^3,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 - 4*x^2*y^2 + x*y^4,
    x^3*y*B,
    x^7 + 2*x^6 + 2*x^5*y + 9*x^5 - 2*x^4*y^2 + 2*x^4*y + 8*x^4 - x^3*y^2 + 
        8*x^3*y + 16*x^3 - 2*x^2*y^3 - 8*x^2*y^2 + x*y^4,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5)/x,
    -x^4*B - x^3*B - x^2*y*B - 4*x^2*B + x*y^2*B,
    x*y^4,
    (-x^3*y^3 - x^2*y^3 - x*y^4 - 4*x*y^3 + y^5)/x,
    x*y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x^3,
    (-x^3*y*B - x^2*y*B - x*y^2*B - 4*x*y*B + y^3*B)/x,
    x*B^2,
    (-x^9 - 3*x^8 - 3*x^7*y - 15*x^7 + 3*x^6*y^2 - 6*x^6*y - 25*x^6 + 3*x^5*y^2 
        - 27*x^5*y - 60*x^5 + 6*x^4*y^3 + 24*x^4*y^2 - 24*x^4*y - 48*x^4 - 
        3*x^3*y^4 + 5*x^3*y^3 + 12*x^3*y^2 - 48*x^3*y - 64*x^3 + 24*x^2*y^3 + 
        48*x^2*y^2 - 3*x*y^5 - 12*x*y^4 + y^6)/x^3,
    A
@}
{@
    x^10,
    x^8*y,
    -x^9 - x^8 - x^7*y - 4*x^7 + x^6*y^2,
    x^6*y^2,
    -x^7*y - x^6*y - x^5*y^2 - 4*x^5*y + x^4*y^3,
    x^6*B,
    x^4*y^3,
    -x^5*y^2 - x^4*y^2 - x^3*y^3 - 4*x^3*y^2 + x^2*y^4,
    x^4*y*B,
    x^8 + 2*x^7 + 2*x^6*y + 9*x^6 - 2*x^5*y^2 + 2*x^5*y + 8*x^5 - x^4*y^2 + 
        8*x^4*y + 16*x^4 - 2*x^3*y^3 - 8*x^3*y^2 + x^2*y^4,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + 9*x^4*y - 2*x^3*y^3 + 2*x^3*y^2 + 8*x^3*y - 
        x^2*y^3 + 8*x^2*y^2 + 16*x^2*y - 2*x*y^4 - 8*x*y^3 + y^5,
    -x^5*B - x^4*B - x^3*y*B - 4*x^3*B + x^2*y^2*B,
    x^2*y^4,
    -x^3*y^3 - x^2*y^3 - x*y^4 - 4*x*y^3 + y^5,
    x^2*y^2*B,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + 9*x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 + 
        8*x^3*y^2 - x^2*y^4 + 8*x^2*y^3 + 16*x^2*y^2 - 2*x*y^5 - 8*x*y^4 + 
        y^6)/x^2,
    -x^3*y*B - x^2*y*B - x*y^2*B - 4*x*y*B + y^3*B,
    x^2*B^2,
    (-x^9 - 3*x^8 - 3*x^7*y - 15*x^7 + 3*x^6*y^2 - 6*x^6*y - 25*x^6 + 3*x^5*y^2 
        - 27*x^5*y - 60*x^5 + 6*x^4*y^3 + 24*x^4*y^2 - 24*x^4*y - 48*x^4 - 
        3*x^3*y^4 + 5*x^3*y^3 + 12*x^3*y^2 - 48*x^3*y - 64*x^3 + 24*x^2*y^3 + 
        48*x^2*y^2 - 3*x*y^5 - 12*x*y^4 + y^6)/x^2,
    x*A,
    y^5,
    (-x^3*y^4 - x^2*y^4 - x*y^5 - 4*x*y^4 + y^6)/x^2,
    y^3*B,
    (x^6*y^3 + 2*x^5*y^3 + 2*x^4*y^4 + 9*x^4*y^3 - 2*x^3*y^5 + 2*x^3*y^4 + 
        8*x^3*y^3 - x^2*y^5 + 8*x^2*y^4 + 16*x^2*y^3 - 2*x*y^6 - 8*x*y^5 + 
        y^7)/x^4,
    (-x^3*y^2*B - x^2*y^2*B - x*y^3*B - 4*x*y^2*B + y^4*B)/x^2,
    y*B^2,
    (-x^9*y - 3*x^8*y - 3*x^7*y^2 - 15*x^7*y + 3*x^6*y^3 - 6*x^6*y^2 - 25*x^6*y 
        + 3*x^5*y^3 - 27*x^5*y^2 - 60*x^5*y + 6*x^4*y^4 + 24*x^4*y^3 - 
        24*x^4*y^2 - 48*x^4*y - 3*x^3*y^5 + 5*x^3*y^4 + 12*x^3*y^3 - 48*x^3*y^2 
        - 64*x^3*y + 24*x^2*y^4 + 48*x^2*y^3 - 3*x*y^6 - 12*x*y^5 + y^7)/x^4,
    (x^6*B + 2*x^5*B + 2*x^4*y*B + 9*x^4*B - 2*x^3*y^2*B + 2*x^3*y*B + 8*x^3*B -
        x^2*y^2*B + 8*x^2*y*B + 16*x^2*B - 2*x*y^3*B - 8*x*y^2*B + y^4*B)/x^2
@}

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB03a.cache.pol.co.uk. (195.92.168.165)
Time: Thu Aug 26 09:22:53 2004

Input: R<x,y,z,t,C,D>:=PolynomialRing(RationalField(),[1,2,3,4,9,8]);
S<x,y,z,t,C,D>:=FieldOfFractions(R);
subs:=hom<R->S|x,y,y^2/x-(x^2+y+x),y^3/x^2-(x*y+y^2/x+y),C,D>;
for i in [1..10] do
subs(MonomialsOfWeightedDegree(R,i));
end for;


Output: Magma V2.11-2     Thu Aug 26 2004 09:22:52 on modular  [Seed = 1045601105]
   -------------------------------------

{@
    x
@}
{@
    x^2,
    y
@}
{@
    x^3,
    x*y,
    (-x^3 - x^2 - x*y + y^2)/x
@}
{@
    x^4,
    x^2*y,
    -x^3 - x^2 - x*y + y^2,
    y^2,
    (-x^3*y - x^2*y - x*y^2 + y^3)/x^2
@}
{@
    x^5,
    x^3*y,
    -x^4 - x^3 - x^2*y + x*y^2,
    x*y^2,
    (-x^3*y - x^2*y - x*y^2 + y^3)/x
@}
{@
    x^6,
    x^4*y,
    -x^5 - x^4 - x^3*y + x^2*y^2,
    x^2*y^2,
    -x^3*y - x^2*y - x*y^2 + y^3,
    y^3,
    (-x^3*y^2 - x^2*y^2 - x*y^3 + y^4)/x^2,
    (x^6 + 2*x^5 + 2*x^4*y + x^4 - 2*x^3*y^2 + 2*x^3*y - x^2*y^2 - 2*x*y^3 + 
        y^4)/x^2
@}
{@
    x^7,
    x^5*y,
    -x^6 - x^5 - x^4*y + x^3*y^2,
    x^3*y^2,
    -x^4*y - x^3*y - x^2*y^2 + x*y^3,
    x*y^3,
    (-x^3*y^2 - x^2*y^2 - x*y^3 + y^4)/x,
    (x^6 + 2*x^5 + 2*x^4*y + x^4 - 2*x^3*y^2 + 2*x^3*y - x^2*y^2 - 2*x*y^3 + 
        y^4)/x,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y - 2*x^3*y^3 + 2*x^3*y^2 - x^2*y^3 - 
        2*x*y^4 + y^5)/x^3
@}
{@
    x^8,
    x^6*y,
    -x^7 - x^6 - x^5*y + x^4*y^2,
    x^4*y^2,
    -x^5*y - x^4*y - x^3*y^2 + x^2*y^3,
    x^2*y^3,
    -x^3*y^2 - x^2*y^2 - x*y^3 + y^4,
    x^6 + 2*x^5 + 2*x^4*y + x^4 - 2*x^3*y^2 + 2*x^3*y - x^2*y^2 - 2*x*y^3 + y^4,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y - 2*x^3*y^3 + 2*x^3*y^2 - x^2*y^3 - 
        2*x*y^4 + y^5)/x^2,
    y^4,
    (-x^3*y^3 - x^2*y^3 - x*y^4 + y^5)/x^2,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 - x^2*y^4
        - 2*x*y^5 + y^6)/x^4,
    D
@}
{@
    x^9,
    x^7*y,
    -x^8 - x^7 - x^6*y + x^5*y^2,
    x^5*y^2,
    -x^6*y - x^5*y - x^4*y^2 + x^3*y^3,
    x^3*y^3,
    -x^4*y^2 - x^3*y^2 - x^2*y^3 + x*y^4,
    x^7 + 2*x^6 + 2*x^5*y + x^5 - 2*x^4*y^2 + 2*x^4*y - x^3*y^2 - 2*x^2*y^3 + 
        x*y^4,
    (x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y - 2*x^3*y^3 + 2*x^3*y^2 - x^2*y^3 - 
        2*x*y^4 + y^5)/x,
    x*y^4,
    (-x^3*y^3 - x^2*y^3 - x*y^4 + y^5)/x,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 - x^2*y^4
        - 2*x*y^5 + y^6)/x^3,
    x*D,
    (-x^9 - 3*x^8 - 3*x^7*y - 3*x^7 + 3*x^6*y^2 - 6*x^6*y - x^6 + 3*x^5*y^2 - 
        3*x^5*y + 6*x^4*y^3 - 3*x^3*y^4 + 5*x^3*y^3 - 3*x*y^5 + y^6)/x^3,
    C
@}
{@
    x^10,
    x^8*y,
    -x^9 - x^8 - x^7*y + x^6*y^2,
    x^6*y^2,
    -x^7*y - x^6*y - x^5*y^2 + x^4*y^3,
    x^4*y^3,
    -x^5*y^2 - x^4*y^2 - x^3*y^3 + x^2*y^4,
    x^8 + 2*x^7 + 2*x^6*y + x^6 - 2*x^5*y^2 + 2*x^5*y - x^4*y^2 - 2*x^3*y^3 + 
        x^2*y^4,
    x^6*y + 2*x^5*y + 2*x^4*y^2 + x^4*y - 2*x^3*y^3 + 2*x^3*y^2 - x^2*y^3 - 
        2*x*y^4 + y^5,
    x^2*y^4,
    -x^3*y^3 - x^2*y^3 - x*y^4 + y^5,
    (x^6*y^2 + 2*x^5*y^2 + 2*x^4*y^3 + x^4*y^2 - 2*x^3*y^4 + 2*x^3*y^3 - x^2*y^4
        - 2*x*y^5 + y^6)/x^2,
    x^2*D,
    (-x^9 - 3*x^8 - 3*x^7*y - 3*x^7 + 3*x^6*y^2 - 6*x^6*y - x^6 + 3*x^5*y^2 - 
        3*x^5*y + 6*x^4*y^3 - 3*x^3*y^4 + 5*x^3*y^3 - 3*x*y^5 + y^6)/x^2,
    x*C,
    y^5,
    (-x^3*y^4 - x^2*y^4 - x*y^5 + y^6)/x^2,
    (x^6*y^3 + 2*x^5*y^3 + 2*x^4*y^4 + x^4*y^3 - 2*x^3*y^5 + 2*x^3*y^4 - x^2*y^5
        - 2*x*y^6 + y^7)/x^4,
    y*D,
    (-x^9*y - 3*x^8*y - 3*x^7*y^2 - 3*x^7*y + 3*x^6*y^3 - 6*x^6*y^2 - x^6*y + 
        3*x^5*y^3 - 3*x^5*y^2 + 6*x^4*y^4 - 3*x^3*y^5 + 5*x^3*y^4 - 3*x*y^6 + 
        y^7)/x^4
@}

Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:32:53 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^3 - D);
ClassGroup(F)

Output: Magma V2.11-2     Thu Aug 26 2004 10:32:50 on modular  [Seed = 1897776276]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/86 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    86*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/86 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    86*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/86 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    86*$.2 = 0 given by a rule

Total time: 2.049 seconds, Total memory usage: 13.28MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:33:12 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
ClassGroup(F)

Output: Magma V2.11-2     Thu Aug 26 2004 10:33:11 on modular  [Seed = 608735732]
   -------------------------------------

Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0 given by a rule

Total time: 1.540 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:33:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Place(F,2)

Output: Magma V2.11-2     Thu Aug 26 2004 10:33:45 on modular  [Seed = 3017737741]
   -------------------------------------


>> Place(F,2);
        ^
Runtime error in 'Place': Bad argument types
Argument types given: FldFun, RngIntElt

Total time: 1.329 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:34:23 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
NumberOfPlaces(F,2)

Output: Magma V2.11-2     Thu Aug 26 2004 10:34:21 on modular  [Seed = 1177220061]
   -------------------------------------


>> NumberOfPlaces(F,2);
   ^
User error: Identifier 'NumberOfPlaces' has not been declared or assigned

Total time: 1.359 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:34:44 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Places(F,2)

Output: Magma V2.11-2     Thu Aug 26 2004 10:34:43 on modular  [Seed = 241351291]
   -------------------------------------

[ (x + 5), (x + 3), (x^2 + 5*x + 2, alpha + 3*x + 3), (x^2 + 5*x + 2, alpha + 
    4*x + 4), (x^2 + 4*x + 5, alpha + x + 1), (x^2 + 4*x + 5, alpha + 6*x + 6), 
(x^2 + 4*x + 6, alpha + x + 5), (x^2 + 4*x + 6, alpha + 6*x + 2), (x^2 + x + 4, 
alpha + 2*x + 3), (x^2 + x + 4, alpha + 5*x + 4), (x^2 + 3*x + 5, alpha + 2*x + 
    4), (x^2 + 3*x + 5, alpha + 5*x + 3), (x^2 + 2*x + 3, alpha + 2*x + 5), (x^2
    + 2*x + 3, alpha + 5*x + 2), (x^2 + 6*x + 6, alpha + 2*x), (x^2 + 6*x + 6, 
    alpha + 5*x), (x^2 + 6*x + 4, alpha + 3*x + 1), (x^2 + 6*x + 4, alpha + 4*x 
    + 6) ]

Total time: 1.220 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:34:58 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Place(F,2)

Output: Magma V2.11-2     Thu Aug 26 2004 10:34:56 on modular  [Seed = 3702548666]
   -------------------------------------


>> Place(F,2);
        ^
Runtime error in 'Place': Bad argument types
Argument types given: FldFun, RngIntElt

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:35:22 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Places(F,2)

Output: Magma V2.11-2     Thu Aug 26 2004 10:35:21 on modular  [Seed = 2330345173]
   -------------------------------------

[ (x + 5), (x + 3), (x^2 + 5*x + 2, alpha + 3*x + 3), (x^2 + 5*x + 2, alpha + 
    4*x + 4), (x^2 + 4*x + 5, alpha + x + 1), (x^2 + 4*x + 5, alpha + 6*x + 6), 
(x^2 + 4*x + 6, alpha + x + 5), (x^2 + 4*x + 6, alpha + 6*x + 2), (x^2 + x + 4, 
alpha + 2*x + 3), (x^2 + x + 4, alpha + 5*x + 4), (x^2 + 3*x + 5, alpha + 2*x + 
    4), (x^2 + 3*x + 5, alpha + 5*x + 3), (x^2 + 2*x + 3, alpha + 2*x + 5), (x^2
    + 2*x + 3, alpha + 5*x + 2), (x^2 + 6*x + 6, alpha + 2*x), (x^2 + 6*x + 6, 
    alpha + 5*x), (x^2 + 6*x + 4, alpha + 3*x + 1), (x^2 + 6*x + 4, alpha + 4*x 
    + 6) ]

Total time: 1.250 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Thu Aug 26 10:36:03 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Places(F,1)

Output: Magma V2.11-2     Thu Aug 26 2004 10:36:02 on modular  [Seed = 4036773083]
   -------------------------------------

[ (1/x, 1/x^2*alpha + (x + 1)/x), (1/x, 1/x^2*alpha + (6*x + 1)/x), (x, alpha + 
    3), (x, alpha + 4), (x + 4, alpha + 3), (x + 4, alpha + 4), (x + 1, alpha + 
    3), (x + 1, alpha + 4), (x + 2, alpha + 3), (x + 2, alpha + 4), (x + 6, 
    alpha + 2), (x + 6, alpha + 5) ]

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:26:26 2004

Input: G<e> := DirichletGroup(73,CyclotomicField(3));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
save "191.session";
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;
save "191w.session";

Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed.

************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:26:56 2004

Input: G<e> := DirichletGroup(73,CyclotomicField(3));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;
save "191w.session";

Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed.

************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:27:05 2004

Input: G<e> := DirichletGroup(73,CyclotomicField(3));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;
save "191w.session";

Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed.

************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:27:21 2004

Input: G<e> := DirichletGroup(73,CyclotomicField(3));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:27:20 on modular  [Seed = 3299574913]
   -------------------------------------

Time: 0.110
Time: 0.030
Time: 0.090
D =  [
    Modular symbols space of level 73, weight 2, character e^2, and dimension 4 
    over Cyclotomic Field of order 3 and degree 2
]
A =  Modular symbols space of level 73, weight 2, character e^2, and dimension 4
over Cyclotomic Field of order 3 and degree 2
e =  (1/553*(184*zeta_3 + 34) 1/553*(228*zeta_3 - 30) 1/553*(54*zeta_3 + 22) 
    1/553*(-2*zeta_3 + 204))

Total time: 0.830 seconds, Total memory usage: 3.91MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:30:53 2004

Input: G<e> := DirichletGroup(61,CyclotomicField(6));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:30:52 on modular  [Seed = 3635911637]
   -------------------------------------

Time: 0.110
Time: 0.030
Time: 0.070
D =  [
    Modular symbols space of level 61, weight 2, character e^2, and dimension 4 
    over Cyclotomic Field of order 6 and degree 2
]
A =  Modular symbols space of level 61, weight 2, character e^2, and dimension 4
over Cyclotomic Field of order 6 and degree 2
e =  (1/399*(-20*zeta_6 + 88) 1/399*(-26*zeta_6 + 8) 1/399*(-72*zeta_6 + 104) 
    1/399*(-40*zeta_6 + 176))

Total time: 0.819 seconds, Total memory usage: 3.90MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:32:41 2004

Input: G<e> := DirichletGroup(61,CyclotomicField(3));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:32:40 on modular  [Seed = 57426105]
   -------------------------------------

Time: 0.110
Time: 0.020
Time: 0.080
D =  [
    Modular symbols space of level 61, weight 2, character e^2, and dimension 4 
    over Cyclotomic Field of order 3 and degree 2
]
A =  Modular symbols space of level 61, weight 2, character e^2, and dimension 4
over Cyclotomic Field of order 3 and degree 2
e =  (1/399*(-20*zeta_3 + 68) 1/399*(-26*zeta_3 - 18) 1/399*(-72*zeta_3 + 32) 
    1/399*(-40*zeta_3 + 136))

Total time: 0.809 seconds, Total memory usage: 3.90MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:32:53 2004

Input: G<e> := DirichletGroup(61,CyclotomicField(6));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:32:52 on modular  [Seed = 2031500031]
   -------------------------------------

Time: 0.110
Time: 0.020
Time: 0.080
D =  [
    Modular symbols space of level 61, weight 2, character e^2, and dimension 4 
    over Cyclotomic Field of order 6 and degree 2
]
A =  Modular symbols space of level 61, weight 2, character e^2, and dimension 4
over Cyclotomic Field of order 6 and degree 2
e =  (1/399*(-20*zeta_6 + 88) 1/399*(-26*zeta_6 + 8) 1/399*(-72*zeta_6 + 104) 
    1/399*(-40*zeta_6 + 176))

Total time: 0.820 seconds, Total memory usage: 3.90MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:34:33 2004

Input: G<e> := DirichletGroup(61,CyclotomicField(6));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:34:33 on modular  [Seed = 2098347856]
   -------------------------------------

Time: 0.130
Time: 0.020
Time: 0.080

>> for A in D do
   ^
User error: bad syntax

>>    print "A = ", A;
                    ^
User error: Identifier 'A' has not been declared or assigned

>>    print "e = ", WindingElementProjection(A);
                                             ^
User error: Identifier 'A' has not been declared or assigned

>> end for;;
   ^
User error: bad syntax

Total time: 0.829 seconds, Total memory usage: 3.70MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:34:46 2004

Input: G<e> := DirichletGroup(61,CyclotomicField(6));
f := e^2;
time M := ModularSymbols(f,2,+1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:34:45 on modular  [Seed = 3151296906]
   -------------------------------------

Time: 0.110
Time: 0.030
Time: 0.080
D =  [
    Modular symbols space of level 61, weight 2, character e^2, and dimension 4 
    over Cyclotomic Field of order 6 and degree 2
]
A =  Modular symbols space of level 61, weight 2, character e^2, and dimension 4
over Cyclotomic Field of order 6 and degree 2
e =  (1/399*(-20*zeta_6 + 88) 1/399*(-26*zeta_6 + 8) 1/399*(-72*zeta_6 + 104) 
    1/399*(-40*zeta_6 + 176))

Total time: 0.830 seconds, Total memory usage: 3.90MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:37:38 2004

Input: time M := ModularSymbols(Gamma1(73));
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:37:18 on modular  [Seed = 1496718302]
   -------------------------------------

Time: 0.660
Time: 1.090
Time: 7.230
D =  [
    Modular symbols space for Gamma_0(73) of weight 2 and dimension 2 over 
    Rational Field,
    Modular symbols space for Gamma_0(73) of weight 2 and dimension 4 over 
    Rational Field,
    Modular symbols space for Gamma_0(73) of weight 2 and dimension 4 over 
    Rational Field,
    Modular symbols space of level 73, weight 2, and dimension 4 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 16 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 16 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 16 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 40 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 60 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 60 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 144 over Rational
    Field (multi-character)
]
A =  Modular symbols space for Gamma_0(73) of weight 2 and dimension 2 over 
Rational Field
e =  (1/2  -1)
A =  Modular symbols space for Gamma_0(73) of weight 2 and dimension 4 over 
Rational Field
e =  (0 0 0 0)
A =  Modular symbols space for Gamma_0(73) of weight 2 and dimension 4 over 
Rational Field


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:40:14 2004

Input: time M := ModularSymbols(Gamma1(73), 6);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:39:53 on modular  [Seed = 2931944397]
   -------------------------------------



************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:40:31 2004

Input: time M := ModularSymbols(Gamma1(73), 2, 6);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:40:30 on modular  [Seed = 360337494]
   -------------------------------------


>> time M := ModularSymbols(Gamma1(73), 2, 6);
                           ^
Runtime error in 'ModularSymbols': Argument 3 must be either -1, 0, or 1.

>> time S := CuspidalSubspace(M);
                              ^
User error: Identifier 'M' has not been declared or assigned

>> time D := NewformDecomposition(S);
                                  ^
User error: Identifier 'S' has not been declared or assigned

>> print "D = ", D;
                 ^
User error: Identifier 'D' has not been declared or assigned

>> for A in D do
            ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:41:07 2004

Input: time M := ModularSymbols(Gamma1(73), 2, 1);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:40:47 on modular  [Seed = 1363022851]
   -------------------------------------

Time: 0.890
Time: 0.390
Time: 2.470
D =  [
    Modular symbols space for Gamma_0(73) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(73) of weight 2 and dimension 2 over 
    Rational Field,
    Modular symbols space for Gamma_0(73) of weight 2 and dimension 2 over 
    Rational Field,
    Modular symbols space of level 73, weight 2, and dimension 2 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 4 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 20 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 30 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 30 over Rational 
    Field (multi-character),
    Modular symbols space of level 73, weight 2, and dimension 72 over Rational 
    Field (multi-character)
]
A =  Modular symbols space for Gamma_0(73) of weight 2 and dimension 1 over 
Rational Field
e =  (1)
A =  Modular symbols space for Gamma_0(73) of weight 2 and dimension 2 over 
Rational Field
e =  (0 0)
A =  Modular symbols space for Gamma_0(73) of weight 2 and dimension 2 over 
Rational Field
e =  (-4/3  4/3)
A =  Modular symbols space of level 73, weight 2, and dimension 2 over Rational 
Field (multi-character)
e =  (-1 -1)
A =  Modular symbols space of level 73, weight 2, and dimension 4 over Rational 
Field (multi-character)
e =  ( 3/22  6/11 21/22     1)
A =  Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
Field (multi-character)
e =  ( 0  0  0  0  0  0 -1  0)
A =  Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
Field (multi-character)
e =  ( 0  0  0  0  0 -1  0  0)
A =  Modular symbols space of level 73, weight 2, and dimension 8 over Rational 
Field (multi-character)
e =  ( 0  0  0  0  0 -1  0  0)
A =  Modular symbols space of level 73, weight 2, and dimension 20 over Rational
Field (multi-character)


************** MAGMA *****************
Host d306wh.math.msu.edu. (35.8.72.106)
Time: Thu Aug 26 11:41:56 2004

Input: time M := ModularSymbols(Gamma1(73), 2, 6);
time S := CuspidalSubspace(M);
time D := NewformDecomposition(S);
print "D = ", D;
for A in D do
   print "A = ", A;
   print "e = ", WindingElementProjection(A);
end for;

Output: Magma V2.11-2     Thu Aug 26 2004 11:41:55 on modular  [Seed = 3000891229]
   -------------------------------------


>> time M := ModularSymbols(Gamma1(73), 2, 6);
                           ^
Runtime error in 'ModularSymbols': Argument 3 must be either -1, 0, or 1.

>> time S := CuspidalSubspace(M);
                              ^
User error: Identifier 'M' has not been declared or assigned

>> time D := NewformDecomposition(S);
                                  ^
User error: Identifier 'S' has not been declared or assigned

>> print "D = ", D;
                 ^
User error: Identifier 'D' has not been declared or assigned

>> for A in D do
            ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.569 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host ce3.net.hrz.tu-darmstadt.de. (130.83.244.131)
Time: Thu Aug 26 12:54:48 2004

Input: F := GF(2^21);
K := GF(2^7);
IP := { MinimalPolynomial(w,K) : w in F | not w in K };
#IP;

Output: Magma V2.11-2     Thu Aug 26 2004 12:54:25 on modular  [Seed = 2714694925]
   -------------------------------------



************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Thu Aug 26 22:40:43 2004

Input: 5+1


Output: Magma V2.11-2     Thu Aug 26 2004 22:40:42 on modular  [Seed = 1294111570]
   -------------------------------------

6

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Thu Aug 26 22:41:05 2004

Input: x^5/x^2



Output: Magma V2.11-2     Thu Aug 26 2004 22:41:05 on modular  [Seed = 2516208609]
   -------------------------------------


>> x^5/x^2
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.141.145.35)
Time: Thu Aug 26 23:43:11 2004

Input: 5+4

Output: Magma V2.11-2     Thu Aug 26 2004 23:43:11 on modular  [Seed = 978704058]
   -------------------------------------

9

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.141.145.35)
Time: Thu Aug 26 23:43:37 2004

Input: 66^{55}

Output: Magma V2.11-2     Thu Aug 26 2004 23:43:36 on modular  [Seed = 3851028803]
   -------------------------------------


>> 66^{55};
     ^
Runtime error in '^': Bad argument types
Argument types given: RngIntElt, SetEnum[RngIntElt]

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 3(NXDOMAIN) (202.141.145.35)
Time: Thu Aug 26 23:44:06 2004

Input: 66*66

Output: Magma V2.11-2     Thu Aug 26 2004 23:44:05 on modular  [Seed = 2931900900]
   -------------------------------------

4356

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host rimmer.cs.mu.OZ.AU. (128.250.37.73)
Time: Fri Aug 27 01:01:29 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Fri Aug 27 2004 01:01:28 on modular  [Seed = 2196571122]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:31:45 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Places(F,1)




Output: Magma V2.11-2     Fri Aug 27 2004 05:31:39 on modular  [Seed = 2967408279]
   -------------------------------------

[ (1/x, 1/x^2*alpha + (x + 1)/x), (1/x, 1/x^2*alpha + (6*x + 1)/x), (x, alpha + 
    3), (x, alpha + 4), (x + 4, alpha + 3), (x + 4, alpha + 4), (x + 1, alpha + 
    3), (x + 1, alpha + 4), (x + 2, alpha + 3), (x + 2, alpha + 4), (x + 6, 
    alpha + 2), (x + 6, alpha + 5) ]

Total time: 1.460 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:46:37 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Places(F,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:46:35 on modular  [Seed = 1327566059]
   -------------------------------------

[ (x^2 + 6*x + 3), (x^2 + x + 6), (x^2 + 4), (x^2 + 4*x + 1), (x^2 + 1), (x^2 + 
    5*x + 3), (x^2 + 5*x + 5), (x^2 + 3*x + 1), (x^2 + 2), (x^2 + x + 3), (x^2 +
    2*x + 2), (x^2 + 3*x + 6), (x^2 + 2*x + 5), (x^4 + 5*x^2 + 4*x + 3, alpha + 
    3*x^3 + 2*x^2 + 5*x + 1), (x^4 + 5*x^2 + 4*x + 3, alpha + 4*x^3 + 5*x^2 + 
    2*x + 6), (x^4 + 3*x^3 + 3*x^2 + 2, alpha + 3*x^3 + 6*x^2 + 6*x + 1), (x^4 +
    3*x^3 + 3*x^2 + 2, alpha + 4*x^3 + x^2 + x + 6), (x^4 + 4*x^3 + 6*x^2 + 5*x 
    + 4, alpha + x^3 + 4*x), (x^4 + 4*x^3 + 6*x^2 + 5*x + 4, alpha + 6*x^3 + 
    3*x), (x^4 + x + 1, alpha + 1), (x^4 + x + 1, alpha + 6), (x^4 + 6*x^3 + 
    2*x^2 + 4*x + 6, alpha + 3*x^2 + x + 6), (x^4 + 6*x^3 + 2*x^2 + 4*x + 6, 
    alpha + 4*x^2 + 6*x + 1), (x^4 + 6*x^3 + x^2 + 4*x + 4, alpha + 2*x^3 + x^2 
    + 5), (x^4 + 6*x^3 + x^2 + 4*x + 4, alpha + 5*x^3 + 6*x^2 + 2), (x^4 + 5*x^2
    + 5*x + 5, alpha + 3*x^3 + 4*x^2 + 4*x), (x^4 + 5*x^2 + 5*x + 5, alpha + 
    4*x^3 + 3*x^2 + 3*x), (x^4 + 2*x + 6, alpha + 3*x^3 + 2*x^2 + x), (x^4 + 2*x
    + 6, alpha + 4*x^3 + 5*x^2 + 6*x), (x^4 + 3*x^3 + 3*x^2 + x + 1, alpha + 
    2*x^3 + 4*x^2 + 2*x + 1), (x^4 + 3*x^3 + 3*x^2 + x + 1, alpha + 5*x^3 + 
    3*x^2 + 5*x + 6), (x^4 + x^3 + 2*x^2 + 3*x + 3, alpha + 2*x^3 + x^2 + x + 
    5), (x^4 + x^3 + 2*x^2 + 3*x + 3, alpha + 5*x^3 + 6*x^2 + 6*x + 2), (x^4 + 
    x^3 + 3*x^2 + 6*x + 2, alpha + 3*x^3 + 6*x^2 + 3*x), (x^4 + x^3 + 3*x^2 + 
    6*x + 2, alpha + 4*x^3 + x^2 + 4*x), (x^4 + 3*x^3 + x^2 + 5*x + 5, alpha + 
    3*x^3 + x + 3), (x^4 + 3*x^3 + x^2 + 5*x + 5, alpha + 4*x^3 + 6*x + 4), (x^4
    + x^3 + x^2 + x + 2, alpha + 2*x^3 + 4*x^2 + 4*x + 5), (x^4 + x^3 + x^2 + x 
    + 2, alpha + 5*x^3 + 3*x^2 + 3*x + 2), (x^4 + 2*x^3 + 2*x^2 + 5, alpha + x^3
    + 4*x^2 + 6*x + 2), (x^4 + 2*x^3 + 2*x^2 + 5, alpha + 6*x^3 + 3*x^2 + x + 
    5), (x^4 + 5*x^2 + 3*x + 1, alpha + 3*x^3 + 3*x^2 + 5*x + 4), (x^4 + 5*x^2 +
    3*x + 1, alpha + 4*x^3 + 4*x^2 + 2*x + 3), (x^4 + 3*x^2 + 3*x + 3, alpha + 
    x^3 + 5*x^2 + x + 1), (x^4 + 3*x^2 + 3*x + 3, alpha + 6*x^3 + 2*x^2 + 6*x + 
    6), (x^4 + x^3 + 6*x^2 + 2*x + 6, alpha + x^3 + x^2 + 4), (x^4 + x^3 + 6*x^2
    + 2*x + 6, alpha + 6*x^3 + 6*x^2 + 3), (x^4 + 2*x^3 + 4*x^2 + 5*x + 4, alpha
    + x^3 + 5*x^2 + 5*x + 4), (x^4 + 2*x^3 + 4*x^2 + 5*x + 4, alpha + 6*x^3 + 
    2*x^2 + 2*x + 3), (x^4 + 6*x^3 + x + 3, alpha + 2*x^3 + 6*x^2 + 6*x + 5), 
(x^4 + 6*x^3 + x + 3, alpha + 5*x^3 + x^2 + x + 2), (x^4 + 2*x^3 + 6*x^2 + 3*x +
    6, alpha + 3*x^3 + 2*x^2 + 5*x + 5), (x^4 + 2*x^3 + 6*x^2 + 3*x + 6, alpha +
    4*x^3 + 5*x^2 + 2*x + 2), (x^4 + 5*x^3 + x^2 + 4*x + 4, alpha + 3*x^3 + 
    2*x^2 + 5*x + 3), (x^4 + 5*x^3 + x^2 + 4*x + 4, alpha + 4*x^3 + 5*x^2 + 2*x 
    + 4), (x^4 + 2*x^3 + x^2 + 3*x + 5, alpha + 2*x^3 + 3*x^2 + 6*x + 5), (x^4 +
    2*x^3 + x^2 + 3*x + 5, alpha + 5*x^3 + 4*x^2 + x + 2), (x^4 + 5*x^3 + 5*x^2 
    + 5*x + 2, alpha + 2*x^3 + 4*x^2 + 4*x + 1), (x^4 + 5*x^3 + 5*x^2 + 5*x + 2,
alpha + 5*x^3 + 3*x^2 + 3*x + 6), (x^4 + 2*x^2 + 6*x + 4, alpha + x^3 + 3*x^2 + 
    4*x + 4), (x^4 + 2*x^2 + 6*x + 4, alpha + 6*x^3 + 4*x^2 + 3*x + 3), (x^4 + 
    2*x^3 + 3*x^2 + 6*x + 5, alpha + 3*x^3 + 6*x^2 + 4), (x^4 + 2*x^3 + 3*x^2 + 
    6*x + 5, alpha + 4*x^3 + x^2 + 3), (x^4 + 3*x^3 + 3*x + 1, alpha + 2*x^3 + 
    x^2 + 5*x + 2), (x^4 + 3*x^3 + 3*x + 1, alpha + 5*x^3 + 6*x^2 + 2*x + 5), 
(x^4 + 4*x^3 + x^2 + 6, alpha + 3*x^3 + x^2 + 5*x + 1), (x^4 + 4*x^3 + x^2 + 6, 
alpha + 4*x^3 + 6*x^2 + 2*x + 6), (x^4 + 6*x + 4, alpha + 2*x^3 + 4*x^2 + 5*x + 
    3), (x^4 + 6*x + 4, alpha + 5*x^3 + 3*x^2 + 2*x + 4), (x^4 + x^2 + 4*x + 5, 
alpha + x^3 + 3*x^2 + 4*x), (x^4 + x^2 + 4*x + 5, alpha + 6*x^3 + 4*x^2 + 3*x), 
(x^4 + 3*x^3 + 6*x^2 + x + 1, alpha + x^3 + 2*x^2 + 2*x), (x^4 + 3*x^3 + 6*x^2 +
    x + 1, alpha + 6*x^3 + 5*x^2 + 5*x), (x^4 + 2*x^3 + 5*x^2 + 6*x + 3, alpha +
    x^3 + 2*x^2 + x + 2), (x^4 + 2*x^3 + 5*x^2 + 6*x + 3, alpha + 6*x^3 + 5*x^2 
    + 6*x + 5), (x^4 + 6*x^3 + x^2 + 2*x + 2, alpha + x^3 + 6*x^2 + 5*x + 5), 
(x^4 + 6*x^3 + x^2 + 2*x + 2, alpha + 6*x^3 + x^2 + 2*x + 2), (x^4 + 3*x^3 + 5, 
alpha + x^3 + 5*x^2 + 5*x + 5), (x^4 + 3*x^3 + 5, alpha + 6*x^3 + 2*x^2 + 2*x + 
    2), (x^4 + 4*x^3 + 2*x^2 + 5*x + 1, alpha + 2*x^3 + 3*x^2 + 5), (x^4 + 4*x^3
    + 2*x^2 + 5*x + 1, alpha + 5*x^3 + 4*x^2 + 2), (x^4 + 4*x^3 + 4*x^2 + 2, 
    alpha + 2*x^2 + 3*x + 6), (x^4 + 4*x^3 + 4*x^2 + 2, alpha + 5*x^2 + 4*x + 
    1), (x^4 + 5*x^3 + 4*x^2 + 2*x + 6, alpha + x^3 + 2*x^2 + 2*x + 1), (x^4 + 
    5*x^3 + 4*x^2 + 2*x + 6, alpha + 6*x^3 + 5*x^2 + 5*x + 6), (x^4 + 6*x^3 + 
    3*x^2 + 5*x + 3, alpha + x^3 + 6*x^2 + 2*x + 3), (x^4 + 6*x^3 + 3*x^2 + 5*x 
    + 3, alpha + 6*x^3 + x^2 + 5*x + 4), (x^4 + 6*x^3 + x^2 + 6*x + 2, alpha + 
    x^3 + 6*x^2 + 4*x), (x^4 + 6*x^3 + x^2 + 6*x + 2, alpha + 6*x^3 + x^2 + 
    3*x), (x^4 + x^2 + 6, alpha + x^3 + 4*x^2 + x), (x^4 + x^2 + 6, alpha + 
    6*x^3 + 3*x^2 + 6*x), (x^4 + 6*x^3 + 2*x^2 + 4, alpha + 2*x^3 + 5*x^2 + 5*x 
    + 2), (x^4 + 6*x^3 + 2*x^2 + 4, alpha + 5*x^3 + 2*x^2 + 2*x + 5), (x^4 + x^3
    + x^2 + 1, alpha + x^3 + 6), (x^4 + x^3 + x^2 + 1, alpha + 6*x^3 + 1), (x^4 
    + 4*x^3 + 2*x + 3, alpha + 3*x^3 + 4*x^2 + 3), (x^4 + 4*x^3 + 2*x + 3, alpha
    + 4*x^3 + 3*x^2 + 4), (x^4 + 5*x^3 + 4*x^2 + 6*x + 2, alpha + 3*x^3 + 5*x^2 
    + x), (x^4 + 5*x^3 + 4*x^2 + 6*x + 2, alpha + 4*x^3 + 2*x^2 + 6*x), (x^4 + 
    4*x^3 + 2*x^2 + 6, alpha + 3*x^3 + 6*x^2 + 5*x + 5), (x^4 + 4*x^3 + 2*x^2 + 
    6, alpha + 4*x^3 + x^2 + 2*x + 2), (x^4 + 5*x^3 + 6*x^2 + x + 4, alpha + 
    2*x^3 + 4*x^2 + 6*x + 4), (x^4 + 5*x^3 + 6*x^2 + x + 4, alpha + 5*x^3 + 
    3*x^2 + x + 3), (x^4 + 4*x^3 + 2*x^2 + 5*x + 5, alpha + 2*x^3 + 3*x^2 + 4*x 
    + 1), (x^4 + 4*x^3 + 2*x^2 + 5*x + 5, alpha + 5*x^3 + 4*x^2 + 3*x + 6), (x^4
    + 6*x^3 + 2*x + 4, alpha + x^3 + x^2 + x + 1), (x^4 + 6*x^3 + 2*x + 4, alpha
    + 6*x^3 + 6*x^2 + 6*x + 6), (x^4 + 2*x^3 + 4*x^2 + 3*x + 1, alpha + 2*x^3 + 
    5*x^2 + 2*x + 6), (x^4 + 2*x^3 + 4*x^2 + 3*x + 1, alpha + 5*x^3 + 2*x^2 + 
    5*x + 1), (x^4 + 5*x^3 + 5*x^2 + 5*x + 1, alpha + 3*x^3 + 2*x + 2), (x^4 + 
    5*x^3 + 5*x^2 + 5*x + 1, alpha + 4*x^3 + 5*x + 5), (x^4 + 3*x^3 + 4*x^2 + 
    5*x + 5, alpha + 3*x^3 + 5*x^2 + 6*x), (x^4 + 3*x^3 + 4*x^2 + 5*x + 5, alpha
    + 4*x^3 + 2*x^2 + x), (x^4 + 6*x^3 + 6*x + 3, alpha + x^3 + x^2 + 3*x + 6), 
(x^4 + 6*x^3 + 6*x + 3, alpha + 6*x^3 + 6*x^2 + 4*x + 1), (x^4 + 3*x^3 + 2*x + 
    3, alpha + x^3 + 5*x), (x^4 + 3*x^3 + 2*x + 3, alpha + 6*x^3 + 2*x), (x^4 + 
    6*x^3 + 6*x^2 + 2, alpha + 2*x^3 + x^2 + 4*x + 3), (x^4 + 6*x^3 + 6*x^2 + 2,
alpha + 5*x^3 + 6*x^2 + 3*x + 4), (x^4 + 2*x^3 + 5*x^2 + 2*x + 6, alpha + 2*x^3 
    + 6*x^2 + 6*x + 4), (x^4 + 2*x^3 + 5*x^2 + 2*x + 6, alpha + 5*x^3 + x^2 + x 
    + 3), (x^4 + 6*x^3 + 6*x^2 + x + 5, alpha + 2*x^3 + 5*x + 2), (x^4 + 6*x^3 +
    6*x^2 + x + 5, alpha + 5*x^3 + 2*x + 5), (x^4 + 2*x^3 + 4*x^2 + x + 4, alpha
    + 3*x^3 + 5*x^2 + x + 6), (x^4 + 2*x^3 + 4*x^2 + x + 4, alpha + 4*x^3 + 
    2*x^2 + 6*x + 1), (x^4 + 3*x^3 + 4*x^2 + 4*x + 1, alpha + 3*x^3 + x^2 + x), 
(x^4 + 3*x^3 + 4*x^2 + 4*x + 1, alpha + 4*x^3 + 6*x^2 + 6*x), (x^4 + 4*x^3 + 
    5*x^2 + 6*x + 3, alpha + 2*x^3 + x^2 + 6*x + 5), (x^4 + 4*x^3 + 5*x^2 + 6*x 
    + 3, alpha + 5*x^3 + 6*x^2 + x + 2), (x^4 + 6*x^3 + x + 2, alpha + 3*x^3 + 
    6*x^2 + 2*x + 2), (x^4 + 6*x^3 + x + 2, alpha + 4*x^3 + x^2 + 5*x + 5), (x^4
    + 4*x^3 + 6*x^2 + 6*x + 6, alpha + 2*x^3 + 2*x^2 + 3*x), (x^4 + 4*x^3 + 
    6*x^2 + 6*x + 6, alpha + 5*x^3 + 5*x^2 + 4*x), (x^4 + 5*x^3 + 2*x^2 + 2*x + 
    3, alpha + 3*x^3 + x^2 + 1), (x^4 + 5*x^3 + 2*x^2 + 2*x + 3, alpha + 4*x^3 +
    6*x^2 + 6), (x^4 + 5*x^3 + 6*x + 6, alpha + 2*x^3 + x^2 + 4*x + 5), (x^4 + 
    5*x^3 + 6*x + 6, alpha + 5*x^3 + 6*x^2 + 3*x + 2), (x^4 + 4*x^3 + 4*x^2 + 
    3*x + 5, alpha + x^3 + 3*x^2 + 6*x), (x^4 + 4*x^3 + 4*x^2 + 3*x + 5, alpha +
    6*x^3 + 4*x^2 + x), (x^4 + 3*x^3 + x^2 + 6*x + 6, alpha + 2*x^3 + x + 3), 
(x^4 + 3*x^3 + x^2 + 6*x + 6, alpha + 5*x^3 + 6*x + 4), (x^4 + 6*x^3 + 6*x^2 + 
    2*x + 4, alpha + 3*x^3 + 6*x + 2), (x^4 + 6*x^3 + 6*x^2 + 2*x + 4, alpha + 
    4*x^3 + x + 5), (x^4 + 6*x^3 + 2*x^2 + 3*x + 5, alpha + 3*x^3 + 4*x + 4), 
(x^4 + 6*x^3 + 2*x^2 + 3*x + 5, alpha + 4*x^3 + 3*x + 3), (x^4 + 6*x^2 + 2*x + 
    3, alpha + x^3 + 6*x^2 + 4*x + 6), (x^4 + 6*x^2 + 2*x + 3, alpha + 6*x^3 + 
    x^2 + 3*x + 1), (x^4 + 5*x^3 + 4*x^2 + 2, alpha + 2*x^3 + 6*x^2 + 4*x + 2), 
(x^4 + 5*x^3 + 4*x^2 + 2, alpha + 5*x^3 + x^2 + 3*x + 5), (x^4 + x^3 + 4*x^2 + 
    6*x + 3, alpha + 3*x^3 + 6*x^2 + 4*x + 2), (x^4 + x^3 + 4*x^2 + 6*x + 3, 
    alpha + 4*x^3 + x^2 + 3*x + 5), (x^4 + 3*x^3 + 5*x^2 + 2*x + 2, alpha + 
    3*x^3 + 6*x^2 + 2*x + 1), (x^4 + 3*x^3 + 5*x^2 + 2*x + 2, alpha + 4*x^3 + 
    x^2 + 5*x + 6), (x^4 + 6*x^3 + 5*x + 6, alpha + 3*x^3 + 5*x^2 + 5*x), (x^4 +
    6*x^3 + 5*x + 6, alpha + 4*x^3 + 2*x^2 + 2*x), (x^4 + 4*x^3 + 2*x^2 + 6*x + 
    5, alpha + 3*x^2 + 3*x), (x^4 + 4*x^3 + 2*x^2 + 6*x + 5, alpha + 4*x^2 + 
    4*x), (x^4 + 4*x^3 + 2*x^2 + x + 4, alpha + x^3 + 4*x^2 + 2), (x^4 + 4*x^3 +
    2*x^2 + x + 4, alpha + 6*x^3 + 3*x^2 + 5), (x^4 + 2*x^3 + 2*x^2 + 3*x + 1, 
    alpha + 3*x^3 + x + 5), (x^4 + 2*x^3 + 2*x^2 + 3*x + 1, alpha + 4*x^3 + 6*x 
    + 2), (x^4 + 2*x^3 + 3*x^2 + 3, alpha + 3*x^3 + 5*x^2 + 6*x + 6), (x^4 + 
    2*x^3 + 3*x^2 + 3, alpha + 4*x^3 + 2*x^2 + x + 1), (x^4 + x^3 + 6*x^2 + 5*x 
    + 2, alpha + 2*x^2 + 6*x + 6), (x^4 + x^3 + 6*x^2 + 5*x + 2, alpha + 5*x^2 +
    x + 1), (x^4 + x^3 + 2*x^2 + 6*x + 6, alpha + x^3 + 2*x^2 + 5), (x^4 + x^3 +
    2*x^2 + 6*x + 6, alpha + 6*x^3 + 5*x^2 + 2), (x^4 + 6*x^3 + x^2 + 5, alpha +
    3*x^3 + 2*x^2 + x + 4), (x^4 + 6*x^3 + x^2 + 5, alpha + 4*x^3 + 5*x^2 + 6*x 
    + 3), (x^4 + x^3 + 2*x^2 + x + 3, alpha + 2*x^3 + 4*x), (x^4 + x^3 + 2*x^2 +
    x + 3, alpha + 5*x^3 + 3*x), (x^4 + 5*x^2 + 2*x + 5, alpha + 2*x^3 + 6*x^2 +
    5*x + 3), (x^4 + 5*x^2 + 2*x + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:47:27 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Place(F,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:47:26 on modular  [Seed = 1193870646]
   -------------------------------------


