CoCalc Shared Fileswww / cgi-bin / old_logs / until2004-09-07_magma.txt
Author: William A. Stein

************** 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;

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

^
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
^

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
^

>>          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;
^

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
^

>>          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;
^

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
^

>>          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;
^

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 ;
^

>> end for;
^

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
^

>>          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;
^

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!;;
^

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 !;;
^

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
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
soluble-quotients/print-access/PrintCollector
soluble-quotients/print-access/PrintExtensions
soluble-quotients/print-access/PrintModules
soluble-quotients/print-access/PrintPrimes
soluble-quotients/print-access/PrintProcess
soluble-quotients/print-access/PrintProcess
soluble-quotients/print-access/PrintQuotient
soluble-quotients/print-access/PrintRelat
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
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
soluble-quotients/print-access/PrintCollector
soluble-quotients/print-access/PrintExtensions
soluble-quotients/print-access/PrintModules
soluble-quotients/print-access/PrintPrimes
soluble-quotients/print-access/PrintProcess
soluble-quotients/print-access/PrintProcess
soluble-quotients/print-access/PrintQuotient
soluble-quotients/print-access/PrintRelat
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);
^

>> 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;
^

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

************** MAGMA *****************
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];

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));

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));

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));

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));

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));

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));

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));

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));

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));

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));

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 * [email protected] */ /* * 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 [email protected]; 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 + 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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 + 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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 + 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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 + 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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 + 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+ 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>;

Output: Magma V2.10-22    Mon Jun 28 2004 08:16:38 on modular  [Seed = 2301216166]
-------------------------------------

^

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>;

Output: Magma V2.10-22    Mon Jun 28 2004 08:16:48 on modular  [Seed = 2233846204]
-------------------------------------

^
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>;

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>;

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)
^

>> I3=ideal(x_2,x_1)
^

>> hilbertSeries I ;
^

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 *****************
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):
^

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>;
^

>> (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;
^

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
^

>> 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);
^

>> 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);
^
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);
^
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);
^

>> 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);
^

>> 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 [email protected]
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);;
^

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 *****************
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
^

>>  n=n+1;
^
User error: Identifier 'n' has not been declared or assigned

>> end while
^

>> 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
^

>> end while;
^
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
^

>> end while;
^
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);
^
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);
^
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));
^
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
^
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
^
X^9 + X^4 + 1

>> end if;
^

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
^

>> 6.88=11u+4v+2w+6x+y+2z
^

>> 25.44=2u+2v+4z
^

>> 18.65=u+2w+y;
^

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

Output: Magma V2.10-22    Fri Jul  2 2004 15:28:20 on modular  [Seed = 2519949815]
-------------------------------------

^
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

Output: Magma V2.10-22    Fri Jul  2 2004 15:28:51 on modular  [Seed = 2654693848]
-------------------------------------

^
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

Output: Magma V2.10-22    Fri Jul  2 2004 15:29:14 on modular  [Seed = 2250469689]
-------------------------------------

^
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

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 *****************
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 *****************
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);
^

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);;
^

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 *****************
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!;
^

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

************** MAGMA *****************
Time: Sun Jul  4 21:15:04 2004

Output: Magma V2.10-22    Sun Jul  4 2004 21:15:02 on modular  [Seed = 3648074277]
-------------------------------------

^
User error: Identifier 'Q' has not been declared or assigned

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

************** MAGMA *****************
Time: Sun Jul  4 21:15:42 2004

Output: Magma V2.10-22    Sun Jul  4 2004 21:15:40 on modular  [Seed = 3514382855]
-------------------------------------

^

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

************** MAGMA *****************
Time: Sun Jul  4 21:15:54 2004

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 *****************
Time: Sun Jul  4 21:16:25 2004

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

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

************** MAGMA *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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());
^

>> K<a> = NumberField(x^2-14);
^

>> 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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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 *****************
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
^

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]>;

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]>;
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]>;
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]>;

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]

^
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]>;

Output: Magma V2.10-22    Tue Jul  6 2004 01:22:15 on modular  [Seed = 4082730231]
-------------------------------------

^
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]>;

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]>;

Output: Magma V2.10-22    Tue Jul  6 2004 01:30:18 on modular  [Seed = 4283795222]
-------------------------------------

^
Runtime error in 'CoveringRadius': Arguments too large

^
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);
^

>> 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);
^

>> 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 *****************
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 *****************
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 *****************
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 *****************
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`