>> Place(F,4)
        ^
Runtime error in 'Place': Bad argument types
Argument types given: FldFun, RngIntElt

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:47:44 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
HasPlace(F,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:47:43 on modular  [Seed = 2131836191]
   -------------------------------------

true

Total time: 1.250 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:48:09 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
RandomPlace(F,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:48:08 on modular  [Seed = 1981297777]
   -------------------------------------

true (x^4 + 4*x^3 + 2*x + 3, alpha + 3*x^3 + 4*x^2 + 3)

Total time: 1.220 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:50:43 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
Places(R,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:50:42 on modular  [Seed = 1828925376]
   -------------------------------------


>> Places(R,4)
         ^
Runtime error in 'Places': Bad argument types
Argument types given: RngUPol[FldFin], RngIntElt

Total time: 1.250 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:51:49 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
Places(F0,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:51:48 on modular  [Seed = 1678385423]
   -------------------------------------

[ (x^4 + 5*x^2 + 4*x + 3), (x^4 + 3*x^3 + 3*x^2 + 2), (x^4 + 5*x^3 + 2*x^2 + 3*x
    + 6), (x^4 + 4*x^3 + 6*x^2 + 5*x + 4), (x^4 + 5*x^3 + 5*x^2 + 2*x + 5), (x^4
    + x + 1), (x^4 + 3*x^3 + 4*x^2 + 2*x + 2), (x^4 + 6*x^3 + 2*x^2 + 4*x + 6), 
(x^4 + 6*x^3 + x^2 + 4*x + 4), (x^4 + 5*x^2 + 5*x + 5), (x^4 + 2*x^2 + 6*x + 1),
(x^4 + 4*x^2 + 3*x + 3), (x^4 + 2*x + 6), (x^4 + 6*x^3 + x^2 + 5*x + 4), (x^4 + 
    2*x^3 + 3*x^2 + 2*x + 5), (x^4 + 3*x^3 + 3*x^2 + x + 1), (x^4 + x^3 + 2*x^2 
    + 3*x + 3), (x^4 + x^3 + 3*x^2 + 6*x + 2), (x^4 + 3*x^3 + 4*x + 4), (x^4 + 
    3*x^3 + x^2 + 5*x + 5), (x^4 + 4*x^3 + 6*x^2 + 3*x + 1), (x^4 + 6*x^2 + 3), 
(x^4 + x^3 + x^2 + x + 2), (x^4 + 3*x^3 + 6*x^2 + x + 6), (x^4 + 2*x^3 + 2*x^2 +
    5), (x^4 + 5*x^2 + 3*x + 1), (x^4 + 3*x^2 + 3*x + 3), (x^4 + x^3 + 5*x^2 + 
    4*x + 2), (x^4 + x^3 + 6*x^2 + 2*x + 6), (x^4 + 2*x^3 + 4*x^2 + 5*x + 4), 
(x^4 + 4*x^3 + 5*x^2 + 5*x + 1), (x^4 + 6*x^3 + x + 3), (x^4 + 3*x^3 + 4*x^2 + 
    3*x + 2), (x^4 + 2*x^3 + 6*x^2 + 3*x + 6), (x^4 + 5*x^3 + x^2 + 4*x + 4), 
(x^4 + 2*x^3 + x^2 + 3*x + 5), (x^4 + 6*x^3 + 6*x^2 + 3*x + 3), (x^4 + 5*x^3 + 
    5*x^2 + 5*x + 2), (x^4 + 6*x^3 + 5*x^2 + x + 6), (x^4 + 2*x^2 + 6*x + 4), 
(x^4 + 2*x^3 + 3*x^2 + 6*x + 5), (x^4 + 3*x^3 + 3*x + 1), (x^4 + 3*x^3 + 4*x^2 +
    5*x + 6), (x^4 + x^3 + 3*x^2 + 3*x + 4), (x^4 + 5*x^2 + x + 5), (x^4 + 3*x^3
    + x + 1), (x^4 + x^3 + 3), (x^4 + 4*x^3 + x^2 + 6), (x^4 + 6*x + 4), (x^4 + 
    x^2 + 4*x + 5), (x^4 + 3*x^3 + 6*x^2 + x + 1), (x^4 + 2*x^3 + 5*x^2 + 6*x + 
    3), (x^4 + 6*x^3 + x^2 + 2*x + 2), (x^4 + 2*x^3 + 4*x + 4), (x^4 + 3*x^3 + 
    5), (x^4 + 4*x^3 + 2*x^2 + 5*x + 1), (x^4 + x^3 + x^2 + 5*x + 3), (x^4 + 
    4*x^3 + 4*x^2 + 2), (x^4 + 5*x^3 + 4*x^2 + 2*x + 6), (x^4 + 5*x^3 + 4*x^2 + 
    x + 5), (x^4 + x^3 + x^2 + 6*x + 1), (x^4 + 6*x^3 + 3*x^2 + 5*x + 3), (x^4 +
    6*x^3 + x^2 + 6*x + 2), (x^4 + x^2 + 6), (x^4 + 6*x^3 + 2*x^2 + 4), (x^4 + 
    x^3 + x^2 + 1), (x^4 + 4*x^3 + 2*x + 3), (x^4 + 5*x^3 + 4*x^2 + 6*x + 2), 
(x^4 + 4*x^3 + 2*x^2 + 6), (x^4 + 5*x^3 + 6*x^2 + x + 4), (x^4 + 4*x^3 + 2*x^2 +
    5*x + 5), (x^4 + 4*x^3 + 4*x^2 + 6*x + 3), (x^4 + 4*x^3 + 6*x^2 + 6*x + 2), 
(x^4 + 3*x^3 + 3*x^2 + 3*x + 6), (x^4 + 6*x^3 + 2*x + 4), (x^4 + 6*x^3 + 4*x^2 +
    2*x + 5), (x^4 + 2*x^3 + 4*x^2 + 3*x + 1), (x^4 + 4*x^3 + 5*x^2 + x + 2), 
(x^4 + 2*x^3 + 6*x^2 + 2*x + 6), (x^4 + 2*x^3 + 2*x^2 + x + 4), (x^4 + 2*x^3 + 
    3*x^2 + 4*x + 5), (x^4 + 5*x^3 + 5*x^2 + 5*x + 1), (x^4 + 4*x^3 + 2*x^2 + 
    6*x + 3), (x^4 + 3*x^3 + 4*x^2 + 5*x + 5), (x^4 + 6*x^3 + 5*x^2 + 2*x + 1), 
(x^4 + 6*x^3 + 6*x + 3), (x^4 + 5*x^3 + 4*x^2 + x + 2), (x^4 + 3*x^3 + 4), (x^4 
    + 4*x^3 + 5*x^2 + 4*x + 5), (x^4 + 5*x^3 + 3*x^2 + 6*x + 1), (x^4 + 3*x^3 + 
    2*x + 3), (x^4 + 6*x^3 + 6*x^2 + 2), (x^4 + 2*x^3 + 5*x^2 + 2*x + 6), (x^4 +
    6*x^3 + 6*x^2 + x + 5), (x^4 + 6*x^2 + 5*x + 1), (x^4 + 3*x^3 + 6*x^2 + 2*x 
    + 3), (x^4 + x^2 + 6*x + 2), (x^4 + 2*x^3 + x^2 + 3*x + 6), (x^4 + 2*x^3 + 
    4*x^2 + x + 4), (x^4 + 3*x^3 + 4*x^2 + 4*x + 1), (x^4 + 4*x^3 + 5*x^2 + 6*x 
    + 3), (x^4 + 6*x^3 + x + 2), (x^4 + 4*x^3 + 6*x^2 + 6*x + 6), (x^4 + x^3 + 
    2*x^2 + 4), (x^4 + 4*x^2 + 5), (x^4 + 5*x^3 + 2*x^2 + 2*x + 3), (x^4 + 3*x^3
    + 6*x^2 + 5*x + 2), (x^4 + 5*x^3 + 6*x + 6), (x^4 + 5*x^3 + 3*x^2 + 4), (x^4
    + 4*x^3 + 4*x^2 + 3*x + 5), (x^4 + 2*x^3 + x^2 + 1), (x^4 + x^3 + 4*x^2 + 
    2*x + 2), (x^4 + 3*x^3 + x^2 + 6*x + 6), (x^4 + 6*x^3 + 6*x^2 + 2*x + 4), 
(x^4 + 6*x^3 + 2*x^2 + 3*x + 5), (x^4 + 4*x^3 + x^2 + 2*x + 1), (x^4 + 6*x^2 + 
    2*x + 3), (x^4 + x^3 + 5*x + 6), (x^4 + 4*x^3 + 2*x^2 + 4*x + 4), (x^4 + 
    5*x^3 + 6*x^2 + 2*x + 5), (x^4 + x^3 + 5*x^2 + x + 1), (x^4 + 5*x^3 + 2*x^2 
    + 6*x + 3), (x^4 + 5*x^3 + 4*x^2 + 2), (x^4 + x^3 + 4*x^2 + 6*x + 3), (x^4 +
    3*x^3 + 5*x^2 + 2*x + 2), (x^4 + 6*x^3 + 5*x + 6), (x^4 + 4*x^3 + 2*x^2 + 
    6*x + 5), (x^4 + x^3 + 3*x^2 + 2*x + 1), (x^4 + 6*x^3 + 5*x^2 + 5*x + 3), 
(x^4 + 5*x^3 + 4*x^2 + 3*x + 2), (x^4 + 3*x^3 + 4*x^2 + 3*x + 6), (x^4 + 4*x^3 +
    2*x^2 + x + 4), (x^4 + 2*x^3 + 2*x^2 + 3*x + 1), (x^4 + 2*x^3 + 3*x^2 + 3), 
(x^4 + x^3 + 6*x^2 + 5*x + 2), (x^4 + x^3 + 2*x^2 + 6*x + 6), (x^4 + 2*x^3 + 
    2*x^2 + 2*x + 4), (x^4 + 6*x^3 + x^2 + 5), (x^4 + x^3 + 2*x^2 + x + 3), (x^4
    + 6*x^3 + 2*x^2 + 2*x + 2), (x^4 + 3*x^3 + 5*x^2 + 5*x + 6), (x^4 + 3*x^3 + 
    6*x^2 + 2*x + 4), (x^4 + 5*x^2 + 2*x + 5), (x^4 + 4*x^3 + 3*x^2 + 6*x + 1), 
(x^4 + 6*x^3 + 5*x^2 + 3*x + 2), (x^4 + 5*x^3 + 6*x^2 + 4*x + 6), (x^4 + 2*x^2 +
    x + 4), (x^4 + 5*x^2 + 6*x + 5), (x^4 + 4*x^3 + 6*x^2 + 6*x + 1), (x^4 + 
    6*x^3 + x^2 + 2*x + 3), (x^4 + 3*x^3 + 2*x^2 + 6), (x^4 + x^3 + 5*x + 4), 
(x^4 + 5*x^3 + 3*x^2 + 3*x + 5), (x^4 + x^3 + 5*x^2 + 5*x + 1), (x^4 + 4*x^3 + 
    5*x + 3), (x^4 + x^2 + x + 2), (x^4 + 2*x^3 + 3*x^2 + 4), (x^4 + x^3 + 2*x^2
    + 4*x + 5), (x^4 + 6*x^3 + 5*x^2 + 6*x + 1), (x^4 + 6*x^3 + 4*x^2 + x + 3), 
(x^4 + 2*x^3 + 4*x^2 + 4*x + 2), (x^4 + 6*x^3 + 2*x^2 + x + 6), (x^4 + 6*x^3 + 
    5*x^2 + 2*x + 6), (x^4 + 6*x^3 + 3*x^2 + x + 4), (x^4 + 2*x^3 + 3*x^2 + 6*x 
    + 1), (x^4 + 4*x^3 + 3*x^2 + 6*x + 3), (x^4 + 6*x^3 + 4*x^2 + 6*x + 2), (x^4
    + x^3 + 5*x^2 + 5*x + 6), (x^4 + 4*x^3 + 3*x^2 + x + 4), (x^4 + x^3 + 5*x^2 
    + 4*x + 5), (x^4 + 4*x^3 + 2*x^2 + 3*x + 3), (x^4 + 5*x^3 + x^2 + 2), (x^4 +
    5*x^3 + x + 6), (x^4 + x^3 + 3*x^2 + 6*x + 4), (x^4 + 6*x^3 + 4*x^2 + 6*x + 
    5), (x^4 + 2*x^3 + 5*x + 1), (x^4 + 5*x^3 + x^2 + 3*x + 2), (x^4 + 2*x^3 + 
    3*x^2 + 5*x + 6), (x^4 + 4*x^3 + 5*x^2 + 3*x + 4), (x^4 + 5*x^3 + 2*x^2 + 
    5), (x^4 + 6*x^3 + x^2 + 1), (x^4 + 2*x^3 + 2*x^2 + 5*x + 3), (x^4 + 4*x^2 +
    6), (x^4 + 4*x^3 + 6*x^2 + 3*x + 4), (x^4 + 4*x^3 + 2*x^2 + 5), (x^4 + 5*x^3
    + 3*x^2 + x + 1), (x^4 + 6*x^3 + 4*x^2 + 3*x + 3), (x^4 + 3*x^3 + 2*x^2 + 
    4*x + 2), (x^4 + 2*x^3 + 5*x^2 + 3*x + 4), (x^4 + 6*x^2 + 3*x + 5), (x^4 + 
    5*x^3 + x^2 + 3*x + 1), (x^4 + 3*x^3 + 3*x^2 + x + 3), (x^4 + 4*x^3 + 6*x^2 
    + 3*x + 2), (x^4 + 2*x^2 + 4*x + 6), (x^4 + 3*x^3 + 6*x^2 + 5*x + 5), (x^4 +
    6*x^3 + x^2 + 6*x + 1), (x^4 + 5*x^3 + 6*x^2 + 3*x + 3), (x^4 + x^3 + 4*x^2 
    + x + 2), (x^4 + 5*x^3 + x^2 + 5*x + 6), (x^4 + 6*x^3 + 6*x^2 + 6*x + 4), 
(x^4 + 3*x^3 + 3*x^2 + 5*x + 5), (x^4 + 5*x^3 + 3*x^2 + 5*x + 3), (x^4 + 4*x^2 +
    x + 2), (x^4 + 6*x^3 + 6*x^2 + 3*x + 6), (x^4 + 3*x^3 + 3*x^2 + 6*x + 4), 
(x^4 + 4*x^3 + x^2 + 6*x + 5), (x^4 + 3*x^3 + x^2 + 6*x + 1), (x^4 + 2*x^3 + 
    3*x^2 + 3*x + 2), (x^4 + 2*x^3 + 4*x^2 + 6), (x^4 + 6*x^3 + 2*x^2 + 3*x + 
    4), (x^4 + 6*x^3 + 5*x^2 + 3*x + 5), (x^4 + 5*x^3 + 3*x^2 + 2*x + 1), (x^4 +
    3*x^3 + 5*x^2 + 3*x + 3), (x^4 + 3*x^3 + 6*x^2 + 2*x + 6), (x^4 + 2*x^2 + 
    5*x + 4), (x^4 + 6*x^3 + 3*x^2 + 2*x + 5), (x^4 + 5*x^2 + 4*x + 1), (x^4 + 
    3*x^3 + 5*x + 3), (x^4 + 4*x^3 + 6*x^2 + 2*x + 2), (x^4 + 3*x^3 + 6*x^2 + 
    4*x + 4), (x^4 + 3*x^2 + 5), (x^4 + x^2 + 5*x + 1), (x^4 + 3*x^3 + 2*x^2 + 
    4*x + 3), (x^4 + 5*x^3 + 4*x + 2), (x^4 + 6*x^3 + x^2 + x + 6), (x^4 + 4*x^3
    + 4*x^2 + x + 5), (x^4 + 6*x^3 + 2*x^2 + 3*x + 1), (x^4 + 5*x^3 + 5*x^2 + 
    2*x + 3), (x^4 + 2*x^3 + x^2 + 2), (x^4 + 2*x^3 + 4*x^2 + 6*x + 6), (x^4 + 
    x^3 + 5*x^2 + 4), (x^4 + 2*x^3 + 4*x^2 + 2*x + 1), (x^4 + x^3 + 4*x^2 + 2*x 
    + 3), (x^4 + 6*x^2 + 4*x + 2), (x^4 + 2*x^3 + 6*x + 6), (x^4 + 4*x^3 + 6*x^2
    + 2*x + 4), (x^4 + x^3 + 2*x^2 + 2*x + 5), (x^4 + 3*x^2 + 2*x + 2), (x^4 + 
    6*x^3 + 6*x^2 + x + 6), (x^4 + x^3 + 3*x^2 + 2*x + 4), (x^4 + x^3 + 4*x^2 + 
    x + 5), (x^4 + 6*x^3 + x^2 + 3*x + 1), (x^4 + x^3 + 2*x^2 + 2*x + 3), (x^4 +
    3*x^3 + 5*x^2 + 6), (x^4 + 2*x^3 + x^2 + 5*x + 4), (x^4 + 4*x^3 + 3*x^2 + 
    3*x + 5), (x^4 + 5*x^3 + 2*x + 1), (x^4 + 5*x^3 + x^2 + 3*x + 3), (x^4 + 
    2*x^3 + 6*x^2 + 5*x + 2), (x^4 + 4*x^3 + 4*x^2 + 4), (x^4 + 3*x^3 + 5*x^2 + 
    2*x + 5), (x^4 + 6*x^3 + 3*x^2 + 4*x + 1), (x^4 + 3*x^2 + 4*x + 3), (x^4 + 
    2*x^3 + 4*x^2 + x + 2), (x^4 + 2*x^3 + x + 6), (x^4 + 3*x^3 + 2*x^2 + 5), 
(x^4 + x^2 + 2*x + 1), (x^4 + 5*x^2 + 3), (x^4 + 2*x^3 + x^2 + 4*x + 2), (x^4 + 
    5*x^3 + 2*x^2 + 5*x + 6), (x^4 + 4*x^3 + 2*x^2 + 6*x + 4), (x^4 + 3*x^3 + 
    4*x^2 + 2*x + 1), (x^4 + x^3 + 6*x^2 + 5*x + 3), (x^4 + 4*x^2 + 5*x + 2), 
(x^4 + 5*x^3 + 3*x^2 + 2*x + 6), (x^4 + x^3 + 4*x^2 + 3*x + 4), (x^4 + 5*x + 5),
(x^4 + 2*x^3 + 3*x^2 + 6*x + 3), (x^4 + 3*x^3 + x^2 + 4*x + 2), (x^4 + 6*x^3 + 
    x^2 + 4*x + 6), (x^4 + 3*x^3 + 5*x^2 + 4*x + 4), (x^4 + x^3 + 6*x^2 + 5), 
(x^4 + x^3 + 1), (x^4 + 3*x^2 + 3*x + 5), (x^4 + 2*x^3 + 6*x^2 + 1), (x^4 + x^3 
    + 4*x^2 + 4*x + 3), (x^4 + 5*x^3 + 5*x^2 + 2*x + 2), (x^4 + x^3 + 3*x^2 + 
    5*x + 6), (x^4 + 2*x^3 + x^2 + 5*x + 1), (x^4 + 4*x^3 + 4*x^2 + 3*x + 3), 
(x^4 + 4*x^3 + 2*x^2 + 3*x + 2), (x^4 + 3*x^2 + 2*x + 6), (x^4 + 4*x^2 + x + 4),
(x^4 + 5*x + 3), (x^4 + 4*x^3 + 2*x^2 + 2*x + 2), (x^4 + 6*x^3 + 6*x^2 + 5*x + 
    6), (x^4 + 2*x^3 + 6*x^2 + 6*x + 4), (x^4 + 3*x^3 + 4*x^2 + 4*x + 5), (x^4 +
    2*x^3 + 3*x + 2), (x^4 + 2*x^3 + 2*x^2 + 2*x + 6), (x^4 + 5*x^3 + 5*x^2 + 
    4*x + 4), (x^4 + 5*x^2 + 5), (x^4 + 3*x^3 + 2*x^2 + 6*x + 1), (x^4 + 6*x^3 +
    4*x^2 + 6), (x^4 + 3*x^2 + 4*x + 4), (x^4 + 6*x^2 + 4*x + 5), (x^4 + 3*x^3 +
    3*x^2 + 3*x + 1), (x^4 + 3*x^3 + 5*x^2 + 5*x + 3), (x^4 + 5*x^3 + 3*x^2 + 
    2*x + 4), (x^4 + 4*x^3 + 6*x + 5), (x^4 + 2*x^3 + x^2 + 4*x + 1), (x^4 + 
    6*x^3 + 5*x^2 + 4*x + 3), (x^4 + x^3 + 2*x^2 + 3*x + 2), (x^4 + 2*x^3 + x^2 
    + 2*x + 3), (x^4 + 3*x^3 + 6*x^2 + 4*x + 2), (x^4 + 3*x^2 + 6*x + 6), (x^4 +
    2*x^3 + 6*x + 4), (x^4 + 5*x^3 + 2*x^2 + 3), (x^4 + x + 2), (x^4 + 2*x^2 + 
    3*x + 6), (x^4 + 2*x^3 + 5*x^2 + 6*x + 4), (x^4 + 6*x^3 + 3*x^2 + x + 5), 
(x^4 + 6*x^3 + 3*x + 2), (x^4 + 2*x^3 + 6), (x^4 + 5*x^3 + 4*x^2 + 2*x + 4), 
(x^4 + 3*x^3 + 2*x^2 + 2*x + 5), (x^4 + 5*x^3 + x^2 + 1), (x^4 + x^3 + x^2 + 6*x
    + 6), (x^4 + 3*x^3 + 2*x^2 + x + 4), (x^4 + 4*x^3 + 6*x^2 + 2*x + 5), (x^4 +
    4*x^3 + 2*x^2 + x + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:52:12 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
RandomPlace(F0,4)




Output: Magma V2.11-2     Fri Aug 27 2004 05:52:11 on modular  [Seed = 477255944]
   -------------------------------------

true (x^4 + 4*x^3 + 3*x^2 + 5*x + 3)

Total time: 1.250 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:53:16 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := D;
F<alpha> := FunctionField(y^2 - D);
Decomposition(F, pl)




Output: Magma V2.11-2     Fri Aug 27 2004 05:53:14 on modular  [Seed = 310138822]
   -------------------------------------


>> Decomposition(F, pl)
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFun, RngUPolElt[FldFin]

Total time: 1.210 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:53:46 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
Decomposition(F, pl)




Output: Magma V2.11-2     Fri Aug 27 2004 05:53:44 on modular  [Seed = 174346237]
   -------------------------------------


>> Decomposition(F, pl)
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFun, RngUPolElt[FldFin]

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:53:53 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
Decomposition(F, pl)




Output: Magma V2.11-2     Fri Aug 27 2004 05:53:52 on modular  [Seed = 40650733]
   -------------------------------------


>> Decomposition(F, pl)
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFun, RngUPolElt[FldFin]

Total time: 1.220 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:54:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
Place(F,4)





Output: Magma V2.11-2     Fri Aug 27 2004 05:54:58 on modular  [Seed = 962034836]
   -------------------------------------


>> Place(F,4)
        ^
Runtime error in 'Place': Bad argument types
Argument types given: FldFun, RngIntElt

Total time: 1.270 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:55:10 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
RandomPlace(F,4)





Output: Magma V2.11-2     Fri Aug 27 2004 05:55:09 on modular  [Seed = 828339347]
   -------------------------------------

true (x^4 + 3*x^3 + 5*x^2 + x + 6, alpha + 4*x^3 + 2*x^2 + 3*x + 1)

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:55:19 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
RandomPlace(F0,4)





Output: Magma V2.11-2     Fri Aug 27 2004 05:55:18 on modular  [Seed = 692546928]
   -------------------------------------

true (x^4 + 4*x^3 + 4*x^2 + 5*x + 2)

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:55:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
pl := RandomPlace(F0,4);
Decomposition(F,pl)





Output: Magma V2.11-2     Fri Aug 27 2004 05:55:46 on modular  [Seed = 558851420]
   -------------------------------------


>> Decomposition(F,pl)
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFun, BoolElt

Total time: 1.260 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:56:30 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
pl := (x^4 + 4*x^3 + 4*x^2 + 5*x + 2);
Decomposition(F,pl)





Output: Magma V2.11-2     Fri Aug 27 2004 05:56:29 on modular  [Seed = 3635846346]
   -------------------------------------


>> Decomposition(F,pl)
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFun, RngUPolElt[FldFin]

Total time: 1.220 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:56:54 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
pl := x^4 + 4*x^3 + 4*x^2 + 5*x + 2;
Decomposition(F,pl)





Output: Magma V2.11-2     Fri Aug 27 2004 05:56:53 on modular  [Seed = 3502150890]
   -------------------------------------


>> Decomposition(F,pl)
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFun, RngUPolElt[FldFin]

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:58:05 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
pl := x^4 + 4*x^3 + 4*x^2 + 5*x + 2;
Decomposition(F,$1[1])





Output: Magma V2.11-2     Fri Aug 27 2004 05:58:04 on modular  [Seed = 3349775156]
   -------------------------------------


>> Decomposition(F,$1[1])
                   ^
Runtime error: Previous value number (1) should be in the range [1 .. 0]

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:59:33 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F0,4);






Output: Magma V2.11-2     Fri Aug 27 2004 05:59:32 on modular  [Seed = 4254317222]
   -------------------------------------


Total time: 1.250 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:59:41 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F0,4);
pl





Output: Magma V2.11-2     Fri Aug 27 2004 05:59:40 on modular  [Seed = 4120621734]
   -------------------------------------

(x^4 + 2*x^3 + 3*x^2 + 4)

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 05:59:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F0,4);
pl





Output: Magma V2.11-2     Fri Aug 27 2004 05:59:46 on modular  [Seed = 3984829088]
   -------------------------------------

(x^4 + x^3 + 6*x^2 + 5*x + 3)

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 06:00:22 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);






Output: Magma V2.11-2     Fri Aug 27 2004 06:00:20 on modular  [Seed = 2397096421]
   -------------------------------------


Total time: 1.270 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 06:00:30 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
R<x> := PolynomialRing(GF(7));
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
pl





Output: Magma V2.11-2     Fri Aug 27 2004 06:00:28 on modular  [Seed = 2263400933]
   -------------------------------------

(x^4 + 5*x^3 + 3*x^2 + 3*x + 6, alpha + 3*x^2 + 2*x + 1)

Total time: 1.280 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 06:03:11 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);

D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
pl





Output: Magma V2.11-2     Fri Aug 27 2004 06:03:10 on modular  [Seed = 3167943485]
   -------------------------------------

(x^4 + 5*x^3 + x^2 + 4*x + 4, alpha + 4*x^3 + 5*x^2 + 2*x + 4)

Total time: 1.280 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 06:06:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
Decomposition(F,pl)





Output: Magma V2.11-2     Fri Aug 27 2004 06:06:54 on modular  [Seed = 2848452424]
   -------------------------------------


>> Decomposition(F,pl)
                ^
Runtime error in 'Decomposition': Arguments are not compatible

Total time: 1.439 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 06:08:12 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
Decomposition(F0,pl)





Output: Magma V2.11-2     Fri Aug 27 2004 06:08:11 on modular  [Seed = 1597052426]
   -------------------------------------


>> Decomposition(F0,pl)
                ^
Runtime error in 'Decomposition': Arguments are not compatible

Total time: 1.260 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:39:37 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
pl





Output: Magma V2.11-2     Fri Aug 27 2004 08:39:32 on modular  [Seed = 2196564071]
   -------------------------------------

(x^4 + 3*x^3 + 3*x^2 + x + 1, alpha + 2*x^3 + 4*x^2 + 2*x + 1)

Total time: 1.399 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:41:18 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
SClassGroup(pl)





Output: Magma V2.11-2     Fri Aug 27 2004 08:41:16 on modular  [Seed = 2666591250]
   -------------------------------------


>> SClassGroup(pl)
              ^
Runtime error in 'SClassGroup': Bad argument types
Argument types given: PlcFunElt

Total time: 1.260 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:45:32 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:45:30 on modular  [Seed = 1745225186]
   -------------------------------------

Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0 given by a rule

Total time: 1.560 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:45:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
print(pl);
SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:45:45 on modular  [Seed = 1881021929]
   -------------------------------------

(x^4 + 3*x^2 + 5*x + 2, alpha + 6*x^3 + 6*x^2 + 2*x + 3)
Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.569 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:46:08 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
print(pl);
SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:46:06 on modular  [Seed = 2031555863]
   -------------------------------------

(x^4 + x^3 + 6*x^2 + 2*x + 6, alpha + x^3 + x^2 + 4)
Abelian Group isomorphic to Z/4 + Z/12
Defined on 2 generators
Relations:
    4*$.1 = 0
    12*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/4 + Z/12
Defined on 2 generators
Relations:
    4*$.1 = 0
    12*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/4 + Z/12
Defined on 2 generators
Relations:
    4*$.1 = 0
    12*$.2 = 0 given by a rule

Total time: 1.550 seconds, Total memory usage: 13.17MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:46:14 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
print(pl);
SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:46:12 on modular  [Seed = 1093610805]
   -------------------------------------

(x^4 + 4*x^3 + 6*x^2 + 5*x + 3, alpha + 2*x^3 + 2*x^2 + 3*x + 6)
Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.589 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:46:49 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
IsPlace(pl)
print(pl);
SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:46:47 on modular  [Seed = 1227302174]
   -------------------------------------


>> print(pl);
   ^
User error: bad syntax
Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0 given by a rule

Total time: 1.599 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:46:58 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
IsPlace(pl);
print(pl);
SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:46:57 on modular  [Seed = 1363098992]
   -------------------------------------


>> IsPlace(pl);
   ^
User error: Identifier 'IsPlace' has not been declared or assigned
(x^4 + 5*x^3 + x^2 + x + 5, alpha + x^3 + 6*x^2 + 5)
Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/48
Defined on 1 generator
Relations:
    48*$.1 = 0 given by a rule

Total time: 1.560 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:47:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);

* print(pl);
* SClassGroup({pl})





Output: Magma V2.11-2     Fri Aug 27 2004 08:47:46 on modular  [Seed = 542002226]
   -------------------------------------


>> * print(pl);
   ^
User error: bad syntax

>> * SClassGroup({pl})
   ^
User error: bad syntax

Total time: 1.250 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:47:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);

% print(pl);
%* SClassGroup({pl})





Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:49:43 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
pl := (x^4 + x+ 2);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
print(pl);
Ideal(pl)

Output: Magma V2.11-2     Fri Aug 27 2004 08:49:41 on modular  [Seed = 828333492]
   -------------------------------------

(x^4 + 3*x^3 + x^2 + 6, alpha + 3*x^2 + 4*x + 1)
Prime Ideal of Maximal Equation Order of F over Univariate Polynomial Ring in x 
over GF(7)
Generators:
x^4 + 3*x^3 + x^2 + 6
alpha + 3*x^2 + 4*x + 1

Total time: 1.260 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:54:01 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
pl := (x^4 + x + 2, alpha);
Ideal(pl)

Output: Magma V2.11-2     Fri Aug 27 2004 08:53:59 on modular  [Seed = 1012028347]
   -------------------------------------


>> pl := (x^4 + x + 2, alpha);
         ^
Runtime error in elt< ... >: Bad arguments
Prime Ideal of Maximal Equation Order of F over Univariate Polynomial Ring in x 
over GF(7)
Generators:
x^4 + 3*x^3 + 5*x^2 + 2*x + 1
alpha + 2*x^3 + 5*x^2 + 5*x + 3

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:56:19 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
Zeros(alpha)

Output: Magma V2.11-2     Fri Aug 27 2004 08:56:18 on modular  [Seed = 174351384]
   -------------------------------------

[ (x^4 + x + 2, alpha) ]

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:56:37 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
Poles(alpha)

Output: Magma V2.11-2     Fri Aug 27 2004 08:56:36 on modular  [Seed = 310148342]
   -------------------------------------

[ (1/x, 1/x^2*alpha + (x + 1)/x), (1/x, 1/x^2*alpha + (6*x + 1)/x) ]

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:58:13 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
Place((D, alpha))

Output: Magma V2.11-2     Fri Aug 27 2004 08:58:12 on modular  [Seed = 477262488]
   -------------------------------------


>> Place((D, alpha));
         ^
Runtime error in elt< ... >: Bad arguments

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 08:58:26 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
_, pl := RandomPlace(F,4);
Place(alpha)

Output: Magma V2.11-2     Fri Aug 27 2004 08:58:25 on modular  [Seed = 3834284661]
   -------------------------------------


>> Place(alpha);
        ^
Runtime error in 'Place': Bad argument types
Argument types given: FldFunElt

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:00:24 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
Factorization(alpha*O)

Output: Magma V2.11-2     Fri Aug 27 2004 09:00:23 on modular  [Seed = 3232674247]
   -------------------------------------

[ <Prime Ideal of O
Generators:
x^4 + x + 2
alpha, 1> ]

Total time: 1.280 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:00:58 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
L[1]

Output: Magma V2.11-2     Fri Aug 27 2004 09:00:57 on modular  [Seed = 3399793443]
   -------------------------------------

<Prime Ideal of O
Generators:
x^4 + x + 2
alpha, 1>

Total time: 1.260 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:01:07 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
L[2]

Output: Magma V2.11-2     Fri Aug 27 2004 09:01:06 on modular  [Seed = 3569001766]
   -------------------------------------


>> L[2];
    ^
Runtime error in '[]': Sequence element 2 not defined

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:01:36 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
L[1]

Output: Magma V2.11-2     Fri Aug 27 2004 09:01:35 on modular  [Seed = 3719539730]
   -------------------------------------

<Prime Ideal of O
Generators:
x^4 + x + 2
alpha, 1>

Total time: 1.290 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:01:52 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
L[1][1]

Output: Magma V2.11-2     Fri Aug 27 2004 09:01:51 on modular  [Seed = 2781598842]
   -------------------------------------

Prime Ideal of O
Generators:
x^4 + x + 2
alpha

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:02:11 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F0 := FunctionField(y);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
Place(I)

Output: Magma V2.11-2     Fri Aug 27 2004 09:02:10 on modular  [Seed = 2915294239]
   -------------------------------------

(x^4 + x + 2, alpha)

Total time: 1.230 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:02:46 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup(pl)

Output: Magma V2.11-2     Fri Aug 27 2004 09:02:45 on modular  [Seed = 3051078688]
   -------------------------------------


>> SClassGroup(pl);
              ^
Runtime error in 'SClassGroup': Bad argument types
Argument types given: PlcFunElt

Total time: 1.240 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:02:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 09:02:58 on modular  [Seed = 2179985891]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.589 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:05:57 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - 3*D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 09:05:56 on modular  [Seed = 2397109850]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/8
Defined on 2 generators
Relations:
    2*$.1 = 0
    8*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/8
Defined on 2 generators
Relations:
    2*$.1 = 0
    8*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/8
Defined on 2 generators
Relations:
    2*$.1 = 0
    8*$.2 = 0 given by a rule

Total time: 1.389 seconds, Total memory usage: 12.97MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 09:06:02 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - 3*D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 09:06:00 on modular  [Seed = 2532894286]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/8
Defined on 2 generators
Relations:
    2*$.1 = 0
    8*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/8
Defined on 2 generators
Relations:
    2*$.1 = 0
    8*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/8
Defined on 2 generators
Relations:
    2*$.1 = 0
    8*$.2 = 0 given by a rule

Total time: 1.409 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:01:19 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;
SetOfMonomials;

Output: Magma V2.11-2     Fri Aug 27 2004 10:01:19 on modular  [Seed = 4204037430]
   -------------------------------------

{
    y*u,
    x^2*y*v,
    x*B^2,
    x^7*B,
    x*y^3*B,
    y^2*B/x,
    y^5/x,
    x^4*y^2,
    x*y^2*u,
    y*B^2,
    x*y,
    x^2*A,
    y*v,
    y^5/x^2,
    x^5*B,
    x^11,
    x^2*u*B,
    x^5*y^3,
    x^2*y^2,
    x*y^2*v,
    y^5/x^3,
    x^6*y*B,
    A,
    y^4*B,
    x^2*u^2,
    x^3*B,
    x^9,
    u*B,
    x^3*y^3,
    x^6*u,
    x^2*v*B,
    y^3*u,
    y^2,
    x*y*A,
    y^4*B/x,
    x^4*y*B,
    u^2,
    x^10*y,
    y^9/x^6,
    x*y*u*B,
    x^4*y^4,
    y^3*u/x,
    x*B,
    B^3,
    x^7,
    x*y^3,
    x^4*u,
    y^2/x,
    v*B,
    x^6*v,
    y^3*v,
    y^4*B/x^2,
    y^7/x^2,
    y^3*u/x^2,
    x^2*y*B,
    x^8*y,
    x^2*y^4,
    x^5*y*u,
    y^3*v/x,
    x^5,
    x^4*B^2,
    x^2*u,
    y^7/x^3,
    x^4*v,
    y^6/x^4,
    x*u*v,
    x^3*y^2*B,
    y^3*B^2/x^2,
    y*B,
    y^3*v/x^2,
    x^6*y,
    y^4,
    x^3*y*u,
    y^2*A/x,
    x^3,
    x^2*B^2,
    u,
    x^2*v,
    y^2*u*B/x,
    x*y^2*B,
    x^7*y^2,
    x*y^5,
    y^4/x,
    x^4*y,
    x*y*u,
    x^3*y*v,
    B^2,
    x,
    x^8*B,
    x^2*y^3*B,
    v,
    y^4/x^2,
    x^5*y^2,
    x^2*y^2*u,
    y^8/x^4,
    x^2*y,
    x^3*A,
    x*y*v,
    y^5*u/x^3,
    x^6*B,
    y^3*B,
    x^12,
    x^3*u*B,
    x^6*y^3,
    y^6*B/x^4,
    y^6,
    y^8/x^5,
    x^3*y^2,
    y^2*u,
    x^2*y^2*v,
    x*y*B^2,
    y,
    x*A,
    y^3*B/x,
    y^6/x,
    x^4*B,
    x^10,
    x*u*B,
    x^4*y^3,
    x^7*u,
    x*y^3*u,
    y^2*u/x,
    x*y^2,
    y^2*B^2,
    y^2*v,
    y^3*B/x^2,
    y^6/x^2,
    x^5*y*B,
    x*u^2,
    x^2*B,
    x^8,
    x^2*y^3,
    y^2*B^2/x,
    x*v*B,
    x^5*u,
    y^2*v/x,
    y^6/x^3,
    y*A,
    x^3*y*B,
    x^9*y,
    y*u*B,
    x^3*y^4,
    B,
    x^6,
    y^3,
    x^3*u,
    x^5*v,
    x^4*y^2*B,
    y*u^2,
    y^4*u/x,
    x*y*B,
    x^7*y,
    x*y^4,
    x^4*y*u,
    y^3/x,
    y*v*B,
    y^5*B/x^2,
    x^4,
    x*u,
    x^3*v,
    u*v,
    x^2*y^2*B,
    y^4*u/x^2,
    x^8*y^2,
    x^2*y^5,
    y^3/x^2,
    x^5*y,
    y^5*B/x^3,
    x^2*y*u,
    y^7/x^4,
    x^4*y*v,
    x^2,
    x^3*B^2,
    x*v,
    v^2,
    y^2*B,
    x^6*y^2,
    y^4*v/x^2,
    y^5,
    x^3*y^2*u,
    x^3*y,
    x^2*y*B^2
}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:06:52 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
for i in I do
if IsDivisibleBy(i,m) then
Exclude(~I,i);
Include(~I,m);
end if;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:06:51 on modular  [Seed = 3483480407]
   -------------------------------------

{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:07:07 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
for i in I do
if IsDivisibleBy(i,m) then
Exclude(~I,i);
Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:07:07 on modular  [Seed = 3619280575]
   -------------------------------------

{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:07:43 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
for j in I do
if I:={} then I:={m};
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:07:42 on modular  [Seed = 3719552144]
   -------------------------------------


>> if I:={} then I:={m};
       ^
User error: bad syntax

>> if IsDivisibleBy(j,m) then
                    ^
User error: Identifier 'j' has not been declared or assigned
{}

>> end for;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:07:59 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
for j in I do
if I eq {} then I:={m};
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:07:59 on modular  [Seed = 2764744184]
   -------------------------------------


>> end for;
       ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:08:38 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
for j in I do
if I eq {} then
I:={m};
end if;
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:08:37 on modular  [Seed = 2984226999]
   -------------------------------------

{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:09:03 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
m;
for j in I do
if I eq {} then
I:={m};
end if;
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:09:03 on modular  [Seed = 3117922469]
   -------------------------------------

y*u
x^2*y*v
x*B^2
x^7*B
x*y^3*B
y^2*B/x
y^5/x
x^4*y^2
x*y^2*u
y*B^2
x*y
x^2*A
y*v
y^5/x^2
x^5*B
x^11
x^2*u*B
x^5*y^3
x^2*y^2
x*y^2*v
y^5/x^3
x^6*y*B
A
y^4*B
x^2*u^2
x^3*B
x^9
u*B
x^3*y^3
x^6*u
x^2*v*B
y^3*u
y^2
x*y*A
y^4*B/x
x^4*y*B
u^2
x^10*y
y^9/x^6
x*y*u*B
x^4*y^4
y^3*u/x
x*B
B^3
x^7
x*y^3
x^4*u
y^2/x
v*B
x^6*v
y^3*v
y^4*B/x^2
y^7/x^2
y^3*u/x^2
x^2*y*B
x^8*y
x^2*y^4
x^5*y*u
y^3*v/x
x^5
x^4*B^2
x^2*u
y^7/x^3
x^4*v
y^6/x^4
x*u*v
x^3*y^2*B
y^3*B^2/x^2
y*B
y^3*v/x^2
x^6*y
y^4
x^3*y*u
y^2*A/x
x^3
x^2*B^2
u
x^2*v
y^2*u*B/x
x*y^2*B
x^7*y^2
x*y^5
y^4/x
x^4*y
x*y*u
x^3*y*v
B^2
x
x^8*B
x^2*y^3*B
v
y^4/x^2
x^5*y^2
x^2*y^2*u
y^8/x^4
x^2*y
x^3*A
x*y*v
y^5*u/x^3
x^6*B
y^3*B
x^12
x^3*u*B
x^6*y^3
y^6*B/x^4
y^6
y^8/x^5
x^3*y^2
y^2*u
x^2*y^2*v
x*y*B^2
y
x*A
y^3*B/x
y^6/x
x^4*B
x^10
x*u*B
x^4*y^3
x^7*u
x*y^3*u
y^2*u/x
x*y^2
y^2*B^2
y^2*v
y^3*B/x^2
y^6/x^2
x^5*y*B
x*u^2
x^2*B
x^8
x^2*y^3
y^2*B^2/x
x*v*B
x^5*u
y^2*v/x
y^6/x^3
y*A
x^3*y*B
x^9*y
y*u*B
x^3*y^4
B
x^6
y^3
x^3*u
x^5*v
x^4*y^2*B
y*u^2
y^4*u/x
x*y*B
x^7*y
x*y^4
x^4*y*u
y^3/x
y*v*B
y^5*B/x^2
x^4
x*u
x^3*v
u*v
x^2*y^2*B
y^4*u/x^2
x^8*y^2
x^2*y^5
y^3/x^2
x^5*y
y^5*B/x^3
x^2*y*u
y^7/x^4
x^4*y*v
x^2
x^3*B^2
x*v
v^2
y^2*B
x^6*y^2
y^4*v/x^2
y^5
x^3*y^2*u
x^3*y
x^2*y*B^2
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:09:21 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
m;
for j in I do
if I={} then
I:={m};
end if;
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:09:20 on modular  [Seed = 2163114355]
   -------------------------------------

y*u
x^2*y*v
x*B^2
x^7*B
x*y^3*B
y^2*B/x
y^5/x
x^4*y^2
x*y^2*u
y*B^2
x*y
x^2*A
y*v
y^5/x^2
x^5*B
x^11
x^2*u*B
x^5*y^3
x^2*y^2
x*y^2*v
y^5/x^3
x^6*y*B
A
y^4*B
x^2*u^2
x^3*B
x^9
u*B
x^3*y^3
x^6*u
x^2*v*B
y^3*u
y^2
x*y*A
y^4*B/x
x^4*y*B
u^2
x^10*y
y^9/x^6
x*y*u*B
x^4*y^4
y^3*u/x
x*B
B^3
x^7
x*y^3
x^4*u
y^2/x
v*B
x^6*v
y^3*v
y^4*B/x^2
y^7/x^2
y^3*u/x^2
x^2*y*B
x^8*y
x^2*y^4
x^5*y*u
y^3*v/x
x^5
x^4*B^2
x^2*u
y^7/x^3
x^4*v
y^6/x^4
x*u*v
x^3*y^2*B
y^3*B^2/x^2
y*B
y^3*v/x^2
x^6*y
y^4
x^3*y*u
y^2*A/x
x^3
x^2*B^2
u
x^2*v
y^2*u*B/x
x*y^2*B
x^7*y^2
x*y^5
y^4/x
x^4*y
x*y*u
x^3*y*v
B^2
x
x^8*B
x^2*y^3*B
v
y^4/x^2
x^5*y^2
x^2*y^2*u
y^8/x^4
x^2*y
x^3*A
x*y*v
y^5*u/x^3
x^6*B
y^3*B
x^12
x^3*u*B
x^6*y^3
y^6*B/x^4
y^6
y^8/x^5
x^3*y^2
y^2*u
x^2*y^2*v
x*y*B^2
y
x*A
y^3*B/x
y^6/x
x^4*B
x^10
x*u*B
x^4*y^3
x^7*u
x*y^3*u
y^2*u/x
x*y^2
y^2*B^2
y^2*v
y^3*B/x^2
y^6/x^2
x^5*y*B
x*u^2
x^2*B
x^8
x^2*y^3
y^2*B^2/x
x*v*B
x^5*u
y^2*v/x
y^6/x^3
y*A
x^3*y*B
x^9*y
y*u*B
x^3*y^4
B
x^6
y^3
x^3*u
x^5*v
x^4*y^2*B
y*u^2
y^4*u/x
x*y*B
x^7*y
x*y^4
x^4*y*u
y^3/x
y*v*B
y^5*B/x^2
x^4
x*u
x^3*v
u*v
x^2*y^2*B
y^4*u/x^2
x^8*y^2
x^2*y^5
y^3/x^2
x^5*y
y^5*B/x^3
x^2*y*u
y^7/x^4
x^4*y*v
x^2
x^3*B^2
x*v
v^2
y^2*B
x^6*y^2
y^4*v/x^2
y^5
x^3*y^2*u
x^3*y
x^2*y*B^2
{}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:09:54 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
if I={} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:09:54 on modular  [Seed = 2397081439]
   -------------------------------------


>> if I={} then
   ^
Runtime error in if: Logical expected
{}

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:10:09 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
if I=={} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:10:08 on modular  [Seed = 2616564280]
   -------------------------------------


>> if I=={} then
        ^
User error: bad syntax

>> I:={m};
       ^
User error: Identifier 'm' has not been declared or assigned

>> end if;
   ^
User error: bad syntax

>> if IsDivisibleBy(j,m) then
                      ^
User error: Identifier 'm' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:10:25 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
if I eq {} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:10:24 on modular  [Seed = 1644979152]
   -------------------------------------

{
    x^2*y*B^2
}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:10:54 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
if I eq {} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:10:54 on modular  [Seed = 1778674662]
   -------------------------------------

{
    y*u
}
{
    x^2*y*v
}
{
    x*B^2
}
{
    x^7*B
}
{
    x*y^3*B
}
{
    y^2*B/x
}
{
    y^5/x
}
{
    x^4*y^2
}
{
    x*y^2*u
}
{
    y*B^2
}
{
    x*y
}
{
    x^2*A
}
{
    y*v
}
{
    y^5/x^2
}
{
    x^5*B
}
{
    x^11
}
{
    x^2*u*B
}
{
    x^5*y^3
}
{
    x^2*y^2
}
{
    x*y^2*v
}
{
    y^5/x^3
}
{
    x^6*y*B
}
{
    A
}
{
    y^4*B
}
{
    x^2*u^2
}
{
    x^3*B
}
{
    x^9
}
{
    u*B
}
{
    x^3*y^3
}
{
    x^6*u
}
{
    x^2*v*B
}
{
    y^3*u
}
{
    y^2
}
{
    x*y*A
}
{
    y^4*B/x
}
{
    x^4*y*B
}
{
    u^2
}
{
    x^10*y
}
{
    y^9/x^6
}
{
    x*y*u*B
}
{
    x^4*y^4
}
{
    y^3*u/x
}
{
    x*B
}
{
    B^3
}
{
    x^7
}
{
    x*y^3
}
{
    x^4*u
}
{
    y^2/x
}
{
    v*B
}
{
    x^6*v
}
{
    y^3*v
}
{
    y^4*B/x^2
}
{
    y^7/x^2
}
{
    y^3*u/x^2
}
{
    x^2*y*B
}
{
    x^8*y
}
{
    x^2*y^4
}
{
    x^5*y*u
}
{
    y^3*v/x
}
{
    x^5
}
{
    x^4*B^2
}
{
    x^2*u
}
{
    y^7/x^3
}
{
    x^4*v
}
{
    y^6/x^4
}
{
    x*u*v
}
{
    x^3*y^2*B
}
{
    y^3*B^2/x^2
}
{
    y*B
}
{
    y^3*v/x^2
}
{
    x^6*y
}
{
    y^4
}
{
    x^3*y*u
}
{
    y^2*A/x
}
{
    x^3
}
{
    x^2*B^2
}
{
    u
}
{
    x^2*v
}
{
    y^2*u*B/x
}
{
    x*y^2*B
}
{
    x^7*y^2
}
{
    x*y^5
}
{
    y^4/x
}
{
    x^4*y
}
{
    x*y*u
}
{
    x^3*y*v
}
{
    B^2
}
{
    x
}
{
    x^8*B
}
{
    x^2*y^3*B
}
{
    v
}
{
    y^4/x^2
}
{
    x^5*y^2
}
{
    x^2*y^2*u
}
{
    y^8/x^4
}
{
    x^2*y
}
{
    x^3*A
}
{
    x*y*v
}
{
    y^5*u/x^3
}
{
    x^6*B
}
{
    y^3*B
}
{
    x^12
}
{
    x^3*u*B
}
{
    x^6*y^3
}
{
    y^6*B/x^4
}
{
    y^6
}
{
    y^8/x^5
}
{
    x^3*y^2
}
{
    y^2*u
}
{
    x^2*y^2*v
}
{
    x*y*B^2
}
{
    y
}
{
    x*A
}
{
    y^3*B/x
}
{
    y^6/x
}
{
    x^4*B
}
{
    x^10
}
{
    x*u*B
}
{
    x^4*y^3
}
{
    x^7*u
}
{
    x*y^3*u
}
{
    y^2*u/x
}
{
    x*y^2
}
{
    y^2*B^2
}
{
    y^2*v
}
{
    y^3*B/x^2
}
{
    y^6/x^2
}
{
    x^5*y*B
}
{
    x*u^2
}
{
    x^2*B
}
{
    x^8
}
{
    x^2*y^3
}
{
    y^2*B^2/x
}
{
    x*v*B
}
{
    x^5*u
}
{
    y^2*v/x
}
{
    y^6/x^3
}
{
    y*A
}
{
    x^3*y*B
}
{
    x^9*y
}
{
    y*u*B
}
{
    x^3*y^4
}
{
    B
}
{
    x^6
}
{
    y^3
}
{
    x^3*u
}
{
    x^5*v
}
{
    x^4*y^2*B
}
{
    y*u^2
}
{
    y^4*u/x
}
{
    x*y*B
}
{
    x^7*y
}
{
    x*y^4
}
{
    x^4*y*u
}
{
    y^3/x
}
{
    y*v*B
}
{
    y^5*B/x^2
}
{
    x^4
}
{
    x*u
}
{
    x^3*v
}
{
    u*v
}
{
    x^2*y^2*B
}
{
    y^4*u/x^2
}
{
    x^8*y^2
}
{
    x^2*y^5
}
{
    y^3/x^2
}
{
    x^5*y
}
{
    y^5*B/x^3
}
{
    x^2*y*u
}
{
    y^7/x^4
}
{
    x^4*y*v
}
{
    x^2
}
{
    x^3*B^2
}
{
    x*v
}
{
    v^2
}
{
    y^2*B
}
{
    x^6*y^2
}
{
    y^4*v/x^2
}
{
    y^5
}
{
    x^3*y^2*u
}
{
    x^3*y
}
{
    x^2*y*B^2
}
{
    x^2*y*B^2
}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:11:22 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={@@};
for m in SetOfMonomials do
if I eq {@@} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:11:21 on modular  [Seed = 1914466841]
   -------------------------------------

{
    y*u
}
{
    x^2*y*v
}
{
    x*B^2
}
{
    x^7*B
}
{
    x*y^3*B
}
{
    y^2*B/x
}
{
    y^5/x
}
{
    x^4*y^2
}
{
    x*y^2*u
}
{
    y*B^2
}
{
    x*y
}
{
    x^2*A
}
{
    y*v
}
{
    y^5/x^2
}
{
    x^5*B
}
{
    x^11
}
{
    x^2*u*B
}
{
    x^5*y^3
}
{
    x^2*y^2
}
{
    x*y^2*v
}
{
    y^5/x^3
}
{
    x^6*y*B
}
{
    A
}
{
    y^4*B
}
{
    x^2*u^2
}
{
    x^3*B
}
{
    x^9
}
{
    u*B
}
{
    x^3*y^3
}
{
    x^6*u
}
{
    x^2*v*B
}
{
    y^3*u
}
{
    y^2
}
{
    x*y*A
}
{
    y^4*B/x
}
{
    x^4*y*B
}
{
    u^2
}
{
    x^10*y
}
{
    y^9/x^6
}
{
    x*y*u*B
}
{
    x^4*y^4
}
{
    y^3*u/x
}
{
    x*B
}
{
    B^3
}
{
    x^7
}
{
    x*y^3
}
{
    x^4*u
}
{
    y^2/x
}
{
    v*B
}
{
    x^6*v
}
{
    y^3*v
}
{
    y^4*B/x^2
}
{
    y^7/x^2
}
{
    y^3*u/x^2
}
{
    x^2*y*B
}
{
    x^8*y
}
{
    x^2*y^4
}
{
    x^5*y*u
}
{
    y^3*v/x
}
{
    x^5
}
{
    x^4*B^2
}
{
    x^2*u
}
{
    y^7/x^3
}
{
    x^4*v
}
{
    y^6/x^4
}
{
    x*u*v
}
{
    x^3*y^2*B
}
{
    y^3*B^2/x^2
}
{
    y*B
}
{
    y^3*v/x^2
}
{
    x^6*y
}
{
    y^4
}
{
    x^3*y*u
}
{
    y^2*A/x
}
{
    x^3
}
{
    x^2*B^2
}
{
    u
}
{
    x^2*v
}
{
    y^2*u*B/x
}
{
    x*y^2*B
}
{
    x^7*y^2
}
{
    x*y^5
}
{
    y^4/x
}
{
    x^4*y
}
{
    x*y*u
}
{
    x^3*y*v
}
{
    B^2
}
{
    x
}
{
    x^8*B
}
{
    x^2*y^3*B
}
{
    v
}
{
    y^4/x^2
}
{
    x^5*y^2
}
{
    x^2*y^2*u
}
{
    y^8/x^4
}
{
    x^2*y
}
{
    x^3*A
}
{
    x*y*v
}
{
    y^5*u/x^3
}
{
    x^6*B
}
{
    y^3*B
}
{
    x^12
}
{
    x^3*u*B
}
{
    x^6*y^3
}
{
    y^6*B/x^4
}
{
    y^6
}
{
    y^8/x^5
}
{
    x^3*y^2
}
{
    y^2*u
}
{
    x^2*y^2*v
}
{
    x*y*B^2
}
{
    y
}
{
    x*A
}
{
    y^3*B/x
}
{
    y^6/x
}
{
    x^4*B
}
{
    x^10
}
{
    x*u*B
}
{
    x^4*y^3
}
{
    x^7*u
}
{
    x*y^3*u
}
{
    y^2*u/x
}
{
    x*y^2
}
{
    y^2*B^2
}
{
    y^2*v
}
{
    y^3*B/x^2
}
{
    y^6/x^2
}
{
    x^5*y*B
}
{
    x*u^2
}
{
    x^2*B
}
{
    x^8
}
{
    x^2*y^3
}
{
    y^2*B^2/x
}
{
    x*v*B
}
{
    x^5*u
}
{
    y^2*v/x
}
{
    y^6/x^3
}
{
    y*A
}
{
    x^3*y*B
}
{
    x^9*y
}
{
    y*u*B
}
{
    x^3*y^4
}
{
    B
}
{
    x^6
}
{
    y^3
}
{
    x^3*u
}
{
    x^5*v
}
{
    x^4*y^2*B
}
{
    y*u^2
}
{
    y^4*u/x
}
{
    x*y*B
}
{
    x^7*y
}
{
    x*y^4
}
{
    x^4*y*u
}
{
    y^3/x
}
{
    y*v*B
}
{
    y^5*B/x^2
}
{
    x^4
}
{
    x*u
}
{
    x^3*v
}
{
    u*v
}
{
    x^2*y^2*B
}
{
    y^4*u/x^2
}
{
    x^8*y^2
}
{
    x^2*y^5
}
{
    y^3/x^2
}
{
    x^5*y
}
{
    y^5*B/x^3
}
{
    x^2*y*u
}
{
    y^7/x^4
}
{
    x^4*y*v
}
{
    x^2
}
{
    x^3*B^2
}
{
    x*v
}
{
    v^2
}
{
    y^2*B
}
{
    x^6*y^2
}
{
    y^4*v/x^2
}
{
    y^5
}
{
    x^3*y^2*u
}
{
    x^3*y
}
{
    x^2*y*B^2
}
{
    x^2*y*B^2
}

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 10:11:26 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroupAbelianInvariants({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 10:11:25 on modular  [Seed = 2048162325]
   -------------------------------------

[ 2, 24 ]

Total time: 1.500 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 10:12:15 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroupExactSequence({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 10:12:14 on modular  [Seed = 1076772892]
   -------------------------------------

Mapping from: Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0 to FldFun: F given by a rule
Mapping from: FldFun: F to Divisor group of F given by a rule
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.500 seconds, Total memory usage: 13.17MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:13:05 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={@@};
for m in SetOfMonomials do
if I eq {@@} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
else if IsDivisibleBy(m,j) then
else Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:13:04 on modular  [Seed = 1210468442]
   -------------------------------------


>> end for;
       ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
{@ @}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 10:13:30 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 10:13:28 on modular  [Seed = 1363104187]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.520 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:14:30 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={@@};
for m in SetOfMonomials do
if I eq {@@} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(~I,j);
Include(~I,m);
elif IsDivisibleBy(m,j) then
else Include(~I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:14:29 on modular  [Seed = 1580228345]
   -------------------------------------

{
    y*u
}
{
    x^2*y*v
}
{
    x*B^2
}
{
    x^7*B
}
{
    x*y^3*B
}
{
    y^2*B/x
}
{
    y^5/x
}
{
    x^4*y^2
}
{
    x*y^2*u
}
{
    y*B^2
}
{
    x*y
}
{
    x^2*A
}
{
    y*v
}
{
    y^5/x^2
}
{
    x^5*B
}
{
    x^11
}
{
    x^2*u*B
}
{
    x^5*y^3
}
{
    x^2*y^2
}
{
    x*y^2*v
}
{
    y^5/x^3
}
{
    x^6*y*B
}
{
    A
}
{
    y^4*B
}
{
    x^2*u^2
}
{
    x^3*B
}
{
    x^9
}
{
    u*B
}
{
    x^3*y^3
}
{
    x^6*u
}
{
    x^2*v*B
}
{
    y^3*u
}
{
    y^2
}
{
    x*y*A
}
{
    y^4*B/x
}
{
    x^4*y*B
}
{
    u^2
}
{
    x^10*y
}
{
    y^9/x^6
}
{
    x*y*u*B
}
{
    x^4*y^4
}
{
    y^3*u/x
}
{
    x*B
}
{
    B^3
}
{
    x^7
}
{
    x*y^3
}
{
    x^4*u
}
{
    y^2/x
}
{
    v*B
}
{
    x^6*v
}
{
    y^3*v
}
{
    y^4*B/x^2
}
{
    y^7/x^2
}
{
    y^3*u/x^2
}
{
    x^2*y*B
}
{
    x^8*y
}
{
    x^2*y^4
}
{
    x^5*y*u
}
{
    y^3*v/x
}
{
    x^5
}
{
    x^4*B^2
}
{
    x^2*u
}
{
    y^7/x^3
}
{
    x^4*v
}
{
    y^6/x^4
}
{
    x*u*v
}
{
    x^3*y^2*B
}
{
    y^3*B^2/x^2
}
{
    y*B
}
{
    y^3*v/x^2
}
{
    x^6*y
}
{
    y^4
}
{
    x^3*y*u
}
{
    y^2*A/x
}
{
    x^3
}
{
    x^2*B^2
}
{
    u
}
{
    x^2*v
}
{
    y^2*u*B/x
}
{
    x*y^2*B
}
{
    x^7*y^2
}
{
    x*y^5
}
{
    y^4/x
}
{
    x^4*y
}
{
    x*y*u
}
{
    x^3*y*v
}
{
    B^2
}
{
    x
}
{
    x^8*B
}
{
    x^2*y^3*B
}
{
    v
}
{
    y^4/x^2
}
{
    x^5*y^2
}
{
    x^2*y^2*u
}
{
    y^8/x^4
}
{
    x^2*y
}
{
    x^3*A
}
{
    x*y*v
}
{
    y^5*u/x^3
}
{
    x^6*B
}
{
    y^3*B
}
{
    x^12
}
{
    x^3*u*B
}
{
    x^6*y^3
}
{
    y^6*B/x^4
}
{
    y^6
}
{
    y^8/x^5
}
{
    x^3*y^2
}
{
    y^2*u
}
{
    x^2*y^2*v
}
{
    x*y*B^2
}
{
    y
}
{
    x*A
}
{
    y^3*B/x
}
{
    y^6/x
}
{
    x^4*B
}
{
    x^10
}
{
    x*u*B
}
{
    x^4*y^3
}
{
    x^7*u
}
{
    x*y^3*u
}
{
    y^2*u/x
}
{
    x*y^2
}
{
    y^2*B^2
}
{
    y^2*v
}
{
    y^3*B/x^2
}
{
    y^6/x^2
}
{
    x^5*y*B
}
{
    x*u^2
}
{
    x^2*B
}
{
    x^8
}
{
    x^2*y^3
}
{
    y^2*B^2/x
}
{
    x*v*B
}
{
    x^5*u
}
{
    y^2*v/x
}
{
    y^6/x^3
}
{
    y*A
}
{
    x^3*y*B
}
{
    x^9*y
}
{
    y*u*B
}
{
    x^3*y^4
}
{
    B
}
{
    x^6
}
{
    y^3
}
{
    x^3*u
}
{
    x^5*v
}
{
    x^4*y^2*B
}
{
    y*u^2
}
{
    y^4*u/x
}
{
    x*y*B
}
{
    x^7*y
}
{
    x*y^4
}
{
    x^4*y*u
}
{
    y^3/x
}
{
    y*v*B
}
{
    y^5*B/x^2
}
{
    x^4
}
{
    x*u
}
{
    x^3*v
}
{
    u*v
}
{
    x^2*y^2*B
}
{
    y^4*u/x^2
}
{
    x^8*y^2
}
{
    x^2*y^5
}
{
    y^3/x^2
}
{
    x^5*y
}
{
    y^5*B/x^3
}
{
    x^2*y*u
}
{
    y^7/x^4
}
{
    x^4*y*v
}
{
    x^2
}
{
    x^3*B^2
}
{
    x*v
}
{
    v^2
}
{
    y^2*B
}
{
    x^6*y^2
}
{
    y^4*v/x^2
}
{
    y^5
}
{
    x^3*y^2*u
}
{
    x^3*y
}
{
    x^2*y*B^2
}
{
    x^2*y*B^2
}

Total time: 0.590 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 10:14:45 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
ClassGroup({pl})

Output: Magma V2.11-2     Fri Aug 27 2004 10:14:44 on modular  [Seed = 642262672]
   -------------------------------------


>> ClassGroup({pl});
             ^
Runtime error in 'ClassGroup': Bad argument types
Argument types given: SetEnum[PlcFunElt]

Total time: 1.199 seconds, Total memory usage: 12.67MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:14:48 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={@@};
for m in SetOfMonomials do
if I eq {@@} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(I,j);
Include(I,m);
elif IsDivisibleBy(m,j) then
else Include(I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:14:47 on modular  [Seed = 792801178]
   -------------------------------------

{}
{
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*v
}
{
    y*u
}
{}
{
    y*u,
    x*B^2
}
{
    y*u
}
{}
{
    y*u,
    x^7*B
}
{
    y*u
}
{}
{
    y*u,
    x*y^3*B
}
{
    y*u
}
{}
{
    y*u,
    y^2*B/x
}
{
    y*u
}
{}
{
    y*u,
    y^5/x
}
{
    y*u
}
{}
{
    y*u,
    x^4*y^2
}
{
    y*u
}
{}
{
    y*u,
    x*y^2*u
}
{
    y*u
}
{}
{
    y*u,
    y*B^2
}
{
    y*u
}
{}
{
    y*u,
    x*y
}
{
    y*u
}
{}
{
    x^2*A,
    y*u
}
{
    y*u
}
{}
{
    y*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^5/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^5*B
}
{
    y*u
}
{}
{
    y*u,
    x^11
}
{
    y*u
}
{}
{
    y*u,
    x^2*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^5*y^3
}
{
    y*u
}
{}
{
    x^2*y^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x*y^2*v
}
{
    y*u
}
{}
{
    y*u,
    y^5/x^3
}
{
    y*u
}
{}
{
    x^6*y*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    A
}
{
    y*u
}
{}
{
    y*u,
    y^4*B
}
{
    y*u
}
{}
{
    x^2*u^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*B
}
{
    y*u
}
{}
{
    y*u,
    x^9
}
{
    y*u
}
{}
{
    y*u,
    u*B
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^3
}
{
    y*u
}
{}
{
    y*u,
    x^6*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*v*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*u
}
{
    y*u
}
{}
{
    y*u,
    y^2
}
{
    y*u
}
{}
{
    y*u,
    x*y*A
}
{
    y*u
}
{}
{
    y^4*B/x,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^4*y*B
}
{
    y*u
}
{}
{
    y*u,
    u^2
}
{
    y*u
}
{}
{
    y*u,
    x^10*y
}
{
    y*u
}
{}
{
    y*u,
    y^9/x^6
}
{
    y*u
}
{}
{
    x*y*u*B,
    y*u
}
{
    y*u
}
{}
{
    x^4*y^4,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3*u/x
}
{
    y*u
}
{}
{
    x*B,
    y*u
}
{
    y*u
}
{}
{
    B^3,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^7
}
{
    y*u
}
{}
{
    y*u,
    x*y^3
}
{
    y*u
}
{}
{
    y*u,
    x^4*u
}
{
    y*u
}
{}
{
    y*u,
    y^2/x
}
{
    y*u
}
{}
{
    y*u,
    v*B
}
{
    y*u
}
{}
{
    x^6*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3*v
}
{
    y*u
}
{}
{
    y*u,
    y^4*B/x^2
}
{
    y*u
}
{}
{
    y*u,
    y^7/x^2
}
{
    y*u
}
{}
{
    y*u,
    y^3*u/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*B
}
{
    y*u
}
{}
{
    x^8*y,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^4
}
{
    y*u
}
{}
{
    y*u,
    x^5*y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3*v/x
}
{
    y*u
}
{}
{
    y*u,
    x^5
}
{
    y*u
}
{}
{
    y*u,
    x^4*B^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*u
}
{
    y*u
}
{}
{
    y*u,
    y^7/x^3
}
{
    y*u
}
{}
{
    y*u,
    x^4*v
}
{
    y*u
}
{}
{
    y*u,
    y^6/x^4
}
{
    y*u
}
{}
{
    x*u*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*B^2/x^2
}
{
    y*u
}
{}
{
    y*u,
    y*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*v/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^6*y
}
{
    y*u
}
{}
{
    y*u,
    y^4
}
{
    y*u
}
{}
{
    x^3*y*u,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^2*A/x
}
{
    y*u
}
{}
{
    x^3,
    y*u
}
{
    y*u
}
{}
{
    x^2*B^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    u
}
{
    y*u
}
{}
{
    y*u,
    x^2*v
}
{
    y*u
}
{}
{
    y*u,
    y^2*u*B/x
}
{
    y*u
}
{}
{
    y*u,
    x*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    x^7*y^2
}
{
    y*u
}
{}
{
    y*u,
    x*y^5
}
{
    y*u
}
{}
{
    y*u,
    y^4/x
}
{
    y*u
}
{}
{
    y*u,
    x^4*y
}
{
    y*u
}
{}
{
    y*u,
    x*y*u
}
{
    y*u
}
{}
{
    x^3*y*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    B^2
}
{
    y*u
}
{}
{
    y*u,
    x
}
{
    y*u
}
{}
{
    y*u,
    x^8*B
}
{
    y*u
}
{}
{
    x^2*y^3*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    v
}
{
    y*u
}
{}
{
    y*u,
    y^4/x^2
}
{
    y*u
}
{}
{
    x^5*y^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^2*u
}
{
    y*u
}
{}
{
    y*u,
    y^8/x^4
}
{
    y*u
}
{}
{
    y*u,
    x^2*y
}
{
    y*u
}
{}
{
    y*u,
    x^3*A
}
{
    y*u
}
{}
{
    y*u,
    x*y*v
}
{
    y*u
}
{}
{
    y*u,
    y^5*u/x^3
}
{
    y*u
}
{}
{
    y*u,
    x^6*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*B
}
{
    y*u
}
{}
{
    y*u,
    x^12
}
{
    y*u
}
{}
{
    y*u,
    x^3*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^6*y^3
}
{
    y*u
}
{}
{
    y^6*B/x^4,
    y*u
}
{
    y*u
}
{}
{
    y^6,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^8/x^5
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^2
}
{
    y*u
}
{}
{
    y^2*u,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^2*v
}
{
    y*u
}
{}
{
    x*y*B^2,
    y*u
}
{
    y*u
}
{}
{
    y,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x*A
}
{
    y*u
}
{}
{
    y*u,
    y^3*B/x
}
{
    y*u
}
{}
{
    y*u,
    y^6/x
}
{
    y*u
}
{}
{
    y*u,
    x^4*B
}
{
    y*u
}
{}
{
    y*u,
    x^10
}
{
    y*u
}
{}
{
    y*u,
    x*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^4*y^3
}
{
    y*u
}
{}
{
    y*u,
    x^7*u
}
{
    y*u
}
{}
{
    y*u,
    x*y^3*u
}
{
    y*u
}
{}
{
    y*u,
    y^2*u/x
}
{
    y*u
}
{}
{
    y*u,
    x*y^2
}
{
    y*u
}
{}
{
    y*u,
    y^2*B^2
}
{
    y*u
}
{}
{
    y*u,
    y^2*v
}
{
    y*u
}
{}
{
    y*u,
    y^3*B/x^2
}
{
    y*u
}
{}
{
    y^6/x^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^5*y*B
}
{
    y*u
}
{}
{
    y*u,
    x*u^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*B
}
{
    y*u
}
{}
{
    y*u,
    x^8
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^3
}
{
    y*u
}
{}
{
    y*u,
    y^2*B^2/x
}
{
    y*u
}
{}
{
    x*v*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^5*u
}
{
    y*u
}
{}
{
    y*u,
    y^2*v/x
}
{
    y*u
}
{}
{
    y*u,
    y^6/x^3
}
{
    y*u
}
{}
{
    y*u,
    y*A
}
{
    y*u
}
{}
{
    x^3*y*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^9*y
}
{
    y*u
}
{}
{
    y*u,
    y*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^4
}
{
    y*u
}
{}
{
    y*u,
    B
}
{
    y*u
}
{}
{
    x^6,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3
}
{
    y*u
}
{}
{
    y*u,
    x^3*u
}
{
    y*u
}
{}
{
    y*u,
    x^5*v
}
{
    y*u
}
{}
{
    y*u,
    x^4*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    y*u^2
}
{
    y*u
}
{}
{
    y^4*u/x,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x*y*B
}
{
    y*u
}
{}
{
    y*u,
    x^7*y
}
{
    y*u
}
{}
{
    x*y^4,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^4*y*u
}
{
    y*u
}
{}
{
    y^3/x,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y*v*B
}
{
    y*u
}
{}
{
    y*u,
    y^5*B/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^4
}
{
    y*u
}
{}
{
    x*u,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*v
}
{
    y*u
}
{}
{
    y*u,
    u*v
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    y^4*u/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^8*y^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^5
}
{
    y*u
}
{}
{
    y*u,
    y^3/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^5*y
}
{
    y*u
}
{}
{
    y*u,
    y^5*B/x^3
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*u
}
{
    y*u
}
{}
{
    y^7/x^4,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^4*y*v
}
{
    y*u
}
{}
{
    y*u,
    x^2
}
{
    y*u
}
{}
{
    y*u,
    x^3*B^2
}
{
    y*u
}
{}
{
    y*u,
    x*v
}
{
    y*u
}
{}
{
    y*u,
    v^2
}
{
    y*u
}
{}
{
    y^2*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^6*y^2
}
{
    y*u
}
{}
{
    y*u,
    y^4*v/x^2
}
{
    y*u
}
{}
{
    y*u,
    y^5
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^2*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*y
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*B^2
}
{
    y*u
}
{
    y*u
}

Total time: 0.590 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Fri Aug 27 10:15:10 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
ClassGroup(F)

Output: Magma V2.11-2     Fri Aug 27 2004 10:15:09 on modular  [Seed = 878326971]
   -------------------------------------

Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
    12*$.1 = 0 given by a rule

Total time: 1.510 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:15:28 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
if I eq {} then
I:={m};
end if;
for j in I do
if IsDivisibleBy(j,m) then
Exclude(I,j);
Include(I,m);
elif IsDivisibleBy(m,j) then
else Include(I,m);
end if;
I;
end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:15:27 on modular  [Seed = 1012022433]
   -------------------------------------

{}
{
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*v
}
{
    y*u
}
{}
{
    y*u,
    x*B^2
}
{
    y*u
}
{}
{
    y*u,
    x^7*B
}
{
    y*u
}
{}
{
    y*u,
    x*y^3*B
}
{
    y*u
}
{}
{
    y*u,
    y^2*B/x
}
{
    y*u
}
{}
{
    y*u,
    y^5/x
}
{
    y*u
}
{}
{
    y*u,
    x^4*y^2
}
{
    y*u
}
{}
{
    y*u,
    x*y^2*u
}
{
    y*u
}
{}
{
    y*u,
    y*B^2
}
{
    y*u
}
{}
{
    y*u,
    x*y
}
{
    y*u
}
{}
{
    x^2*A,
    y*u
}
{
    y*u
}
{}
{
    y*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^5/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^5*B
}
{
    y*u
}
{}
{
    y*u,
    x^11
}
{
    y*u
}
{}
{
    y*u,
    x^2*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^5*y^3
}
{
    y*u
}
{}
{
    x^2*y^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x*y^2*v
}
{
    y*u
}
{}
{
    y*u,
    y^5/x^3
}
{
    y*u
}
{}
{
    x^6*y*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    A
}
{
    y*u
}
{}
{
    y*u,
    y^4*B
}
{
    y*u
}
{}
{
    x^2*u^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*B
}
{
    y*u
}
{}
{
    y*u,
    x^9
}
{
    y*u
}
{}
{
    y*u,
    u*B
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^3
}
{
    y*u
}
{}
{
    y*u,
    x^6*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*v*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*u
}
{
    y*u
}
{}
{
    y*u,
    y^2
}
{
    y*u
}
{}
{
    y*u,
    x*y*A
}
{
    y*u
}
{}
{
    y^4*B/x,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^4*y*B
}
{
    y*u
}
{}
{
    y*u,
    u^2
}
{
    y*u
}
{}
{
    y*u,
    x^10*y
}
{
    y*u
}
{}
{
    y*u,
    y^9/x^6
}
{
    y*u
}
{}
{
    x*y*u*B,
    y*u
}
{
    y*u
}
{}
{
    x^4*y^4,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3*u/x
}
{
    y*u
}
{}
{
    x*B,
    y*u
}
{
    y*u
}
{}
{
    B^3,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^7
}
{
    y*u
}
{}
{
    y*u,
    x*y^3
}
{
    y*u
}
{}
{
    y*u,
    x^4*u
}
{
    y*u
}
{}
{
    y*u,
    y^2/x
}
{
    y*u
}
{}
{
    y*u,
    v*B
}
{
    y*u
}
{}
{
    x^6*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3*v
}
{
    y*u
}
{}
{
    y*u,
    y^4*B/x^2
}
{
    y*u
}
{}
{
    y*u,
    y^7/x^2
}
{
    y*u
}
{}
{
    y*u,
    y^3*u/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*B
}
{
    y*u
}
{}
{
    x^8*y,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^4
}
{
    y*u
}
{}
{
    y*u,
    x^5*y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3*v/x
}
{
    y*u
}
{}
{
    y*u,
    x^5
}
{
    y*u
}
{}
{
    y*u,
    x^4*B^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*u
}
{
    y*u
}
{}
{
    y*u,
    y^7/x^3
}
{
    y*u
}
{}
{
    y*u,
    x^4*v
}
{
    y*u
}
{}
{
    y*u,
    y^6/x^4
}
{
    y*u
}
{}
{
    x*u*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*B^2/x^2
}
{
    y*u
}
{}
{
    y*u,
    y*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*v/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^6*y
}
{
    y*u
}
{}
{
    y*u,
    y^4
}
{
    y*u
}
{}
{
    x^3*y*u,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^2*A/x
}
{
    y*u
}
{}
{
    x^3,
    y*u
}
{
    y*u
}
{}
{
    x^2*B^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    u
}
{
    y*u
}
{}
{
    y*u,
    x^2*v
}
{
    y*u
}
{}
{
    y*u,
    y^2*u*B/x
}
{
    y*u
}
{}
{
    y*u,
    x*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    x^7*y^2
}
{
    y*u
}
{}
{
    y*u,
    x*y^5
}
{
    y*u
}
{}
{
    y*u,
    y^4/x
}
{
    y*u
}
{}
{
    y*u,
    x^4*y
}
{
    y*u
}
{}
{
    y*u,
    x*y*u
}
{
    y*u
}
{}
{
    x^3*y*v,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    B^2
}
{
    y*u
}
{}
{
    y*u,
    x
}
{
    y*u
}
{}
{
    y*u,
    x^8*B
}
{
    y*u
}
{}
{
    x^2*y^3*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    v
}
{
    y*u
}
{}
{
    y*u,
    y^4/x^2
}
{
    y*u
}
{}
{
    x^5*y^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^2*u
}
{
    y*u
}
{}
{
    y*u,
    y^8/x^4
}
{
    y*u
}
{}
{
    y*u,
    x^2*y
}
{
    y*u
}
{}
{
    y*u,
    x^3*A
}
{
    y*u
}
{}
{
    y*u,
    x*y*v
}
{
    y*u
}
{}
{
    y*u,
    y^5*u/x^3
}
{
    y*u
}
{}
{
    y*u,
    x^6*B
}
{
    y*u
}
{}
{
    y*u,
    y^3*B
}
{
    y*u
}
{}
{
    y*u,
    x^12
}
{
    y*u
}
{}
{
    y*u,
    x^3*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^6*y^3
}
{
    y*u
}
{}
{
    y^6*B/x^4,
    y*u
}
{
    y*u
}
{}
{
    y^6,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^8/x^5
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^2
}
{
    y*u
}
{}
{
    y^2*u,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^2*v
}
{
    y*u
}
{}
{
    x*y*B^2,
    y*u
}
{
    y*u
}
{}
{
    y,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x*A
}
{
    y*u
}
{}
{
    y*u,
    y^3*B/x
}
{
    y*u
}
{}
{
    y*u,
    y^6/x
}
{
    y*u
}
{}
{
    y*u,
    x^4*B
}
{
    y*u
}
{}
{
    y*u,
    x^10
}
{
    y*u
}
{}
{
    y*u,
    x*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^4*y^3
}
{
    y*u
}
{}
{
    y*u,
    x^7*u
}
{
    y*u
}
{}
{
    y*u,
    x*y^3*u
}
{
    y*u
}
{}
{
    y*u,
    y^2*u/x
}
{
    y*u
}
{}
{
    y*u,
    x*y^2
}
{
    y*u
}
{}
{
    y*u,
    y^2*B^2
}
{
    y*u
}
{}
{
    y*u,
    y^2*v
}
{
    y*u
}
{}
{
    y*u,
    y^3*B/x^2
}
{
    y*u
}
{}
{
    y^6/x^2,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^5*y*B
}
{
    y*u
}
{}
{
    y*u,
    x*u^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*B
}
{
    y*u
}
{}
{
    y*u,
    x^8
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^3
}
{
    y*u
}
{}
{
    y*u,
    y^2*B^2/x
}
{
    y*u
}
{}
{
    x*v*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^5*u
}
{
    y*u
}
{}
{
    y*u,
    y^2*v/x
}
{
    y*u
}
{}
{
    y*u,
    y^6/x^3
}
{
    y*u
}
{}
{
    y*u,
    y*A
}
{
    y*u
}
{}
{
    x^3*y*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^9*y
}
{
    y*u
}
{}
{
    y*u,
    y*u*B
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^4
}
{
    y*u
}
{}
{
    y*u,
    B
}
{
    y*u
}
{}
{
    x^6,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y^3
}
{
    y*u
}
{}
{
    y*u,
    x^3*u
}
{
    y*u
}
{}
{
    y*u,
    x^5*v
}
{
    y*u
}
{}
{
    y*u,
    x^4*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    y*u^2
}
{
    y*u
}
{}
{
    y^4*u/x,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x*y*B
}
{
    y*u
}
{}
{
    y*u,
    x^7*y
}
{
    y*u
}
{}
{
    x*y^4,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^4*y*u
}
{
    y*u
}
{}
{
    y^3/x,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    y*v*B
}
{
    y*u
}
{}
{
    y*u,
    y^5*B/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^4
}
{
    y*u
}
{}
{
    x*u,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*v
}
{
    y*u
}
{}
{
    y*u,
    u*v
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^2*B
}
{
    y*u
}
{}
{
    y*u,
    y^4*u/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^8*y^2
}
{
    y*u
}
{}
{
    y*u,
    x^2*y^5
}
{
    y*u
}
{}
{
    y*u,
    y^3/x^2
}
{
    y*u
}
{}
{
    y*u,
    x^5*y
}
{
    y*u
}
{}
{
    y*u,
    y^5*B/x^3
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*u
}
{
    y*u
}
{}
{
    y^7/x^4,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^4*y*v
}
{
    y*u
}
{}
{
    y*u,
    x^2
}
{
    y*u
}
{}
{
    y*u,
    x^3*B^2
}
{
    y*u
}
{}
{
    y*u,
    x*v
}
{
    y*u
}
{}
{
    y*u,
    v^2
}
{
    y*u
}
{}
{
    y^2*B,
    y*u
}
{
    y*u
}
{}
{
    y*u,
    x^6*y^2
}
{
    y*u
}
{}
{
    y*u,
    y^4*v/x^2
}
{
    y*u
}
{}
{
    y*u,
    y^5
}
{
    y*u
}
{}
{
    y*u,
    x^3*y^2*u
}
{
    y*u
}
{}
{
    y*u,
    x^3*y
}
{
    y*u
}
{}
{
    y*u,
    x^2*y*B^2
}
{
    y*u
}
{
    y*u
}

Total time: 0.610 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:20:00 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
	if I eq {} then
		I:={x^4*m};
	end if;
	for j in I do
		if IsDivisibleBy(j,x^4*m) then
			Exclude(I,j);
			Include(I,x^4*m);
		elif IsDivisibleBy(x^4*m,j) then
			// do nothing
		else Include(I,(x^4*m);
		end if;
	end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:19:59 on modular  [Seed = 224595808]
   -------------------------------------


>>                 else Include(I,(x^4*m);
                                         ^
User error: bad syntax

>>                 end if;
                   ^
User error: bad syntax

>>         end for;
           ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:20:33 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
	if I eq {} then
		I:={x^4*m};
	end if;
	for j in I do
		if IsDivisibleBy(j,x^4*m) then
			Exclude(I,j);
			Include(I,x^4*m);
		elif IsDivisibleBy(x^4*m,j) then
			// do nothing
		else
			Include(I,(x^4*m);
		end if;
	end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:20:32 on modular  [Seed = 3901156027]
   -------------------------------------


>>                         Include(I,(x^4*m);
                                            ^
User error: bad syntax

>>                 end if;
                   ^
User error: bad syntax

>>         end for;
           ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.580 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:21:40 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
	if I eq {} then
		I:={x^4*m};
	end if;
	for j in I do
		if IsDivisibleBy(j,x^4*m) then
			Exclude(I,j);
			Include(I,x^4*m);
		elif IsDivisibleBy(x^4*m,j) then
			// do nothing
		else
			Include(I,x^4*m);
		end if;
	end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:21:39 on modular  [Seed = 4036948705]
   -------------------------------------

{}
{
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^6*y*v
}
{}
{
    x^4*y*u,
    x^5*B^2
}
{}
{
    x^11*B,
    x^4*y*u
}
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{}
{
    x^3*y^5,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^8*y^2
}
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{}
{
    x^5*y,
    x^4*y*u
}
{}
{
    x^6*A,
    x^4*y*u
}
{}
{
    x^4*y*v,
    x^4*y*u
}
{}
{
    x^2*y^5,
    x^4*y*u
}
{}
{
    x^9*B,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^15
}
{}
{
    x^6*u*B,
    x^4*y*u
}
{}
{
    x^9*y^3,
    x^4*y*u
}
{}
{
    x^6*y^2,
    x^4*y*u
}
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x*y^5
}
{}
{
    x^10*y*B,
    x^4*y*u
}
{}
{
    x^4*A,
    x^4*y*u
}
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{}
{
    x^6*u^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^7*B
}
{}
{
    x^13,
    x^4*y*u
}
{}
{
    x^4*u*B,
    x^4*y*u
}
{}
{
    x^7*y^3,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^10*u
}
{}
{
    x^6*v*B,
    x^4*y*u
}
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{}
{
    x^4*y^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^5*y*A
}
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{}
{
    x^8*y*B,
    x^4*y*u
}
{}
{
    x^4*u^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^14*y
}
{}
{
    y^9/x^2,
    x^4*y*u
}
{}
{
    x^5*y*u*B,
    x^4*y*u
}
{}
{
    x^8*y^4,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^3*y^3*u
}
{}
{
    x^5*B,
    x^4*y*u
}
{}
{
    x^4*B^3,
    x^4*y*u
}
{}
{
    x^11,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^5*y^3
}
{}
{
    x^8*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^3*y^2
}
{}
{
    x^4*v*B,
    x^4*y*u
}
{}
{
    x^10*v,
    x^4*y*u
}
{}
{
    x^4*y^3*v,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^2*y^4*B
}
{}
{
    x^2*y^7,
    x^4*y*u
}
{}
{
    x^2*y^3*u,
    x^4*y*u
}
{}
{
    x^6*y*B,
    x^4*y*u
}
{}
{
    x^12*y,
    x^4*y*u
}
{}
{
    x^6*y^4,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^9*y*u
}
{}
{
    x^3*y^3*v,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^9
}
{}
{
    x^4*y*u,
    x^8*B^2
}
{}
{
    x^6*u,
    x^4*y*u
}
{}
{
    x*y^7,
    x^4*y*u
}
{}
{
    x^8*v,
    x^4*y*u
}
{}
{
    y^6,
    x^4*y*u
}
{}
{
    x^5*u*v,
    x^4*y*u
}
{}
{
    x^7*y^2*B,
    x^4*y*u
}
{}
{
    x^2*y^3*B^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^4*y*B
}
{}
{
    x^2*y^3*v,
    x^4*y*u
}
{}
{
    x^10*y,
    x^4*y*u
}
{}
{
    x^4*y^4,
    x^4*y*u
}
{}
{
    x^7*y*u,
    x^4*y*u
}
{}
{
    x^3*y^2*A,
    x^4*y*u
}
{}
{
    x^7,
    x^4*y*u
}
{}
{
    x^6*B^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^4*u
}
{}
{
    x^6*v,
    x^4*y*u
}
{}
{
    x^3*y^2*u*B,
    x^4*y*u
}
{}
{
    x^5*y^2*B,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^11*y^2
}
{}
{
    x^5*y^5,
    x^4*y*u
}
{}
{
    x^3*y^4,
    x^4*y*u
}
{}
{
    x^8*y,
    x^4*y*u
}
{}
{
    x^5*y*u,
    x^4*y*u
}
{}
{
    x^7*y*v,
    x^4*y*u
}
{}
{
    x^4*B^2,
    x^4*y*u
}
{}
{
    x^5,
    x^4*y*u
}
{}
{
    x^12*B,
    x^4*y*u
}
{}
{
    x^6*y^3*B,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^4*v
}
{}
{
    x^4*y*u,
    x^2*y^4
}
{}
{
    x^9*y^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^6*y^2*u
}
{}
{
    x^4*y*u,
    y^8
}
{}
{
    x^4*y*u,
    x^6*y
}
{}
{
    x^7*A,
    x^4*y*u
}
{}
{
    x^5*y*v,
    x^4*y*u
}
{}
{
    x*y^5*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^10*B
}
{}
{
    x^4*y^3*B,
    x^4*y*u
}
{}
{
    x^16,
    x^4*y*u
}
{}
{
    x^7*u*B,
    x^4*y*u
}
{}
{
    x^10*y^3,
    x^4*y*u
}
{}
{
    y^6*B,
    x^4*y*u
}
{}
{
    x^4*y^6,
    x^4*y*u
}
{}
{
    y^8/x,
    x^4*y*u
}
{}
{
    x^7*y^2,
    x^4*y*u
}
{}
{
    x^4*y^2*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^6*y^2*v
}
{}
{
    x^5*y*B^2,
    x^4*y*u
}
{}
{
    x^4*y,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^5*A
}
{}
{
    x^4*y*u,
    x^3*y^3*B
}
{}
{
    x^3*y^6,
    x^4*y*u
}
{}
{
    x^8*B,
    x^4*y*u
}
{}
{
    x^14,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^5*u*B
}
{}
{
    x^4*y*u,
    x^8*y^3
}
{}
{
    x^11*u,
    x^4*y*u
}
{}
{
    x^5*y^3*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^3*y^2*u
}
{}
{
    x^5*y^2,
    x^4*y*u
}
{}
{
    x^4*y^2*B^2,
    x^4*y*u
}
{}
{
    x^4*y^2*v,
    x^4*y*u
}
{}
{
    x^2*y^3*B,
    x^4*y*u
}
{}
{
    x^2*y^6,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^9*y*B
}
{}
{
    x^5*u^2,
    x^4*y*u
}
{}
{
    x^6*B,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^12
}
{}
{
    x^6*y^3,
    x^4*y*u
}
{}
{
    x^3*y^2*B^2,
    x^4*y*u
}
{}
{
    x^5*v*B,
    x^4*y*u
}
{}
{
    x^9*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^3*y^2*v
}
{}
{
    x^4*y*u,
    x*y^6
}
{}
{
    x^4*y*A,
    x^4*y*u
}
{}
{
    x^7*y*B,
    x^4*y*u
}
{}
{
    x^13*y,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^4*y*u*B
}
{}
{
    x^4*y*u,
    x^7*y^4
}
{}
{
    x^4*y*u,
    x^4*B
}
{}
{
    x^10,
    x^4*y*u
}
{}
{
    x^4*y^3,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^7*u
}
{}
{
    x^9*v,
    x^4*y*u
}
{}
{
    x^8*y^2*B,
    x^4*y*u
}
{}
{
    x^4*y*u^2,
    x^4*y*u
}
{}
{
    x^3*y^4*u,
    x^4*y*u
}
{}
{
    x^5*y*B,
    x^4*y*u
}
{}
{
    x^11*y,
    x^4*y*u
}
{}
{
    x^5*y^4,
    x^4*y*u
}
{}
{
    x^8*y*u,
    x^4*y*u
}
{}
{
    x^3*y^3,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^4*y*v*B
}
{}
{
    x^4*y*u,
    x^2*y^5*B
}
{}
{
    x^8,
    x^4*y*u
}
{}
{
    x^5*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^7*v
}
{}
{
    x^4*u*v,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^6*y^2*B
}
{}
{
    x^4*y*u,
    x^2*y^4*u
}
{}
{
    x^12*y^2,
    x^4*y*u
}
{}
{
    x^6*y^5,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^2*y^3
}
{}
{
    x^4*y*u,
    x^9*y
}
{}
{
    x*y^5*B,
    x^4*y*u
}
{}
{
    x^6*y*u,
    x^4*y*u
}
{}
{
    x^4*y*u,
    y^7
}
{}
{
    x^8*y*v,
    x^4*y*u
}
{}
{
    x^6,
    x^4*y*u
}
{}
{
    x^7*B^2,
    x^4*y*u
}
{}
{
    x^5*v,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^4*v^2
}
{}
{
    x^4*y^2*B,
    x^4*y*u
}
{}
{
    x^10*y^2,
    x^4*y*u
}
{}
{
    x^4*y*u,
    x^2*y^4*v
}
{}
{
    x^4*y*u,
    x^4*y^5
}
{}
{
    x^7*y^2*u,
    x^4*y*u
}
{}
{
    x^7*y,
    x^4*y*u
}
{}
{
    x^6*y*B^2,
    x^4*y*u
}
{
    x^4*y*u
}

Total time: 0.600 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:24:09 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
	if I eq {} then
		I:={x^4*m};
	end if;
	R!j;
	m:=x^4*m;
	R!m;
	for j in I do
		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			// do nothing
		else Include(I,m);
		end if;
	end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:24:09 on modular  [Seed = 4254333078]
   -------------------------------------


>>         R!j;
             ^
User error: Identifier 'j' has not been declared or assigned
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:24:52 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for m in SetOfMonomials do
	if I eq {} then
		I:={x^4*m};
	end if;
	for j in I do

		R!j;
		m:=x^4*m;
		R!m;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			// do nothing
		else Include(I,m);
		end if;
	end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:24:51 on modular  [Seed = 3399798683]
   -------------------------------------


>>                 m:=x^4*m;
                   ^
User error: Bad use of identifier 'm'
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:26:35 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for n in SetOfMonomials do
	if I eq {} then
		I:={x^4*n};
	end if;
	for j in I do

		R!j;
		m:=x^4*n;
		R!m;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			// do nothing
		else Include(I,m);
		end if;
	end for;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:26:34 on modular  [Seed = 3502167336]
   -------------------------------------

x^4*y*u
x^4*y*u
{}
{
    x^4*y*u
}
x^4*y*u
x^6*y*v
{}
{
    x^4*y*u,
    x^6*y*v
}
x^4*y*u
x^5*B^2
{}
{
    x^4*y*u,
    x^5*B^2
}
x^4*y*u
x^11*B
{}
{
    x^11*B,
    x^4*y*u
}
x^4*y*u
x^5*y^3*B
{}
{
    x^5*y^3*B,
    x^4*y*u
}
x^4*y*u
x^3*y^2*B
{}
{
    x^4*y*u,
    x^3*y^2*B
}
x^4*y*u
x^3*y^5
{}
{
    x^3*y^5,
    x^4*y*u
}
x^4*y*u
x^8*y^2
{}
{
    x^4*y*u,
    x^8*y^2
}
x^4*y*u
x^5*y^2*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*u
x^4*y*B^2
{}
{
    x^4*y*B^2,
    x^4*y*u
}
x^4*y*u
x^5*y
{}
{
    x^5*y,
    x^4*y*u
}
x^4*y*u
x^6*A
{}
{
    x^6*A,
    x^4*y*u
}
x^4*y*u
x^4*y*v
{}
{
    x^4*y*v,
    x^4*y*u
}
x^4*y*u
x^2*y^5
{}
{
    x^2*y^5,
    x^4*y*u
}
x^4*y*u
x^9*B
{}
{
    x^9*B,
    x^4*y*u
}
x^4*y*u
x^15
{}
{
    x^4*y*u,
    x^15
}
x^4*y*u
x^6*u*B
{}
{
    x^6*u*B,
    x^4*y*u
}
x^4*y*u
x^9*y^3
{}
{
    x^9*y^3,
    x^4*y*u
}
x^4*y*u
x^6*y^2
{}
{
    x^6*y^2,
    x^4*y*u
}
x^4*y*u
x^5*y^2*v
{}
{
    x^5*y^2*v,
    x^4*y*u
}
x^4*y*u
x*y^5
{}
{
    x^4*y*u,
    x*y^5
}
x^4*y*u
x^10*y*B
{}
{
    x^10*y*B,
    x^4*y*u
}
x^4*y*u
x^4*A
{}
{
    x^4*A,
    x^4*y*u
}
x^4*y*u
x^4*y^4*B
{}
{
    x^4*y^4*B,
    x^4*y*u
}
x^4*y*u
x^6*u^2
{}
{
    x^6*u^2,
    x^4*y*u
}
x^4*y*u
x^7*B
{}
{
    x^4*y*u,
    x^7*B
}
x^4*y*u
x^13
{}
{
    x^13,
    x^4*y*u
}
x^4*y*u
x^4*u*B
{}
{
    x^4*u*B,
    x^4*y*u
}
x^4*y*u
x^7*y^3
{}
{
    x^7*y^3,
    x^4*y*u
}
x^4*y*u
x^10*u
{}
{
    x^4*y*u,
    x^10*u
}
x^4*y*u
x^6*v*B
{}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y*u
x^4*y^3*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y*u
x^4*y^2
{}
{
    x^4*y^2,
    x^4*y*u
}
x^4*y*u
x^5*y*A
{}
{
    x^4*y*u,
    x^5*y*A
}
x^4*y*u
x^3*y^4*B
{}
{
    x^3*y^4*B,
    x^4*y*u
}
x^4*y*u
x^8*y*B
{}
{
    x^8*y*B,
    x^4*y*u
}
x^4*y*u
x^4*u^2
{}
{
    x^4*u^2,
    x^4*y*u
}
x^4*y*u
x^14*y
{}
{
    x^4*y*u,
    x^14*y
}
x^4*y*u

>>                 R!m;
                    ^
Runtime error in '!': Illegal coercion
{
    x^4*y*u
}

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:31:14 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for n in SetOfMonomials do

	m:=x^4*n:
	R!m:

	if I eq {} then
		I:={m}:
	end if;

	flag:=0;

	for j in I do
		R!j:

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
			flag:=1;
		elif IsDivisibleBy(m,j) then
			// do nothing
		end if;
	end for;

	if flag then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:31:13 on modular  [Seed = 2748163952]
   -------------------------------------


>>         m:=x^4*n:
                   ^
User error: bad syntax

>>         if I eq {} then
           ^
User error: bad syntax

>>                 I:={m}:
                         ^
User error: bad syntax

>>         end if;
           ^
User error: bad syntax

>>                 if IsDivisibleBy(j,m) then
                   ^
User error: bad syntax

>>                         Exclude(I,j);
                                     ^
User error: Identifier 'j' has not been declared or assigned

>>                         Include(I,m);
                                     ^
User error: Identifier 'm' has not been declared or assigned

>>                 elif IsDivisibleBy(m,j) then
                   ^
User error: bad syntax

>>                 end if;
                   ^
User error: bad syntax

>>         end for;
           ^
User error: bad syntax

>>                 Include(I,m);
                             ^
User error: Identifier 'm' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:31:47 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for n in SetOfMonomials do

	m:=x^4*n;
	R!m;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do
		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
			flag:=1;
		elif IsDivisibleBy(m,j) then
			// do nothing
		end if;
	end for;

	if flag then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:31:46 on modular  [Seed = 2881859355]
   -------------------------------------

x^4*y*u
x^4*y*u
{}
{
    x^4*y*u
}

>>         if flag then
           ^
Runtime error in if: Logical expected
{
    x^4*y*u
}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:32:03 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for n in SetOfMonomials do

	m:=x^4*n;
	R!m;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do
		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
			flag:=1;
		elif IsDivisibleBy(m,j) then
			// do nothing
		end if;
	end for;

	if flag eq 1 then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:32:02 on modular  [Seed = 3017652019]
   -------------------------------------

x^4*y*u
x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^6*y*v
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^5*B^2
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^11*B
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^5*y^3*B
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^3*y^2*B
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^3*y^5
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^8*y^2
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^5*y^2*u
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*B^2
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^5*y
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^6*A
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*v
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^2*y^5
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^9*B
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^15
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^6*u*B
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^9*y^3
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^6*y^2
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^5*y^2*v
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x*y^5
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^10*y*B
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*A
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y^4*B
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^6*u^2
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^7*B
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^13
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*u*B
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^7*y^3
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^10*u
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^6*v*B
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y^3*u
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y^2
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^5*y*A
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^3*y^4*B
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^8*y*B
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*u^2
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^14*y
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}

>>         R!m;
            ^
Runtime error in '!': Illegal coercion
{
    x^4*y*u
}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:34:15 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for n in SetOfMonomials do

	m:=x^4*n:
	R!m:

	if I eq {} then
		I:={m}:
	end if;

	flag:=0;

	for j in I do
		R!j:

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:34:15 on modular  [Seed = 3201350075]
   -------------------------------------


>>         m:=x^4*n:
                   ^
User error: bad syntax

>>         if I eq {} then
           ^
User error: bad syntax

>>                 I:={m}:
                         ^
User error: bad syntax

>>         end if;
           ^
User error: bad syntax

>>                 if IsDivisibleBy(j,m) then
                   ^
User error: bad syntax

>>                         Exclude(I,j);
                                     ^
User error: Identifier 'j' has not been declared or assigned

>>                         Include(I,m);
                                     ^
User error: Identifier 'm' has not been declared or assigned

>>                 elif IsDivisibleBy(m,j) then
                   ^
User error: bad syntax

>>                 end if;
                   ^
User error: bad syntax

>>         end for;
           ^
User error: bad syntax

>>                 Include(I,m);
                             ^
User error: Identifier 'm' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
{}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:34:47 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={};
for n in SetOfMonomials do

	m:=x^4*n;
	R!m;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do
		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:34:46 on modular  [Seed = 2280226915]
   -------------------------------------

x^4*y*u
x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^6*y*v
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^5*B^2
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^11*B
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^5*y^3*B
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^3*y^2*B
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^3*y^5
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^8*y^2
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^5*y^2*u
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*B^2
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^5*y
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^6*A
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*v
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^2*y^5
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^9*B
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^15
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^6*u*B
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^9*y^3
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^6*y^2
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^5*y^2*v
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x*y^5
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^10*y*B
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*A
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y^4*B
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^6*u^2
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^7*B
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^13
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*u*B
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^7*y^3
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^10*u
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^6*v*B
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y^3*u
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y^2
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^5*y*A
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^3*y^4*B
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^8*y*B
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*u^2
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^14*y
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}

>>         R!m;
            ^
Runtime error in '!': Illegal coercion
{
    x^4*y*u
}

Total time: 0.579 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:38:03 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={R|};
for n in SetOfMonomials do

	m:=x^4*n;
	R!m;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do
		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:38:02 on modular  [Seed = 2466026682]
   -------------------------------------

x^4*y*u
x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^6*y*v
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^5*B^2
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^11*B
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^5*y^3*B
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^3*y^2*B
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^3*y^5
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^8*y^2
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^5*y^2*u
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*B^2
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^5*y
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^6*A
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*v
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^2*y^5
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^9*B
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^15
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^6*u*B
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^9*y^3
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^6*y^2
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^5*y^2*v
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x*y^5
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^10*y*B
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*A
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y^4*B
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^6*u^2
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^7*B
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^13
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*u*B
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^7*y^3
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^10*u
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^6*v*B
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y^3*u
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y^2
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^5*y*A
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^3*y^4*B
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^8*y*B
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*u^2
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^14*y
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}

>>         R!m;
            ^
Runtime error in '!': Illegal coercion
{
    x^4*y*u
}

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:38:43 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

I:={R|};
for n in SetOfMonomials do

	m:=x^4*n;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do
		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;
I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:38:42 on modular  [Seed = 2599722122]
   -------------------------------------

x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}
x^4*y*u
{}
{
    y^9/x^2,
    x^4*y*u
}
{
    y^9/x^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u*B,
    x^4*y*u
}
{
    x^5*y*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y^4,
    x^4*y*u
}
{
    x^8*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*u
}
{
    x^4*y*u,
    x^3*y^3*u
}
x^4*y*u
{}
{
    x^5*B,
    x^4*y*u
}
{
    x^5*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^3,
    x^4*y*u
}
{
    x^4*B^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^11,
    x^4*y*u
}
{
    x^11,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y^3
}
{
    x^4*y*u,
    x^5*y^3
}
x^4*y*u
{}
{
    x^8*u,
    x^4*y*u
}
{
    x^8*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2
}
{
    x^4*y*u,
    x^3*y^2
}
x^4*y*u
{}
{
    x^4*v*B,
    x^4*y*u
}
{
    x^4*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*v,
    x^4*y*u
}
{
    x^10*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*v,
    x^4*y*u
}
{
    x^4*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4*B
}
{
    x^4*y*u,
    x^2*y^4*B
}
x^4*y*u
{}
{
    x^2*y^7,
    x^4*y*u
}
{
    x^2*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*u,
    x^4*y*u
}
{
    x^2*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y*B,
    x^4*y*u
}
{
    x^6*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*y,
    x^4*y*u
}
{
    x^12*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^4,
    x^4*y*u
}
{
    x^6*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*u
}
{
    x^4*y*u,
    x^9*y*u
}
x^4*y*u
{}
{
    x^3*y^3*v,
    x^4*y*u
}
{
    x^3*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9
}
{
    x^4*y*u,
    x^9
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*B^2
}
{
    x^4*y*u,
    x^8*B^2
}
x^4*y*u
{}
{
    x^6*u,
    x^4*y*u
}
{
    x^6*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^7,
    x^4*y*u
}
{
    x*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*v,
    x^4*y*u
}
{
    x^8*v,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6,
    x^4*y*u
}
{
    y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*u*v,
    x^4*y*u
}
{
    x^5*u*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2*B,
    x^4*y*u
}
{
    x^7*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B^2,
    x^4*y*u
}
{
    x^2*y^3*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*B
}
{
    x^4*y*u,
    x^4*y*B
}
x^4*y*u
{}
{
    x^2*y^3*v,
    x^4*y*u
}
{
    x^2*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y,
    x^4*y*u
}
{
    x^10*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4,
    x^4*y*u
}
{
    x^4*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*u,
    x^4*y*u
}
{
    x^7*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*A,
    x^4*y*u
}
{
    x^3*y^2*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7,
    x^4*y*u
}
{
    x^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B^2,
    x^4*y*u
}
{
    x^6*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*u
}
{
    x^4*y*u,
    x^4*u
}
x^4*y*u
{}
{
    x^6*v,
    x^4*y*u
}
{
    x^6*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*u*B,
    x^4*y*u
}
{
    x^3*y^2*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*B,
    x^4*y*u
}
{
    x^5*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^11*y^2
}
{
    x^4*y*u,
    x^11*y^2
}
x^4*y*u
{}
{
    x^5*y^5,
    x^4*y*u
}
{
    x^5*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^4,
    x^4*y*u
}
{
    x^3*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y,
    x^4*y*u
}
{
    x^8*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u,
    x^4*y*u
}
{
    x^5*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*v,
    x^4*y*u
}
{
    x^7*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^2,
    x^4*y*u
}
{
    x^4*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5,
    x^4*y*u
}
{
    x^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*B,
    x^4*y*u
}
{
    x^12*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^3*B,
    x^4*y*u
}
{
    x^6*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*v
}
{
    x^4*y*u,
    x^4*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4
}
{
    x^4*y*u,
    x^2*y^4
}
x^4*y*u
{}
{
    x^9*y^2,
    x^4*y*u
}
{
    x^9*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*u
}
{
    x^4*y*u,
    x^6*y^2*u
}
x^4*y*u
{}
{
    x^4*y*u,
    y^8
}
{
    x^4*y*u,
    y^8
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y
}
{
    x^4*y*u,
    x^6*y
}
x^4*y*u
{}
{
    x^7*A,
    x^4*y*u
}
{
    x^7*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*v,
    x^4*y*u
}
{
    x^5*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^5*u,
    x^4*y*u
}
{
    x*y^5*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*B
}
{
    x^4*y*u,
    x^10*B
}
x^4*y*u
{}
{
    x^4*y^3*B,
    x^4*y*u
}
{
    x^4*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^16,
    x^4*y*u
}
{
    x^16,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*u*B,
    x^4*y*u
}
{
    x^7*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y^3,
    x^4*y*u
}
{
    x^10*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6*B,
    x^4*y*u
}
{
    y^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^6,
    x^4*y*u
}
{
    x^4*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    y^8/x,
    x^4*y*u
}
{
    y^8/x,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2,
    x^4*y*u
}
{
    x^7*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*u,
    x^4*y*u
}
{
    x^4*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*v
}
{
    x^4*y*u,
    x^6*y^2*v
}
x^4*y*u
{}
{
    x^5*y*B^2,
    x^4*y*u
}
{
    x^5*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y,
    x^4*y*u
}
{
    x^4*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*A
}
{
    x^4*y*u,
    x^5*A
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*B
}
{
    x^4*y*u,
    x^3*y^3*B
}
x^4*y*u
{}
{
    x^3*y^6,
    x^4*y*u
}
{
    x^3*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*B,
    x^4*y*u
}
{
    x^8*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^14,
    x^4*y*u
}
{
    x^14,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*u*B
}
{
    x^4*y*u,
    x^5*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^3
}
{
    x^4*y*u,
    x^8*y^3
}
x^4*y*u
{}
{
    x^11*u,
    x^4*y*u
}
{
    x^11*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*u,
    x^4*y*u
}
{
    x^5*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*u
}
{
    x^4*y*u,
    x^3*y^2*u
}
x^4*y*u
{}
{
    x^5*y^2,
    x^4*y*u
}
{
    x^5*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*B^2,
    x^4*y*u
}
{
    x^4*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*v,
    x^4*y*u
}
{
    x^4*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B,
    x^4*y*u
}
{
    x^2*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^6,
    x^4*y*u
}
{
    x^2*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*B
}
{
    x^4*y*u,
    x^9*y*B
}
x^4*y*u
{}
{
    x^5*u^2,
    x^4*y*u
}
{
    x^5*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B,
    x^4*y*u
}
{
    x^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^12
}
{
    x^4*y*u,
    x^12
}
x^4*y*u
{}
{
    x^6*y^3,
    x^4*y*u
}
{
    x^6*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*B^2,
    x^4*y*u
}
{
    x^3*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*v*B,
    x^4*y*u
}
{
    x^5*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*u,
    x^4*y*u
}
{
    x^9*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*v
}
{
    x^4*y*u,
    x^3*y^2*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^6
}
{
    x^4*y*u,
    x*y^6
}
x^4*y*u
{}
{
    x^4*y*A,
    x^4*y*u
}
{
    x^4*y*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*B,
    x^4*y*u
}
{
    x^7*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^13*y,
    x^4*y*u
}
{
    x^13*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*u*B
}
{
    x^4*y*u,
    x^4*y*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*y^4
}
{
    x^4*y*u,
    x^7*y^4
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*B
}
{
    x^4*y*u,
    x^4*B
}
x^4*y*u
{}
{
    x^10,
    x^4*y*u
}
{
    x^10,
    x^4*y*u
}
x^4*y*u
{}
{
    
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:41:13 2004

Input: GetVerbose(0);


Output: Magma V2.11-2     Fri Aug 27 2004 10:41:13 on modular  [Seed = 1881045276]
   -------------------------------------


>> GetVerbose(0);
             ^
Runtime error in 'GetVerbose': Bad argument types
Argument types given: RngIntElt

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:42:06 2004

Input: GetVerbose("Usern");

Output: Magma V2.11-2     Fri Aug 27 2004 10:42:05 on modular  [Seed = 2014736672]
   -------------------------------------


>> GetVerbose("Usern");;
             ^
Runtime error in 'GetVerbose': Unknown verbose flag "Usern"

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:43:11 2004

Input: GetPrintLevel();

Output: Magma V2.11-2     Fri Aug 27 2004 10:43:10 on modular  [Seed = 1076775258]
   -------------------------------------

Default

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:43:23 2004

Input: SetPrintLevel(Minimal);

Output: Magma V2.11-2     Fri Aug 27 2004 10:43:22 on modular  [Seed = 1210466727]
   -------------------------------------


>> SetPrintLevel(Minimal);;
                 ^
User error: Identifier 'Minimal' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:43:32 2004

Input: SetPrintLevel("Minimal");

Output: Magma V2.11-2     Fri Aug 27 2004 10:43:31 on modular  [Seed = 1346263462]
   -------------------------------------


Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:43:44 2004

Input: x;

Output: Magma V2.11-2     Fri Aug 27 2004 10:43:43 on modular  [Seed = 1479954850]
   -------------------------------------


>> x;;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:43:53 2004

Input: 22222;

Output: Magma V2.11-2     Fri Aug 27 2004 10:43:52 on modular  [Seed = 541993453]
   -------------------------------------

22222

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:44:40 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

SetPrintLevel("Minimal");

I:={R|};
for n in SetOfMonomials do

	m:=x^4*n;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do
		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;

SetPrintLevel("Default");

I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:44:39 on modular  [Seed = 709108632]
   -------------------------------------

x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}
x^4*y*u
{}
{
    y^9/x^2,
    x^4*y*u
}
{
    y^9/x^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u*B,
    x^4*y*u
}
{
    x^5*y*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y^4,
    x^4*y*u
}
{
    x^8*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*u
}
{
    x^4*y*u,
    x^3*y^3*u
}
x^4*y*u
{}
{
    x^5*B,
    x^4*y*u
}
{
    x^5*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^3,
    x^4*y*u
}
{
    x^4*B^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^11,
    x^4*y*u
}
{
    x^11,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y^3
}
{
    x^4*y*u,
    x^5*y^3
}
x^4*y*u
{}
{
    x^8*u,
    x^4*y*u
}
{
    x^8*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2
}
{
    x^4*y*u,
    x^3*y^2
}
x^4*y*u
{}
{
    x^4*v*B,
    x^4*y*u
}
{
    x^4*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*v,
    x^4*y*u
}
{
    x^10*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*v,
    x^4*y*u
}
{
    x^4*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4*B
}
{
    x^4*y*u,
    x^2*y^4*B
}
x^4*y*u
{}
{
    x^2*y^7,
    x^4*y*u
}
{
    x^2*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*u,
    x^4*y*u
}
{
    x^2*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y*B,
    x^4*y*u
}
{
    x^6*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*y,
    x^4*y*u
}
{
    x^12*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^4,
    x^4*y*u
}
{
    x^6*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*u
}
{
    x^4*y*u,
    x^9*y*u
}
x^4*y*u
{}
{
    x^3*y^3*v,
    x^4*y*u
}
{
    x^3*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9
}
{
    x^4*y*u,
    x^9
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*B^2
}
{
    x^4*y*u,
    x^8*B^2
}
x^4*y*u
{}
{
    x^6*u,
    x^4*y*u
}
{
    x^6*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^7,
    x^4*y*u
}
{
    x*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*v,
    x^4*y*u
}
{
    x^8*v,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6,
    x^4*y*u
}
{
    y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*u*v,
    x^4*y*u
}
{
    x^5*u*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2*B,
    x^4*y*u
}
{
    x^7*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B^2,
    x^4*y*u
}
{
    x^2*y^3*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*B
}
{
    x^4*y*u,
    x^4*y*B
}
x^4*y*u
{}
{
    x^2*y^3*v,
    x^4*y*u
}
{
    x^2*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y,
    x^4*y*u
}
{
    x^10*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4,
    x^4*y*u
}
{
    x^4*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*u,
    x^4*y*u
}
{
    x^7*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*A,
    x^4*y*u
}
{
    x^3*y^2*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7,
    x^4*y*u
}
{
    x^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B^2,
    x^4*y*u
}
{
    x^6*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*u
}
{
    x^4*y*u,
    x^4*u
}
x^4*y*u
{}
{
    x^6*v,
    x^4*y*u
}
{
    x^6*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*u*B,
    x^4*y*u
}
{
    x^3*y^2*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*B,
    x^4*y*u
}
{
    x^5*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^11*y^2
}
{
    x^4*y*u,
    x^11*y^2
}
x^4*y*u
{}
{
    x^5*y^5,
    x^4*y*u
}
{
    x^5*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^4,
    x^4*y*u
}
{
    x^3*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y,
    x^4*y*u
}
{
    x^8*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u,
    x^4*y*u
}
{
    x^5*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*v,
    x^4*y*u
}
{
    x^7*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^2,
    x^4*y*u
}
{
    x^4*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5,
    x^4*y*u
}
{
    x^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*B,
    x^4*y*u
}
{
    x^12*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^3*B,
    x^4*y*u
}
{
    x^6*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*v
}
{
    x^4*y*u,
    x^4*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4
}
{
    x^4*y*u,
    x^2*y^4
}
x^4*y*u
{}
{
    x^9*y^2,
    x^4*y*u
}
{
    x^9*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*u
}
{
    x^4*y*u,
    x^6*y^2*u
}
x^4*y*u
{}
{
    x^4*y*u,
    y^8
}
{
    x^4*y*u,
    y^8
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y
}
{
    x^4*y*u,
    x^6*y
}
x^4*y*u
{}
{
    x^7*A,
    x^4*y*u
}
{
    x^7*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*v,
    x^4*y*u
}
{
    x^5*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^5*u,
    x^4*y*u
}
{
    x*y^5*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*B
}
{
    x^4*y*u,
    x^10*B
}
x^4*y*u
{}
{
    x^4*y^3*B,
    x^4*y*u
}
{
    x^4*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^16,
    x^4*y*u
}
{
    x^16,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*u*B,
    x^4*y*u
}
{
    x^7*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y^3,
    x^4*y*u
}
{
    x^10*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6*B,
    x^4*y*u
}
{
    y^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^6,
    x^4*y*u
}
{
    x^4*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    y^8/x,
    x^4*y*u
}
{
    y^8/x,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2,
    x^4*y*u
}
{
    x^7*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*u,
    x^4*y*u
}
{
    x^4*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*v
}
{
    x^4*y*u,
    x^6*y^2*v
}
x^4*y*u
{}
{
    x^5*y*B^2,
    x^4*y*u
}
{
    x^5*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y,
    x^4*y*u
}
{
    x^4*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*A
}
{
    x^4*y*u,
    x^5*A
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*B
}
{
    x^4*y*u,
    x^3*y^3*B
}
x^4*y*u
{}
{
    x^3*y^6,
    x^4*y*u
}
{
    x^3*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*B,
    x^4*y*u
}
{
    x^8*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^14,
    x^4*y*u
}
{
    x^14,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*u*B
}
{
    x^4*y*u,
    x^5*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^3
}
{
    x^4*y*u,
    x^8*y^3
}
x^4*y*u
{}
{
    x^11*u,
    x^4*y*u
}
{
    x^11*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*u,
    x^4*y*u
}
{
    x^5*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*u
}
{
    x^4*y*u,
    x^3*y^2*u
}
x^4*y*u
{}
{
    x^5*y^2,
    x^4*y*u
}
{
    x^5*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*B^2,
    x^4*y*u
}
{
    x^4*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*v,
    x^4*y*u
}
{
    x^4*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B,
    x^4*y*u
}
{
    x^2*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^6,
    x^4*y*u
}
{
    x^2*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*B
}
{
    x^4*y*u,
    x^9*y*B
}
x^4*y*u
{}
{
    x^5*u^2,
    x^4*y*u
}
{
    x^5*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B,
    x^4*y*u
}
{
    x^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^12
}
{
    x^4*y*u,
    x^12
}
x^4*y*u
{}
{
    x^6*y^3,
    x^4*y*u
}
{
    x^6*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*B^2,
    x^4*y*u
}
{
    x^3*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*v*B,
    x^4*y*u
}
{
    x^5*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*u,
    x^4*y*u
}
{
    x^9*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*v
}
{
    x^4*y*u,
    x^3*y^2*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^6
}
{
    x^4*y*u,
    x*y^6
}
x^4*y*u
{}
{
    x^4*y*A,
    x^4*y*u
}
{
    x^4*y*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*B,
    x^4*y*u
}
{
    x^7*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^13*y,
    x^4*y*u
}
{
    x^13*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*u*B
}
{
    x^4*y*u,
    x^4*y*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*y^4
}
{
    x^4*y*u,
    x^7*y^4
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*B
}
{
    x^4*y*u,
    x^4*B
}
x^4*y*u
{}
{
    x^10,
    x^4*y*u
}
{
    x^10,
    x^4*y*u
}
x^4*y*u
{}
{
    x
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:45:08 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

SetPrintLevel("Minimal");

I:={R|};
for n in SetOfMonomials do
SetPrintLevel("Minimal");

	m:=x^4*n;

	if I eq {} then
		I:={m};
	end if;

	flag:=0;

	for j in I do

SetPrintLevel("Minimal");

		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;

SetPrintLevel("Default");

I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:45:07 on modular  [Seed = 844905379]
   -------------------------------------

x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}
x^4*y*u
{}
{
    y^9/x^2,
    x^4*y*u
}
{
    y^9/x^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u*B,
    x^4*y*u
}
{
    x^5*y*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y^4,
    x^4*y*u
}
{
    x^8*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*u
}
{
    x^4*y*u,
    x^3*y^3*u
}
x^4*y*u
{}
{
    x^5*B,
    x^4*y*u
}
{
    x^5*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^3,
    x^4*y*u
}
{
    x^4*B^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^11,
    x^4*y*u
}
{
    x^11,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y^3
}
{
    x^4*y*u,
    x^5*y^3
}
x^4*y*u
{}
{
    x^8*u,
    x^4*y*u
}
{
    x^8*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2
}
{
    x^4*y*u,
    x^3*y^2
}
x^4*y*u
{}
{
    x^4*v*B,
    x^4*y*u
}
{
    x^4*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*v,
    x^4*y*u
}
{
    x^10*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*v,
    x^4*y*u
}
{
    x^4*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4*B
}
{
    x^4*y*u,
    x^2*y^4*B
}
x^4*y*u
{}
{
    x^2*y^7,
    x^4*y*u
}
{
    x^2*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*u,
    x^4*y*u
}
{
    x^2*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y*B,
    x^4*y*u
}
{
    x^6*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*y,
    x^4*y*u
}
{
    x^12*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^4,
    x^4*y*u
}
{
    x^6*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*u
}
{
    x^4*y*u,
    x^9*y*u
}
x^4*y*u
{}
{
    x^3*y^3*v,
    x^4*y*u
}
{
    x^3*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9
}
{
    x^4*y*u,
    x^9
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*B^2
}
{
    x^4*y*u,
    x^8*B^2
}
x^4*y*u
{}
{
    x^6*u,
    x^4*y*u
}
{
    x^6*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^7,
    x^4*y*u
}
{
    x*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*v,
    x^4*y*u
}
{
    x^8*v,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6,
    x^4*y*u
}
{
    y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*u*v,
    x^4*y*u
}
{
    x^5*u*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2*B,
    x^4*y*u
}
{
    x^7*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B^2,
    x^4*y*u
}
{
    x^2*y^3*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*B
}
{
    x^4*y*u,
    x^4*y*B
}
x^4*y*u
{}
{
    x^2*y^3*v,
    x^4*y*u
}
{
    x^2*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y,
    x^4*y*u
}
{
    x^10*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4,
    x^4*y*u
}
{
    x^4*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*u,
    x^4*y*u
}
{
    x^7*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*A,
    x^4*y*u
}
{
    x^3*y^2*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7,
    x^4*y*u
}
{
    x^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B^2,
    x^4*y*u
}
{
    x^6*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*u
}
{
    x^4*y*u,
    x^4*u
}
x^4*y*u
{}
{
    x^6*v,
    x^4*y*u
}
{
    x^6*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*u*B,
    x^4*y*u
}
{
    x^3*y^2*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*B,
    x^4*y*u
}
{
    x^5*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^11*y^2
}
{
    x^4*y*u,
    x^11*y^2
}
x^4*y*u
{}
{
    x^5*y^5,
    x^4*y*u
}
{
    x^5*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^4,
    x^4*y*u
}
{
    x^3*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y,
    x^4*y*u
}
{
    x^8*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u,
    x^4*y*u
}
{
    x^5*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*v,
    x^4*y*u
}
{
    x^7*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^2,
    x^4*y*u
}
{
    x^4*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5,
    x^4*y*u
}
{
    x^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*B,
    x^4*y*u
}
{
    x^12*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^3*B,
    x^4*y*u
}
{
    x^6*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*v
}
{
    x^4*y*u,
    x^4*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4
}
{
    x^4*y*u,
    x^2*y^4
}
x^4*y*u
{}
{
    x^9*y^2,
    x^4*y*u
}
{
    x^9*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*u
}
{
    x^4*y*u,
    x^6*y^2*u
}
x^4*y*u
{}
{
    x^4*y*u,
    y^8
}
{
    x^4*y*u,
    y^8
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y
}
{
    x^4*y*u,
    x^6*y
}
x^4*y*u
{}
{
    x^7*A,
    x^4*y*u
}
{
    x^7*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*v,
    x^4*y*u
}
{
    x^5*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^5*u,
    x^4*y*u
}
{
    x*y^5*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*B
}
{
    x^4*y*u,
    x^10*B
}
x^4*y*u
{}
{
    x^4*y^3*B,
    x^4*y*u
}
{
    x^4*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^16,
    x^4*y*u
}
{
    x^16,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*u*B,
    x^4*y*u
}
{
    x^7*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y^3,
    x^4*y*u
}
{
    x^10*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6*B,
    x^4*y*u
}
{
    y^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^6,
    x^4*y*u
}
{
    x^4*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    y^8/x,
    x^4*y*u
}
{
    y^8/x,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2,
    x^4*y*u
}
{
    x^7*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*u,
    x^4*y*u
}
{
    x^4*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*v
}
{
    x^4*y*u,
    x^6*y^2*v
}
x^4*y*u
{}
{
    x^5*y*B^2,
    x^4*y*u
}
{
    x^5*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y,
    x^4*y*u
}
{
    x^4*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*A
}
{
    x^4*y*u,
    x^5*A
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*B
}
{
    x^4*y*u,
    x^3*y^3*B
}
x^4*y*u
{}
{
    x^3*y^6,
    x^4*y*u
}
{
    x^3*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*B,
    x^4*y*u
}
{
    x^8*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^14,
    x^4*y*u
}
{
    x^14,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*u*B
}
{
    x^4*y*u,
    x^5*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^3
}
{
    x^4*y*u,
    x^8*y^3
}
x^4*y*u
{}
{
    x^11*u,
    x^4*y*u
}
{
    x^11*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*u,
    x^4*y*u
}
{
    x^5*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*u
}
{
    x^4*y*u,
    x^3*y^2*u
}
x^4*y*u
{}
{
    x^5*y^2,
    x^4*y*u
}
{
    x^5*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*B^2,
    x^4*y*u
}
{
    x^4*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*v,
    x^4*y*u
}
{
    x^4*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B,
    x^4*y*u
}
{
    x^2*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^6,
    x^4*y*u
}
{
    x^2*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*B
}
{
    x^4*y*u,
    x^9*y*B
}
x^4*y*u
{}
{
    x^5*u^2,
    x^4*y*u
}
{
    x^5*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B,
    x^4*y*u
}
{
    x^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^12
}
{
    x^4*y*u,
    x^12
}
x^4*y*u
{}
{
    x^6*y^3,
    x^4*y*u
}
{
    x^6*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*B^2,
    x^4*y*u
}
{
    x^3*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*v*B,
    x^4*y*u
}
{
    x^5*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*u,
    x^4*y*u
}
{
    x^9*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*v
}
{
    x^4*y*u,
    x^3*y^2*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^6
}
{
    x^4*y*u,
    x*y^6
}
x^4*y*u
{}
{
    x^4*y*A,
    x^4*y*u
}
{
    x^4*y*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*B,
    x^4*y*u
}
{
    x^7*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^13*y,
    x^4*y*u
}
{
    x^13*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*u*B
}
{
    x^4*y*u,
    x^4*y*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*y^4
}
{
    x^4*y*u,
    x^7*y^4
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*B
}
{
    x^4*y*u,
    x^4*B
}
x^4*y*u
{}
{
    x^10,
    x^4*y*u
}
{
    x^10,
    x^4*y*u
}
x^4*y*u
{}
{
    x
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host webcacheB06a.cache.pol.co.uk. (195.92.168.168)
Time: Fri Aug 27 10:45:46 2004

Input: R<x,y,z,t,u,v,A,B>:=PolynomialRing(RationalField(),[1,2,3,4,5,6,9,4]);
S<x,y,z,t,u,v,A,B>:=FieldOfFractions(R);
SetOfMonomials:={};
subs:=hom<R->S|x,y,y^2/x,y^3/x^2,u,v,A,B>;
for i in [1..12] do
SetOfMonomials:=SetOfMonomials join subs(MonomialsOfWeightedDegree(R,i));
end for;

SetPrintLevel("Minimal");

I:={R|};
for n in SetOfMonomials do
SetPrintLevel("Minimal");

	m:=x^4*n;

	if I eq {R|} then
		I:={m};
	end if;

	flag:=0;

	for j in I do

SetPrintLevel("Minimal");

		R!j;

		if IsDivisibleBy(j,m) then
			Exclude(I,j);
			Include(I,m);
		elif IsDivisibleBy(m,j) then
			flag:=1;
		end if;
	end for;

	if flag eq 0 then
		Include(I,m);
	end if;
end for;

SetPrintLevel("Default");

I;

Output: Magma V2.11-2     Fri Aug 27 2004 10:45:46 on modular  [Seed = 978596421]
   -------------------------------------

x^4*y*u
{}
{
    x^4*y*u
}
{
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y*v
}
{
    x^4*y*u,
    x^6*y*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*B^2
}
{
    x^4*y*u,
    x^5*B^2
}
x^4*y*u
{}
{
    x^11*B,
    x^4*y*u
}
{
    x^11*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*B,
    x^4*y*u
}
{
    x^5*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*B
}
{
    x^4*y*u,
    x^3*y^2*B
}
x^4*y*u
{}
{
    x^3*y^5,
    x^4*y*u
}
{
    x^3*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^2
}
{
    x^4*y*u,
    x^8*y^2
}
x^4*y*u
{}
{
    x^5*y^2*u,
    x^4*y*u
}
{
    x^5*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*B^2,
    x^4*y*u
}
{
    x^4*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y,
    x^4*y*u
}
{
    x^5*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*A,
    x^4*y*u
}
{
    x^6*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*v,
    x^4*y*u
}
{
    x^4*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^5,
    x^4*y*u
}
{
    x^2*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*B,
    x^4*y*u
}
{
    x^9*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^15
}
{
    x^4*y*u,
    x^15
}
x^4*y*u
{}
{
    x^6*u*B,
    x^4*y*u
}
{
    x^6*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*y^3,
    x^4*y*u
}
{
    x^9*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^2,
    x^4*y*u
}
{
    x^6*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*v,
    x^4*y*u
}
{
    x^5*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^5
}
{
    x^4*y*u,
    x*y^5
}
x^4*y*u
{}
{
    x^10*y*B,
    x^4*y*u
}
{
    x^10*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*A,
    x^4*y*u
}
{
    x^4*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4*B,
    x^4*y*u
}
{
    x^4*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*u^2,
    x^4*y*u
}
{
    x^6*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*B
}
{
    x^4*y*u,
    x^7*B
}
x^4*y*u
{}
{
    x^13,
    x^4*y*u
}
{
    x^13,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u*B,
    x^4*y*u
}
{
    x^4*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^3,
    x^4*y*u
}
{
    x^7*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*u
}
{
    x^4*y*u,
    x^10*u
}
x^4*y*u
{}
{
    x^6*v*B,
    x^4*y*u
}
{
    x^6*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*u,
    x^4*y*u
}
{
    x^4*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2,
    x^4*y*u
}
{
    x^4*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y*A
}
{
    x^4*y*u,
    x^5*y*A
}
x^4*y*u
{}
{
    x^3*y^4*B,
    x^4*y*u
}
{
    x^3*y^4*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y*B,
    x^4*y*u
}
{
    x^8*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*u^2,
    x^4*y*u
}
{
    x^4*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^14*y
}
{
    x^4*y*u,
    x^14*y
}
x^4*y*u
{}
{
    y^9/x^2,
    x^4*y*u
}
{
    y^9/x^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u*B,
    x^4*y*u
}
{
    x^5*y*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y^4,
    x^4*y*u
}
{
    x^8*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*u
}
{
    x^4*y*u,
    x^3*y^3*u
}
x^4*y*u
{}
{
    x^5*B,
    x^4*y*u
}
{
    x^5*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^3,
    x^4*y*u
}
{
    x^4*B^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^11,
    x^4*y*u
}
{
    x^11,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*y^3
}
{
    x^4*y*u,
    x^5*y^3
}
x^4*y*u
{}
{
    x^8*u,
    x^4*y*u
}
{
    x^8*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2
}
{
    x^4*y*u,
    x^3*y^2
}
x^4*y*u
{}
{
    x^4*v*B,
    x^4*y*u
}
{
    x^4*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*v,
    x^4*y*u
}
{
    x^10*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^3*v,
    x^4*y*u
}
{
    x^4*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4*B
}
{
    x^4*y*u,
    x^2*y^4*B
}
x^4*y*u
{}
{
    x^2*y^7,
    x^4*y*u
}
{
    x^2*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*u,
    x^4*y*u
}
{
    x^2*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y*B,
    x^4*y*u
}
{
    x^6*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*y,
    x^4*y*u
}
{
    x^12*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^4,
    x^4*y*u
}
{
    x^6*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*u
}
{
    x^4*y*u,
    x^9*y*u
}
x^4*y*u
{}
{
    x^3*y^3*v,
    x^4*y*u
}
{
    x^3*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9
}
{
    x^4*y*u,
    x^9
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*B^2
}
{
    x^4*y*u,
    x^8*B^2
}
x^4*y*u
{}
{
    x^6*u,
    x^4*y*u
}
{
    x^6*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^7,
    x^4*y*u
}
{
    x*y^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*v,
    x^4*y*u
}
{
    x^8*v,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6,
    x^4*y*u
}
{
    y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*u*v,
    x^4*y*u
}
{
    x^5*u*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2*B,
    x^4*y*u
}
{
    x^7*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B^2,
    x^4*y*u
}
{
    x^2*y^3*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*B
}
{
    x^4*y*u,
    x^4*y*B
}
x^4*y*u
{}
{
    x^2*y^3*v,
    x^4*y*u
}
{
    x^2*y^3*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y,
    x^4*y*u
}
{
    x^10*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^4,
    x^4*y*u
}
{
    x^4*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*u,
    x^4*y*u
}
{
    x^7*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*A,
    x^4*y*u
}
{
    x^3*y^2*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7,
    x^4*y*u
}
{
    x^7,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B^2,
    x^4*y*u
}
{
    x^6*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*u
}
{
    x^4*y*u,
    x^4*u
}
x^4*y*u
{}
{
    x^6*v,
    x^4*y*u
}
{
    x^6*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*u*B,
    x^4*y*u
}
{
    x^3*y^2*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^2*B,
    x^4*y*u
}
{
    x^5*y^2*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^11*y^2
}
{
    x^4*y*u,
    x^11*y^2
}
x^4*y*u
{}
{
    x^5*y^5,
    x^4*y*u
}
{
    x^5*y^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^4,
    x^4*y*u
}
{
    x^3*y^4,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*y,
    x^4*y*u
}
{
    x^8*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*u,
    x^4*y*u
}
{
    x^5*y*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*v,
    x^4*y*u
}
{
    x^7*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*B^2,
    x^4*y*u
}
{
    x^4*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5,
    x^4*y*u
}
{
    x^5,
    x^4*y*u
}
x^4*y*u
{}
{
    x^12*B,
    x^4*y*u
}
{
    x^12*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*y^3*B,
    x^4*y*u
}
{
    x^6*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*v
}
{
    x^4*y*u,
    x^4*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x^2*y^4
}
{
    x^4*y*u,
    x^2*y^4
}
x^4*y*u
{}
{
    x^9*y^2,
    x^4*y*u
}
{
    x^9*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*u
}
{
    x^4*y*u,
    x^6*y^2*u
}
x^4*y*u
{}
{
    x^4*y*u,
    y^8
}
{
    x^4*y*u,
    y^8
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y
}
{
    x^4*y*u,
    x^6*y
}
x^4*y*u
{}
{
    x^7*A,
    x^4*y*u
}
{
    x^7*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y*v,
    x^4*y*u
}
{
    x^5*y*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x*y^5*u,
    x^4*y*u
}
{
    x*y^5*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^10*B
}
{
    x^4*y*u,
    x^10*B
}
x^4*y*u
{}
{
    x^4*y^3*B,
    x^4*y*u
}
{
    x^4*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^16,
    x^4*y*u
}
{
    x^16,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*u*B,
    x^4*y*u
}
{
    x^7*u*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^10*y^3,
    x^4*y*u
}
{
    x^10*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    y^6*B,
    x^4*y*u
}
{
    y^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^6,
    x^4*y*u
}
{
    x^4*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    y^8/x,
    x^4*y*u
}
{
    y^8/x,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y^2,
    x^4*y*u
}
{
    x^7*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*u,
    x^4*y*u
}
{
    x^4*y^2*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^6*y^2*v
}
{
    x^4*y*u,
    x^6*y^2*v
}
x^4*y*u
{}
{
    x^5*y*B^2,
    x^4*y*u
}
{
    x^5*y*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y,
    x^4*y*u
}
{
    x^4*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*A
}
{
    x^4*y*u,
    x^5*A
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^3*B
}
{
    x^4*y*u,
    x^3*y^3*B
}
x^4*y*u
{}
{
    x^3*y^6,
    x^4*y*u
}
{
    x^3*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^8*B,
    x^4*y*u
}
{
    x^8*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^14,
    x^4*y*u
}
{
    x^14,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^5*u*B
}
{
    x^4*y*u,
    x^5*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^8*y^3
}
{
    x^4*y*u,
    x^8*y^3
}
x^4*y*u
{}
{
    x^11*u,
    x^4*y*u
}
{
    x^11*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*y^3*u,
    x^4*y*u
}
{
    x^5*y^3*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*u
}
{
    x^4*y*u,
    x^3*y^2*u
}
x^4*y*u
{}
{
    x^5*y^2,
    x^4*y*u
}
{
    x^5*y^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*B^2,
    x^4*y*u
}
{
    x^4*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y^2*v,
    x^4*y*u
}
{
    x^4*y^2*v,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^3*B,
    x^4*y*u
}
{
    x^2*y^3*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^2*y^6,
    x^4*y*u
}
{
    x^2*y^6,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^9*y*B
}
{
    x^4*y*u,
    x^9*y*B
}
x^4*y*u
{}
{
    x^5*u^2,
    x^4*y*u
}
{
    x^5*u^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^6*B,
    x^4*y*u
}
{
    x^6*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^12
}
{
    x^4*y*u,
    x^12
}
x^4*y*u
{}
{
    x^6*y^3,
    x^4*y*u
}
{
    x^6*y^3,
    x^4*y*u
}
x^4*y*u
{}
{
    x^3*y^2*B^2,
    x^4*y*u
}
{
    x^3*y^2*B^2,
    x^4*y*u
}
x^4*y*u
{}
{
    x^5*v*B,
    x^4*y*u
}
{
    x^5*v*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^9*u,
    x^4*y*u
}
{
    x^9*u,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^3*y^2*v
}
{
    x^4*y*u,
    x^3*y^2*v
}
x^4*y*u
{}
{
    x^4*y*u,
    x*y^6
}
{
    x^4*y*u,
    x*y^6
}
x^4*y*u
{}
{
    x^4*y*A,
    x^4*y*u
}
{
    x^4*y*A,
    x^4*y*u
}
x^4*y*u
{}
{
    x^7*y*B,
    x^4*y*u
}
{
    x^7*y*B,
    x^4*y*u
}
x^4*y*u
{}
{
    x^13*y,
    x^4*y*u
}
{
    x^13*y,
    x^4*y*u
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*y*u*B
}
{
    x^4*y*u,
    x^4*y*u*B
}
x^4*y*u
{}
{
    x^4*y*u,
    x^7*y^4
}
{
    x^4*y*u,
    x^7*y^4
}
x^4*y*u
{}
{
    x^4*y*u,
    x^4*B
}
{
    x^4*y*u,
    x^4*B
}
x^4*y*u
{}
{
    x^10,
    x^4*y*u
}
{
    x^10,
    x^4*y*u
}
x^4*y*u
{}
{
    x
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:53:59 2004

Input: InfiniteSum(1/i,i)

Output: Magma V2.11-2     Fri Aug 27 2004 10:53:58 on modular  [Seed = 343547511]
   -------------------------------------


>> InfiniteSum(1/i,i);
                 ^
User error: Identifier 'i' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:54:37 2004

Input: InfiniteSum(i,1)

Output: Magma V2.11-2     Fri Aug 27 2004 10:54:37 on modular  [Seed = 410391120]
   -------------------------------------


>> InfiniteSum(i,1);
               ^
User error: Identifier 'i' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:55:00 2004

Input: m(i)=1/i; InfiniteSum(,1)

Output: Magma V2.11-2     Fri Aug 27 2004 10:54:59 on modular  [Seed = 3767462598]
   -------------------------------------


>> m(i)=1/i; InfiniteSum(,1);
          ^
User error: Identifier 'i' has not been declared or assigned

>> m(i)=1/i; InfiniteSum(,1);
                         ^
User error: bad syntax

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:55:20 2004

Input: m(i):=1/i; InfiniteSum(m,1)

Output: Magma V2.11-2     Fri Aug 27 2004 10:55:20 on modular  [Seed = 3901154005]
   -------------------------------------


>> m(i):=1/i; InfiniteSum(m,1);
           ^
User error: Identifier 'i' has not been declared or assigned

>> m(i):=1/i; InfiniteSum(m,1);
                          ^
User error: Identifier 'm' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:55:56 2004

Input: m:=1/i; InfiniteSum(m,1)

Output: Magma V2.11-2     Fri Aug 27 2004 10:55:55 on modular  [Seed = 4187485159]
   -------------------------------------


>> m:=1/i; InfiniteSum(m,1);
        ^
User error: Identifier 'i' has not been declared or assigned

>> m:=1/i; InfiniteSum(m,1);
                       ^
User error: Identifier 'm' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:56:14 2004

Input: m<i>:=1/i; InfiniteSum(m,1)

Output: Magma V2.11-2     Fri Aug 27 2004 10:56:13 on modular  [Seed = 3249523497]
   -------------------------------------


>> m<i>:=1/i; InfiniteSum(m,1);
           ^
User error: Identifier 'i' has not been declared or assigned

>> m<i>:=1/i; InfiniteSum(m,1);
                          ^
User error: Identifier 'm' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:58:45 2004

Input: m := function(i) return 1/i; end function;
InfiniteSum(m,1);

Output: Magma V2.11-2     Fri Aug 27 2004 10:58:44 on modular  [Seed = 3585857684]
   -------------------------------------


>> InfiniteSum(m,1);;
              ^
Runtime error in 'InfiniteSum': Bad argument types
Argument types given: UserProgram, RngIntElt

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 10:59:17 2004

Input: m := function(i) return 1/i; end function;
InfiniteSum(1/,1);

Output: Magma V2.11-2     Fri Aug 27 2004 10:59:16 on modular  [Seed = 3752973054]
   -------------------------------------


>> InfiniteSum(1/,1);;
                 ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 11:00:10 2004

Input: m := func<i,1/i>;
InfiniteSum(,1);

Output: Magma V2.11-2     Fri Aug 27 2004 11:00:09 on modular  [Seed = 3017653935]
   -------------------------------------


>> m := func<i,1/i>;
               ^
User error: bad syntax

>> InfiniteSum(,1);;
               ^
User error: bad syntax

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host p83.129.237.9.tisdip.tiscali.de. (83.129.237.9)
Time: Fri Aug 27 11:00:25 2004

Input: m := func<i|1/i>;
InfiniteSum(m,1);

Output: Magma V2.11-2     Fri Aug 27 2004 11:00:24 on modular  [Seed = 3151345238]
   -------------------------------------


>> InfiniteSum(m,1);;
              ^
Runtime error in 'InfiniteSum': Bad argument types
Argument types given: UserProgram, RngIntElt

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 19:54:35 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
			Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ S*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 19:54:30 on modular  [Seed = 2831556716]
   -------------------------------------


>> f :=x^6 + 2*x^5+ S*x^3 + 3*x + 1;
                     ^
Runtime error in '*': Bad argument types
Argument types given: SeqEnum[FldFunRatUElt], RngUPolElt[FldFunRat]
Done.

Total time: 0.809 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 19:55:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
			Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ b*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 19:55:15 on modular  [Seed = 2432571393]
   -------------------------------------

x^6 + 2*x^5 + 3*x + 1
x^6 + 2*x^5 + x^3 + 3*x + 1
x^6 + 2*x^5 + 2*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*x^3 + 3*x + 1
Done.

Total time: 7.629 seconds, Total memory usage: 8.16MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 19:57:28 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
			for v in [0..p-1] do
				Append(~S, v*t^3+u*t^2+r*t+s);
			end for;
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ b*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 19:57:07 on modular  [Seed = 2583106232]
   -------------------------------------

x^6 + 2*x^5 + 3*x + 1
x^6 + 2*x^5 + x^3 + 3*x + 1
x^6 + 2*x^5 + 2*x^3 + 3*x + 1
x^6 + 2*x^5 + 3*x^3 + 3*x + 1
x^6 + 2*x^5 + 4*x^3 + 3*x + 1


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 19:59:00 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
			for v in [1..p-1] do
				Append(~S, v*t^3+u*t^2+r*t+s);
			end for;
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ b*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 19:58:39 on modular  [Seed = 2280197210]
   -------------------------------------



************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:00:10 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ (t^3+b)*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:00:03 on modular  [Seed = 1862395161]
   -------------------------------------

Done.

Total time: 6.610 seconds, Total memory usage: 8.16MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:01:48 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ (2*t^3+b)*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:01:37 on modular  [Seed = 1177078866]
   -------------------------------------

Done.

Total time: 7.129 seconds, Total memory usage: 8.15MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:02:51 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ (3*t^3+b)*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:02:40 on modular  [Seed = 945205997]
   -------------------------------------

Done.

Total time: 7.100 seconds, Total memory usage: 8.16MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:03:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ (4*t^3+b)*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f;
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) and not isSS(f, p) then
	print f;
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:03:12 on modular  [Seed = 675717789]
   -------------------------------------

Done.

Total time: 7.159 seconds, Total memory usage: 8.16MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:14:19 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^4+ (b)*x^3 + x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if not isSS(G) then
	print f, " - not SS";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:14:18 on modular  [Seed = 1012052754]
   -------------------------------------


>> if not isSS(G) then
              ^
Runtime error: Number of arguments (1) does not equal expected number of 
arguments (2)
Done.

Total time: 1.089 seconds, Total memory usage: 7.56MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:14:43 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^4+ (b)*x^3 + x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if not isSS(f, p) then
	print f, " - not SS";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:14:36 on modular  [Seed = 608873276]
   -------------------------------------

x^6 + 2*x^4 + t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 2*t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 3*t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 4*t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
Done.

Total time: 6.969 seconds, Total memory usage: 8.26MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:15:04 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^4+ (b)*x^3 + x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if isSS(f, p) then
	print f, " - SS";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:14:57 on modular  [Seed = 742564825]
   -------------------------------------

Done.

Total time: 6.969 seconds, Total memory usage: 8.26MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:15:38 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [1..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ (b)*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if not isSS(f, p) then
	print f, " - not SS";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:15:32 on modular  [Seed = 343579588]
   -------------------------------------

Done.

Total time: 6.659 seconds, Total memory usage: 8.16MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:15:57 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^5+ (b)*x^3 + 3*x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if not isSS(f, p) then
	print f, " - not SS";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:15:49 on modular  [Seed = 477271005]
   -------------------------------------

x^6 + 2*x^5 + 3*x + 1
 - not IRR
x^6 + 2*x^5 + x^3 + 3*x + 1
 - not IRR
x^6 + 2*x^5 + 2*x^3 + 3*x + 1
 - not IRR
x^6 + 2*x^5 + 3*x^3 + 3*x + 1
 - not IRR
x^6 + 2*x^5 + 4*x^3 + 3*x + 1
 - not IRR
Done.

Total time: 7.600 seconds, Total memory usage: 8.16MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:16:34 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^4+ (b)*x^3 + x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if not isSS(f, p) then
	print f, " - not SS";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:16:26 on modular  [Seed = 74091434]
   -------------------------------------

x^6 + 2*x^4 + x + 1
 - not IRR
x^6 + 2*x^4 + t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 2*t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 3*t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 4*t^2*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + (t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 2*x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + (t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 3*x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + (t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 4*x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + (t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + t*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 2*t*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 2*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 3*t*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 3*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + 4*t*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 1)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 2)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 3)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (2*t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (3*t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
x^6 + 2*x^4 + (4*t^2 + 4*t + 4)*x^3 + x + 1
 - not SS
Done.

Total time: 8.030 seconds, Total memory usage: 8.26MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:16:59 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		for u in [0..p-1] do
				Append(~S, u*t^2+r*t+s);
		end for;
	end for;
end for;
 
for b in S do

f :=x^6 + 2*x^4+ (b)*x^3 + x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

end for;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 20:16:51 on modular  [Seed = 241205641]
   -------------------------------------

x^6 + 2*x^4 + x + 1
 - not IRR
x^6 + 2*x^4 + x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + 2*x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + 3*x^3 + x + 1
 - not IRR
x^6 + 2*x^4 + 4*x^3 + x + 1
 - not IRR
Done.

Total time: 7.940 seconds, Total memory usage: 8.26MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:26:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) and isA5(f) then
print "OK";
endif;


Output: Magma V2.11-2     Fri Aug 27 2004 20:26:22 on modular  [Seed = 1597099782]
   -------------------------------------


User error: syntax error at end of input

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:28:06 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) and isA5(f) then
       print "OK";
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:28:06 on modular  [Seed = 1177081511]
   -------------------------------------


Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:29:48 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) and isA5(f) then
	G, R :=  GaloisGroup(f);
	if isA5(G) then
		print "OK";
	end if;
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:29:47 on modular  [Seed = 1210505412]
   -------------------------------------


Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:30:03 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	if isA5(G) then
		print "OK";
	end if;
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:30:02 on modular  [Seed = 811508557]
   -------------------------------------


Total time: 0.710 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:30:20 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:30:20 on modular  [Seed = 945204051]
   -------------------------------------


Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:30:57 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
else if
	print "Not irreducible"
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:30:57 on modular  [Seed = 542028566]
   -------------------------------------


>>         print "Not irreducible"
           ^
User error: bad syntax

>> end if;;
   ^
User error: bad syntax

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:31:05 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
else if
	print "Not irreducible";
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:31:04 on modular  [Seed = 675724055]
   -------------------------------------


>>         print "Not irreducible";
           ^
User error: bad syntax

>> end if;;
   ^
User error: bad syntax

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:31:24 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 6*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
else
	print "Not irreducible";
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:31:23 on modular  [Seed = 258055203]
   -------------------------------------

Not irreducible

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:31:33 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * x^5 + 5 * x^4 + 2*x^3 + 10 * x^2 + 8 * x + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
else
	print "Not irreducible";
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:31:33 on modular  [Seed = 4103759846]
   -------------------------------------

Not irreducible

Total time: 0.710 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:33:00 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * u^5 + 5 * u^4 + 2*u^3 + 10 * u^2 + 8 * u + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
else
	print "Not irreducible";
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:32:59 on modular  [Seed = 3884545067]
   -------------------------------------

Permutation group G acting on a set of cardinality 6
    (1, 2, 3, 4, 6)
    (1, 4)(5, 6)
OK

Total time: 0.829 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Fri Aug 27 20:33:15 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

f:=u^6 + 2 * u^5 + 5 * u^4 + 6*u^3 + 10 * u^2 + 8 * u + 1;

if IsIrreducible(f) then
	G, R :=  GaloisGroup(f);
	print G;
	if isA5(G) then
		print "OK";
	end if;
else
	print "Not irreducible";
end if;

Output: Magma V2.11-2     Fri Aug 27 2004 20:33:14 on modular  [Seed = 4018240594]
   -------------------------------------

Permutation group G acting on a set of cardinality 6
    (1, 2, 3, 4, 6)
    (1, 4)(5, 6)
OK

Total time: 0.840 seconds, Total memory usage: 2.95MB


************** MAGMA *****************
Host 69-162-39-86.stcgpa.adelphia.net. (69.162.39.86)
Time: Fri Aug 27 22:54:46 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;
 
f :=x^6 + 2*x^4 + (-4*t+2)*x^3 + 5*x^2 + 6*x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
	continue;
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if isSS(f, p) then
	print f, " - SS";
end if;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 22:54:44 on modular  [Seed = 4154017146]
   -------------------------------------


>>         continue;
           ^
User error: A 'continue' can only be used inside a loop
Done.

Total time: 1.089 seconds, Total memory usage: 7.55MB


************** MAGMA *****************
Host 69-162-39-86.stcgpa.adelphia.net. (69.162.39.86)
Time: Fri Aug 27 22:55:05 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;
 
f :=x^6 + 2*x^4 + (-4*t+2)*x^3 + 5*x^2 + 6*x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
end if;

G, R:= GaloisGroup(f);

if not isA5(G) then
	print f, " - not A5";
end if;

if isSS(f, p) then
	print f, " - SS";
end if;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 22:55:04 on modular  [Seed = 4001389471]
   -------------------------------------

Done.

Total time: 1.089 seconds, Total memory usage: 7.56MB


************** MAGMA *****************
Host 69-162-39-86.stcgpa.adelphia.net. (69.162.39.86)
Time: Fri Aug 27 22:56:03 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;
 
f :=x^6 + 2*x^4 + (-4*t+2)*x^3 + 5*x^2 + 6*x + 1;

if not IsIrreducible(f) then 
	print f, " - not IRR";
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	print f, " - A5";
end if;

if isSS(f, p) then
	print f, " - SS";
end if;

print "Done."

Output: Magma V2.11-2     Fri Aug 27 2004 22:56:02 on modular  [Seed = 3867694045]
   -------------------------------------

x^6 + 2*x^4 + (t + 2)*x^3 + x + 1
 - A5
Done.

Total time: 1.079 seconds, Total memory usage: 7.56MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:38:42 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := [ Q | ];

for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

Append(~R, f);

end for;
end for;
end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:38:25 on modular  [Seed = 4203451360]
   -------------------------------------

[
    x^6 + 2*x^4 + 2*x^3 + x + 1,
    x^6 + 2*x^4 + 3*x^3 + x + 1,
    x^6 + 2*x^4 + 4*x^3 + x + 1,
    x^6 + 2*x^4 + x + 1,
    x^6 + 2*x^4 + x^3 + x + 1,
    x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + t*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 3*t*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
    x^6 + 2*x^5 + x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 2*x^2 + 1,
    x^6 + 4*x^5 + x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 3*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,
    x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 3*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
    x^6 + 3*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 3*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 4*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 2)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 1)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + 2*t^2*x^3 + (t^2 + 4*t)*x^2 + (2*t + 
        1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 4*t)*x^2 
        + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 4*t)*x^2 
        + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 4*t)*x^2 
        + (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + 4*t)*x^2 
        + (2*t + 1)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + t)*x^2 
        + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + t)*x^2 
        + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + t)*x^2 
        + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + t)*x^2 
        + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t)*x^3 + (t^2 + t)*x^2 + 
        (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + t)*x^2 + 
        (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t)*x^3 + (t
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:49:10 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

Include(~R, f);

end for;
end for;
end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:48:53 on modular  [Seed = 3651711607]
   -------------------------------------

{
    x^6 + (4*t + 2)*x^5 + (t + 1)*x^4 + (4*t + 2)*x^3 + (4*t + 2)*x^2 + (3*t + 
        4)*x + 3*t + 3,
    x^6 + 2*x^5 + (4*t^2 + 3*t + 3)*x^4 + (3*t^2 + 4*t)*x^3 + (4*t^2 + 1)*x^2 + 
        (2*t + 1)*x + 4*t + 2,
    x^6 + (3*t^2 + 2*t + 1)*x^4 + (t^2 + 2*t)*x^3 + (3*t^2 + 3)*x^2 + 3*t*x + t 
        + 4,
    x^6 + t*x^5 + (2*t^2 + 4*t + 2)*x^4 + (4*t^2 + 4*t + 1)*x^3 + (2*t^2 + 2*t +
        2)*x^2 + (3*t + 3)*x + 4*t,
    x^6 + (2*t + 3)*x^5 + (3*t^2 + t)*x^4 + (t^2 + t)*x^3 + (3*t^2 + 4*t + 
        2)*x^2 + 3*t*x + 2*t + 3,
    x^6 + (4*t + 2)*x^5 + (t^2 + 3*t + 3)*x^4 + (2*t^2 + t)*x^3 + (t^2 + t + 
        4)*x^2 + (3*t + 4)*x + 3*t + 3,
    x^6 + 4*t*x^5 + (2*t + 2)*x^4 + 3*t*x^2 + (t + 1)*x + 4*t + 1,
    x^6 + (4*t + 3)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 3*t + 2)*x^3 + (4*t^2 + 
        4)*x^2 + (3*t + 2)*x + 3*t + 2,
    x^6 + (t + 1)*x^5 + (3*t^2 + 2*t)*x^4 + (t^2 + 3*t + 4)*x^3 + (3*t^2 + 2*t +
        1)*x^2 + 4*x + 3*t,
    x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + 4*x^3 + (3*t + 4)*x^2 + (t + 3)*x + 
        4*t + 2,
    x^6 + 4*t*x^5 + (3*t^2 + 2*t + 2)*x^4 + (t^2 + 3)*x^3 + (3*t^2 + 3)*x^2 + 
        (3*t + 4)*x + 3*t + 2,
    x^6 + 2*x^5 + (4*t + 2)*x^4 + (t + 1)*x^3 + (4*t + 3)*x^2 + 4*x + 3,
    x^6 + (t + 1)*x^5 + 2*x^4 + (3*t + 3)*x^3 + (2*t + 2)*x^2 + (2*t + 3)*x + 
        2*t + 3,
    x^6 + (t + 2)*x^5 + (3*t + 3)*x^4 + 4*x^3 + (t + 2)*x^2 + (3*t + 2)*x + 4*t 
        + 4,
    x^6 + (2*t + 2)*x^5 + (3*t^2 + t + 1)*x^4 + (t^2 + 4*t + 3)*x^3 + (3*t^2 + t
        + 3)*x^2 + t,
    x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t)*x^3 + (t^2 + t)*x^2 + 3*x 
        + t + 2,
    x^6 + 3*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 3*t + 1,
    x^6 + (3*t + 1)*x^5 + (2*t^2 + t + 2)*x^4 + (4*t^2 + 3*t + 4)*x^3 + 
        2*t^2*x^2 + (4*t + 1)*x + 2*t + 4,
    x^6 + (4*t + 3)*x^4 + (t + 3)*x^3 + (3*t + 2)*x^2 + (4*t + 2)*x + 3*t + 3,
    x^6 + (2*t^2 + t + 1)*x^4 + (4*t^2 + 3*t + 3)*x^3 + (2*t^2 + 3*t + 1)*x^2 + 
        (2*t + 3)*x + 4*t,
    x^6 + (4*t + 1)*x^5 + 2*t*x^4 + (4*t + 4)*x^3 + (2*t + 1)*x^2 + 4*x + 2*t,
    x^6 + (4*t + 4)*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 2*t + 2)*x^3 + (4*t^2
        + 2*t + 3)*x^2 + (3*t + 4)*x + 3*t + 4,
    x^6 + (2*t + 4)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 4*t + 2)*x^3 + (4*t^2 + t
        + 1)*x^2 + (4*t + 4)*x + 4*t + 4,
    x^6 + (t + 1)*x^5 + (4*t + 3)*x^4 + (2*t + 4)*x^3 + (3*t + 1)*x^2 + (4*t + 
        1)*x + t + 4,
    x^6 + (2*t + 3)*x^5 + (4*t^2 + t + 4)*x^4 + (3*t^2 + 3*t + 1)*x^3 + (4*t^2 +
        4*t + 1)*x^2 + 3*t*x + 2*t + 3,
    x^6 + (t + 2)*x^5 + (t^2 + 2*t + 3)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 
        t)*x^2 + 4*t*x + t,
    x^6 + 2*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (2*t + 1)*x^2,
    x^6 + 3*x^5 + (2*t^2 + 3*t + 1)*x^4 + (4*t^2 + 1)*x^3 + (2*t^2 + 2*t + 
        2)*x^2 + (4*t + 4)*x + 3*t + 1,
    x^6 + 3*t*x^5 + 2*x^2 + 4*t + 4,
    x^6 + 4*t*x^5 + (2*t^2 + t + 1)*x^4 + (4*t^2 + t + 2)*x^3 + (2*t^2 + 3*t + 
        2)*x^2 + (2*t + 4)*x + t + 2,
    x^6 + (2*t^2 + t + 4)*x^4 + (4*t^2 + 3*t)*x^3 + (2*t^2 + 3*t)*x^2 + (2*t + 
        4)*x + 4*t + 2,
    x^6 + 4*t*x^5 + (4*t^2 + 3*t + 3)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 2*t
        + 4)*x^2 + (4*t + 4)*x + 2,
    x^6 + (t + 4)*x^5 + (4*t^2 + 4*t)*x^4 + (3*t^2 + t)*x^3 + 4*t^2*x^2 + (t + 
        3)*x + 2,
    x^6 + (t + 2)*x^5 + (3*t^2 + 3*t)*x^4 + (t^2 + 3*t + 2)*x^3 + (3*t^2 + t + 
        3)*x^2 + (3*t + 1)*x + 4*t + 2,
    x^6 + (t + 2)*x^5 + 2*x^4 + (4*t + 4)*x^3 + 4*t*x^2 + (4*t + 1)*x + t + 2,
    x^6 + 4*t*x^5 + (3*t^2 + t + 1)*x^4 + (t^2 + 3)*x^3 + (3*t^2 + 3*t + 1)*x^2 
        + (2*t + 3)*x + t,
    x^6 + (3*t + 2)*x^5 + (2*t^2 + 4*t + 1)*x^4 + (4*t^2 + 3)*x^3 + (2*t^2 + 4*t
        + 4)*x^2 + x + 4*t + 2,
    x^6 + 4*x^5 + (t^2 + 3*t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 2*t + 4)*x^2 
        + (4*t + 2)*x + 3*t,
    x^6 + x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 2*t + 1)*x^2 
        + (2*t + 3)*x + 4*t + 3,
    x^6 + (t + 4)*x^5 + (3*t^2 + 4*t + 1)*x^4 + (t^2 + 2*t + 1)*x^3 + (3*t^2 + 
        t)*x^2 + (2*t + 2)*x + 2*t,
    x^6 + 2*t*x^5 + (3*t^2 + 2)*x^4 + (t^2 + 2*t + 1)*x^3 + (3*t^2 + 2)*x^2 + 
        3*x + t,
    x^6 + (4*t + 4)*x^5 + (3*t^2 + 4)*x^4 + (t^2 + t + 2)*x^3 + (3*t^2 + 
        3*t)*x^2 + (3*t + 4)*x + 3*t + 4,
    x^6 + (t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 1)*x^3 + (4*t^2 + 4*t + 
        4)*x^2 + (4*t + 1)*x + t,
    x^6 + (t + 1)*x^5 + (2*t^2 + 2*t + 1)*x^4 + (4*t^2 + 4)*x^3 + (2*t^2 + 2*t +
        1)*x^2 + 3*x + 3*t + 3,
    x^6 + 2*t*x^5 + (2*t^2 + 3*t + 2)*x^4 + (4*t^2 + 4*t + 1)*x^3 + (2*t^2 + 
        3*t)*x^2 + x + t + 1,
    x^6 + (t + 3)*x^5 + (3*t^2 + 2*t + 1)*x^4 + (t^2 + 3*t + 3)*x^3 + (3*t^2 + 
        2*t + 2)*x^2 + 4*x + 3*t + 1,
    x^6 + x^5 + (4*t^2 + 4*t + 4)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 2)*x^2 
        + (t + 1)*x + 2*t + 4,
    x^6 + 3*x^5 + 2*t*x^4 + (t + 3)*x^3 + (3*t + 3)*x^2 + (t + 1)*x + 2*t,
    x^6 + (3*t + 3)*x^5 + x^4 + 2*x^3 + 2*x^2 + 4*x + 4*t + 1,
    x^6 + (4*t + 1)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + t + 
        3)*x^2 + t*x + 4*t + 2,
    x^6 + 2*x^5 + (t^2 + t + 3)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 4*t)*x^2 + 
        3*t*x + t,
    x^6 + 2*t*x^5 + (3*t^2 + 3*t + 4)*x^4 + (t^2 + 3*t + 2)*x^3 + (3*t^2 + 3*t +
        4)*x^2 + 3*x + t,
    x^6 + 4*x^5 + (2*t^2 + 2*t + 1)*x^4 + (4*t^2 + 2)*x^3 + (2*t^2 + 4*t + 
        2)*x^2 + (2*t + 4)*x + 4*t + 4,
    x^6 + (2*t + 1)*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 
        1)*x^2 + (3*t + 2)*x + 2*t + 1,
    x^6 + (2*t + 3)*x^5 + (4*t + 3)*x^4 + (t + 2)*x^3 + (2*t + 1)*x^2 + (3*t + 
        1)*x + 2*t,
    x^6 + 3*t*x^5 + (4*t^2 + 2*t + 3)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 4*t
        + 4)*x^2 + (2*t + 4)*x + 3*t + 2,
    x^6 + (3*t + 4)*x^5 + (3*t^2 + 2*t)*x^4 + (t^2 + 3)*x^3 + (3*t^2 + 3*t + 
        4)*x^2 + (t + 2)*x + t,
    x^6 + 3*t*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + t)*x^2 + 3*x + 
        4*t,
    x^6 + 4*t*x^5 + (2*t^2 + t + 4)*x^4 + 4*t^2*x^3 + (2*t^2 + 4*t)*x^2 + (3*t +
        4)*x + 3*t + 2,
    x^6 + (2*t + 3)*x^5 + (4*t^2 + 3)*x^4 + 3*t^2*x^3 + (4*t^2 + t + 3)*x^2 + (t
        + 3)*x + 3*t + 4,
    x^6 + 3*t*x^5 + (3*t + 3)*x^4 + 4*x^3 + (4*t + 4)*x^2 + (t + 4)*x + t + 2,
    x^6 + (t + 3)*x^5 + (2*t^2 + 4)*x^4 + (4*t^2 + t + 1)*x^3 + (2*t^2 + 3*t + 
        1)*x^2 + 3*t*x + 4*t + 3,
    x^6 + 4*x^5 + (3*t + 3)*x^4 + (2*t + 3)*x^3 + (3*t + 1)*x^2 + x + 3,
    x^6 + (3*t + 1)*x^5 + (3*t^2 + t + 4)*x^4 + (t^2 + 3*t + 4)*x^3 + (3*t^2 + 
        3*t + 2)*x^2 + (2*t + 1)*x + 3*t + 4,
    x^6 + (t + 2)*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 2*t + 2,
    x^6 + (2*t + 2)*x^5 + (t^2 + 2)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 2*t + 3)*x^2 
        + (2*t + 4)*x + 3,
    x^6 + (4*t + 3)*x^5 + (3*t^2 + 4*t + 2)*x^4 + (t^2 + 2*t + 3)*x^3 + (3*t^2 +
        4)*x^2 + t*x + 4*t + 3,
    x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (2*t + 3)*x^2 + (t + 2)*x + 3*t,
    x^6 + (2*t^2 + 4*t + 1)*x^4 + (4*t^2 + 2*t + 3)*x^3 + (2*t^2 + 2*t + 1)*x^2 
        + (3*t + 3)*x + t,
    x^6 + (t + 1)*x^5 + (3*t^2 + t + 2)*x^4 + (t^2 + t + 2)*x^3 + (3*t^2 + t + 
        1)*x^2 + 2*x + 3*t + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 4*t +
        1)*x^2 + 4*x + t + 3,
    x^6 + x^5 + (3*t + 3)*x^4 + (3*t + 3)*x^3 + 3*t*x^2 + 2,
    x^6 + 3*x^5 + (3*t + 4)*x^4 + 4*t*x^3 + (3*t + 2)*x^2 + x,
    x^6 + 2*x^5 + (t^2 + t + 3)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 1)*x^2 + (4*t +
        1)*x + 3*t + 2,
    x^6 + x^5 + (4*t^2 + t + 4)*x^4 + (3*t^2 + 4*t + 4)*x^3 + (4*t^2 + 4*t + 
        1)*x^2 + 3*t*x + t + 2,
    x^6 + (t + 3)*x^5 + (4*t + 1)*x^4 + t*x^3 + (t + 1)*x^2 + (2*t + 3)*x + 2*t 
        + 4,
    x^6 + (4*t^2 + 4*t + 4)*x^4 + (3*t^2 + t)*x^3 + (4*t^2 + t)*x^2 + (2*t + 
        4)*x + 4*t + 2,
    x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
    x^6 + (2*t + 3)*x^5 + (3*t^2 + t + 3)*x^4 + (t^2 + 4*t + 2)*x^3 + (3*t^2 + t
        + 1)*x^2 + x + t,
    x^6 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 4*t + 3)*x^2 + (t + 
        4)*x + 2*t + 2,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 
        4*t)*x^2 + (3*t + 3)*x + 1,
    x^6 + (2*t + 3)*x^5 + (2*t^2 + 2*t + 3)*x^4 + (4*t^2 + 3*t + 2)*x^3 + (2*t^2
        + 3*t)*x^2 + t*x + 3*t + 3,
    x^6 + (2*t + 1)*x^5 + (2*t^2 + 2*t + 1)*x^4 + (4*t^2 + 2*t + 4)*x^3 + (2*t^2
        + 2*t + 1)*x^2 + 3*x + t + 3,
    x^6 + (t + 3)*x^5 + (3*t^2 + 2*t)*x^4 + (t^2 + t + 2)*x^3 + (3*t^2 + 4)*x^2 
        + (3*t + 2)*x + 4*t + 2,
    x^6 + (2*t + 1)*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 3*t + 2)*x^3 + (4*t^2 +
        t + 4)*x^2 + t + 2,
    x^6 + (4*t + 3)*x^5 + (t + 4)*x^4 + 3*t*x^3 + (2*t + 4)*x^2 + (t + 3)*x + 
        4*t + 4,
    x^6 + (3*t + 3)*x^5 + (3*t^2 + 4*t + 3)*x^4 + (t^2 + t + 2)*x^3 + (3*t^2 + 
        4*t + 1)*x^2 + x + 4*t,
    x^6 + (3*t + 2)*x^5 + (t^2 + 2)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 3*t + 3)*x^2 
        + (3*t + 4)*x + 3,
    x^6 + (3*t + 2)*x^5 + (t^2 + 3*t + 3)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 4)*x^2 
        + (2*t + 4)*x + 3*t + 3,
    x^6 + (3*t + 2)*x^5 + 4*t^2*x^4 + (3*t^2 + 4*t + 3)*x^3 + (4*t^2 + 1)*x^2 + 
        4*x + 4*t + 3,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 4*t)*x^2 + 
        (3*t + 3)*x + 1,
    x^6 + 4*t*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + t)*x^3 + (4*t^2 + 4*t + 2)*x^2 
        + t*x + 4*t + 4,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 2*t +
        2)*x^2 + 3*t*x + 1,
    x^6 + (2*t + 3)*x^5 + (3*t^2 + 2*t + 4)*x^4 + (t^2 + 3*t + 1)*x^3 + (3*t^2 +
        t + 1)*x^2 + 4*t*x + 4*t + 3,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + t)*x^2 
        + 3*x + 4*t + 1,
    x^6 + (t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 3*t + 
        2)*x^2 + 4*t
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:49:46 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

b=0;
for c in S do
for d in S do

f := brumer(b, c, d);

Include(~R, f);

end for;
end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:49:45 on modular  [Seed = 3618028965]
   -------------------------------------


>> b=0;
   ^
User error: Identifier 'b' has not been declared or assigned

>> f := brumer(b, c, d);
               ^
User error: Identifier 'b' has not been declared or assigned
{}
Done.

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:50:01 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

b := 0;
for c in S do
for d in S do

f := brumer(b, c, d);

Include(~R, f);

end for;
end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:49:59 on modular  [Seed = 3485377955]
   -------------------------------------

{
    x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
    x^6 + t*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 2*t + 4)*x^3 + (4*t^2 + 
        2*t)*x^2 + (t + 1)*x + 1,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 2*t + 
        2)*x^2 + 3*t*x + 1,
    x^6 + (t + 2)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 4*t + 4)*x^3 + (4*t^2 + 
        3*t)*x^2 + (t + 3)*x + 1,
    x^6 + 4*t*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 3*t + 3)*x^3 + (4*t^2 + 
        3*t)*x^2 + (4*t + 1)*x + 1,
    x^6 + (4*t + 1)*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + t + 1)*x^3 + (4*t^2 + 
        1)*x^2 + (4*t + 2)*x + 1,
    x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1,
    x^6 + (4*t + 2)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + 2*t)*x^3 + (4*t^2 + 
        2*t)*x^2 + (4*t + 3)*x + 1,
    x^6 + t*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 3*t)*x^3 + (4*t^2 + 2*t)*x^2 + 
        (t + 1)*x + 1,
    x^6 + 3*t*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 2*t + 2)*x^3 + (t^2 + t)*x^2 
        + (3*t + 1)*x + 1,
    x^6 + (3*t + 1)*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 
        1)*x^2 + (3*t + 2)*x + 1,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 
        4*t)*x^2 + (3*t + 3)*x + 1,
    x^6 + (4*t + 2)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 
        2*t)*x^2 + (4*t + 3)*x + 1,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 2*t +
        2)*x^2 + 3*t*x + 1,
    x^6 + (2*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 2*t + 
        2)*x^2 + (2*t + 4)*x + 1,
    x^6 + (4*t + 1)*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 4*t + 3)*x^3 + (4*t^2 +
        1)*x^2 + (4*t + 2)*x + 1,
    x^6 + 3*t*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 4)*x^3 + (t^2 + t)*x^2 + (3*t
        + 1)*x + 1,
    x^6 + 4*x^5 + 2*x^2 + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + (3*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 3*t + 
        2)*x^2 + (3*t + 4)*x + 1,
    x^6 + (2*t + 1)*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 
        1)*x^2 + (2*t + 2)*x + 1,
    x^6 + (4*t + 4)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + t)*x^3 + (4*t^2 + t + 
        2)*x^2 + 4*t*x + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + (2*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 2*t + 
        2)*x^2 + (2*t + 4)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + 2*x^4 + 3*x^3 + x + 1,
    x^6 + (3*t + 1)*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 1)*x^3 + (t^2 + 
        1)*x^2 + (3*t + 2)*x + 1,
    x^6 + (t + 4)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + t + 2)*x^3 + (4*t^2 + 4*t +
        2)*x^2 + t*x + 1,
    x^6 + (t + 1)*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 4)*x^3 + (4*t^2 + 
        1)*x^2 + (t + 2)*x + 1,
    x^6 + (4*t + 4)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 2*t + 4)*x^3 + (4*t^2 + t
        + 2)*x^2 + 4*t*x + 1,
    x^6 + (t + 2)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + t + 1)*x^3 + (4*t^2 + 
        3*t)*x^2 + (t + 3)*x + 1,
    x^6 + (t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 3*t + 2)*x^3 + (4*t^2 + t + 
        2)*x^2 + (t + 4)*x + 1,
    x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
    x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + 3*t + 2)*x^2 
        + 2*t*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 3*t + 3)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (t + 1)*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + t)*x^3 + (4*t^2 + 
        1)*x^2 + (t + 2)*x + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + (4*t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 4*t
        + 2)*x^2 + (4*t + 4)*x + 1,
    x^6 + (4*t + 4)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 4*t + 2)*x^3 + (4*t^2 + t
        + 2)*x^2 + 4*t*x + 1,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 2*t + 
        2)*x^2 + 3*t*x + 1,
    x^6 + 4*t*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 2*t)*x^3 + (4*t^2 + 
        3*t)*x^2 + (4*t + 1)*x + 1,
    x^6 + (4*t + 1)*x^5 + (4*t^2 + t + 2)*x^4 + 3*t^2*x^3 + (4*t^2 + 1)*x^2 + 
        (4*t + 2)*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + (4*t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 2*t)*x^3 + (4*t^2 + 4*t + 
        2)*x^2 + (4*t + 4)*x + 1,
    x^6 + t*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 2*t + 1)*x^3 + (4*t^2 + 
        2*t)*x^2 + (t + 1)*x + 1,
    x^6 + (t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 4*t + 4)*x^3 + (4*t^2 + t + 
        2)*x^2 + (t + 4)*x + 1,
    x^6 + 4*t*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 
        3*t)*x^2 + (4*t + 1)*x + 1,
    x^6 + (4*t + 1)*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + t + 4)*x^3 + (4*t^2 + 
        1)*x^2 + (4*t + 2)*x + 1,
    x^6 + 3*t*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + t)*x^2 
        + (3*t + 1)*x + 1,
    x^6 + (3*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 3*t + 
        2)*x^2 + (3*t + 4)*x + 1,
    x^6 + (t + 1)*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 4*t + 2)*x^3 + (4*t^2 +
        1)*x^2 + (t + 2)*x + 1,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 3*t)*x^3 + (t^2 + 4*t)*x^2 + 
        (3*t + 3)*x + 1,
    x^6 + (4*t + 2)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + 2*t + 3)*x^3 + (4*t^2 + 
        2*t)*x^2 + (4*t + 3)*x + 1,
    x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 4*t + 2)*x^3 + (t^2 + 3*t + 
        2)*x^2 + 2*t*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + (3*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 3*t + 
        2)*x^2 + (3*t + 4)*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + (2*t + 1)*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 3*t + 2)*x^3 + (t^2 + 
        1)*x^2 + (2*t + 2)*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + (4*t + 4)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 1)*x^3 + (4*t^2 + t + 
        2)*x^2 + 4*t*x + 1,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (3*t + 3)*x + 1,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 2*t + 
        2)*x^2 + 3*t*x + 1,
    x^6 + (2*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 2*t + 
        2)*x^2 + (2*t + 4)*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + t)*x^2 
        + (2*t + 3)*x + 1,
    x^6 + (t + 4)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + 3)*x^3 + (4*t^2 + 4*t + 
        2)*x^2 + t*x + 1,
    x^6 + (2*t + 1)*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 
        1)*x^2 + (2*t + 2)*x + 1,
    x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1,
    x^6 + (t + 2)*x^5 + (4*t^2 + 2*t)*x^4 + 3*t^2*x^3 + (4*t^2 + 3*t)*x^2 + (t +
        3)*x + 1,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3*t + 4)*x^3 + (t^2 + 
        4*t)*x^2 + (2*t + 1)*x + 1,
    x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + (2*t^2 + t + 4)*x^3 + (t^2 + 3*t + 
        2)*x^2 + 2*t*x + 1,
    x^6 + (3*t + 1)*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 
        1)*x^2 + (3*t + 2)*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + 2*t^2*x^3 + (t^2 + t)*x^2 + (2*t + 
        3)*x + 1,
    x^6 + (t + 1)*x^5 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 1)*x^3 + (4*t^2 + 
        1)*x^2 + (t + 2)*x + 1,
    x^6 + (2*t + 1)*x^5 + (t^2 + 3*t + 2)*x^4 + 2*t^2*x^3 + (t^2 + 1)*x^2 + (2*t
        + 2)*x + 1,
    x^6 + (4*t + 4)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 3*t + 3)*x^3 + (4*t^2 + t
        + 2)*x^2 + 4*t*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + t + 2)*x^3 + (t^2 + 2*t + 
        2)*x^2 + 3*t*x + 1,
    x^6 + (2*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 2*t + 
        2)*x^2 + (2*t + 4)*x + 1,
    x^6 + 4*x^5 + 2*x^3 + 2*x^2 + 1,
    x^6 + (t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 3*t + 1)*x^3 + (4*t^2 + t + 
        2)*x^2 + (t + 4)*x + 1,
    x^6 + (2*t + 4)*x^5 + (t^2 + t)*x^4 + 2*t^2*x^3 + (t^2 + 3*t + 2)*x^2 + 
        2*t*x + 1,
    x^6 + (4*t + 1)*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 3*t + 3)*x^3 + (4*t^2 +
        1)*x^2 + (4*t + 2)*x + 1,
    x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + (4*t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 3*t + 3)*x^3 + (4*t^2 + 4*t
        + 2)*x^2 + (4*t + 4)*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + 2*t*x^5 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 1,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + 3*t*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + t)*x^2 + 
        (3*t + 1)*x + 1,
    x^6 + (t + 4)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + 4*t + 1)*x^3 + (4*t^2 + 4*t
        + 2)*x^2 + t*x + 1,
    x^6 + (3*t + 2)*x^5 + (t^2 + t)*x^4 + (2*t^2 + 1)*x^3 + (t^2 + 4*t)*x^2 + 
        (3*t + 3)*x + 1,
    x^6 + (4*t + 2)*x^5 + (4*t^2 + 3*t)*x^4 + (3*t^2 + t + 2)*x^3 + (4*t^2 + 
        2*t)*x^2 + (4*t + 3)*x + 1,
    x^6 + 2*x^4 + x^3 + x + 1,
    x^6 + (3*t + 4)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 2*t + 4)*x^3 + (t^2 + 2*t +
        2)*x^2 + 3*t*x + 1,
    x^6 + t*x^5 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 2*t + 2)*x^3 + (4*t^2 + 
        2*t)*x^2 + (t + 1)*x + 1,
    x^6 + (t + 2)*x^5 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 4*t + 2)*x^3 + (4*t^2 + 
        3*t)*x^2 + (t + 3)*x + 1,
    x^6 + (t + 3)*x^5 + (4*t^2 + 1)*x^4 + (3*t^2 + 4*t + 3)*x^3 + (4*t^2 + t + 
        2)*x^2 + (t + 4)*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + (2*t + 2)*x^5 + (t^2 + 4*t)*x^4 + (2*t^2 + 4*t + 3)*x^3 + (t^2 + 
        t)*x^2 + (2*t + 3)*x + 1,
    x^6 + (3*t + 3)*x^5 + (t^2 + 1)*x^4 + (2*t^2 + t + 3)*x^3 + (t^2 + 3*t + 
        2)*x^2 + (3*t + 4)*x + 1,
    x^6 + (2*t + 1)*x^5 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 4*t + 1)*x^3 + (t^2 + 
        1)*x^2 + (2*t + 2)*x + 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:51:12 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

c := 0;
for b in S do
for d in S do

f := brumer(b, c, d);

Include(~R, f);

end for;
end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:51:10 on modular  [Seed = 3350638050]
   -------------------------------------

{
    x^6 + (t^2 + 4*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (3*t^2 + 3*t + 2)*x^4 + (t^2 + 3*t)*x^3 + (3*t^2 + 2*t + 4)*x^2 + 
        4*t*x + 3*t + 4,
    x^6 + (t + 1)*x^4 + (t + 2)*x^3 + (t + 2)*x^2 + 4*x + 2,
    x^6 + (3*t + 2)*x^4 + (2*t + 4)*x^3 + (3*t + 1)*x^2 + 2*x + 3,
    x^6 + (2*t + 3)*x^4 + (3*t + 3)*x^3 + (2*t + 2)*x^2 + 2*x + 3,
    x^6 + (2*t^2 + t + 1)*x^4 + (4*t^2 + t + 2)*x^3 + (2*t^2 + 4*t + 2)*x^2 + 
        (3*t + 4)*x + t + 2,
    x^6 + (2*t^2 + 4)*x^4 + (4*t^2 + 4*t + 2)*x^3 + (2*t^2 + 3*t + 3)*x^2 + (3*t
        + 2)*x + t + 3,
    x^6 + (t^2 + t)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + 1)*x^2 + (4*t + 4)*x + 
        3*t + 2,
    x^6 + (4*t^2 + 3)*x^4 + 3*t^2*x^3 + (4*t^2 + t)*x^2 + t*x + 2*t + 4,
    x^6 + (4*t^2 + 1)*x^4 + (3*t^2 + 2*t)*x^3 + (4*t^2 + 3*t + 3)*x^2 + 3*t*x + 
        t + 4,
    x^6 + (3*t^2 + 4*t + 2)*x^4 + (t^2 + t + 3)*x^3 + (3*t^2 + 2*t)*x^2 + (3*t +
        1)*x + t + 1,
    x^6 + 2*t^2*x^4 + (4*t^2 + 4*t + 1)*x^3 + (2*t^2 + 4*t + 4)*x^2 + (4*t + 
        2)*x + 3*t + 3,
    x^6 + (t^2 + t)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 4*t + 4)*x^2 + (3*t + 
        2)*x + t + 3,
    x^6 + (t^2 + t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 3*t + 2)*x^2 + 2*t*x + 4*t 
        + 4,
    x^6 + (t^2 + 1)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + t + 3)*x^2 + t*x + 2*t + 4,
    x^6 + (3*t^2 + 3*t + 1)*x^4 + (t^2 + 3*t)*x^3 + (3*t^2 + 3)*x^2 + 2*t*x + 
        4*t + 4,
    x^6 + (4*t + 1)*x^4 + t*x^3 + (3*t + 3)*x^2 + 4*t*x + 3*t + 4,
    x^6 + (2*t^2 + 3*t + 3)*x^4 + 4*t^2*x^3 + (2*t^2 + 2*t)*x^2 + 4*t*x + 3*t + 
        4,
    x^6 + (3*t^2 + 4)*x^4 + (t^2 + 2*t + 2)*x^3 + (3*t^2 + 2*t + 4)*x^2 + (2*t +
        3)*x + 4*t,
    x^6 + (2*t^2 + 2*t + 2)*x^4 + (4*t^2 + 3*t)*x^3 + 2*t^2*x^2 + (3*t + 1)*x + 
        t + 1,
    x^6 + x^4 + 2*x^3 + 2*x^2 + 4*x + 2,
    x^6 + (3*t + 3)*x^4 + (3*t + 4)*x^3 + (4*t + 3)*x^2 + (t + 3)*x + 2*t,
    x^6 + (4*t^2 + 4*t + 3)*x^4 + (3*t^2 + 3*t + 4)*x^3 + (4*t^2 + 3*t + 3)*x^2 
        + (4*t + 3)*x + 3*t,
    x^6 + (4*t^2 + 3)*x^4 + (3*t^2 + 2*t + 4)*x^3 + (4*t^2 + 3*t + 3)*x^2 + (3*t
        + 3)*x + t,
    x^6 + (3*t^2 + t)*x^4 + (t^2 + 1)*x^3 + (3*t^2 + 4*t + 1)*x^2 + (3*t + 4)*x 
        + t + 2,
    x^6 + (3*t^2 + 2*t + 1)*x^4 + (t^2 + t)*x^3 + (3*t^2 + 4*t)*x^2 + (2*t + 
        2)*x + 4*t + 3,
    x^6 + (2*t^2 + 2*t + 3)*x^4 + 4*t^2*x^3 + (2*t^2 + 3*t)*x^2 + t*x + 2*t + 4,
    x^6 + (3*t^2 + 2*t + 4)*x^4 + (t^2 + 2*t + 2)*x^3 + (3*t^2 + 3*t + 4)*x^2 + 
        (t + 3)*x + 2*t,
    x^6 + (t + 4)*x^4 + (t + 1)*x^2 + 4,
    x^6 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 3)*x^3 + (4*t^2 + 3*t + 3)*x^2 + (2*t +
        4)*x + 4*t + 2,
    x^6 + (t^2 + 1)*x^4 + (2*t^2 + t)*x^3 + (t^2 + 4*t)*x^2 + (4*t + 2)*x + 3*t 
        + 3,
    x^6 + (2*t^2 + 4*t + 2)*x^4 + (4*t^2 + 4*t)*x^3 + 2*t^2*x^2 + (t + 1)*x + 
        2*t + 1,
    x^6 + (4*t^2 + 4*t + 3)*x^4 + 3*t^2*x^3 + (4*t^2 + 2*t)*x^2 + 3*t*x + t + 4,
    x^6 + 2*x^4 + (2*t + 2)*x^3 + t*x^2 + (t + 1)*x + 2*t + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + (2*t + 4)*x^4 + 2*t*x^3 + 2*t*x^2 + 4*x + 2,
    x^6 + 3*t*x^4 + (3*t + 2)*x^2 + 4,
    x^6 + 2*x^4 + 3*x^3 + x + 1,
    x^6 + (t^2 + 4*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 3*t + 1)*x^2 + 
        (4*t + 2)*x + 3*t + 3,
    x^6 + 2*x^4 + (t + 4)*x^3 + (3*t + 1)*x^2 + (3*t + 2)*x + t + 3,
    x^6 + 4*t*x^4 + 2*t*x^3 + 4*t*x^2 + 3*x,
    x^6 + t*x^4 + 3*t*x^3 + (4*t + 2)*x^2 + 3*t*x + t + 4,
    x^6 + (t^2 + 3*t + 4)*x^4 + (2*t^2 + t)*x^3 + (t^2 + t)*x^2 + (3*t + 4)*x + 
        t + 2,
    x^6 + (3*t^2 + 2)*x^4 + (t^2 + 3*t + 2)*x^3 + (3*t^2 + 3*t)*x^2 + (3*t + 
        1)*x + t + 1,
    x^6 + (3*t + 2)*x^4 + (3*t + 3)*x^3 + (3*t + 3)*x^2 + 4*x + 2,
    x^6 + (t + 2)*x^4 + (4*t + 1)*x + 3*t + 1,
    x^6 + (3*t + 3)*x^4 + (3*t + 4)*x^3 + (3*t + 4)*x^2 + 4*x + 2,
    x^6 + (2*t^2 + 4*t + 2)*x^4 + (4*t^2 + 2*t + 3)*x^3 + (2*t^2 + 2*t)*x^2 + 
        (3*t + 1)*x + t + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + (2*t + 4)*x^4 + (t + 2)*x^3 + (2*t + 4)*x^2 + 3*x,
    x^6 + (t^2 + 2*t + 4)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 1)*x^2 + 3*t*x + t + 
        4,
    x^6 + 2*t^2*x^4 + (4*t^2 + 4*t + 1)*x^3 + (2*t^2 + 3*t + 1)*x^2 + (3*t + 
        4)*x + t + 2,
    x^6 + (3*t + 2)*x^4 + (2*t + 4)*x^3 + t*x^2 + (3*t + 1)*x + t + 1,
    x^6 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 4*t + 1)*x^3 + (4*t^2 + 4*t)*x^2 + (3*t
        + 1)*x + t + 1,
    x^6 + (3*t + 2)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + 3*x,
    x^6 + (2*t^2 + 4)*x^4 + (4*t^2 + t + 2)*x^3 + (2*t^2 + 2*t + 3)*x^2 + (2*t +
        2)*x + 4*t + 3,
    x^6 + (t^2 + 1)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + t)*x^2 + (t + 2)*x + 2*t + 
        3,
    x^6 + (t + 1)*x^4 + 4*t*x^3 + (2*t + 3)*x^2 + t*x + 2*t + 4,
    x^6 + (2*t^2 + 2*t + 3)*x^4 + (4*t^2 + 4)*x^3 + (2*t^2 + 4*t + 4)*x^2 + (2*t
        + 4)*x + 4*t + 2,
    x^6 + (t + 4)*x^4 + (4*t + 2)*x^3 + (t + 3)*x^2 + 2*x + 3,
    x^6 + (2*t^2 + 3*t + 2)*x^4 + (4*t^2 + 2*t + 3)*x^3 + (2*t^2 + 3)*x^2 + (2*t
        + 4)*x + 4*t + 2,
    x^6 + (3*t^2 + 3*t + 2)*x^4 + (t^2 + 4*t + 4)*x^3 + (3*t^2 + t)*x^2 + (3*t +
        1)*x + t + 1,
    x^6 + t*x^4 + 3*t*x^3 + t*x^2 + 3*x,
    x^6 + (3*t^2 + 2*t + 4)*x^4 + (t^2 + t)*x^3 + (3*t^2 + t)*x^2 + (4*t + 4)*x 
        + 3*t + 2,
    x^6 + 2*t^2*x^4 + (4*t^2 + 4*t)*x^3 + (2*t^2 + 3*t)*x^2 + (3*t + 3)*x + t,
    x^6 + 4*t*x^4 + (4*t + 2)*x^2 + 4,
    x^6 + (3*t^2 + 3*t + 2)*x^4 + (t^2 + 3*t + 1)*x^3 + (3*t^2 + 2*t)*x^2 + (4*t
        + 1)*x + 3*t + 1,
    x^6 + (t^2 + 2*t + 3)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 4)*x^2 + (3*t + 
        4)*x + t + 2,
    x^6 + (t^2 + t)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 4*t)*x^2 + (3*t + 3)*x + t,
    x^6 + (3*t^2 + t + 3)*x^4 + (t^2 + 4)*x^3 + (3*t^2 + 4*t + 3)*x^2 + (3*t + 
        3)*x + t,
    x^6 + (2*t^2 + t + 2)*x^4 + (4*t^2 + t + 1)*x^3 + (2*t^2 + 2)*x^2 + (4*t + 
        3)*x + 3*t,
    x^6 + (2*t + 3)*x^4 + 3*t*x + t + 4,
    x^6 + (4*t^2 + 3*t + 1)*x^4 + (3*t^2 + 3*t + 2)*x^3 + (4*t^2 + t + 2)*x^2 + 
        (3*t + 4)*x + t + 2,
    x^6 + (t^2 + 2*t + 4)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + t + 4)*x^2 + (4*t + 
        3)*x + 3*t,
    x^6 + 2*x^4 + (4*t + 1)*x^3 + (2*t + 2)*x^2 + (2*t + 3)*x + 4*t,
    x^6 + (2*t^2 + 4)*x^4 + (4*t^2 + t)*x^3 + (2*t^2 + t)*x^2 + (t + 4)*x + 2*t 
        + 2,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
    x^6 + (t + 3)*x^4 + (t + 4)*x^3 + (t + 4)*x^2 + 4*x + 2,
    x^6 + (2*t^2 + 2*t + 2)*x^4 + (4*t^2 + 3*t)*x^3 + (2*t^2 + t + 4)*x^2 + 
        4*t*x + 3*t + 4,
    x^6 + (3*t^2 + t)*x^4 + (t^2 + 4*t)*x^3 + (3*t^2 + 3*t)*x^2 + (2*t + 3)*x + 
        4*t,
    x^6 + (4*t^2 + 2*t)*x^4 + (3*t^2 + 4*t)*x^3 + (4*t^2 + t + 2)*x^2 + 4*t*x + 
        3*t + 4,
    x^6 + (t^2 + 3)*x^4 + 2*t^2*x^3 + (t^2 + 2*t)*x^2 + 2*t*x + 4*t + 4,
    x^6 + (4*t + 3)*x^4 + t*x + 2*t + 4,
    x^6 + (2*t^2 + t + 4)*x^4 + (4*t^2 + t + 2)*x^3 + (2*t^2 + 3)*x^2 + (4*t + 
        2)*x + 3*t + 3,
    x^6 + (3*t + 1)*x^4 + (3*t + 3)*x^2 + 4,
    x^6 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 3)*x^2 + (t + 2)*x + 2*t + 3,
    x^6 + (4*t^2 + 3*t)*x^4 + (3*t^2 + 4*t + 1)*x^3 + (4*t^2 + 1)*x^2 + (2*t + 
        4)*x + 4*t + 2,
    x^6 + (4*t^2 + 4*t + 4)*x^4 + (3*t^2 + t)*x^3 + (4*t^2 + t)*x^2 + (2*t + 
        4)*x + 4*t + 2,
    x^6 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 3)*x^3 + (t^2 + t + 3)*x^2 + (4*t + 
        4)*x + 3*t + 2,
    x^6 + (t^2 + 2)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 3*t)*x^2 + (3*t + 1)*x + t + 
        1,
    x^6 + (3*t^2 + t + 2)*x^4 + (t^2 + 1)*x^3 + (3*t^2 + 2*t + 2)*x^2 + (t + 
        3)*x + 2*t,
    x^6 + (4*t^2 + 4*t + 4)*x^4 + (3*t^2 + 3*t)*x^3 + (4*t^2 + 3*t)*x^2 + (4*t +
        4)*x + 3*t + 2,
    x^6 + (4*t^2 + t + 4)*x^4 + (3*t^2 + 2*t + 2)*x^3 + (4*t^2 + 2*t + 3)*x^2 + 
        (t + 2)*x + 2*t + 3,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + (t^2 + 2*t + 4)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + t + 3)*x^2 + (4*t + 
        2)*x + 3*t + 3,
    x^6 + (2*t^2 + 3*t + 2)*x^4 + (4*t^2 + 1)*x^3 + (2*t^2 + 2*t)*x^2 + (4*t + 
        1)*x + 3*t + 1,
    x^6 + (3*t^2 + t + 2)*x^4 + (t^2 + 4)*x^3 + (3*t^2 + 4*t + 1)*x^2 + (3*t + 
        2)*x + t + 3,
    x^6 + (2*t^2 + 3*t + 3)*x^4 + (4*t^2 + 4)*x^3 + (2*t^2 + 2*t + 3)*x^2 + (4*t
        + 3)*x + 3*t,
    x^6 + (t^2 + 3*t + 4)*x^4 + (2*t^2 + 2*t)*x^3 + (t^2 + 2*t)*x^2 + (4*t + 
        4)*x + 3*t + 2,
    x^6 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 3)*x^3 + (4*t^2 + 3*t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + 2*x^4 + x^3 + x + 1,
    x^6 + (2*t^2 + t + 2)*x^4 + (4*t^2 + 3*t + 3)*x^3 + (2*t^2 + 3*t)*x^2 + (2*t
        + 1)*x + 4*t + 1,
    x^6 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t)*x^3 + (t^2 + 4*t + 4)*x^2 + 2*t*x 
        + 4*t + 4,
    x^6 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + 2*t + 1)*x^3 + (t^2 + 2*t + 2)*x^2 + 
        (4*t + 3)*x + 3*t,
    x^6 + (3*t^2 + t + 2)*x^4 + (t^2 + 4*t + 3)*x^3 + (3*t^2 + 3)*x^2 + (4*t + 
        4)*x + 3*t + 2,
    x^6 + (t + 3)*x^4 + (4*t + 3)*x^3 + (2*t + 2)*x^2 + (t + 2)*x + 2*t + 3,
    x^6 + (4*t^2 + 4*t + 4)*x^4 + (3*t^2 + 3*t + 2)*x^3 + (4*t^2 + 4)*x^2 + (t +
        3)*x + 2*t,
    x^6 + (3*t^2 + 2*t + 2)*x^4 + (t^2 + t + 3)*x^3 + (3*t^2 + t)*x^2 + (4*t + 
        1)*x + 3*t + 1,
    x^6 + (3*t^2 + 2*t + 1)*x^4 + (t^2 + t + 3)*x^3 + (3*t^2 + 4*t + 1)*x^2 + 
        (2*t + 3)*x + 4*t,
    x^6 + (t^2 + 4*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 3*t)*x^2 + (4*t +
        1)*x + 3*t + 1,
    x^6 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + 3)*x^3 + (4*t^2 + 2*t)*x^2 + (3*t + 
        1)*x + t + 1,
    x^6 + (2*t^2 + t + 2)*x^4 + (4*t^2 + 3*t + 4)*x^3 + (2*t^2 + 2*t)*x^2 + (t +
        1)*x + 2*t + 1,
    x^6 + (3*t^2 + 4)*x^4 + (t^2 + 2*t)*x^3 + (3*t^2 + 4*t + 1)*x^2 + 4*t*x + 
        3*t + 4,
    x^6 + (4*t + 1)*x^4 + (4*t + 3)*x^2 + 4,
    x^6 + (t + 2)*x^4 + (t + 3)*x^3 + 3*t*x^2 + (2*t + 1)*x + 4*t + 1,
    x^6 + (4*t^2 + 2*t + 2)*x^4 + (3*t^2 + 2*t + 4)*x^3 + (4*t^2 + 4*t + 1)*x^2 
        + (2*t + 2)*x + 4*t + 3,
    x^6 + (t^2 + 1)*x^4 + (2*t^2 + 3)
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:51:43 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

b := 0;
c := 0;
for d in S do

f := brumer(b, c, d);
Include(~R, f);

end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:51:43 on modular  [Seed = 3218003387]
   -------------------------------------

{
    x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + 2*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + 3*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + t*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + 4*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + x + 1,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 3*t*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1
}
Done.

Total time: 0.730 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:58:36 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

b := 0;
c := 0;
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	print f "aa";
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	
end if;



end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:58:35 on modular  [Seed = 2933899982]
   -------------------------------------


>>         print f "aa";
                   ^
User error: bad syntax

>>         continue;
           ^
User error: A 'continue' can only be used inside a loop

>> end if;
   ^
User error: bad syntax

>> G, R:= GaloisGroup(f);
                      ^
User error: Identifier 'f' has not been declared or assigned

>> if isA5(G) then
           ^
User error: Identifier 'G' has not been declared or assigned

>> end for;
   ^
User error: bad syntax
{}
Done.

Total time: 0.720 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 02:59:05 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

R := { Q | };

b := 0;
c := 0;
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	print f, "aa";
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	
end if;

end for;

print R;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 02:59:02 on modular  [Seed = 2599155414]
   -------------------------------------

x^6 + 2*x^4 + 2*x^3 + x + 1
aa
x^6 + 2*x^4 + 3*x^3 + x + 1
aa
x^6 + 2*x^4 + 4*x^3 + x + 1
aa
x^6 + 2*x^4 + x + 1
aa
x^6 + 2*x^4 + x^3 + x + 1
aa
[
    w^130*$.1^7 + w^78*$.1^6 + w^208*$.1^5 + w^286*$.1^3 + w^572*$.1^2 + 
        w^442*$.1 + w^442,
    w^26*$.1^7 + w^494*$.1^6 + w^208*$.1^5 + w^182*$.1^3 + w^234*$.1^2 + 
        w^338*$.1 + w^78,
    w^339*$.1^7 + w^496*$.1^6 + w^436*$.1^5 + w^466*$.1^3 + w^62*$.1^2 + 
        w^572*$.1 + w^174,
    w^48*$.1^7 + w^75*$.1^6 + w^327*$.1^5 + w^94*$.1^3 + w^319*$.1^2 + w^38*$.1 
        + w^262,
    w^576*$.1^7 + w^3*$.1^6 + w^63*$.1^5 + w^478*$.1^3 + w^487*$.1^2 + w^326*$.1
        + w^310,
    w^363*$.1^7 + w^544*$.1^6 + w^292*$.1^5 + w^418*$.1^3 + w^302*$.1^2 + 
        w^572*$.1 + w^606
]
Done.

Total time: 2.070 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:01:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

b := 0;
c := 0;
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	print f, "aa";
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Insert(~SS, f);
	else
		Insert(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:01:21 on modular  [Seed = 2047547074]
   -------------------------------------

x^6 + 2*x^4 + 2*x^3 + x + 1
aa
x^6 + 2*x^4 + 3*x^3 + x + 1
aa
x^6 + 2*x^4 + 4*x^3 + x + 1
aa
x^6 + 2*x^4 + x + 1
aa
x^6 + 2*x^4 + x^3 + x + 1
aa

>>                 Insert(~NSS, f);
                         ^
Runtime error in 'Insert': Bad argument types
Argument types given: SetEnum[RngUPolElt] ~, RngUPolElt[FldFunRat]
{}
{}
Done.

Total time: 1.089 seconds, Total memory usage: 7.56MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:01:57 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

b := 0;
c := 0;
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then 
	print f, "aa";
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:01:55 on modular  [Seed = 1912807147]
   -------------------------------------

x^6 + 2*x^4 + 2*x^3 + x + 1
aa
x^6 + 2*x^4 + 3*x^3 + x + 1
aa
x^6 + 2*x^4 + 4*x^3 + x + 1
aa
x^6 + 2*x^4 + x + 1
aa
x^6 + 2*x^4 + x^3 + x + 1
aa
{}
{
    x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + t*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + 3*t*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
}
Done.

Total time: 2.079 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:02:40 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

b := 0;
c := 0;
for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:02:38 on modular  [Seed = 1780155678]
   -------------------------------------

{}
{
    x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + t*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + 3*t*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
}
Done.

Total time: 2.069 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:03:30 2004

Input: b := 1;
c := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:03:29 on modular  [Seed = 1645415769]
   -------------------------------------

{}
{}
Done.

Total time: 1.070 seconds, Total memory usage: 7.46MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:03:40 2004

Input: b := 2;
c := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:03:37 on modular  [Seed = 1512781161]
   -------------------------------------

{}
{}
Done.

Total time: 2.599 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:03:56 2004

Input: b := 3;
c := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:03:54 on modular  [Seed = 1378041202]
   -------------------------------------

{}
{
    x^6 + (3*t + 2)*x^4 + (2*t + 4)*x^3 + (3*t + 1)*x^2 + 2*x + 3,
    x^6 + (3*t + 1)*x^4 + 2*t*x^3 + 3*t*x^2 + 2*x + 3,
    x^6 + (2*t + 1)*x^4 + 3*t*x^3 + 2*t*x^2 + 2*x + 3,
    x^6 + (t + 2)*x^4 + (4*t + 4)*x^3 + (t + 1)*x^2 + 2*x + 3,
    x^6 + (t + 1)*x^4 + 4*t*x^3 + t*x^2 + 2*x + 3,
    x^6 + 2*t*x^4 + (3*t + 1)*x^3 + (2*t + 4)*x^2 + 2*x + 3,
    x^6 + (3*t + 4)*x^4 + (2*t + 2)*x^3 + (3*t + 3)*x^2 + 2*x + 3,
    x^6 + (3*t + 3)*x^4 + (2*t + 3)*x^3 + (3*t + 2)*x^2 + 2*x + 3,
    x^6 + 3*t*x^4 + (2*t + 1)*x^3 + (3*t + 4)*x^2 + 2*x + 3,
    x^6 + (t + 4)*x^4 + (4*t + 2)*x^3 + (t + 3)*x^2 + 2*x + 3,
    x^6 + (2*t + 2)*x^4 + (3*t + 4)*x^3 + (2*t + 1)*x^2 + 2*x + 3,
    x^6 + (4*t + 3)*x^4 + (t + 3)*x^3 + (4*t + 2)*x^2 + 2*x + 3,
    x^6 + t*x^4 + (4*t + 1)*x^3 + (t + 4)*x^2 + 2*x + 3,
    x^6 + (2*t + 3)*x^4 + (3*t + 3)*x^3 + (2*t + 2)*x^2 + 2*x + 3,
    x^6 + (4*t + 2)*x^4 + (t + 4)*x^3 + (4*t + 1)*x^2 + 2*x + 3,
    x^6 + (4*t + 4)*x^4 + (t + 2)*x^3 + (4*t + 3)*x^2 + 2*x + 3,
    x^6 + (2*t + 4)*x^4 + (3*t + 2)*x^3 + (2*t + 3)*x^2 + 2*x + 3,
    x^6 + (t + 3)*x^4 + (4*t + 3)*x^3 + (t + 2)*x^2 + 2*x + 3,
    x^6 + (4*t + 1)*x^4 + t*x^3 + 4*t*x^2 + 2*x + 3,
    x^6 + 4*t*x^4 + (t + 1)*x^3 + (4*t + 4)*x^2 + 2*x + 3
}
Done.

Total time: 2.260 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:04:38 2004

Input: b := 4;
c := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:04:36 on modular  [Seed = 1211705270]
   -------------------------------------

{}
{
    x^6 + (3*t + 2)*x^4 + (3*t + 3)*x^3 + (3*t + 3)*x^2 + 4*x + 2,
    x^6 + (4*t + 4)*x^4 + 4*t*x^3 + 4*t*x^2 + 4*x + 2,
    x^6 + (3*t + 3)*x^4 + (3*t + 4)*x^3 + (3*t + 4)*x^2 + 4*x + 2,
    x^6 + (t + 3)*x^4 + (t + 4)*x^3 + (t + 4)*x^2 + 4*x + 2,
    x^6 + (2*t + 2)*x^4 + (2*t + 3)*x^3 + (2*t + 3)*x^2 + 4*x + 2,
    x^6 + (4*t + 2)*x^4 + (4*t + 3)*x^3 + (4*t + 3)*x^2 + 4*x + 2,
    x^6 + (t + 1)*x^4 + (t + 2)*x^3 + (t + 2)*x^2 + 4*x + 2,
    x^6 + (t + 2)*x^4 + (t + 3)*x^3 + (t + 3)*x^2 + 4*x + 2,
    x^6 + (2*t + 1)*x^4 + (2*t + 2)*x^3 + (2*t + 2)*x^2 + 4*x + 2,
    x^6 + (3*t + 4)*x^4 + 3*t*x^3 + 3*t*x^2 + 4*x + 2,
    x^6 + (2*t + 4)*x^4 + 2*t*x^3 + 2*t*x^2 + 4*x + 2,
    x^6 + (4*t + 1)*x^4 + (4*t + 2)*x^3 + (4*t + 2)*x^2 + 4*x + 2,
    x^6 + (t + 4)*x^4 + t*x^3 + t*x^2 + 4*x + 2,
    x^6 + (2*t + 3)*x^4 + (2*t + 4)*x^3 + (2*t + 4)*x^2 + 4*x + 2,
    x^6 + 4*t*x^4 + (4*t + 1)*x^3 + (4*t + 1)*x^2 + 4*x + 2,
    x^6 + 3*t*x^4 + (3*t + 1)*x^3 + (3*t + 1)*x^2 + 4*x + 2,
    x^6 + t*x^4 + (t + 1)*x^3 + (t + 1)*x^2 + 4*x + 2,
    x^6 + (4*t + 3)*x^4 + (4*t + 4)*x^3 + (4*t + 4)*x^2 + 4*x + 2,
    x^6 + (3*t + 1)*x^4 + (3*t + 2)*x^3 + (3*t + 2)*x^2 + 4*x + 2,
    x^6 + 2*t*x^4 + (2*t + 1)*x^3 + (2*t + 1)*x^2 + 4*x + 2
}
Done.

Total time: 2.299 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:05:10 2004

Input: b := 0;
c := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:05:08 on modular  [Seed = 1076965278]
   -------------------------------------

{}
{
    x^6 + 2*x^4 + (4*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + 4*t*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + t*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (2*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 4)*x^3 + x + 1,
    x^6 + 2*x^4 + 2*t*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 3)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 2)*x^3 + x + 1,
    x^6 + 2*x^4 + (3*t + 1)*x^3 + x + 1,
    x^6 + 2*x^4 + 3*t*x^3 + x + 1,
    x^6 + 2*x^4 + (4*t + 4)*x^3 + x + 1
}
Done.

Total time: 2.090 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:05:38 2004

Input: b := 0;
c := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:05:35 on modular  [Seed = 944330626]
   -------------------------------------

{
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
}
{}
Done.

Total time: 2.099 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:06:12 2004

Input: b := 1;
c := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print SS;
print NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:06:11 on modular  [Seed = 809590697]
   -------------------------------------

{}
{}
Done.

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:06:40 2004

Input: b := 1;
c := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:06:40 on modular  [Seed = 676939346]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 0.740 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:06:50 2004

Input: b := 2;
c := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:06:48 on modular  [Seed = 542199378]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 2*x^5 + (3*t + 1)*x^4 + 4*x^3 + 3*t*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (2*t + 3)*x^4 + 4*x^3 + (2*t + 2)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (3*t + 4)*x^4 + 4*x^3 + (3*t + 3)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (4*t + 3)*x^4 + 4*x^3 + (4*t + 2)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (t + 2)*x^4 + 4*x^3 + (t + 1)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + 3*t*x^4 + 4*x^3 + (3*t + 4)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (t + 3)*x^4 + 4*x^3 + (t + 2)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (2*t + 1)*x^4 + 4*x^3 + 2*t*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (3*t + 2)*x^4 + 4*x^3 + (3*t + 1)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (4*t + 1)*x^4 + 4*x^3 + 4*t*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (2*t + 4)*x^4 + 4*x^3 + (2*t + 3)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + 2*t*x^4 + 4*x^3 + (2*t + 4)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (4*t + 4)*x^4 + 4*x^3 + (4*t + 3)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + 4*t*x^4 + 4*x^3 + (4*t + 4)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (3*t + 3)*x^4 + 4*x^3 + (3*t + 2)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (t + 1)*x^4 + 4*x^3 + t*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (t + 4)*x^4 + 4*x^3 + (t + 3)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (2*t + 2)*x^4 + 4*x^3 + (2*t + 1)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + t*x^4 + 4*x^3 + (t + 4)*x^2 + 2*x + 4,
    x^6 + 2*x^5 + (4*t + 2)*x^4 + 4*x^3 + (4*t + 1)*x^2 + 2*x + 4
}
Done.

Total time: 2.179 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:07:31 2004

Input: b := 3;
c := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:07:29 on modular  [Seed = 426276690]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 2*x^5 + (2*t + 2)*x^4 + (3*t + 1)*x^3 + (2*t + 3)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + t*x^4 + (4*t + 3)*x^3 + (t + 1)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (t + 3)*x^4 + 4*t*x^3 + (t + 4)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (2*t + 3)*x^4 + 3*t*x^3 + (2*t + 4)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (3*t + 1)*x^4 + (2*t + 2)*x^3 + (3*t + 2)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (2*t + 4)*x^4 + (3*t + 4)*x^3 + 2*t*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (4*t + 2)*x^4 + (t + 1)*x^3 + (4*t + 3)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (3*t + 3)*x^4 + 2*t*x^3 + (3*t + 4)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (4*t + 3)*x^4 + t*x^3 + (4*t + 4)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (t + 2)*x^4 + (4*t + 1)*x^3 + (t + 3)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + 3*t*x^4 + (2*t + 3)*x^3 + (3*t + 1)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (3*t + 2)*x^4 + (2*t + 1)*x^3 + (3*t + 3)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (t + 4)*x^4 + (4*t + 4)*x^3 + t*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (t + 1)*x^4 + (4*t + 2)*x^3 + (t + 2)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (4*t + 4)*x^4 + (t + 4)*x^3 + 4*t*x^2 + 4*x + 3,
    x^6 + 2*x^5 + 2*t*x^4 + (3*t + 3)*x^3 + (2*t + 1)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (3*t + 4)*x^4 + (2*t + 4)*x^3 + 3*t*x^2 + 4*x + 3,
    x^6 + 2*x^5 + 4*t*x^4 + (t + 3)*x^3 + (4*t + 1)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (2*t + 1)*x^4 + (3*t + 2)*x^3 + (2*t + 2)*x^2 + 4*x + 3,
    x^6 + 2*x^5 + (4*t + 1)*x^4 + (t + 2)*x^3 + (4*t + 2)*x^2 + 4*x + 3
}
Done.

Total time: 2.229 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:08:16 2004

Input: b := 4;
c := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:08:14 on modular  [Seed = 342194736]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 2*x^5 + (4*t + 4)*x^4 + (4*t + 1)*x^3 + (4*t + 2)*x^2 + x + 2,
    x^6 + 2*x^5 + (3*t + 3)*x^4 + 3*t*x^3 + (3*t + 1)*x^2 + x + 2,
    x^6 + 2*x^5 + (t + 1)*x^4 + (t + 3)*x^3 + (t + 4)*x^2 + x + 2,
    x^6 + 2*x^5 + t*x^4 + (t + 2)*x^3 + (t + 3)*x^2 + x + 2,
    x^6 + 2*x^5 + (t + 2)*x^4 + (t + 4)*x^3 + t*x^2 + x + 2,
    x^6 + 2*x^5 + (2*t + 2)*x^4 + (2*t + 4)*x^3 + 2*t*x^2 + x + 2,
    x^6 + 2*x^5 + (2*t + 3)*x^4 + 2*t*x^3 + (2*t + 1)*x^2 + x + 2,
    x^6 + 2*x^5 + 2*t*x^4 + (2*t + 2)*x^3 + (2*t + 3)*x^2 + x + 2,
    x^6 + 2*x^5 + (3*t + 1)*x^4 + (3*t + 3)*x^3 + (3*t + 4)*x^2 + x + 2,
    x^6 + 2*x^5 + 4*t*x^4 + (4*t + 2)*x^3 + (4*t + 3)*x^2 + x + 2,
    x^6 + 2*x^5 + (3*t + 2)*x^4 + (3*t + 4)*x^3 + 3*t*x^2 + x + 2,
    x^6 + 2*x^5 + (4*t + 3)*x^4 + 4*t*x^3 + (4*t + 1)*x^2 + x + 2,
    x^6 + 2*x^5 + 3*t*x^4 + (3*t + 2)*x^3 + (3*t + 3)*x^2 + x + 2,
    x^6 + 2*x^5 + (t + 4)*x^4 + (t + 1)*x^3 + (t + 2)*x^2 + x + 2,
    x^6 + 2*x^5 + (2*t + 4)*x^4 + (2*t + 1)*x^3 + (2*t + 2)*x^2 + x + 2,
    x^6 + 2*x^5 + (t + 3)*x^4 + t*x^3 + (t + 1)*x^2 + x + 2,
    x^6 + 2*x^5 + (2*t + 1)*x^4 + (2*t + 3)*x^3 + (2*t + 4)*x^2 + x + 2,
    x^6 + 2*x^5 + (4*t + 2)*x^4 + (4*t + 4)*x^3 + 4*t*x^2 + x + 2,
    x^6 + 2*x^5 + (3*t + 4)*x^4 + (3*t + 1)*x^3 + (3*t + 2)*x^2 + x + 2,
    x^6 + 2*x^5 + (4*t + 1)*x^4 + (4*t + 3)*x^3 + (4*t + 4)*x^2 + x + 2
}
Done.

Total time: 2.240 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:08:49 2004

Input: b := 0;
c := 2;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:08:47 on modular  [Seed = 209543689]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 4*x^5 + (t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 4*t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 3*t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (4*t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + 2*t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (3*t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 1)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 2)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 3)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (2*t + 4)*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + t*x^3 + 2*x^2 + 1,
    x^6 + 4*x^5 + (t + 1)*x^3 + 2*x^2 + 1
}
Done.

Total time: 2.089 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:09:16 2004

Input: b := 1;
c := 2;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:09:15 on modular  [Seed = 74803941]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 1.060 seconds, Total memory usage: 7.46MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:09:22 2004

Input: b := 2;
c := 2;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:09:21 on modular  [Seed = 4253848358]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 1.080 seconds, Total memory usage: 7.46MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:09:29 2004

Input: b := 3;
c := 2;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:09:27 on modular  [Seed = 4119108392]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 4*x^5 + (t + 4)*x^4 + (4*t + 2)*x^3 + (t + 2)*x^2 + x + 3,
    x^6 + 4*x^5 + (4*t + 1)*x^4 + t*x^3 + (4*t + 4)*x^2 + x + 3,
    x^6 + 4*x^5 + (3*t + 3)*x^4 + (2*t + 3)*x^3 + (3*t + 1)*x^2 + x + 3,
    x^6 + 4*x^5 + (2*t + 1)*x^4 + 3*t*x^3 + (2*t + 4)*x^2 + x + 3,
    x^6 + 4*x^5 + (2*t + 3)*x^4 + (3*t + 3)*x^3 + (2*t + 1)*x^2 + x + 3,
    x^6 + 4*x^5 + (2*t + 4)*x^4 + (3*t + 2)*x^3 + (2*t + 2)*x^2 + x + 3,
    x^6 + 4*x^5 + (2*t + 2)*x^4 + (3*t + 4)*x^3 + 2*t*x^2 + x + 3,
    x^6 + 4*x^5 + (4*t + 3)*x^4 + (t + 3)*x^3 + (4*t + 1)*x^2 + x + 3,
    x^6 + 4*x^5 + t*x^4 + (4*t + 1)*x^3 + (t + 3)*x^2 + x + 3,
    x^6 + 4*x^5 + (t + 3)*x^4 + (4*t + 3)*x^3 + (t + 1)*x^2 + x + 3,
    x^6 + 4*x^5 + 3*t*x^4 + (2*t + 1)*x^3 + (3*t + 3)*x^2 + x + 3,
    x^6 + 4*x^5 + (4*t + 4)*x^4 + (t + 2)*x^3 + (4*t + 2)*x^2 + x + 3,
    x^6 + 4*x^5 + (3*t + 4)*x^4 + (2*t + 2)*x^3 + (3*t + 2)*x^2 + x + 3,
    x^6 + 4*x^5 + (3*t + 2)*x^4 + (2*t + 4)*x^3 + 3*t*x^2 + x + 3,
    x^6 + 4*x^5 + (t + 2)*x^4 + (4*t + 4)*x^3 + t*x^2 + x + 3,
    x^6 + 4*x^5 + (4*t + 2)*x^4 + (t + 4)*x^3 + 4*t*x^2 + x + 3,
    x^6 + 4*x^5 + 4*t*x^4 + (t + 1)*x^3 + (4*t + 3)*x^2 + x + 3,
    x^6 + 4*x^5 + (3*t + 1)*x^4 + 2*t*x^3 + (3*t + 4)*x^2 + x + 3,
    x^6 + 4*x^5 + (t + 1)*x^4 + 4*t*x^3 + (t + 4)*x^2 + x + 3,
    x^6 + 4*x^5 + 2*t*x^4 + (3*t + 1)*x^3 + (2*t + 3)*x^2 + x + 3
}
Done.

Total time: 2.179 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:09:55 2004

Input: b := 4;
c := 2;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:09:52 on modular  [Seed = 3767635546]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 4*x^5 + 4*t*x^4 + 4*t*x^3 + 4*t*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (t + 4)*x^4 + (t + 4)*x^3 + (t + 4)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (2*t + 4)*x^4 + (2*t + 4)*x^3 + (2*t + 4)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (t + 1)*x^4 + (t + 1)*x^3 + (t + 1)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (3*t + 3)*x^4 + (3*t + 3)*x^3 + (3*t + 3)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (3*t + 4)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (3*t + 1)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (t + 2)*x^4 + (t + 2)*x^3 + (t + 2)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (2*t + 3)*x^4 + (2*t + 3)*x^3 + (2*t + 3)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (4*t + 3)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (2*t + 2)*x^4 + (2*t + 2)*x^3 + (2*t + 2)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (4*t + 4)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (4*t + 2)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (2*t + 1)*x^4 + (2*t + 1)*x^3 + (2*t + 1)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (t + 3)*x^4 + (t + 3)*x^3 + (t + 3)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + t*x^4 + t*x^3 + t*x^2 + 3*x + 2,
    x^6 + 4*x^5 + 2*t*x^4 + 2*t*x^3 + 2*t*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (3*t + 2)*x^4 + (3*t + 2)*x^3 + (3*t + 2)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (4*t + 1)*x^2 + 3*x + 2,
    x^6 + 4*x^5 + 3*t*x^4 + 3*t*x^3 + 3*t*x^2 + 3*x + 2
}
Done.

Total time: 2.159 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:10:26 2004

Input: b := 0;
c := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:10:24 on modular  [Seed = 3651712835]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + x^5 + 2*x^4 + (4*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 3*t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 2*t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (2*t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 2)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (t + 3)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (3*t + 4)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + 4*t*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 1)*x^3 + x^2 + 2*x + 1,
    x^6 + x^5 + 2*x^4 + (4*t + 2)*x^3 + x^2 + 2*x + 1
}
Done.

Total time: 2.139 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:11:04 2004

Input: b := 1;
c := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:11:03 on modular  [Seed = 3516965036]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 1.079 seconds, Total memory usage: 7.46MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:12:34 2004

Input: b := 1;
c := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:12:33 on modular  [Seed = 3384326354]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 1.070 seconds, Total memory usage: 7.45MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:12:40 2004

Input: b := 2;
c := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:12:38 on modular  [Seed = 3249582301]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + x^5 + (3*t + 3)*x^4 + 4*x^3 + (3*t + 1)*x^2 + x + 4,
    x^6 + x^5 + 3*t*x^4 + 4*x^3 + (3*t + 3)*x^2 + x + 4,
    x^6 + x^5 + (4*t + 4)*x^4 + 4*x^3 + (4*t + 2)*x^2 + x + 4,
    x^6 + x^5 + (4*t + 1)*x^4 + 4*x^3 + (4*t + 4)*x^2 + x + 4,
    x^6 + x^5 + (t + 3)*x^4 + 4*x^3 + (t + 1)*x^2 + x + 4,
    x^6 + x^5 + t*x^4 + 4*x^3 + (t + 3)*x^2 + x + 4,
    x^6 + x^5 + (3*t + 2)*x^4 + 4*x^3 + 3*t*x^2 + x + 4,
    x^6 + x^5 + (2*t + 3)*x^4 + 4*x^3 + (2*t + 1)*x^2 + x + 4,
    x^6 + x^5 + 2*t*x^4 + 4*x^3 + (2*t + 3)*x^2 + x + 4,
    x^6 + x^5 + (t + 2)*x^4 + 4*x^3 + t*x^2 + x + 4,
    x^6 + x^5 + (2*t + 2)*x^4 + 4*x^3 + 2*t*x^2 + x + 4,
    x^6 + x^5 + (3*t + 4)*x^4 + 4*x^3 + (3*t + 2)*x^2 + x + 4,
    x^6 + x^5 + (3*t + 1)*x^4 + 4*x^3 + (3*t + 4)*x^2 + x + 4,
    x^6 + x^5 + (t + 4)*x^4 + 4*x^3 + (t + 2)*x^2 + x + 4,
    x^6 + x^5 + (2*t + 4)*x^4 + 4*x^3 + (2*t + 2)*x^2 + x + 4,
    x^6 + x^5 + (t + 1)*x^4 + 4*x^3 + (t + 4)*x^2 + x + 4,
    x^6 + x^5 + (2*t + 1)*x^4 + 4*x^3 + (2*t + 4)*x^2 + x + 4,
    x^6 + x^5 + (4*t + 3)*x^4 + 4*x^3 + (4*t + 1)*x^2 + x + 4,
    x^6 + x^5 + 4*t*x^4 + 4*x^3 + (4*t + 3)*x^2 + x + 4,
    x^6 + x^5 + (4*t + 2)*x^4 + 4*x^3 + 4*t*x^2 + x + 4
}
Done.

Total time: 2.150 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:13:16 2004

Input: b := 3;
c := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:13:14 on modular  [Seed = 3201290062]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + x^5 + 3*t*x^4 + 2*t*x^3 + 3*t*x^2 + 3*x + 3,
    x^6 + x^5 + (4*t + 4)*x^4 + (t + 1)*x^3 + (4*t + 4)*x^2 + 3*x + 3,
    x^6 + x^5 + (4*t + 1)*x^4 + (t + 4)*x^3 + (4*t + 1)*x^2 + 3*x + 3,
    x^6 + x^5 + (2*t + 2)*x^4 + (3*t + 3)*x^3 + (2*t + 2)*x^2 + 3*x + 3,
    x^6 + x^5 + (4*t + 2)*x^4 + (t + 3)*x^3 + (4*t + 2)*x^2 + 3*x + 3,
    x^6 + x^5 + (t + 4)*x^4 + (4*t + 1)*x^3 + (t + 4)*x^2 + 3*x + 3,
    x^6 + x^5 + 2*t*x^4 + 3*t*x^3 + 2*t*x^2 + 3*x + 3,
    x^6 + x^5 + (t + 3)*x^4 + (4*t + 2)*x^3 + (t + 3)*x^2 + 3*x + 3,
    x^6 + x^5 + (t + 2)*x^4 + (4*t + 3)*x^3 + (t + 2)*x^2 + 3*x + 3,
    x^6 + x^5 + (3*t + 4)*x^4 + (2*t + 1)*x^3 + (3*t + 4)*x^2 + 3*x + 3,
    x^6 + x^5 + (2*t + 1)*x^4 + (3*t + 4)*x^3 + (2*t + 1)*x^2 + 3*x + 3,
    x^6 + x^5 + (t + 1)*x^4 + (4*t + 4)*x^3 + (t + 1)*x^2 + 3*x + 3,
    x^6 + x^5 + (2*t + 3)*x^4 + (3*t + 2)*x^3 + (2*t + 3)*x^2 + 3*x + 3,
    x^6 + x^5 + 4*t*x^4 + t*x^3 + 4*t*x^2 + 3*x + 3,
    x^6 + x^5 + (4*t + 3)*x^4 + (t + 2)*x^3 + (4*t + 3)*x^2 + 3*x + 3,
    x^6 + x^5 + (3*t + 1)*x^4 + (2*t + 4)*x^3 + (3*t + 1)*x^2 + 3*x + 3,
    x^6 + x^5 + (3*t + 3)*x^4 + (2*t + 2)*x^3 + (3*t + 3)*x^2 + 3*x + 3,
    x^6 + x^5 + (3*t + 2)*x^4 + (2*t + 3)*x^3 + (3*t + 2)*x^2 + 3*x + 3,
    x^6 + x^5 + t*x^4 + 4*t*x^3 + t*x^2 + 3*x + 3,
    x^6 + x^5 + (2*t + 4)*x^4 + (3*t + 1)*x^3 + (2*t + 4)*x^2 + 3*x + 3
}
Done.

Total time: 2.180 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:13:58 2004

Input: b := 4;
c := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:13:56 on modular  [Seed = 3066546040]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + x^5 + (3*t + 2)*x^4 + (3*t + 2)*x^3 + (3*t + 4)*x^2 + 2,
    x^6 + x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (3*t + 3)*x^2 + 2,
    x^6 + x^5 + (2*t + 4)*x^4 + (2*t + 4)*x^3 + (2*t + 1)*x^2 + 2,
    x^6 + x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (4*t + 3)*x^2 + 2,
    x^6 + x^5 + 2*t*x^4 + 2*t*x^3 + (2*t + 2)*x^2 + 2,
    x^6 + x^5 + (t + 4)*x^4 + (t + 4)*x^3 + (t + 1)*x^2 + 2,
    x^6 + x^5 + (2*t + 1)*x^4 + (2*t + 1)*x^3 + (2*t + 3)*x^2 + 2,
    x^6 + x^5 + t*x^4 + t*x^3 + (t + 2)*x^2 + 2,
    x^6 + x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (4*t + 4)*x^2 + 2,
    x^6 + x^5 + (2*t + 2)*x^4 + (2*t + 2)*x^3 + (2*t + 4)*x^2 + 2,
    x^6 + x^5 + (t + 3)*x^4 + (t + 3)*x^3 + t*x^2 + 2,
    x^6 + x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (4*t + 1)*x^2 + 2,
    x^6 + x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (3*t + 1)*x^2 + 2,
    x^6 + x^5 + 3*t*x^4 + 3*t*x^3 + (3*t + 2)*x^2 + 2,
    x^6 + x^5 + (3*t + 3)*x^4 + (3*t + 3)*x^3 + 3*t*x^2 + 2,
    x^6 + x^5 + (t + 1)*x^4 + (t + 1)*x^3 + (t + 3)*x^2 + 2,
    x^6 + x^5 + (t + 2)*x^4 + (t + 2)*x^3 + (t + 4)*x^2 + 2,
    x^6 + x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + 4*t*x^2 + 2,
    x^6 + x^5 + 4*t*x^4 + 4*t*x^3 + (4*t + 2)*x^2 + 2,
    x^6 + x^5 + (2*t + 3)*x^4 + (2*t + 3)*x^3 + 2*t*x^2 + 2
}
Done.

Total time: 2.280 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:14:31 2004

Input: b := 0;
c := 4;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:14:29 on modular  [Seed = 2950618624]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 3*x^5 + x^4 + t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 4*t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (3*t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 3*t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (2*t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 4)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + 2*t*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 3)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 2)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (t + 1)*x^3 + 2*x^2 + 4*x + 1,
    x^6 + 3*x^5 + x^4 + (4*t + 4)*x^3 + 2*x^2 + 4*x + 1
}
Done.

Total time: 2.110 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:15:01 2004

Input: b := 1;
c := 4;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:14:59 on modular  [Seed = 2815874606]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 1.070 seconds, Total memory usage: 7.46MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:15:07 2004

Input: b := 2;
c := 4;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:15:06 on modular  [Seed = 2683235871]
   -------------------------------------

Supersingular {}
Non-Supersingular {}
Done.

Total time: 1.050 seconds, Total memory usage: 7.46MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:15:14 2004

Input: b := 3;
c := 4;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:15:11 on modular  [Seed = 2548491794]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 3*x^5 + (t + 2)*x^4 + (4*t + 3)*x^3 + (t + 4)*x^2 + 3,
    x^6 + 3*x^5 + (3*t + 4)*x^4 + (2*t + 1)*x^3 + (3*t + 1)*x^2 + 3,
    x^6 + 3*x^5 + (t + 4)*x^4 + (4*t + 1)*x^3 + (t + 1)*x^2 + 3,
    x^6 + 3*x^5 + 4*t*x^4 + t*x^3 + (4*t + 2)*x^2 + 3,
    x^6 + 3*x^5 + (3*t + 3)*x^4 + (2*t + 2)*x^3 + 3*t*x^2 + 3,
    x^6 + 3*x^5 + (4*t + 1)*x^4 + (t + 4)*x^3 + (4*t + 3)*x^2 + 3,
    x^6 + 3*x^5 + 2*t*x^4 + 3*t*x^3 + (2*t + 2)*x^2 + 3,
    x^6 + 3*x^5 + (2*t + 3)*x^4 + (3*t + 2)*x^3 + 2*t*x^2 + 3,
    x^6 + 3*x^5 + (2*t + 2)*x^4 + (3*t + 3)*x^3 + (2*t + 4)*x^2 + 3,
    x^6 + 3*x^5 + (4*t + 3)*x^4 + (t + 2)*x^3 + 4*t*x^2 + 3,
    x^6 + 3*x^5 + (t + 3)*x^4 + (4*t + 2)*x^3 + t*x^2 + 3,
    x^6 + 3*x^5 + (4*t + 2)*x^4 + (t + 3)*x^3 + (4*t + 4)*x^2 + 3,
    x^6 + 3*x^5 + (4*t + 4)*x^4 + (t + 1)*x^3 + (4*t + 1)*x^2 + 3,
    x^6 + 3*x^5 + (3*t + 2)*x^4 + (2*t + 3)*x^3 + (3*t + 4)*x^2 + 3,
    x^6 + 3*x^5 + 3*t*x^4 + 2*t*x^3 + (3*t + 2)*x^2 + 3,
    x^6 + 3*x^5 + t*x^4 + 4*t*x^3 + (t + 2)*x^2 + 3,
    x^6 + 3*x^5 + (2*t + 4)*x^4 + (3*t + 1)*x^3 + (2*t + 1)*x^2 + 3,
    x^6 + 3*x^5 + (t + 1)*x^4 + (4*t + 4)*x^3 + (t + 3)*x^2 + 3,
    x^6 + 3*x^5 + (3*t + 1)*x^4 + (2*t + 4)*x^3 + (3*t + 3)*x^2 + 3,
    x^6 + 3*x^5 + (2*t + 1)*x^4 + (3*t + 4)*x^3 + (2*t + 3)*x^2 + 3
}
Done.

Total time: 2.299 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:15:50 2004

Input: b := 4;
c := 4;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));
Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:15:47 on modular  [Seed = 2415853526]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + 3*x^5 + (4*t + 3)*x^4 + 4*t*x^3 + (4*t + 2)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (4*t + 2)*x^4 + (4*t + 4)*x^3 + (4*t + 1)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + t*x^4 + (t + 2)*x^3 + (t + 4)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (2*t + 1)*x^4 + (2*t + 3)*x^3 + 2*t*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (4*t + 1)*x^4 + (4*t + 3)*x^3 + 4*t*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (t + 3)*x^4 + t*x^3 + (t + 2)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + 2*t*x^4 + (2*t + 2)*x^3 + (2*t + 4)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (t + 1)*x^4 + (t + 3)*x^3 + t*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (t + 4)*x^4 + (t + 1)*x^3 + (t + 3)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + 4*t*x^4 + (4*t + 2)*x^3 + (4*t + 4)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (t + 2)*x^4 + (t + 4)*x^3 + (t + 1)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (2*t + 2)*x^4 + (2*t + 4)*x^3 + (2*t + 1)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (2*t + 4)*x^4 + (2*t + 1)*x^3 + (2*t + 3)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (3*t + 3)*x^4 + 3*t*x^3 + (3*t + 2)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + 3*t*x^4 + (3*t + 2)*x^3 + (3*t + 4)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (3*t + 4)*x^4 + (3*t + 1)*x^3 + (3*t + 3)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (4*t + 4)*x^4 + (4*t + 1)*x^3 + (4*t + 3)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (3*t + 2)*x^4 + (3*t + 4)*x^3 + (3*t + 1)*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (3*t + 1)*x^4 + (3*t + 3)*x^3 + 3*t*x^2 + 2*x + 2,
    x^6 + 3*x^5 + (2*t + 3)*x^4 + 2*t*x^3 + (2*t + 2)*x^2 + 2*x + 2
}
Done.

Total time: 2.199 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:16:51 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := t;
c := 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for d in S do

f := brumer(b, c, d);

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;

end for;

print "Supersingular", SS;
print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:16:48 on modular  [Seed = 2047543911]
   -------------------------------------

Supersingular {}
Non-Supersingular {
    x^6 + (2*t + 2)*x^4 + (3*t + 4)*x^3 + 4*t*x^2 + (2*t + 1)*x + 4*t + 1,
    x^6 + (3*t^2 + 4*t + 2)*x^4 + (t^2 + 1)*x^3 + (3*t^2 + t)*x^2 + (2*t + 1)*x 
        + 4*t + 1,
    x^6 + (3*t^2 + t + 2)*x^4 + (t^2 + 4*t + 3)*x^3 + (3*t^2 + 3*t)*x^2 + (2*t +
        1)*x + 4*t + 1,
    x^6 + (t^2 + 4*t + 2)*x^4 + (2*t^2 + 3*t + 1)*x^3 + (t^2 + t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (4*t^2 + 4*t + 2)*x^4 + (3*t^2 + t + 1)*x^3 + (4*t^2 + t)*x^2 + (2*t +
        1)*x + 4*t + 1,
    x^6 + (4*t^2 + 3*t + 2)*x^4 + (3*t^2 + 4*t)*x^3 + 4*t^2*x^2 + (2*t + 1)*x + 
        4*t + 1,
    x^6 + (2*t^2 + 2)*x^4 + (4*t^2 + t + 2)*x^3 + (2*t^2 + 2*t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (3*t^2 + 3*t + 2)*x^4 + (t^2 + 3*t)*x^3 + 3*t^2*x^2 + (2*t + 1)*x + 
        4*t + 1,
    x^6 + (t^2 + t + 2)*x^4 + (2*t^2 + 2*t + 3)*x^3 + (t^2 + 3*t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (4*t^2 + 2)*x^4 + (3*t^2 + 3*t + 2)*x^3 + (4*t^2 + 2*t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (2*t^2 + t + 2)*x^4 + (4*t^2 + 3*t + 3)*x^3 + (2*t^2 + 3*t)*x^2 + (2*t
        + 1)*x + 4*t + 1,
    x^6 + 2*x^4 + (4*t + 2)*x^3 + 2*t*x^2 + (2*t + 1)*x + 4*t + 1,
    x^6 + (2*t^2 + 4*t + 2)*x^4 + (4*t^2 + 4*t + 1)*x^3 + (2*t^2 + t)*x^2 + (2*t
        + 1)*x + 4*t + 1,
    x^6 + (3*t^2 + 2*t + 2)*x^4 + (t^2 + t + 4)*x^3 + (3*t^2 + 4*t)*x^2 + (2*t +
        1)*x + 4*t + 1,
    x^6 + (t^2 + 2*t + 2)*x^4 + (2*t^2 + 4*t + 4)*x^3 + (t^2 + 4*t)*x^2 + (2*t +
        1)*x + 4*t + 1,
    x^6 + (t^2 + 3*t + 2)*x^4 + (2*t^2 + t)*x^3 + t^2*x^2 + (2*t + 1)*x + 4*t + 
        1,
    x^6 + (3*t + 2)*x^4 + (2*t + 1)*x + 4*t + 1,
    x^6 + (2*t^2 + 2*t + 2)*x^4 + (4*t^2 + 4)*x^3 + (2*t^2 + 4*t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (4*t^2 + 2*t + 2)*x^4 + (3*t^2 + 2*t + 4)*x^3 + (4*t^2 + 4*t)*x^2 + 
        (2*t + 1)*x + 4*t + 1,
    x^6 + (2*t^2 + 3*t + 2)*x^4 + (4*t^2 + 2*t)*x^3 + 2*t^2*x^2 + (2*t + 1)*x + 
        4*t + 1,
    x^6 + (t^2 + 2)*x^4 + (2*t^2 + 2)*x^3 + (t^2 + 2*t)*x^2 + (2*t + 1)*x + 4*t 
        + 1,
    x^6 + (4*t + 2)*x^4 + (2*t + 1)*x^3 + t*x^2 + (2*t + 1)*x + 4*t + 1,
    x^6 + (3*t^2 + 2)*x^4 + (t^2 + 2*t + 2)*x^3 + (3*t^2 + 2*t)*x^2 + (2*t + 
        1)*x + 4*t + 1,
    x^6 + (4*t^2 + t + 2)*x^4 + (3*t^2 + 3)*x^3 + (4*t^2 + 3*t)*x^2 + (2*t + 
        1)*x + 4*t + 1
}
Done.

Total time: 2.570 seconds, Total memory usage: 8.06MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:19:35 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:19:15 on modular  [Seed = 1729501161]
   -------------------------------------



************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:20:11 2004

Input: b := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:20:09 on modular  [Seed = 1262106652]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.750 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:20:18 2004

Input: b := 1;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:20:16 on modular  [Seed = 1127362574]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.689 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:20:24 2004

Input: b := 2;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:20:22 on modular  [Seed = 994723952]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.800 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:20:35 2004

Input: b := 3;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:20:33 on modular  [Seed = 859979791]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.820 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:20:41 2004

Input: b := 4;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:20:39 on modular  [Seed = 727341073]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.820 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:21:43 2004

Input: b := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if isSS(f, p) then 
	Include(~SS, f);
end if;

/*
if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	if isSS(f, p) then
		Include(~SS, f);
	else
		Include(~NSS, f);
	end if;
	
end if;
*/
end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:21:42 on modular  [Seed = 592597208]
   -------------------------------------

Supersingular {
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 3*x^5 + x^4 + x^3 + 2*x^2 + 4*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*x^3 + 3*x + 1,
    x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^4 + x^3 + x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + x^3 + 3*x + 1
}
Done.

Total time: 1.760 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:23:16 2004

Input: b := 0;

Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:23:13 on modular  [Seed = 342189960]
   -------------------------------------

Supersingular {
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
}
Done.

Total time: 3.059 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:23:51 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:23:49 on modular  [Seed = 209550964]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.689 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:23:58 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 2;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:23:56 on modular  [Seed = 74806901]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.780 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:24:08 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 0*t + 3;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:24:06 on modular  [Seed = 4237135511]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.909 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:24:14 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 0*t + 4;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:24:12 on modular  [Seed = 4102391445]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.919 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:24:21 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 0*t + 5;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:24:18 on modular  [Seed = 3969752755]
   -------------------------------------

Supersingular {
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
}
Done.

Total time: 3.090 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:24:36 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 1*t + 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:24:34 on modular  [Seed = 3885405608]
   -------------------------------------

Supersingular {
    x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1,
    x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1,
    x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1,
    x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t +
        4)*x + 4*t + 1
}
Done.

Total time: 2.490 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:25:51 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

b := 1*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for c in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:25:49 on modular  [Seed = 3736055006]
   -------------------------------------

Supersingular {
    x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t,
    x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t,
    x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t,
    x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t
}
Done.

Total time: 2.469 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:26:51 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 0*t + 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:26:49 on modular  [Seed = 3601310738]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.639 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:26:59 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 0*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:26:56 on modular  [Seed = 3468672115]
   -------------------------------------

Supersingular {
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
}
Done.

Total time: 3.179 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:27:53 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 0*t + 2;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:27:49 on modular  [Seed = 3333928013]
   -------------------------------------

Supersingular {
    x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t,
    x^6 + 4*x^5 + 3*t*x^3 + 4*t*x^2 + (4*t + 3)*x + 3*t + 2,
    x^6 + 4*x^5 + (2*t + 1)*x^3 + (t + 3)*x^2 + (t + 1)*x + 2*t + 3,
    x^6 + 4*x^5 + (t + 1)*x^3 + (3*t + 3)*x^2 + (3*t + 1)*x + t + 3,
    x^6 + 4*x^5 + (2*t + 2)*x^3 + (t + 1)*x^2 + (t + 4)*x + 2*t + 4,
    x^6 + 4*x^5 + t*x^3 + 3*t*x^2 + (3*t + 3)*x + t + 2,
    x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4,
    x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1,
    x^6 + 4*x^5 + (t + 2)*x^3 + (3*t + 1)*x^2 + (3*t + 4)*x + t + 4,
    x^6 + 4*x^5 + (2*t + 3)*x^3 + (t + 4)*x^2 + (t + 2)*x + 2*t,
    x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t,
    x^6 + 4*x^5 + 2*t*x^3 + t*x^2 + (t + 3)*x + 2*t + 2,
    x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1,
    x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2,
    x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4,
    x^6 + 4*x^5 + (3*t + 1)*x^3 + (4*t + 3)*x^2 + (4*t + 1)*x + 3*t + 3,
    x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3,
    x^6 + 4*x^5 + (t + 4)*x^3 + (3*t + 2)*x^2 + 3*t*x + t + 1,
    x^6 + 4*x^5 + (2*t + 4)*x^3 + (t + 2)*x^2 + t*x + 2*t + 1,
    x^6 + 4*x^5 + (t + 3)*x^3 + (3*t + 4)*x^2 + (3*t + 2)*x + t
}
Done.

Total time: 3.249 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:28:17 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 0*t + 3;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:28:15 on modular  [Seed = 3100233162]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.879 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:28:24 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 0*t + 4;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:28:22 on modular  [Seed = 2965489115]
   -------------------------------------

Supersingular {}
Done.

Total time: 1.849 seconds, Total memory usage: 2.85MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:28:33 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 1*t + 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:28:30 on modular  [Seed = 2832850379]
   -------------------------------------

Supersingular {
    x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t,
    x^6 + 2*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + t + 3,
    x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1
}
Done.

Total time: 2.409 seconds, Total memory usage: 7.65MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:29:36 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 1*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:29:34 on modular  [Seed = 2748503680]
   -------------------------------------

Supersingular {
    x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t,
    x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t +
        2)*x + 4*t + 4,
    x^6 + (2*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + t + 4
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:30:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 1*t + 2;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:30:21 on modular  [Seed = 2615864939]
   -------------------------------------

Supersingular {
    x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t +
        1)*x + 4*t + 3,
    x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4,
    x^6 + (2*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + t
}
Done.

Total time: 2.440 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:31:10 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 1*t + 3;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:31:07 on modular  [Seed = 1729499808]
   -------------------------------------

Supersingular {
    x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x 
        + 4*t + 2,
    x^6 + (2*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + t + 1,
    x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:31:46 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 1*t + 4;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:31:44 on modular  [Seed = 1127364319]
   -------------------------------------

Supersingular {
    x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2,
    x^6 + (2*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + t + 2,
    x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t +
        4)*x + 4*t + 1
}
Done.

Total time: 2.420 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:32:24 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 2*t + 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:32:22 on modular  [Seed = 643256924]
   -------------------------------------

Supersingular {
    x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t,
    x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1,
    x^6 + 4*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t + 3
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:33:05 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 0*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:33:02 on modular  [Seed = 4203450024]
   -------------------------------------

Supersingular {
    x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1,
    x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1,
    x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1
}
Done.

Total time: 3.190 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:33:56 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 2*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:33:53 on modular  [Seed = 3584336328]
   -------------------------------------

Supersingular {
    x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 
        2)*x + 3*t + 4,
    x^6 + (4*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t + 4,
    x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:34:25 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 2*t + 2;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:34:23 on modular  [Seed = 3485383628]
   -------------------------------------

Supersingular {
    x^6 + (4*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t,
    x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4,
    x^6 + (4*t + 4)*x^5 + (3*t + 3)*x^4 + (3*t + 3)*x^3 + (t + 1)*x^2 + (3*t + 
        1)*x + 3*t + 3
}
Done.

Total time: 2.430 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:34:50 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 2*t + 3;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:34:48 on modular  [Seed = 3350639395]
   -------------------------------------

Supersingular {
    x^6 + (4*t + 1)*x^5 + 2*t*x^4 + t*x^3 + (3*t + 3)*x + 3*t + 3,
    x^6 + (4*t + 1)*x^5 + (3*t + 2)*x^4 + (3*t + 2)*x^3 + (t + 4)*x^2 + 3*t*x + 
        3*t + 2,
    x^6 + (4*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t + 1
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Sat Aug 28 03:35:08 2004

Input: ABC

Output: Magma V2.11-2     Sat Aug 28 2004 03:35:07 on modular  [Seed = 3218000744]
   -------------------------------------


>> ABC;
   ^
User error: Identifier 'ABC' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Sat Aug 28 03:35:12 2004

Input: ABC

Output: Magma V2.11-2     Sat Aug 28 2004 03:35:11 on modular  [Seed = 2832850043]
   -------------------------------------


>> ABC;
   ^
User error: Identifier 'ABC' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:35:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 2*t + 4;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:35:21 on modular  [Seed = 2698105957]
   -------------------------------------

Supersingular {
    x^6 + (4*t + 3)*x^5 + (2*t + 1)*x^4 + (t + 3)*x^3 + (3*t + 2)*x + 3*t + 2,
    x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 
        4)*x + 3*t + 1,
    x^6 + (4*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 2*t + 2
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host ika.cs.mu.OZ.AU. (128.250.37.70)
Time: Sat Aug 28 03:35:46 2004

Input: A

Output: Magma V2.11-2     Sat Aug 28 2004 03:35:46 on modular  [Seed = 2565467190]
   -------------------------------------


>> A;
   ^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:35:50 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 3*t + 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:35:47 on modular  [Seed = 2430723135]
   -------------------------------------

Supersingular {
    x^6 + t*x^5 + 2*t*x^4 + 2*t*x^3 + 4*t*x^2 + (2*t + 3)*x + 2*t,
    x^6 + t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 3,
    x^6 + t*x^5 + (3*t + 2)*x^4 + (4*t + 1)*x^3 + (2*t + 1)*x + 2*t + 1
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:36:55 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 3*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:36:53 on modular  [Seed = 2298085345]
   -------------------------------------

Supersingular {
    x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4,
    x^6 + (t + 2)*x^5 + (3*t + 3)*x^4 + (4*t + 4)*x^3 + 2*t*x + 2*t,
    x^6 + (t + 2)*x^5 + (2*t + 4)*x^4 + (2*t + 4)*x^3 + (4*t + 3)*x^2 + (2*t + 
        2)*x + 2*t + 4
}
Done.

Total time: 2.440 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:37:23 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 3*t + 2;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:37:21 on modular  [Seed = 2180052684]
   -------------------------------------

Supersingular {
    x^6 + (t + 4)*x^5 + (3*t + 4)*x^4 + (4*t + 2)*x^3 + (2*t + 4)*x + 2*t + 4,
    x^6 + (t + 4)*x^5 + (2*t + 3)*x^4 + (2*t + 3)*x^3 + (4*t + 1)*x^2 + (2*t + 
        1)*x + 2*t + 3,
    x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t
}
Done.

Total time: 2.430 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:37:53 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 3*t + 3;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:37:51 on modular  [Seed = 2047544650]
   -------------------------------------

Supersingular {
    x^6 + (t + 1)*x^5 + 3*t*x^4 + 4*t*x^3 + (2*t + 3)*x + 2*t + 3,
    x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1,
    x^6 + (t + 1)*x^5 + (2*t + 2)*x^4 + (2*t + 2)*x^3 + (4*t + 4)*x^2 + 2*t*x + 
        2*t + 2
}
Done.

Total time: 2.420 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:38:12 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 3*t + 4;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:38:09 on modular  [Seed = 1864243313]
   -------------------------------------

Supersingular {
    x^6 + (t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 2,
    x^6 + (t + 3)*x^5 + (2*t + 1)*x^4 + (2*t + 1)*x^3 + (4*t + 2)*x^2 + (2*t + 
        4)*x + 2*t + 1,
    x^6 + (t + 3)*x^5 + (3*t + 1)*x^4 + (4*t + 3)*x^3 + (2*t + 2)*x + 2*t + 2
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:38:35 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 4*t + 0;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:38:32 on modular  [Seed = 1729499232]
   -------------------------------------

Supersingular {
    x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3,
    x^6 + 3*t*x^5 + t*x^4 + t*x^3 + 2*t*x^2 + (t + 3)*x + t,
    x^6 + 3*t*x^5 + (4*t + 2)*x^4 + (2*t + 1)*x^3 + (t + 1)*x + t + 1
}
Done.

Total time: 2.420 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:38:52 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 4*t + 1;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:38:50 on modular  [Seed = 1596860586]
   -------------------------------------

Supersingular {
    x^6 + (3*t + 2)*x^5 + (t + 4)*x^4 + (t + 4)*x^3 + (2*t + 3)*x^2 + (t + 2)*x 
        + t + 4,
    x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4,
    x^6 + (3*t + 2)*x^5 + (4*t + 3)*x^4 + (2*t + 4)*x^3 + t*x + t
}
Done.

Total time: 2.439 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:39:11 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 4*t + 2;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:39:08 on modular  [Seed = 1462116532]
   -------------------------------------

Supersingular {
    x^6 + (3*t + 4)*x^5 + (t + 3)*x^4 + (t + 3)*x^3 + (2*t + 1)*x^2 + (t + 1)*x 
        + t + 3,
    x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t,
    x^6 + (3*t + 4)*x^5 + (4*t + 4)*x^4 + (2*t + 2)*x^3 + (t + 4)*x + t + 4
}
Done.

Total time: 2.429 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:39:30 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 4*t + 3;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:39:27 on modular  [Seed = 1312766366]
   -------------------------------------

Supersingular {
    x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1,
    x^6 + (3*t + 1)*x^5 + 4*t*x^4 + 2*t*x^3 + (t + 3)*x + t + 3,
    x^6 + (3*t + 1)*x^5 + (t + 2)*x^4 + (t + 2)*x^3 + (2*t + 4)*x^2 + t*x + t + 
        2
}
Done.

Total time: 2.420 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host scott-12.math.psu.edu. (146.186.133.122)
Time: Sat Aug 28 03:39:50 2004

Input: Z := Integers();
p := Z ! 5;
P<t> := FunctionField(GF(p));

c := 4*t + 4;

Q<x> := PolynomialRing(P);
T<u> := PolynomialRing(RationalField());
GA, RA :=  GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1);

zeromat := elt<MatrixAlgebra(Q, 2)  | 0, 0, 0, 0>;

polynom := function(a0, a1, a2, a3, a4, a5, a6)
	return  a0*x^6 + a1*x^5 + a2*x^4 + a3*x^3 + a2*x^2  + a1*x + a6;
end function;

brumer := function(b, c, d)
	return x^6 
		+ (2*c)*x^5
		+(2+2*c+c^2-4*b*d)*x^4
		+(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3
		+(5+12*b+4*c+c^2-4*b*d)*x^2
		+(6+12*b+2*c)*x
		+(4*b+1);
end function;

isSS := function(f, p)
	hp:=Z ! ((p-1)/2);
	fp:=f^hp;

	c12:=Coefficient(fp, p-2);
	c11:=Coefficient(fp, p-1);
	c22:=Coefficient(fp, 2*p-2);
	c21:=Coefficient(fp, 2*p-1);

	m:=elt<MatrixAlgebra(Q, 2)  | c11, c12, c21, c22>;
	n:=elt<MatrixAlgebra(Q, 2)  | c11^p, c12^p, c21^p, c22^p>;

	return n*m eq zeromat;
end function;

isA5 := function(G)
	return G eq GA;
end function;

S := [ P | ];
for r in [0..p-1] do
	for s in [0..p-1] do
		Append(~S, r*t+s);
	end for;
end for;

SS := { Q | };
NSS := { Q | };

for b in S do
for d in S do

f := brumer(b, c, d);

if not isSS(f, p) then 
	continue;
end if;

if not IsIrreducible(f) then
	continue;
end if;

G, R:= GaloisGroup(f);

if isA5(G) then
	Include(~SS, f);
end if;

end for;
end for;

print "Supersingular", SS;
// print "Non-Supersingular", NSS;

print "Done."

Output: Magma V2.11-2     Sat Aug 28 2004 03:39:47 on modular  [Seed = 1178022394]
   -------------------------------------

Supersingular {
    x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2,
    x^6 + (3*t + 3)*x^5 + (t + 1)*x^4 + (t + 1)*x^3 + (2*t + 2)*x^2 + (t + 4)*x 
        + t + 1,
    x^6 + (3*t + 3)*x^5 + (4*t + 1)*x^4 + (2*t + 3)*x^3 + (t + 2)*x + t + 2
}
Done.

Total time: 2.420 seconds, Total memory usage: 7.66MB


************** MAGMA *****************
Host 21-BAR2-X73.libre.retevision.es. (62.82.153.21)
Time: Sat Aug 28 13:57:13 2004

Input: 676767

Output: Magma V2.11-2     Sat Aug 28 2004 13:57:13 on modular  [Seed = 1262144823]
   -------------------------------------

676767

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:34:16 2004

Input: C:=GolayCode(23,true);
WeightDistributioin(C);

Output: Magma V2.11-2     Sun Aug 29 2004 11:34:11 on modular  [Seed = 3986512785]
   -------------------------------------


>> C:=GolayCode(23,true);
               ^
Runtime error in 'GolayCode': Bad argument types
Argument types given: RngIntElt, BoolElt

>> WeightDistributioin(C);;
                       ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.850 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:35:51 2004

Input: C:=GolayCode(GF(2),23,true);
WeightDistributioin(C);

Output: Magma V2.11-2     Sun Aug 29 2004 11:35:50 on modular  [Seed = 3834925629]
   -------------------------------------


>> C:=GolayCode(GF(2),23,true);
               ^
Runtime error in 'GolayCode': Bad argument types
Argument types given: FldFin, RngIntElt, BoolElt

>> WeightDistributioin(C);;
                       ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:36:00 2004

Input: C:=GolayCode(GF(2),true);
WeightDistributioin(C);

Output: Magma V2.11-2     Sun Aug 29 2004 11:35:59 on modular  [Seed = 4237052460]
   -------------------------------------


>> WeightDistributioin(C);;
   ^
User error: Identifier 'WeightDistributioin' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:36:15 2004

Input: C:=GolayCode(GF(2),true);
WeightDistribution(C);

Output: Magma V2.11-2     Sun Aug 29 2004 11:36:15 on modular  [Seed = 4102308372]
   -------------------------------------

[ <0, 1>, <8, 759>, <12, 2576>, <16, 759>, <24, 1> ]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:36:48 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
G;

Output: Magma V2.11-2     Sun Aug 29 2004 11:36:47 on modular  [Seed = 226341900]
   -------------------------------------

Permutation group G acting on a set of cardinality 24
Order = 244823040 = 2^10 * 3^3 * 5 * 7 * 11 * 23
    (7, 22, 17)(8, 13, 11)(9, 12, 14)(10, 19, 20)(15, 18, 24)(16, 23, 21)
    (6, 21, 23)(7, 24, 19)(8, 13, 11)(9, 17, 20)(10, 15, 14)(12, 18, 22)
    (6, 20)(7, 21)(9, 15)(10, 19)(12, 22)(14, 23)(16, 18)(17, 24)
    (5, 18, 19)(6, 22, 11)(7, 10, 12)(8, 24, 21)(13, 15, 14)(16, 17, 20)
    (4, 9)(5, 19)(6, 10)(7, 22)(8, 24)(11, 12)(14, 15)(16, 17)
    (3, 5, 16, 7)(6, 9, 22, 20)(8, 10)(11, 14, 21, 12)(13, 15, 18, 23)(19, 24)
    (1, 2, 14, 19, 3, 23, 6, 4, 7, 12, 17, 22, 20, 18, 13, 24, 5, 16, 15, 21, 
        9)(8, 10, 11)
    (2, 14, 19, 4, 12, 16, 24, 5, 17, 22, 9)(3, 10, 11, 8, 23, 18, 13, 15, 21, 
        20, 6)

Total time: 0.569 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:37:20 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
ConjugacyClasses(G);

Output: Magma V2.11-2     Sun Aug 29 2004 11:37:19 on modular  [Seed = 91601956]
   -------------------------------------

Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 11385  
        Rep (2, 17)(3, 14)(6, 22)(9, 13)(10, 19)(11, 21)(12, 16)(18, 20)

[3]     Order 2       Length 31878  
        Rep (1, 9)(2, 6)(3, 12)(4, 21)(5, 17)(7, 23)(8, 14)(10, 13)(11, 18)(15, 
            24)(16, 19)(20, 22)

[4]     Order 3       Length 226688 
        Rep (2, 5, 17)(3, 19, 22)(4, 23, 16)(6, 14, 13)(7, 24, 21)(15, 20, 18)

[5]     Order 3       Length 485760 
        Rep (1, 9, 15)(2, 20, 21)(3, 24, 12)(4, 22, 19)(5, 10, 17)(6, 11, 14)(7,
            23, 13)(8, 18, 16)

[6]     Order 4       Length 637560 
        Rep (1, 9, 24, 14)(2, 7, 11, 4)(3, 13)(5, 18, 15, 12)(6, 10)(8, 22, 23, 
            19)(16, 20)(17, 21)

[7]     Order 4       Length 1912680
        Rep (3, 10, 6, 18)(4, 9, 20, 23)(5, 17, 24, 8)(7, 21)(12, 13)(14, 19, 
            16, 15)

[8]     Order 4       Length 2550240
        Rep (1, 19, 10, 5)(2, 6, 3, 20)(4, 8, 24, 22)(7, 9, 16, 17)(11, 15, 23, 
            14)(12, 18, 21, 13)

[9]     Order 5       Length 4080384
        Rep (1, 9, 10, 11, 12)(3, 13, 21, 23, 15)(4, 18, 22, 14, 24)(6, 7, 16, 
            20, 19)

[10]    Order 6       Length 10200960
        Rep (1, 23)(3, 5, 13, 9, 20, 4)(6, 7, 24)(8, 10, 14, 12, 17, 15)(11, 16,
            22)(19, 21)

[11]    Order 6       Length 10200960
        Rep (1, 7, 11, 9, 23, 18)(2, 14, 16, 6, 8, 19)(3, 4, 22, 12, 21, 20)(5, 
            15, 10, 17, 24, 13)

[12]    Order 7       Length 5829120
        Rep (1, 24, 17, 10, 21, 5, 15)(2, 23, 16, 22, 18, 9, 8)(3, 4, 12, 11, 
            19, 13, 14)

[13]    Order 7       Length 5829120
        Rep (1, 5, 10, 24, 15, 21, 17)(2, 9, 22, 23, 8, 18, 16)(3, 13, 11, 4, 
            14, 19, 12)

[14]    Order 8       Length 15301440
        Rep (1, 22)(3, 14, 10, 19, 6, 16, 18, 15)(4, 24, 9, 8, 20, 5, 23, 17)(7,
            13, 21, 12)

[15]    Order 10      Length 12241152
        Rep (1, 10, 15, 20, 11, 18, 23, 17, 12, 2)(3, 22, 5, 21, 24, 16, 8, 6, 
            14, 4)(7, 13)(9, 19)

[16]    Order 11      Length 22256640
        Rep (1, 21, 17, 10, 7, 13, 6, 24, 16, 2, 22)(4, 20, 9, 12, 14, 5, 19, 
            11, 23, 15, 18)

[17]    Order 12      Length 20401920
        Rep (1, 13, 16, 19, 12, 17, 10, 18, 7, 5, 21, 9)(2, 11, 8, 6, 15, 24, 3,
            23, 22, 20, 14, 4)

[18]    Order 12      Length 20401920
        Rep (1, 14, 24, 9)(2, 15, 22, 7, 12, 23, 11, 5, 19, 4, 18, 8)(3, 13)(6, 
            17, 20, 10, 21, 16)

[19]    Order 14      Length 17487360
        Rep (1, 15, 4, 7, 23, 8, 24)(2, 17)(3, 18, 9, 6, 10, 16, 21, 14, 20, 13,
            22, 19, 12, 11)

[20]    Order 14      Length 17487360
        Rep (1, 7, 24, 4, 8, 15, 23)(2, 17)(3, 6, 21, 13, 12, 18, 10, 14, 22, 
            11, 9, 16, 20, 19)

[21]    Order 15      Length 16321536
        Rep (1, 12, 11, 10, 9)(2, 17, 5)(3, 18, 16, 21, 14, 19, 15, 4, 7, 13, 
            22, 20, 23, 24, 6)

[22]    Order 15      Length 16321536
        Rep (1, 10, 12, 9, 11)(2, 17, 5)(3, 24, 20, 13, 4, 19, 21, 18, 6, 23, 
            22, 7, 15, 14, 16)

[23]    Order 21      Length 11658240
        Rep (1, 10, 19, 14, 24, 2, 7, 9, 17, 4, 6, 12, 20, 23, 15, 5, 22, 11, 3,
            21, 13)(8, 18, 16)

[24]    Order 21      Length 11658240
        Rep (1, 2, 6, 5, 13, 24, 4, 15, 21, 14, 17, 23, 3, 19, 9, 20, 11, 10, 7,
            12, 22)(8, 16, 18)

[25]    Order 23      Length 10644480
        Rep (1, 5, 24, 10, 15, 22, 12, 6, 14, 19, 21, 23, 17, 13, 9, 8, 20, 4, 
            2, 11, 18, 7, 16)

[26]    Order 23      Length 10644480
        Rep (1, 22, 21, 8, 18, 24, 6, 17, 4, 16, 15, 19, 9, 11, 5, 12, 23, 20, 
            7, 10, 14, 13, 2)



Total time: 0.649 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:38:17 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
CC:=ConjugacyClasses(G);
CC[2];CC[3];

Output: Magma V2.11-2     Sun Aug 29 2004 11:38:16 on modular  [Seed = 409510270]
   -------------------------------------

<2, 11385, (1, 10)(2, 22)(3, 13)(4, 18)(7, 9)(11, 20)(15, 17)(16, 19)>
<2, 31878, (1, 8)(2, 22)(3, 7)(4, 13)(5, 14)(6, 12)(9, 18)(10, 11)(15, 19)(16, 
    21)(17, 23)(20, 24)>

Total time: 0.610 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:39:10 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
CC:=ConjugacyClasses(G);
g:=CC[3][3];
Fixed(g,C);

Output: Magma V2.11-2     Sun Aug 29 2004 11:39:09 on modular  [Seed = 291612802]
   -------------------------------------


>> Fixed(g,C);;
   ^
User error: Identifier 'Fixed' has not been declared or assigned

Total time: 0.630 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:39:26 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
CC:=ConjugacyClasses(G);
g:=CC[3][3];
FixedCode(C,g);

Output: Magma V2.11-2     Sun Aug 29 2004 11:39:25 on modular  [Seed = 693735561]
   -------------------------------------


>> FixedCode(C,g);;
   ^
User error: Identifier 'FixedCode' has not been declared or assigned

Total time: 0.630 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:39:45 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
CC:=ConjugacyClasses(G);
g:=CC[3][3];
g;


Output: Magma V2.11-2     Sun Aug 29 2004 11:39:45 on modular  [Seed = 1045334001]
   -------------------------------------

(1, 22)(2, 7)(3, 17)(4, 20)(5, 8)(6, 24)(9, 10)(11, 23)(12, 15)(13, 14)(16, 
    19)(18, 21)

Total time: 0.610 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:40:49 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 22)(2, 7)(3, 17)(4, 20)(5, 8)(6, 24)(9, 10)(11, 23)(12, 15)(13, 14)(16, 19)(18, 21);
C eq C^g;

Output: Magma V2.11-2     Sun Aug 29 2004 11:40:49 on modular  [Seed = 1161166154]
   -------------------------------------

true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:50:22 2004

Input: C:=GolayCode(GF(2),true);
G:=AutomorphismGroup(C);
g:=ConjugacyClasses(G)[3][3];
g;


Output: Magma V2.11-2     Sun Aug 29 2004 11:50:22 on modular  [Seed = 1378019426]
   -------------------------------------

(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10, 12)(13, 16)(17, 18)(19, 
    21)(22, 24)

Total time: 0.620 seconds, Total memory usage: 3.36MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:51:57 2004

Input: C:=GolayCode(GF(2),true);
g:=(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10, 12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,g);
E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);

Output: Magma V2.11-2     Sun Aug 29 2004 11:51:57 on modular  [Seed = 1780142329]
   -------------------------------------


>> g:=(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10, 12)(13,16)(17, 18)(1
      ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

>> D:=Fix(C,g);
            ^
User error: Identifier 'g' has not been declared or assigned

>> E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);;
                   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:52:16 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10, 12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,g);
E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);

Output: Magma V2.11-2     Sun Aug 29 2004 11:52:15 on modular  [Seed = 1645402307]
   -------------------------------------


>> g:=Sym(24)(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10, 12)(13,16)(17
             ^
Runtime error: Attempting to call something that is not callable

>> D:=Fix(C,g);
            ^
User error: Identifier 'g' has not been declared or assigned

>> E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);;
                   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:52:42 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,g);
E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);

Output: Magma V2.11-2     Sun Aug 29 2004 11:52:41 on modular  [Seed = 2047525053]
   -------------------------------------


>> D:=Fix(C,g);
         ^
Runtime error in 'Fix': Bad argument types
Argument types given: CodeLinFld, GrpPermElt

>> E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);;
                   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:53:42 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<G|g>);
E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);

Output: Magma V2.11-2     Sun Aug 29 2004 11:53:42 on modular  [Seed = 1879100792]
   -------------------------------------


>> D:=Fix(C,sub<G|g>);
                ^
User error: Identifier 'G' has not been declared or assigned

>> E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);;
                   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:53:58 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<Sym(24)|g>);
E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);

Output: Magma V2.11-2     Sun Aug 29 2004 11:53:57 on modular  [Seed = 2297968019]
   -------------------------------------


>> E:=PunctureCode(D,[8,20,7,14,15,23,11,12,16,18,21,24]);;
                  ^
Runtime error in 'PunctureCode': Bad argument types
Argument types given: CodeLinFld, SeqEnum[RngIntElt]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:55:18 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<Sym(24)|g>);
E:=PunctureCode(D,{8,20,7,14,15,23,11,12,16,18,21,24});
E;
IsSelfDual(E);


Output: Magma V2.11-2     Sun Aug 29 2004 11:55:17 on modular  [Seed = 2180070634]
   -------------------------------------

[12, 6, 4] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 0 1 0 1 1 1]
[0 1 0 0 0 1 0 0 1 1 1 1]
[0 0 1 0 0 0 0 1 1 0 0 1]
[0 0 0 1 0 1 0 1 1 0 0 0]
[0 0 0 0 1 0 0 1 1 1 0 0]
[0 0 0 0 0 0 1 1 1 0 1 0]
true

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:55:57 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<Sym(24)|g>);
E:=PunctureCode(D,{8,20,7,14,15,23,11,12,16,18,21,24});
WeightDistribution(E);


Output: Magma V2.11-2     Sun Aug 29 2004 11:55:56 on modular  [Seed = 2582193179]
   -------------------------------------

[ <0, 1>, <4, 15>, <6, 32>, <8, 15>, <12, 1> ]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:56:58 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<Sym(24)|g>);
Dimenstion(D);


Output: Magma V2.11-2     Sun Aug 29 2004 11:56:57 on modular  [Seed = 2447453270]
   -------------------------------------


>> Dimenstion(D);
   ^
User error: Identifier 'Dimenstion' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 11:57:09 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<Sym(24)|g>);
Dimension(D);


Output: Magma V2.11-2     Sun Aug 29 2004 11:57:08 on modular  [Seed = 2849576051]
   -------------------------------------

6

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:19:14 2004

Input: C:=GolayCode(GF(2),true);
g:=Sym(24)!(1, 8)(2, 20)(3, 7)(4, 14)(5, 15)(6, 23)(9, 11)(10,12)(13,16)(17, 18)(19, 21)(22, 24);
D:=Fix(C,sub<Sym(24)|g>);
E:=PunctureCode(D,{8,20,7,14,15,23,11,12,16,18,21,24});
WeightDistribution(E);


Output: Magma V2.11-2     Sun Aug 29 2004 12:19:13 on modular  [Seed = 3533803997]
   -------------------------------------

[ <0, 1>, <4, 15>, <6, 32>, <8, 15>, <12, 1> ]

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:20:26 2004

Input: C:=HammingCode(GF(2),true);
C;

Output: Magma V2.11-2     Sun Aug 29 2004 12:20:25 on modular  [Seed = 4135957938]
   -------------------------------------


>> C:=HammingCode(GF(2),true);
                 ^
Runtime error in 'HammingCode': Bad argument types
Argument types given: FldFin, BoolElt

>> C;;
   ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:20:48 2004

Input: C:=ExtendedCode(HammingCode(GF(2)));
C;

Output: Magma V2.11-2     Sun Aug 29 2004 12:20:48 on modular  [Seed = 291656288]
   -------------------------------------


>> C:=ExtendedCode(HammingCode(GF(2)));
      ^
User error: Identifier 'ExtendedCode' has not been declared or assigned

>> C;;
   ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:20:59 2004

Input: C:=ExtendCode(HammingCode(GF(2)));
C;

Output: Magma V2.11-2     Sun Aug 29 2004 12:20:59 on modular  [Seed = 426400355]
   -------------------------------------


>> C:=ExtendCode(HammingCode(GF(2)));
                            ^
Runtime error in 'HammingCode': Bad argument types
Argument types given: FldFin

>> C;;
   ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:22:06 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
C;

Output: Magma V2.11-2     Sun Aug 29 2004 12:22:05 on modular  [Seed = 24265405]
   -------------------------------------

[8, 4, 4] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 1 1 0 1]
[0 1 0 0 0 1 1 1]
[0 0 1 0 1 1 1 0]
[0 0 0 1 1 0 1 1]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:22:28 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
AutomorphismGrou(C);

Output: Magma V2.11-2     Sun Aug 29 2004 12:22:27 on modular  [Seed = 159009499]
   -------------------------------------


>> AutomorphismGrou(C);;
   ^
User error: Identifier 'AutomorphismGrou' has not been declared or assigned

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:23:02 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
G:=AutomorphismGroup(C);
CC:=ConjugacyClasses(G);
CC;

Output: Magma V2.11-2     Sun Aug 29 2004 12:23:01 on modular  [Seed = 826438341]
   -------------------------------------

Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 7      
        Rep (1, 4)(2, 8)(3, 5)(6, 7)

[3]     Order 2       Length 42     
        Rep (1, 4)(2, 3)(5, 8)(6, 7)

[4]     Order 2       Length 42     
        Rep (1, 2)(5, 7)

[5]     Order 3       Length 224    
        Rep (1, 8, 3)(2, 5, 4)

[6]     Order 4       Length 84     
        Rep (1, 8, 7, 3)(2, 6, 5, 4)

[7]     Order 4       Length 168    
        Rep (1, 3, 4, 2)(5, 7, 8, 6)

[8]     Order 4       Length 168    
        Rep (1, 7, 6, 4)(5, 8)

[9]     Order 6       Length 224    
        Rep (1, 5, 8, 4, 3, 2)(6, 7)

[10]    Order 7       Length 192    
        Rep (1, 6, 2, 7, 3, 8, 4)

[11]    Order 7       Length 192    
        Rep (1, 8, 7, 6, 4, 3, 2)



Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:26:13 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
g1:=Sym(8)!(1, 4)(2, 8)(3, 5)(6, 7);
g2:=Sym(8)!(1, 4)(2, 3)(5, 8)(6, 7);
C1:=Fix(C,sub<Sym(8)|g1>);
D1:=PunctureCode(C1,{4,8,5,7});
C2:=Fix(C,sub<Sym(8)|g2>);
D2:=PunctureCode(C1,{4,3,8,7});
IsSelfDual(D1);
IsSelfDual(D2);



Output: Magma V2.11-2     Sun Aug 29 2004 12:26:12 on modular  [Seed = 977893519]
   -------------------------------------

false
false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:26:39 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
g1:=Sym(8)!(1, 4)(2, 8)(3, 5)(6, 7);
g2:=Sym(8)!(1, 4)(2, 3)(5, 8)(6, 7);
C1:=Fix(C,sub<Sym(8)|g1>);
D1:=PunctureCode(C1,{4,8,5,7});
C2:=Fix(C,sub<Sym(8)|g2>);
D2:=PunctureCode(C1,{4,3,8,7});
IsSelfDual(D1);
IsSelfDual(D2);
D1;
D2;



Output: Magma V2.11-2     Sun Aug 29 2004 12:26:38 on modular  [Seed = 659842440]
   -------------------------------------

false
false
[4, 3, 2] Linear Code over GF(2)
Generator matrix:
[1 0 0 1]
[0 1 0 1]
[0 0 1 1]
[4, 3, 2] Cyclic Linear Code over GF(2)
Generator matrix:
[1 0 0 1]
[0 1 0 1]
[0 0 1 1]

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:27:39 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
g1:=Sym(8)!(1, 4)(2, 8)(3, 5)(6, 7);
g2:=Sym(8)!(1, 4)(2, 3)(5, 8)(6, 7);
C^g1 eq C; C^g2 eq C;
C1:=Fix(C,sub<Sym(8)|g1>);
D1:=PunctureCode(C1,{4,8,5,7});
C2:=Fix(C,sub<Sym(8)|g2>);
D2:=PunctureCode(C1,{4,3,8,7});
IsSelfDual(D1);
IsSelfDual(D2);
D1;
D2;



Output: Magma V2.11-2     Sun Aug 29 2004 12:27:38 on modular  [Seed = 794586564]
   -------------------------------------

true
true
false
false
[4, 3, 2] Linear Code over GF(2)
Generator matrix:
[1 0 0 1]
[0 1 0 1]
[0 0 1 1]
[4, 3, 2] Cyclic Linear Code over GF(2)
Generator matrix:
[1 0 0 1]
[0 1 0 1]
[0 0 1 1]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:29:17 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
g1:=Sym(8)!(1, 4)(2, 8)(3, 5)(6, 7);
g2:=Sym(8)!(1, 4)(2, 3)(5, 8)(6, 7);
C^g1 eq C;
C^g2 eq C;
C1:=Fix(C,sub<Sym(8)|g1>);
C2:=Fix(C,sub<Sym(8)|g2>);
Demension(C1);
Demension(C2);



Output: Magma V2.11-2     Sun Aug 29 2004 12:29:17 on modular  [Seed = 1445270298]
   -------------------------------------

true
true

>> Demension(C1);
   ^
User error: Identifier 'Demension' has not been declared or assigned

>> Demension(C2);
   ^
User error: Identifier 'Demension' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:29:33 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
g1:=Sym(8)!(1, 4)(2, 8)(3, 5)(6, 7);
g2:=Sym(8)!(1, 4)(2, 3)(5, 8)(6, 7);
C^g1 eq C;
C^g2 eq C;
C1:=Fix(C,sub<Sym(8)|g1>);
C2:=Fix(C,sub<Sym(8)|g2>);
Dimension(C1);
Dimension(C2);



Output: Magma V2.11-2     Sun Aug 29 2004 12:29:32 on modular  [Seed = 1077085501]
   -------------------------------------

true
true
3
2

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host YahooBB219058078066.bbtec.net. (219.58.78.66)
Time: Sun Aug 29 12:30:35 2004

Input: C:=ExtendCode(HammingCode(GF(2),3));
g1:=Sym(8)!(1, 4)(2, 8)(3, 5)(6, 7);
g2:=Sym(8)!(1, 4)(2, 3)(5, 8)(6, 7);
C^g1 eq C;
C^g2 eq C;
C1:=Fix(C,sub<Sym(8)|g1>);
C2:=Fix(C,sub<Sym(8)|g2>);
Dimension(C1);
Dimension(C2);
D:=PunctureCode(C2,{4,3,8,7});
IsSelfDual(D);

Output: Magma V2.11-2     Sun Aug 29 2004 12:30:34 on modular  [Seed = 1211829747]
   -------------------------------------

true
true
3
2
true

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host diale181.ppp.lrz-muenchen.de. (129.187.28.181)
Time: Sun Aug 29 15:12:50 2004

Input: i = 1;
i*3;

Output: Magma V2.11-2     Sun Aug 29 2004 15:12:50 on modular  [Seed = 1645283776]
   -------------------------------------


>> i = 1;
   ^
User error: Identifier 'i' has not been declared or assigned

>> i*3;;
   ^
User error: Identifier 'i' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 67-137-84-135.dsl2.cok.tn.frontiernet.net. (67.137.84.135)
Time: Sun Aug 29 17:30:24 2004

Input: 1+2

Output: Magma V2.11-2     Sun Aug 29 2004 17:30:23 on modular  [Seed = 1211843508]
   -------------------------------------

3

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 67-137-84-135.dsl2.cok.tn.frontiernet.net. (67.137.84.135)
Time: Sun Aug 29 17:30:49 2004

Input: 1+2+3

Output: Magma V2.11-2     Sun Aug 29 2004 17:30:49 on modular  [Seed = 1879276138]
   -------------------------------------

6

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c-24-10-96-33.client.comcast.net. (24.10.96.33)
Time: Sun Aug 29 21:40:36 2004

Input: 36!/(36-6)

Output: Magma V2.11-2     Sun Aug 29 2004 21:40:36 on modular  [Seed = 1279232205]
   -------------------------------------


>> 36!/(36-6);
      ^
User error: bad syntax

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-253-23-22.VIC.netspace.net.au. (220.253.23.22)
Time: Mon Aug 30 01:40:02 2004

Input: testing

Output: Magma V2.11-2     Mon Aug 30 2004 01:40:00 on modular  [Seed = 1045283481]
   -------------------------------------


>> testing;
   ^
User error: Identifier 'testing' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 04:36:37 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 04:36:35 on modular  [Seed = 3032945329]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.550 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 04:37:02 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({})


Output: Magma V2.11-2     Mon Aug 30 2004 04:37:01 on modular  [Seed = 3167689351]
   -------------------------------------


>> SClassGroup({})
              ^
Runtime error in 'SClassGroup': Set has no universe

Total time: 1.240 seconds, Total memory usage: 12.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 04:37:10 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({})


Output: Magma V2.11-2     Mon Aug 30 2004 04:37:09 on modular  [Seed = 2765554311]
   -------------------------------------


>> SClassGroup({})
              ^
Runtime error in 'SClassGroup': Set has no universe

Total time: 1.240 seconds, Total memory usage: 12.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 04:39:04 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SRegulator({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 04:39:03 on modular  [Seed = 2883063066]
   -------------------------------------

1

Total time: 1.240 seconds, Total memory usage: 12.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 04:40:20 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SUnitGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 04:40:18 on modular  [Seed = 3485231403]
   -------------------------------------

Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0 to FldFun: F given by a rule

Total time: 1.250 seconds, Total memory usage: 12.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:14:45 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
print(L);
I := L[1][1];
pl := Place(I);
SUnitGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 05:14:44 on modular  [Seed = 209698065]
   -------------------------------------

[ <Prime Ideal of O
Generators:
x^4 + x + 2
alpha, 1> ]
Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0 to FldFun: F given by a rule

Total time: 1.260 seconds, Total memory usage: 12.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:15:12 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
print(I);
pl := Place(I);
SUnitGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 05:15:11 on modular  [Seed = 74953986]
   -------------------------------------

Prime Ideal of O
Generators:
x^4 + x + 2
alpha
Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/6
Defined on 1 generator
Relations:
    6*$.1 = 0 to FldFun: F given by a rule

Total time: 1.240 seconds, Total memory usage: 12.87MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:18:53 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^4 + x+ 2;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
print(I);
pl := Place(I);
SClassGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 05:18:51 on modular  [Seed = 809730514]
   -------------------------------------

Prime Ideal of O
Generators:
x^4 + x + 2
alpha
Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
    2*$.1 = 0
    24*$.2 = 0 given by a rule

Total time: 1.500 seconds, Total memory usage: 13.07MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:49:22 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 3;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
% I := L[1][1];
pl := Place(I);
SClassGroup({pl})


Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:49:33 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 3;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
* I := L[1][1];
pl := Place(I);
SClassGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 05:49:32 on modular  [Seed = 1796788830]
   -------------------------------------


>> * I := L[1][1];
   ^
User error: bad syntax

>> pl := Place(I);
               ^
User error: Identifier 'I' has not been declared or assigned

>> SClassGroup({pl})
                ^
User error: Identifier 'pl' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:51:36 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 3;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
// I := L[1][1];
// pl := Place(I);
// SClassGroup({pl})


Output: Magma V2.11-2     Mon Aug 30 2004 05:51:35 on modular  [Seed = 1662048989]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:51:53 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 3;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
// I := L[1][1];
// pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-2     Mon Aug 30 2004 05:51:52 on modular  [Seed = 2615681595]
   -------------------------------------

Abelian Group isomorphic to Z
Defined on 1 generator (free)
Mapping from: Abelian Group isomorphic to Z
Defined on 1 generator (free) to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z
Defined on 1 generator (free) given by a rule

Total time: 0.830 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:53:06 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 3;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Mon Aug 30 2004 05:53:05 on modular  [Seed = 2514890125]
   -------------------------------------

Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0 given by a rule

Total time: 0.730 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:53:13 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 5;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Mon Aug 30 2004 05:53:12 on modular  [Seed = 2382247324]
   -------------------------------------

Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0 given by a rule

Total time: 0.730 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:53:21 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
SClassGroup({pl})

Output: Magma V2.11-2     Mon Aug 30 2004 05:53:20 on modular  [Seed = 2230795404]
   -------------------------------------

Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*$.1 = 0 given by a rule

Total time: 0.789 seconds, Total memory usage: 3.15MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:54:17 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
Factorization(x^4+x+2)

Output: Magma V2.11-2     Mon Aug 30 2004 05:54:17 on modular  [Seed = 3167683820]
   -------------------------------------


>> Factorization(x^4+x+2);
                ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatUElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:54:31 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
Factorize(x^4+x+2)

Output: Magma V2.11-2     Mon Aug 30 2004 05:54:31 on modular  [Seed = 3032943866]
   -------------------------------------


>> Factorize(x^4+x+2);
   ^
User error: Identifier 'Factorize' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:54:40 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
Factor(x^4+x+2)

Output: Magma V2.11-2     Mon Aug 30 2004 05:54:39 on modular  [Seed = 2950436841]
   -------------------------------------


>> Factor(x^4+x+2);
         ^
Runtime error in 'Factor': Bad argument types
Argument types given: FldFunRatUElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:54:56 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
IsIrreducible(x^4+x+2)

Output: Magma V2.11-2     Mon Aug 30 2004 05:54:55 on modular  [Seed = 2815696849]
   -------------------------------------

false

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:56:36 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
Factorization(x^2-2)

Output: Magma V2.11-2     Mon Aug 30 2004 05:56:36 on modular  [Seed = 3517081884]
   -------------------------------------


>> Factorization(x^2-2);
                ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatUElt

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:58:49 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
Factorization(D)

Output: Magma V2.11-2     Mon Aug 30 2004 05:58:48 on modular  [Seed = 3401150859]
   -------------------------------------


>> Factorization(D);
                ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatUElt

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:59:01 2004

Input: R<x> := FunctionField(GF(7));
// P<y> := PolynomialRing(R);
D := x^2 - 6;
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(alpha*O);
I := L[1][1];
pl := Place(I);
// SClassGroup({pl})
Factorization(D)

Output: Magma V2.11-2     Mon Aug 30 2004 05:59:01 on modular  [Seed = 3317071545]
   -------------------------------------


>> F<alpha> := FunctionField(y^2 - D);
                             ^
User error: Identifier 'y' has not been declared or assigned

>> O := MaximalOrderFinite(F);
                           ^
User error: Identifier 'F' has not been declared or assigned

>> L := Factorization(alpha*O);
                      ^
User error: Identifier 'alpha' has not been declared or assigned

>> I := L[1][1];
        ^
User error: Identifier 'L' has not been declared or assigned

>> pl := Place(I);
               ^
User error: Identifier 'I' has not been declared or assigned

>> Factorization(D);
                ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatUElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:59:20 2004

Input: R<x> := FunctionField(GF(7));
// P<y> := PolynomialRing(R);
D := x^2 - 6;
// F<alpha> := FunctionField(y^2 - D);
// O := MaximalOrderFinite(F);
// L := Factorization(alpha*O);
// I := L[1][1];
// pl := Place(I);
// SClassGroup({pl})
Factorization(D)

Output: Magma V2.11-2     Mon Aug 30 2004 05:59:19 on modular  [Seed = 4253959827]
   -------------------------------------


>> Factorization(D);
                ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatUElt

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 05:59:51 2004

Input: R<x> := PolynomialRing(GF(7));
// R<x> := FunctionField(GF(7));
// P<y> := PolynomialRing(R);
D := x^2 - 6;
// F<alpha> := FunctionField(y^2 - D);
// O := MaximalOrderFinite(F);
// L := Factorization(alpha*O);
// I := L[1][1];
// pl := Place(I);
// SClassGroup({pl})
Factorization(D)

Output: Magma V2.11-2     Mon Aug 30 2004 05:59:50 on modular  [Seed = 4102508411]
   -------------------------------------

[
    <x^2 + 1, 1>
]

Total time: 0.539 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 06:00:14 2004

Input: R<x> := PolynomialRing(GF(7));
// R<x> := FunctionField(GF(7));
// P<y> := PolynomialRing(R);
D := x^2 - 6;
// F<alpha> := FunctionField(y^2 - D);
// O := MaximalOrderFinite(F);
// L := Factorization(alpha*O);
// I := L[1][1];
// pl := Place(I);
// SClassGroup({pl})
Factorization(x^2+5)

Output: Magma V2.11-2     Mon Aug 30 2004 06:00:13 on modular  [Seed = 342339489]
   -------------------------------------

[
    <x + 3, 1>,
    <x + 4, 1>
]

Total time: 0.569 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host newton.Informatik.UniBw-Muenchen.de. (137.193.61.16)
Time: Mon Aug 30 06:00:26 2004

Input: R<x> := PolynomialRing(GF(7));
// R<x> := FunctionField(GF(7));
// P<y> := PolynomialRing(R);
D := x^2 - 6;
// F<alpha> := FunctionField(y^2 - D);
// O := MaximalOrderFinite(F);
// L := Factorization(alpha*O);
// I := L[1][1];
// pl := Place(I);
// SClassGroup({pl})
Factorization(x^4+x+2)

Output: Magma V2.11-2     Mon Aug 30 2004 06:00:25 on modular  [Seed = 209696685]
   -------------------------------------

[
    <x^4 + x + 2, 1>
]

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 220-136-166-102.dynamic.hinet.net. (220.136.166.102)
Time: Mon Aug 30 08:39:34 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-2     Mon Aug 30 2004 08:39:32 on modular  [Seed = 3919284470]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.639 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host ti121210a080-4331.bb.online.no. (80.212.48.237)
Time: Mon Aug 30 08:43:42 2004

Input: int(log(x),x)

Output: Magma V2.11-2     Mon Aug 30 2004 08:43:42 on modular  [Seed = 226454761]
   -------------------------------------


>> int(log(x),x);
           ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host CPE-138-217-140-175.vic.bigpond.net.au. (138.217.140.175)
Time: Mon Aug 30 08:50:07 2004

Input: ABC

Output: Magma V2.11-2     Mon Aug 30 2004 08:50:06 on modular  [Seed = 1045192026]
   -------------------------------------


>> ABC;
   ^
User error: Identifier 'ABC' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host CPE-138-217-140-175.vic.bigpond.net.au. (138.217.140.175)
Time: Mon Aug 30 08:50:40 2004

Input: c:=ABC

Output: Magma V2.11-2     Mon Aug 30 2004 08:50:39 on modular  [Seed = 910448051]
   -------------------------------------


>> c:=ABC;
      ^
User error: Identifier 'ABC' has not been declared or assigned

Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host CPE-138-217-140-175.vic.bigpond.net.au. (138.217.140.175)
Time: Mon Aug 30 08:50:53 2004

Input: c:="ABC"

Output: Magma V2.11-2     Mon Aug 30 2004 08:50:53 on modular  [Seed = 777801113]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:19:42 2004

Input: load crcload

Output: WARNING: MAGMA command contains unsafe command 'load', so it will not be executed.

************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:21:29 2004

Input: c = "ABC"

Output: Magma V2.11-2     Mon Aug 30 2004 10:21:28 on modular  [Seed = 1596795306]
   -------------------------------------


>> c = "ABC";
   ^
User error: Identifier 'c' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:21:41 2004

Input: c="ABC"

Output: Magma V2.11-2     Mon Aug 30 2004 10:21:41 on modular  [Seed = 1445208254]
   -------------------------------------


>> c="ABC";
   ^
User error: Identifier 'c' has not been declared or assigned

Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:21:54 2004

Input: c:="ABC"

Output: Magma V2.11-2     Mon Aug 30 2004 10:21:54 on modular  [Seed = 1228615766]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:22:17 2004

Input: c:="BOB"

Output: Magma V2.11-2     Mon Aug 30 2004 10:22:16 on modular  [Seed = 1077033284]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:23:01 2004

Input: c:="ABC"

Output: Magma V2.11-2     Mon Aug 30 2004 10:23:00 on modular  [Seed = 2047345443]
   -------------------------------------


Total time: 0.549 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:24:27 2004

Input: load crcload;
c:="ABC"

Output: WARNING: MAGMA command contains unsafe command 'load', so it will not be executed.

************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:24:40 2004

Input: c:="ABC";
load crcload;

Output: WARNING: MAGMA command contains unsafe command 'load', so it will not be executed.

************** MAGMA *****************
Host c211-28-180-71.mckinn1.vic.optusnet.com.au. (211.28.180.71)
Time: Mon Aug 30 10:24:51 2004

Input: c:="ABC";

Output: Magma V2.11-2     Mon Aug 30 2004 10:24:50 on modular  [Seed = 2666325809]
   -------------------------------------


Total time: 0.559 seconds, Total memory usage: 2.79MB


************** MAGMA *****************
Host 140.247.245.154 (140.247.245.154)
Time: Fri Sep  3 17:42:35 2004

Input: 2+2

Output: Magma V2.11-6     Fri Sep  3 2004 17:42:35 on sha      [Seed = 2965968008]
   -------------------------------------

4

Total time: 0.190 seconds, Total memory usage: 3.51MB


************** MAGMA *****************
Host 140.247.245.154 (140.247.245.154)
Time: Fri Sep  3 17:42:46 2004

Input: ModularSymbols("997E")

Output: Magma V2.11-6     Fri Sep  3 2004 17:42:43 on sha      [Seed = 3050049941]
   -------------------------------------

Modular symbols space for Gamma_0(997) of weight 2 and dimension 10 over 
Rational Field

Total time: 2.570 seconds, Total memory usage: 11.17MB


************** MAGMA *****************
Host 140.247.245.154 (140.247.245.154)
Time: Fri Sep  3 17:42:56 2004

Input: time ModularSymbols("997E")

Output: Magma V2.11-6     Fri Sep  3 2004 17:42:53 on sha      [Seed = 3133349524]
   -------------------------------------

Modular symbols space for Gamma_0(997) of weight 2 and dimension 10 over 
Rational Field
Time: 2.470

Total time: 2.660 seconds, Total memory usage: 11.16MB


************** MAGMA *****************
Host 140.247.245.154 (140.247.245.154)
Time: Fri Sep  3 17:43:14 2004

Input: NewformDecomposition(ModularSymbols(997,2,+1));

Output: Magma V2.11-6     Fri Sep  3 2004 17:43:14 on sha      [Seed = 3217431486]
   -------------------------------------


>> NewformDecomposition(ModularSymbols(997,2,+1));;
                       ^
Runtime error in 'NewformDecomposition': Argument 1 must be cuspidal.

Total time: 0.339 seconds, Total memory usage: 5.86MB


************** MAGMA *****************
Host 140.247.245.154 (140.247.245.154)
Time: Fri Sep  3 17:43:24 2004

Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(997,2,+1)));

Output: Magma V2.11-6     Fri Sep  3 2004 17:43:23 on sha      [Seed = 3167033524]
   -------------------------------------

[
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 4 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 5 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 5 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 23 over 
    Rational Field,
    Modular symbols space for Gamma_0(997) of weight 2 and dimension 42 over 
    Rational Field
]

Total time: 1.030 seconds, Total memory usage: 6.32MB


************** MAGMA *****************
Host 65.96.167.57 (65.96.167.57)
Time: Fri Sep  3 21:54:15 2004

Input: 2+2

Output: Magma V2.11-6     Fri Sep  3 2004 21:54:13 on sha      [Seed = 425818153]
   -------------------------------------

4

Total time: 0.229 seconds, Total memory usage: 3.51MB


************** MAGMA *****************
Host 65.96.167.57 (65.96.167.57)
Time: Tue Sep  7 12:51:31 2004

Input: Factorization(9840984350984343538453453904853)

Output: Magma V2.11-6     Tue Sep  7 2004 12:51:30 on sha      [Seed = 2264539311]
   -------------------------------------

[ <3, 1>, <7, 1>, <241, 1>, <3259517, 1>, <3174224929, 1>, <187936552261, 1> ]

Total time: 0.420 seconds, Total memory usage: 3.51MB


************** MAGMA *****************
Host 65.96.167.57 (65.96.167.57)
Time: Tue Sep  7 12:57:28 2004

Input: Factorization(9048098435094358394);

Output: Magma V2.11-6     Tue Sep  7 2004 12:57:28 on sha      [Seed = 576621408]
   -------------------------------------

[ <2, 1>, <4524049217547179197, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB


************** MAGMA *****************
Host 65.96.167.57 (65.96.167.57)
Time: Tue Sep  7 12:57:46 2004

Input: Factorization(9048098435094358394);

Output: Magma V2.11-6     Tue Sep  7 2004 12:57:46 on sha      [Seed = 559777937]
   -------------------------------------

[ <2, 1>, <4524049217547179197, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB