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Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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************** MAGMA *****************
Host 000-232-076.area1.spcsdns.net. (68.27.135.6)
Time: Wed Dec 24 01:01:43 2003

Input: 2+2;

Output: Magma V2.10-6     Wed Dec 24 2003 01:01:40 on modular  [Seed = 2775822622]
   -------------------------------------

4

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:24:04 2003

Input: a:=5;
a+3;

Output: Magma V2.10-6     Wed Dec 24 2003 05:24:00 on modular  [Seed = 2504246258]
   -------------------------------------

8

Total time: 3.379 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:24:19 2003

Input: a:=5;
a+3;
a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:24:15 on modular  [Seed = 4214074771]
   -------------------------------------

8
7

Total time: 3.239 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:24:33 2003

Input: a:=5;
#a+3;
a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:24:30 on modular  [Seed = 553023064]
   -------------------------------------


>> #a+3;
   ^
Runtime error in '#': Bad argument types
Argument types given: RngIntElt
7

Total time: 2.869 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:24:48 2003

Input: a:=5;
/#a+3;#/
a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:24:45 on modular  [Seed = 199056704]
   -------------------------------------


>> /#a+3;#/
   ^
User error: bad syntax
7

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:25:01 2003

Input: a:=5;
/*a+3;*/
a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:24:58 on modular  [Seed = 1790721078]
   -------------------------------------

7

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:25:20 2003

Input: *a:=5;
*a+3;
*a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:25:17 on modular  [Seed = 1552550647]
   -------------------------------------


>> *a:=5;
   ^
User error: bad syntax

>> *a+3;
   ^
User error: bad syntax

>> *a+2;;
   ^
User error: bad syntax

Total time: 3.209 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:25:32 2003

Input: (*a):=5;
*a+3;
*a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:25:29 on modular  [Seed = 2170017598]
   -------------------------------------


>> (*a):=5;
    ^
User error: bad syntax

>> *a+3;
   ^
User error: bad syntax

>> *a+2;;
   ^
User error: bad syntax

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:25:50 2003

Input: (~a):=5;
~a+3;
~a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:25:47 on modular  [Seed = 4146176378]
   -------------------------------------


>> (~a):=5;
       ^
User error: Illegal left hand side of an assignment statement

>> ~a+3;
     ^
Runtime error in '+': Bad argument types
Argument types given: *nothing ~, RngIntElt

>> ~a+2;;
     ^
Runtime error in '+': Bad argument types
Argument types given: *nothing ~, RngIntElt

Total time: 3.159 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:30:14 2003

Input: a:=5;
//a+3;
a+2;

Output: Magma V2.10-6     Wed Dec 24 2003 05:30:11 on modular  [Seed = 516443022]
   -------------------------------------

7

Total time: 3.299 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 05:58:34 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,llista)));
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(#llista-1)]])+nu(llista[#llista])-interseccioinf(Lconjunts,Linterseccioinf,llista));
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];



Output: Magma V2.10-6     Wed Dec 24 2003 05:58:30 on modular  [Seed = 2058105909]
   -------------------------------------


>>   Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,
                                                       ^
User error: Identifier 'mcinf' has not been declared or assigned

>>     return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(
                              ^
User error: Identifier 'unioinf' has not been declared or assigned

>> Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,
                    ^
User error: Identifier 'actualitzainterseccioinf' has not been declared or 
assigned
CONJUNTS=
<[ 0 ]>
MCINF=
<[ 0 ]>
INTERSECCIOINF=
[ 1 ]
UNIOINF=
[ 1 ]
VEREDICTE:=[]

Total time: 3.859 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:10:48 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,llista)));
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(#llista-1)]])+nu(llista[#llista])-interseccioinf(Lconjunts,Linterseccioinf,llista));
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];



Output: Magma V2.10-6     Wed Dec 24 2003 06:10:45 on modular  [Seed = 3177969308]
   -------------------------------------


>>   Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,
                                                       ^
User error: Identifier 'mcinf' has not been declared or assigned

>>     return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(
                              ^
User error: Identifier 'unioinf' has not been declared or assigned

>> Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,
                    ^
User error: Identifier 'actualitzainterseccioinf' has not been declared or 
assigned
CONJUNTS=
<[ 0 ]>
MCINF=
<[ 0 ]>
INTERSECCIOINF=
[ 1 ]
UNIOINF=
[ 1 ]
VEREDICTE:=[]

Total time: 3.119 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:11:07 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)]));
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/




Output: Magma V2.10-6     Wed Dec 24 2003 06:11:04 on modular  [Seed = 4062493102]
   -------------------------------------


>>   Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)]));
                                                                 ^
User error: bad syntax

>>   end if;
     ^
User error: bad syntax

>> end function;
   ^
User error: bad syntax

>> Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,
                    ^
User error: Identifier 'actualitzainterseccioinf' has not been declared or 
assigned
CONJUNTS=
<[ 0 ]>
MCINF=
<[ 0 ]>
INTERSECCIOINF=
[ 1 ]
UNIOINF=
[ 1 ]
VEREDICTE:=[]

Total time: 3.089 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:12:32 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/




Output: Magma V2.10-6     Wed Dec 24 2003 06:12:29 on modular  [Seed = 3556941658]
   -------------------------------------

CONJUNTS=
<[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 
], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 
4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 
1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0,
2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1,
5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], 
[ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 
1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [
0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 
1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 
4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], 
[ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 
0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 
4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [
1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 
0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 
2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [
0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 
1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 
5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 
1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 
4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 
5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 
2, 3, 4, 5, 6 ]>
MCINF=
<[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 
0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], 
[ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ]>
INTERSECCIOINF=
[ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
UNIOINF=
[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 
5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6,
7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5,
5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 
10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ]
VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 1, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]

Total time: 3.299 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:13:30 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


[index[llista]:llista in Lconjunts];



Output: Magma V2.10-6     Wed Dec 24 2003 06:13:26 on modular  [Seed = 2124953018]
   -------------------------------------

CONJUNTS=
<[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 
], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 
4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 
1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0,
2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1,
5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], 
[ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 
1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [
0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 
1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 
4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], 
[ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 
0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 
4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [
1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 
0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 
2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [
0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 
1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 
5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 
1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 
4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 
5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 
2, 3, 4, 5, 6 ]>
MCINF=
<[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 
0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], 
[ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ]>
INTERSECCIOINF=
[ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
UNIOINF=
[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 
5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6,
7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5,
5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 
10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ]
VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 1, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]

>> [index[llista]:llista in Lconjunts];
         ^
Runtime error in '[]': Bad argument types

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:13:57 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


[index(llista):llista in Lconjunts];



Output: Magma V2.10-6     Wed Dec 24 2003 06:13:53 on modular  [Seed = 3127701849]
   -------------------------------------

CONJUNTS=
<[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 
], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 
4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 
1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0,
2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1,
5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], 
[ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 
1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [
0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 
1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 
4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], 
[ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 
0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 
4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [
1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 
0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 
2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [
0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 
1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 
5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 
1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 
4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 
5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 
2, 3, 4, 5, 6 ]>
MCINF=
<[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 
0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], 
[ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ]>
INTERSECCIOINF=
[ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
UNIOINF=
[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 
5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6,
7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5,
5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 
10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ]
VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 1, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 
63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 
83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 
118, 119, 120, 121, 122, 123, 124, 125, 126, 127 ]

Total time: 3.269 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:14:45 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


[[llista,index(llista)]:llista in Lconjunts];



Output: Magma V2.10-6     Wed Dec 24 2003 06:14:40 on modular  [Seed = 533288238]
   -------------------------------------

CONJUNTS=
<[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 
], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 
4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 
1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0,
2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1,
5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], 
[ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 
1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [
0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 
1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 
4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], 
[ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 
0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 
4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [
1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 
0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 
2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [
0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 
1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 
5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 
1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 
4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 
5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 
2, 3, 4, 5, 6 ]>
MCINF=
<[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 
0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], 
[ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ]>
INTERSECCIOINF=
[ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
UNIOINF=
[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 
5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6,
7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5,
5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 
10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ]
VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 1, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]

>> [[llista,index(llista)]:llista in Lconjunts];
    ^
Runtime error in [ ... ]: Could not find a valid universe

Total time: 3.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:15:38 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
  Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;


for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    
Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];

printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


[<llista,index(llista)>:llista in Lconjunts];



Output: Magma V2.10-6     Wed Dec 24 2003 06:15:34 on modular  [Seed = 1672816932]
   -------------------------------------

CONJUNTS=
<[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 
], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 
4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 
1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0,
2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1,
5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], 
[ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 
1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [
0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 
1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 
4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], 
[ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 
0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 
4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [
1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 
0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 
2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [
0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 
1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 
5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 
1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 
4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 
5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 
2, 3, 4, 5, 6 ]>
MCINF=
<[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 
0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], 
[ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0
], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], 
[ 0 ]>
INTERSECCIOINF=
[ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
UNIOINF=
[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 
5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6,
7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5,
5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 
10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ]
VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 1, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[
    <[ 0 ], 1>,
    <[ 1 ], 2>,
    <[ 0, 1 ], 3>,
    <[ 2 ], 4>,
    <[ 0, 2 ], 5>,
    <[ 1, 2 ], 6>,
    <[ 0, 1, 2 ], 7>,
    <[ 3 ], 8>,
    <[ 0, 3 ], 9>,
    <[ 1, 3 ], 10>,
    <[ 0, 1, 3 ], 11>,
    <[ 2, 3 ], 12>,
    <[ 0, 2, 3 ], 13>,
    <[ 1, 2, 3 ], 14>,
    <[ 0, 1, 2, 3 ], 15>,
    <[ 4 ], 16>,
    <[ 0, 4 ], 17>,
    <[ 1, 4 ], 18>,
    <[ 0, 1, 4 ], 19>,
    <[ 2, 4 ], 20>,
    <[ 0, 2, 4 ], 21>,
    <[ 1, 2, 4 ], 22>,
    <[ 0, 1, 2, 4 ], 23>,
    <[ 3, 4 ], 24>,
    <[ 0, 3, 4 ], 25>,
    <[ 1, 3, 4 ], 26>,
    <[ 0, 1, 3, 4 ], 27>,
    <[ 2, 3, 4 ], 28>,
    <[ 0, 2, 3, 4 ], 29>,
    <[ 1, 2, 3, 4 ], 30>,
    <[ 0, 1, 2, 3, 4 ], 31>,
    <[ 5 ], 32>,
    <[ 0, 5 ], 33>,
    <[ 1, 5 ], 34>,
    <[ 0, 1, 5 ], 35>,
    <[ 2, 5 ], 36>,
    <[ 0, 2, 5 ], 37>,
    <[ 1, 2, 5 ], 38>,
    <[ 0, 1, 2, 5 ], 39>,
    <[ 3, 5 ], 40>,
    <[ 0, 3, 5 ], 41>,
    <[ 1, 3, 5 ], 42>,
    <[ 0, 1, 3, 5 ], 43>,
    <[ 2, 3, 5 ], 44>,
    <[ 0, 2, 3, 5 ], 45>,
    <[ 1, 2, 3, 5 ], 46>,
    <[ 0, 1, 2, 3, 5 ], 47>,
    <[ 4, 5 ], 48>,
    <[ 0, 4, 5 ], 49>,
    <[ 1, 4, 5 ], 50>,
    <[ 0, 1, 4, 5 ], 51>,
    <[ 2, 4, 5 ], 52>,
    <[ 0, 2, 4, 5 ], 53>,
    <[ 1, 2, 4, 5 ], 54>,
    <[ 0, 1, 2, 4, 5 ], 55>,
    <[ 3, 4, 5 ], 56>,
    <[ 0, 3, 4, 5 ], 57>,
    <[ 1, 3, 4, 5 ], 58>,
    <[ 0, 1, 3, 4, 5 ], 59>,
    <[ 2, 3, 4, 5 ], 60>,
    <[ 0, 2, 3, 4, 5 ], 61>,
    <[ 1, 2, 3, 4, 5 ], 62>,
    <[ 0, 1, 2, 3, 4, 5 ], 63>,
    <[ 6 ], 64>,
    <[ 0, 6 ], 65>,
    <[ 1, 6 ], 66>,
    <[ 0, 1, 6 ], 67>,
    <[ 2, 6 ], 68>,
    <[ 0, 2, 6 ], 69>,
    <[ 1, 2, 6 ], 70>,
    <[ 0, 1, 2, 6 ], 71>,
    <[ 3, 6 ], 72>,
    <[ 0, 3, 6 ], 73>,
    <[ 1, 3, 6 ], 74>,
    <[ 0, 1, 3, 6 ], 75>,
    <[ 2, 3, 6 ], 76>,
    <[ 0, 2, 3, 6 ], 77>,
    <[ 1, 2, 3, 6 ], 78>,
    <[ 0, 1, 2, 3, 6 ], 79>,
    <[ 4, 6 ], 80>,
    <[ 0, 4, 6 ], 81>,
    <[ 1, 4, 6 ], 82>,
    <[ 0, 1, 4, 6 ], 83>,
    <[ 2, 4, 6 ], 84>,
    <[ 0, 2, 4, 6 ], 85>,
    <[ 1, 2, 4, 6 ], 86>,
    <[ 0, 1, 2, 4, 6 ], 87>,
    <[ 3, 4, 6 ], 88>,
    <[ 0, 3, 4, 6 ], 89>,
    <[ 1, 3, 4, 6 ], 90>,
    <[ 0, 1, 3, 4, 6 ], 91>,
    <[ 2, 3, 4, 6 ], 92>,
    <[ 0, 2, 3, 4, 6 ], 93>,
    <[ 1, 2, 3, 4, 6 ], 94>,
    <[ 0, 1, 2, 3, 4, 6 ], 95>,
    <[ 5, 6 ], 96>,
    <[ 0, 5, 6 ], 97>,
    <[ 1, 5, 6 ], 98>,
    <[ 0, 1, 5, 6 ], 99>,
    <[ 2, 5, 6 ], 100>,
    <[ 0, 2, 5, 6 ], 101>,
    <[ 1, 2, 5, 6 ], 102>,
    <[ 0, 1, 2, 5, 6 ], 103>,
    <[ 3, 5, 6 ], 104>,
    <[ 0, 3, 5, 6 ], 105>,
    <[ 1, 3, 5, 6 ], 106>,
    <[ 0, 1, 3, 5, 6 ], 107>,
    <[ 2, 3, 5, 6 ], 108>,
    <[ 0, 2, 3, 5, 6 ], 109>,
    <[ 1, 2, 3, 5, 6 ], 110>,
    <[ 0, 1, 2, 3, 5, 6 ], 111>,
    <[ 4, 5, 6 ], 112>,
    <[ 0, 4, 5, 6 ], 113>,
    <[ 1, 4, 5, 6 ], 114>,
    <[ 0, 1, 4, 5, 6 ], 115>,
    <[ 2, 4, 5, 6 ], 116>,
    <[ 0, 2, 4, 5, 6 ], 117>,
    <[ 1, 2, 4, 5, 6 ], 118>,
    <[ 0, 1, 2, 4, 5, 6 ], 119>,
    <[ 3, 4, 5, 6 ], 120>,
    <[ 0, 3, 4, 5, 6 ], 121>,
    <[ 1, 3, 4, 5, 6 ], 122>,
    <[ 0, 1, 3, 4, 5, 6 ], 123>,
    <[ 2, 3, 4, 5, 6 ], 124>,
    <[ 0, 2, 3, 4, 5, 6 ], 125>,
    <[ 1, 2, 3, 4, 5, 6 ], 126>,
    <[ 0, 1, 2, 3, 4, 5, 6 ], 127>
]

Total time: 3.759 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:29:27 2003

Input: 	/* Klein quartic */

MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/




Output: Magma V2.10-6     Wed Dec 24 2003 06:29:20 on modular  [Seed = 2792415546]
   -------------------------------------

VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 1, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]

Total time: 3.339 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:31:20 2003

Input: 	/* Klein quartic */

/*
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];
*/


	/* Hermitian curve */

 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];


	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/




Output: Magma V2.10-6     Wed Dec 24 2003 06:31:13 on modular  [Seed = 3076649402]
   -------------------------------------

VEREDICTE:=[
    [ 0, 1, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 2, 3 ],
    [ 0, 1, 4 ],
    [ 0, 2, 4 ],
    [ 1, 2, 4 ],
    [ 0, 1, 2, 4 ],
    [ 0, 3, 4 ],
    [ 0, 1, 3, 4 ],
    [ 2, 3, 4 ],
    [ 0, 2, 3, 4 ],
    [ 1, 2, 3, 4 ],
    [ 0, 1, 2, 3, 4 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 0, 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 0, 4, 5 ],
    [ 1, 4, 5 ],
    [ 0, 1, 4, 5 ],
    [ 0, 2, 4, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 3, 4, 5 ],
    [ 1, 3, 4, 5 ],
    [ 0, 1, 3, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 1, 2, 6 ],
    [ 0, 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 0, 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 2, 3, 6 ],
    [ 1, 2, 3, 6 ],
    [ 0, 1, 2, 3, 6 ],
    [ 0, 4, 6 ],
    [ 0, 1, 4, 6 ],
    [ 2, 4, 6 ],
    [ 0, 2, 4, 6 ],
    [ 1, 2, 4, 6 ],
    [ 0, 1, 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 3, 4, 6 ],
    [ 1, 3, 4, 6 ],
    [ 0, 1, 3, 4, 6 ],
    [ 2, 3, 4, 6 ],
    [ 0, 2, 3, 4, 6 ],
    [ 1, 2, 3, 4, 6 ],
    [ 0, 1, 2, 3, 4, 6 ],
    [ 1, 5, 6 ],
    [ 0, 1, 5, 6 ],
    [ 0, 2, 5, 6 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 0, 3, 5, 6 ],
    [ 1, 3, 5, 6 ],
    [ 0, 1, 3, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 4, 5, 6 ],
    [ 1, 4, 5, 6 ],
    [ 0, 1, 4, 5, 6 ],
    [ 2, 4, 5, 6 ],
    [ 0, 2, 4, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 3, 4, 5, 6 ],
    [ 0, 3, 4, 5, 6 ],
    [ 1, 3, 4, 5, 6 ],
    [ 0, 1, 3, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]

Total time: 3.519 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:40:32 2003

Input: a:=0;
a_b:=6;

Output: Magma V2.10-6     Wed Dec 24 2003 06:40:29 on modular  [Seed = 4013534158]
   -------------------------------------


Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:40:51 2003

Input: a:=4;
a_b:=6;
a+a_b;

Output: Magma V2.10-6     Wed Dec 24 2003 06:40:48 on modular  [Seed = 3811944367]
   -------------------------------------

10

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:46:22 2003

Input: a:=4;
a_b:=6;
a+a_b;
a eq a_b;


Output: Magma V2.10-6     Wed Dec 24 2003 06:46:19 on modular  [Seed = 433019545]
   -------------------------------------

10
false

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 06:46:36 2003

Input: a:=4;
a_b:=6;
a+a_b;
not(a eq a_b);


Output: Magma V2.10-6     Wed Dec 24 2003 06:46:32 on modular  [Seed = 365123206]
   -------------------------------------

10
true

Total time: 3.549 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:01:51 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  if (maxc eq 0) then
    return ([0]);
  end if;
  maxc:=ultim-2;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(ret);
end function;


actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/




Output: Magma V2.10-6     Wed Dec 24 2003 07:01:44 on modular  [Seed = 2655527357]
   -------------------------------------


>>   if (maxc eq 0) then
         ^
User error: Identifier 'maxc' has not been declared or assigned

>> lista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(ll
                                         ^
User error: Identifier 'interseccio_ultim_unio_dels_altres' has not been 
declared or assigned

>>   Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
               ^
User error: Identifier 'actualitzaunioinf' has not been declared or assigned
VEREDICTE:=[]

Total time: 3.399 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:03:52 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(ret);
end function;


actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/




Output: Magma V2.10-6     Wed Dec 24 2003 07:03:45 on modular  [Seed = 2487364414]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]

Total time: 3.299 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:05:30 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(ret);
end function;


actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


interseccio_ultim_unio_dels_altres([1,2,5]);
[lambda(i):i in [1,2,5]];



Output: Magma V2.10-6     Wed Dec 24 2003 07:05:26 on modular  [Seed = 3127641270]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 2, 1 ]
[ 3, 5, 8 ]

Total time: 3.299 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:13:52 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(ret);
end function;


actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


interseccio_ultim_unio_dels_altres([1,2,5]);
[lambda(i):i in [1,2,5]];
i:=index([1,2,5]);
Lconjunts[i];
Lunioinf[i];
unioasac[i];



Output: Magma V2.10-6     Wed Dec 24 2003 07:13:44 on modular  [Seed = 3913241626]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 2, 1 ]
[ 3, 5, 8 ]
[ 1, 2, 5 ]
6
4

Total time: 3.339 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:20:54 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


llista:=[1,2,5];

[lambda(i):i in llista];

l:=interseccio_ultim_unio_dels_altres(llista);
Lconjunts(l);

Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);


Output: Magma V2.10-6     Wed Dec 24 2003 07:20:51 on modular  [Seed = 988578195]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 3, 5, 8 ]

>> Lconjunts(l);
            ^
Runtime error: Bad argument types
Argument types given: RngIntElt, SeqEnum[SeqEnum]

>> Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);
                                                              ^
User error: bad syntax

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:21:19 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


llista:=[1,2,5];

[lambda(i):i in llista];

l:=interseccio_ultim_unio_dels_altres(llista);
Lconjunts[l];

Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);


Output: Magma V2.10-6     Wed Dec 24 2003 07:21:16 on modular  [Seed = 870680709]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 3, 5, 8 ]
[ 1, 2 ]

>> Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);
                                                              ^
User error: bad syntax

Total time: 3.149 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:21:53 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


llista:=[1,2,5];

[lambda(i):i in llista];

l:=interseccio_ultim_unio_dels_altres(llista);
Lconjunts[l];

Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)];


Output: Magma V2.10-6     Wed Dec 24 2003 07:21:50 on modular  [Seed = 1218376604]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 3, 5, 8 ]
[ 1, 2 ]
1

Total time: 3.189 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:23:08 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


llista:=[1,2,5];

[lambda(i):i in llista];

l:=interseccio_ultim_unio_dels_altres(llista);
Lconjunts[l];

Lunioinf[interseccio_ultim_unio_dels_altres(llista)];


Output: Magma V2.10-6     Wed Dec 24 2003 07:23:05 on modular  [Seed = 1100479330]
   -------------------------------------

VEREDICTE:=[
    [ 1, 2, 5 ],
    [ 0, 1, 2, 5 ],
    [ 2, 3, 5 ],
    [ 0, 2, 3, 5 ],
    [ 1, 2, 3, 5 ],
    [ 0, 1, 2, 3, 5 ],
    [ 1, 2, 4, 5 ],
    [ 0, 1, 2, 4, 5 ],
    [ 2, 3, 4, 5 ],
    [ 0, 2, 3, 4, 5 ],
    [ 1, 2, 3, 4, 5 ],
    [ 0, 1, 2, 3, 4, 5 ],
    [ 1, 2, 5, 6 ],
    [ 0, 1, 2, 5, 6 ],
    [ 2, 3, 5, 6 ],
    [ 0, 2, 3, 5, 6 ],
    [ 1, 2, 3, 5, 6 ],
    [ 0, 1, 2, 3, 5, 6 ],
    [ 1, 2, 4, 5, 6 ],
    [ 0, 1, 2, 4, 5, 6 ],
    [ 2, 3, 4, 5, 6 ],
    [ 0, 2, 3, 4, 5, 6 ],
    [ 1, 2, 3, 4, 5, 6 ],
    [ 0, 1, 2, 3, 4, 5, 6 ]
]
[ 3, 5, 8 ]
[ 1, 2 ]
3

Total time: 3.159 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:23:58 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


llista:=[1,2,5];

[lambda(i):i in llista];

l:=interseccio_ultim_unio_dels_altres(llista);
Lconjunts[l];

Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)];


Output: Magma V2.10-6     Wed Dec 24 2003 07:23:55 on modular  [Seed = 1451289607]
   -------------------------------------

VEREDICTE:=[]
[ 3, 5, 8 ]
[ 1, 2 ]
1

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:34:46 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


Output: Magma V2.10-6     Wed Dec 24 2003 07:34:42 on modular  [Seed = 2404988775]
   -------------------------------------

VEREDICTE:=[]

Total time: 3.389 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:35:14 2003

Input: 	/* Klein quartic */


MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */


MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];


	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


Output: Magma V2.10-6     Wed Dec 24 2003 07:35:07 on modular  [Seed = 2555256937]
   -------------------------------------

VEREDICTE:=[]

Total time: 6.500 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:36:55 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=6;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


Output: Magma V2.10-6     Wed Dec 24 2003 07:36:52 on modular  [Seed = 2943948993]
   -------------------------------------

Klein quarticVEREDICTE:=[]

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:37:29 2003

Input: 	/* Klein quartic */

/*
printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];
*/


	/* Hermitian curve */

 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];


	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


/*r:=2;
Subsets({0..MAX},r);*/


Output: Magma V2.10-6     Wed Dec 24 2003 07:37:23 on modular  [Seed = 3161066293]
   -------------------------------------

hermitian curveVEREDICTE:=[]

Total time: 5.969 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:38:43 2003

Input: 	/* Klein quartic */

/*
printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];
*/


	/* Hermitian curve */

 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];


	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


r:=2;
Subsets({0..MAX},r);


Output: Magma V2.10-6     Wed Dec 24 2003 07:38:37 on modular  [Seed = 3222697735]
   -------------------------------------

hermitian curveVEREDICTE:=[]
{
    { 0, 5 },
    { 4, 8 },
    { 4, 9 },
    { 7, 9 },
    { 2, 10 },
    { 8, 9 },
    { 1, 10 },
    { 1, 2 },
    { 4, 10 },
    { 5, 10 },
    { 1, 6 },
    { 7, 8 },
    { 3, 5 },
    { 2, 6 },
    { 1, 4 },
    { 6, 10 },
    { 4, 7 },
    { 3, 8 },
    { 3, 9 },
    { 6, 7 },
    { 2, 4 },
    { 0, 8 },
    { 5, 8 },
    { 0, 9 },
    { 4, 6 },
    { 5, 9 },
    { 8, 10 },
    { 5, 7 },
    { 1, 7 },
    { 3, 4 },
    { 2, 7 },
    { 7, 10 },
    { 3, 7 },
    { 9, 10 },
    { 2, 3 },
    { 5, 6 },
    { 0, 2 },
    { 2, 5 },
    { 1, 3 },
    { 4, 5 },
    { 1, 5 },
    { 0, 1 },
    { 0, 10 },
    { 3, 6 },
    { 0, 6 },
    { 1, 8 },
    { 0, 4 },
    { 2, 9 },
    { 1, 9 },
    { 2, 8 },
    { 0, 7 },
    { 0, 3 },
    { 6, 8 },
    { 3, 10 },
    { 6, 9 }
}

Total time: 6.069 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:46:47 2003

Input: 2*[1,2,3,4];

Output: Magma V2.10-6     Wed Dec 24 2003 07:46:23 on modular  [Seed = 1117059029]
   -------------------------------------


>> 2*[1,2,3,4];;
    ^
Runtime error in '*': Bad argument types
Argument types given: RngIntElt, SeqEnum[RngIntElt]

Total time: 3.810 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:46:54 2003

Input: 2*[1,2,3,4];

Output: Magma V2.10-6     Wed Dec 24 2003 07:46:43 on modular  [Seed = 2708935706]
   -------------------------------------


>> 2*[1,2,3,4];;
    ^
Runtime error in '*': Bad argument types
Argument types given: RngIntElt, SeqEnum[RngIntElt]

Total time: 3.399 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:50:49 2003

Input: a:=func<{a,b}|a+b>;

Output: Magma V2.10-6     Wed Dec 24 2003 07:50:34 on modular  [Seed = 4163783709]
   -------------------------------------


>> a:=func<{a,b}|a+b>;;
           ^
User error: bad syntax

Total time: 3.829 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:51:25 2003

Input: a:=func<[a,b]|a+b>;

Output: Magma V2.10-6     Wed Dec 24 2003 07:51:02 on modular  [Seed = 1790762658]
   -------------------------------------


>> a:=func<[a,b]|a+b>;;
           ^
User error: bad syntax

Total time: 3.709 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:51:40 2003

Input: a:=func<<a,b>|a+b>;

Output: Magma V2.10-6     Wed Dec 24 2003 07:51:35 on modular  [Seed = 1485761777]
   -------------------------------------


>> a:=func<<a,b>|a+b>;;
           ^
User error: bad syntax

Total time: 3.269 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:52:32 2003

Input: a:=func<l|l[1]+l[2]>;
a([2,3]);
a(<2,3>);
a({2,3});

Output: Magma V2.10-6     Wed Dec 24 2003 07:52:26 on modular  [Seed = 1318649144]
   -------------------------------------

5
5

[<main>:3](
    l: { 2, 3 }
)
>> a:=func<l|l[1]+l[2]>;
              ^
Runtime error in '[]': Bad argument types

Total time: 3.549 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 07:53:15 2003

Input: a:=func<l|l[1]+l[2]>;
a([2,3]);
a(<2,3>);


Output: Magma V2.10-6     Wed Dec 24 2003 07:52:51 on modular  [Seed = 2775783165]
   -------------------------------------

5
5

Total time: 3.779 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:02:21 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


r:=2;
conj_r_elements:=func<r|[index(llista): llista in Subsets({0..MAX},r)]>;
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
conj_r_elements_ge_i(4,3);


Output: Magma V2.10-6     Wed Dec 24 2003 08:02:04 on modular  [Seed = 569872386]
   -------------------------------------

Klein quarticVEREDICTE:=[]

>> conj_r_elements_ge_i(4,3);
                       ^
Runtime error in procedure call: Number of arguments (2) does not equal expected
number of arguments (1)

Total time: 3.889 seconds, Total memory usage: 1.92MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:03:35 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


r:=2;
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
conj_r_elements_ge_i([4,3]);


Output: Magma V2.10-6     Wed Dec 24 2003 08:03:28 on modular  [Seed = 603296494]
   -------------------------------------

Klein quarticVEREDICTE:=[]
[ 120 ]

Total time: 4.099 seconds, Total memory usage: 1.92MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:05:38 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
conj_r_elements(3);
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
conj_r_elements_ge_i([4,3]);


Output: Magma V2.10-6     Wed Dec 24 2003 08:05:34 on modular  [Seed = 3725094571]
   -------------------------------------

Klein quartic[ 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 
49, 50, 52, 56, 67, 69, 70, 73, 74, 76, 81, 82, 84, 88, 97, 98, 100, 104, 112 ]
[ 120 ]

Total time: 3.289 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:06:32 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
conj_r_elements_ge_i([3,3]);


Output: Magma V2.10-6     Wed Dec 24 2003 08:06:28 on modular  [Seed = 2893683859]
   -------------------------------------

Klein quartic[
    [ 0, 1, 2 ],
    [ 0, 1, 3 ],
    [ 0, 2, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 4 ],
    [ 0, 2, 4 ],
    [ 1, 2, 4 ],
    [ 0, 3, 4 ],
    [ 1, 3, 4 ],
    [ 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 4, 5 ],
    [ 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 0, 2, 6 ],
    [ 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 4, 6 ],
    [ 1, 4, 6 ],
    [ 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ]
]
[ 56, 88, 104, 112 ]

Total time: 3.299 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:07:50 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=6;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
conj_r_elements_ge_i([3,3]);
[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];



Output: Magma V2.10-6     Wed Dec 24 2003 08:07:43 on modular  [Seed = 2959474756]
   -------------------------------------

Klein quartic[
    [ 0, 1, 2 ],
    [ 0, 1, 3 ],
    [ 0, 2, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 4 ],
    [ 0, 2, 4 ],
    [ 1, 2, 4 ],
    [ 0, 3, 4 ],
    [ 1, 3, 4 ],
    [ 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 4, 5 ],
    [ 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 0, 2, 6 ],
    [ 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 4, 6 ],
    [ 1, 4, 6 ],
    [ 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ]
]
[ 56, 88, 104, 112 ]
[
    [ 3, 4, 5 ],
    [ 3, 4, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ]
]

Total time: 3.279 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:13:40 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum[Lunioinf[j]:j in conj_r_elements_ge_i(ri)]>;
[gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:13:34 on modular  [Seed = 3127645477]
   -------------------------------------

Klein quartic[
    [ 0, 1, 2 ],
    [ 0, 1, 3 ],
    [ 0, 2, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 4 ],
    [ 0, 2, 4 ],
    [ 1, 2, 4 ],
    [ 0, 3, 4 ],
    [ 1, 3, 4 ],
    [ 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 4, 5 ],
    [ 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 0, 2, 6 ],
    [ 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 4, 6 ],
    [ 1, 4, 6 ],
    [ 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 1, 7 ],
    [ 0, 2, 7 ],
    [ 1, 2, 7 ],
    [ 0, 3, 7 ],
    [ 1, 3, 7 ],
    [ 2, 3, 7 ],
    [ 0, 4, 7 ],
    [ 1, 4, 7 ],
    [ 2, 4, 7 ],
    [ 3, 4, 7 ],
    [ 0, 5, 7 ],
    [ 1, 5, 7 ],
    [ 2, 5, 7 ],
    [ 3, 5, 7 ],
    [ 4, 5, 7 ],
    [ 0, 6, 7 ],
    [ 1, 6, 7 ],
    [ 2, 6, 7 ],
    [ 3, 6, 7 ],
    [ 4, 6, 7 ],
    [ 5, 6, 7 ],
    [ 0, 1, 8 ],
    [ 0, 2, 8 ],
    [ 1, 2, 8 ],
    [ 0, 3, 8 ],
    [ 1, 3, 8 ],
    [ 2, 3, 8 ],
    [ 0, 4, 8 ],
    [ 1, 4, 8 ],
    [ 2, 4, 8 ],
    [ 3, 4, 8 ],
    [ 0, 5, 8 ],
    [ 1, 5, 8 ],
    [ 2, 5, 8 ],
    [ 3, 5, 8 ],
    [ 4, 5, 8 ],
    [ 0, 6, 8 ],
    [ 1, 6, 8 ],
    [ 2, 6, 8 ],
    [ 3, 6, 8 ],
    [ 4, 6, 8 ],
    [ 5, 6, 8 ],
    [ 0, 7, 8 ],
    [ 1, 7, 8 ],
    [ 2, 7, 8 ],
    [ 3, 7, 8 ],
    [ 4, 7, 8 ],
    [ 5, 7, 8 ],
    [ 6, 7, 8 ],
    [ 0, 1, 9 ],
    [ 0, 2, 9 ],
    [ 1, 2, 9 ],
    [ 0, 3, 9 ],
    [ 1, 3, 9 ],
    [ 2, 3, 9 ],
    [ 0, 4, 9 ],
    [ 1, 4, 9 ],
    [ 2, 4, 9 ],
    [ 3, 4, 9 ],
    [ 0, 5, 9 ],
    [ 1, 5, 9 ],
    [ 2, 5, 9 ],
    [ 3, 5, 9 ],
    [ 4, 5, 9 ],
    [ 0, 6, 9 ],
    [ 1, 6, 9 ],
    [ 2, 6, 9 ],
    [ 3, 6, 9 ],
    [ 4, 6, 9 ],
    [ 5, 6, 9 ],
    [ 0, 7, 9 ],
    [ 1, 7, 9 ],
    [ 2, 7, 9 ],
    [ 3, 7, 9 ],
    [ 4, 7, 9 ],
    [ 5, 7, 9 ],
    [ 6, 7, 9 ],
    [ 0, 8, 9 ],
    [ 1, 8, 9 ],
    [ 2, 8, 9 ],
    [ 3, 8, 9 ],
    [ 4, 8, 9 ],
    [ 5, 8, 9 ],
    [ 6, 8, 9 ],
    [ 7, 8, 9 ],
    [ 0, 1, 10 ],
    [ 0, 2, 10 ],
    [ 1, 2, 10 ],
    [ 0, 3, 10 ],
    [ 1, 3, 10 ],
    [ 2, 3, 10 ],
    [ 0, 4, 10 ],
    [ 1, 4, 10 ],
    [ 2, 4, 10 ],
    [ 3, 4, 10 ],
    [ 0, 5, 10 ],
    [ 1, 5, 10 ],
    [ 2, 5, 10 ],
    [ 3, 5, 10 ],
    [ 4, 5, 10 ],
    [ 0, 6, 10 ],
    [ 1, 6, 10 ],
    [ 2, 6, 10 ],
    [ 3, 6, 10 ],
    [ 4, 6, 10 ],
    [ 5, 6, 10 ],
    [ 0, 7, 10 ],
    [ 1, 7, 10 ],
    [ 2, 7, 10 ],
    [ 3, 7, 10 ],
    [ 4, 7, 10 ],
    [ 5, 7, 10 ],
    [ 6, 7, 10 ],
    [ 0, 8, 10 ],
    [ 1, 8, 10 ],
    [ 2, 8, 10 ],
    [ 3, 8, 10 ],
    [ 4, 8, 10 ],
    [ 5, 8, 10 ],
    [ 6, 8, 10 ],
    [ 7, 8, 10 ],
    [ 0, 9, 10 ],
    [ 1, 9, 10 ],
    [ 2, 9, 10 ],
    [ 3, 9, 10 ],
    [ 4, 9, 10 ],
    [ 5, 9, 10 ],
    [ 6, 9, 10 ],
    [ 7, 9, 10 ],
    [ 8, 9, 10 ]
]
[
    [ 3, 4, 5 ],
    [ 3, 4, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 3, 4, 7 ],
    [ 3, 5, 7 ],
    [ 4, 5, 7 ],
    [ 3, 6, 7 ],
    [ 4, 6, 7 ],
    [ 5, 6, 7 ],
    [ 3, 4, 8 ],
    [ 3, 5, 8 ],
    [ 4, 5, 8 ],
    [ 3, 6, 8 ],
    [ 4, 6, 8 ],
    [ 5, 6, 8 ],
    [ 3, 7, 8 ],
    [ 4, 7, 8 ],
    [ 5, 7, 8 ],
    [ 6, 7, 8 ],
    [ 3, 4, 9 ],
    [ 3, 5, 9 ],
    [ 4, 5, 9 ],
    [ 3, 6, 9 ],
    [ 4, 6, 9 ],
    [ 5, 6, 9 ],
    [ 3, 7, 9 ],
    [ 4, 7, 9 ],
    [ 5, 7, 9 ],
    [ 6, 7, 9 ],
    [ 3, 8, 9 ],
    [ 4, 8, 9 ],
    [ 5, 8, 9 ],
    [ 6, 8, 9 ],
    [ 7, 8, 9 ],
    [ 3, 4, 10 ],
    [ 3, 5, 10 ],
    [ 4, 5, 10 ],
    [ 3, 6, 10 ],
    [ 4, 6, 10 ],
    [ 5, 6, 10 ],
    [ 3, 7, 10 ],
    [ 4, 7, 10 ],
    [ 5, 7, 10 ],
    [ 6, 7, 10 ],
    [ 3, 8, 10 ],
    [ 4, 8, 10 ],
    [ 5, 8, 10 ],
    [ 6, 8, 10 ],
    [ 7, 8, 10 ],
    [ 3, 9, 10 ],
    [ 4, 9, 10 ],
    [ 5, 9, 10 ],
    [ 6, 9, 10 ],
    [ 7, 9, 10 ],
    [ 8, 9, 10 ]
]

>> gen_ham_weight:=func<ri|Minimum[Lunioinf[j]:j in conj_r_elements_ge_i(ri)]>
                                              ^
User error: bad syntax

>> [gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; ;
                                           ^
User error: bad syntax

Total time: 5.379 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:15:37 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
// [Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
// [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum([Lunioinf[j] : j in conj_r_elements_ge_i(ri)])>;
[gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:15:32 on modular  [Seed = 2304714652]
   -------------------------------------

Klein quartic
>> [gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; ;
                                           ^
User error: bad syntax

Total time: 5.059 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:16:14 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
// [Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
// [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum([Lunioinf[j] : j in conj_r_elements_ge_i(ri)])>;
[[gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:16:09 on modular  [Seed = 2420522600]
   -------------------------------------

Klein quartic[
    [ 2, 2, 2, 2, 4 ],
    [ 3, 3, 4, 5, 6 ],
    [ 4, 5, 5, 6, 7 ],
    [ 5, 6, 7, 8, 9 ],
    [ 6, 7, 8, 9, 10 ]
]

Total time: 5.269 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:20:06 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
[gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:20:00 on modular  [Seed = 1790756747]
   -------------------------------------

Klein quartic[
    [ 0, 1, 2 ],
    [ 0, 1, 3 ],
    [ 0, 2, 3 ],
    [ 1, 2, 3 ],
    [ 0, 1, 4 ],
    [ 0, 2, 4 ],
    [ 1, 2, 4 ],
    [ 0, 3, 4 ],
    [ 1, 3, 4 ],
    [ 2, 3, 4 ],
    [ 0, 1, 5 ],
    [ 0, 2, 5 ],
    [ 1, 2, 5 ],
    [ 0, 3, 5 ],
    [ 1, 3, 5 ],
    [ 2, 3, 5 ],
    [ 0, 4, 5 ],
    [ 1, 4, 5 ],
    [ 2, 4, 5 ],
    [ 3, 4, 5 ],
    [ 0, 1, 6 ],
    [ 0, 2, 6 ],
    [ 1, 2, 6 ],
    [ 0, 3, 6 ],
    [ 1, 3, 6 ],
    [ 2, 3, 6 ],
    [ 0, 4, 6 ],
    [ 1, 4, 6 ],
    [ 2, 4, 6 ],
    [ 3, 4, 6 ],
    [ 0, 5, 6 ],
    [ 1, 5, 6 ],
    [ 2, 5, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 0, 1, 7 ],
    [ 0, 2, 7 ],
    [ 1, 2, 7 ],
    [ 0, 3, 7 ],
    [ 1, 3, 7 ],
    [ 2, 3, 7 ],
    [ 0, 4, 7 ],
    [ 1, 4, 7 ],
    [ 2, 4, 7 ],
    [ 3, 4, 7 ],
    [ 0, 5, 7 ],
    [ 1, 5, 7 ],
    [ 2, 5, 7 ],
    [ 3, 5, 7 ],
    [ 4, 5, 7 ],
    [ 0, 6, 7 ],
    [ 1, 6, 7 ],
    [ 2, 6, 7 ],
    [ 3, 6, 7 ],
    [ 4, 6, 7 ],
    [ 5, 6, 7 ],
    [ 0, 1, 8 ],
    [ 0, 2, 8 ],
    [ 1, 2, 8 ],
    [ 0, 3, 8 ],
    [ 1, 3, 8 ],
    [ 2, 3, 8 ],
    [ 0, 4, 8 ],
    [ 1, 4, 8 ],
    [ 2, 4, 8 ],
    [ 3, 4, 8 ],
    [ 0, 5, 8 ],
    [ 1, 5, 8 ],
    [ 2, 5, 8 ],
    [ 3, 5, 8 ],
    [ 4, 5, 8 ],
    [ 0, 6, 8 ],
    [ 1, 6, 8 ],
    [ 2, 6, 8 ],
    [ 3, 6, 8 ],
    [ 4, 6, 8 ],
    [ 5, 6, 8 ],
    [ 0, 7, 8 ],
    [ 1, 7, 8 ],
    [ 2, 7, 8 ],
    [ 3, 7, 8 ],
    [ 4, 7, 8 ],
    [ 5, 7, 8 ],
    [ 6, 7, 8 ],
    [ 0, 1, 9 ],
    [ 0, 2, 9 ],
    [ 1, 2, 9 ],
    [ 0, 3, 9 ],
    [ 1, 3, 9 ],
    [ 2, 3, 9 ],
    [ 0, 4, 9 ],
    [ 1, 4, 9 ],
    [ 2, 4, 9 ],
    [ 3, 4, 9 ],
    [ 0, 5, 9 ],
    [ 1, 5, 9 ],
    [ 2, 5, 9 ],
    [ 3, 5, 9 ],
    [ 4, 5, 9 ],
    [ 0, 6, 9 ],
    [ 1, 6, 9 ],
    [ 2, 6, 9 ],
    [ 3, 6, 9 ],
    [ 4, 6, 9 ],
    [ 5, 6, 9 ],
    [ 0, 7, 9 ],
    [ 1, 7, 9 ],
    [ 2, 7, 9 ],
    [ 3, 7, 9 ],
    [ 4, 7, 9 ],
    [ 5, 7, 9 ],
    [ 6, 7, 9 ],
    [ 0, 8, 9 ],
    [ 1, 8, 9 ],
    [ 2, 8, 9 ],
    [ 3, 8, 9 ],
    [ 4, 8, 9 ],
    [ 5, 8, 9 ],
    [ 6, 8, 9 ],
    [ 7, 8, 9 ],
    [ 0, 1, 10 ],
    [ 0, 2, 10 ],
    [ 1, 2, 10 ],
    [ 0, 3, 10 ],
    [ 1, 3, 10 ],
    [ 2, 3, 10 ],
    [ 0, 4, 10 ],
    [ 1, 4, 10 ],
    [ 2, 4, 10 ],
    [ 3, 4, 10 ],
    [ 0, 5, 10 ],
    [ 1, 5, 10 ],
    [ 2, 5, 10 ],
    [ 3, 5, 10 ],
    [ 4, 5, 10 ],
    [ 0, 6, 10 ],
    [ 1, 6, 10 ],
    [ 2, 6, 10 ],
    [ 3, 6, 10 ],
    [ 4, 6, 10 ],
    [ 5, 6, 10 ],
    [ 0, 7, 10 ],
    [ 1, 7, 10 ],
    [ 2, 7, 10 ],
    [ 3, 7, 10 ],
    [ 4, 7, 10 ],
    [ 5, 7, 10 ],
    [ 6, 7, 10 ],
    [ 0, 8, 10 ],
    [ 1, 8, 10 ],
    [ 2, 8, 10 ],
    [ 3, 8, 10 ],
    [ 4, 8, 10 ],
    [ 5, 8, 10 ],
    [ 6, 8, 10 ],
    [ 7, 8, 10 ],
    [ 0, 9, 10 ],
    [ 1, 9, 10 ],
    [ 2, 9, 10 ],
    [ 3, 9, 10 ],
    [ 4, 9, 10 ],
    [ 5, 9, 10 ],
    [ 6, 9, 10 ],
    [ 7, 9, 10 ],
    [ 8, 9, 10 ]
]
[
    [ 3, 4, 5 ],
    [ 3, 4, 6 ],
    [ 3, 5, 6 ],
    [ 4, 5, 6 ],
    [ 3, 4, 7 ],
    [ 3, 5, 7 ],
    [ 4, 5, 7 ],
    [ 3, 6, 7 ],
    [ 4, 6, 7 ],
    [ 5, 6, 7 ],
    [ 3, 4, 8 ],
    [ 3, 5, 8 ],
    [ 4, 5, 8 ],
    [ 3, 6, 8 ],
    [ 4, 6, 8 ],
    [ 5, 6, 8 ],
    [ 3, 7, 8 ],
    [ 4, 7, 8 ],
    [ 5, 7, 8 ],
    [ 6, 7, 8 ],
    [ 3, 4, 9 ],
    [ 3, 5, 9 ],
    [ 4, 5, 9 ],
    [ 3, 6, 9 ],
    [ 4, 6, 9 ],
    [ 5, 6, 9 ],
    [ 3, 7, 9 ],
    [ 4, 7, 9 ],
    [ 5, 7, 9 ],
    [ 6, 7, 9 ],
    [ 3, 8, 9 ],
    [ 4, 8, 9 ],
    [ 5, 8, 9 ],
    [ 6, 8, 9 ],
    [ 7, 8, 9 ],
    [ 3, 4, 10 ],
    [ 3, 5, 10 ],
    [ 4, 5, 10 ],
    [ 3, 6, 10 ],
    [ 4, 6, 10 ],
    [ 5, 6, 10 ],
    [ 3, 7, 10 ],
    [ 4, 7, 10 ],
    [ 5, 7, 10 ],
    [ 6, 7, 10 ],
    [ 3, 8, 10 ],
    [ 4, 8, 10 ],
    [ 5, 8, 10 ],
    [ 6, 8, 10 ],
    [ 7, 8, 10 ],
    [ 3, 9, 10 ],
    [ 4, 9, 10 ],
    [ 5, 9, 10 ],
    [ 6, 9, 10 ],
    [ 7, 9, 10 ],
    [ 8, 9, 10 ]
]

>> gen_ham_weight:=func<ri|Minimum[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1
                                              ^
User error: bad syntax

>> [gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; ;
                                           ^
User error: bad syntax

Total time: 5.279 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:21:05 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
[gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:20:59 on modular  [Seed = 1940250280]
   -------------------------------------

Klein quartic
>> gen_ham_weight:=func<ri|Minimum[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1
                                              ^
User error: bad syntax

>> [gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; ;
                                           ^
User error: bad syntax

Total time: 5.219 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:22:07 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum([Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])])>;
[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:22:02 on modular  [Seed = 2108412135]
   -------------------------------------

Klein quartic
>> [gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; ;
                                           ^
User error: bad syntax

Total time: 5.019 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:22:44 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
gen_ham_weight:=func<ri|Minimum([Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])])>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:22:38 on modular  [Seed = 1183902265]
   -------------------------------------


[<main>:172](
    ri: [ 4, 7 ]
)
>> gen_ham_weight:=func<ri|Minimum([Lunioinf[j]:j in conj_r_elements_ge_i([ri[
                                  ^
Runtime error in 'Minimum': Argument 1 is not non-empty

Total time: 5.429 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 08:28:43 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
Lmcinf:=[[0]];
Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;


/*
mcinf:=function(Lconjunts,Lmcinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lmcinf[p];
  end if;
end function;

interseccioinf:=function(Lconjunts,Linterseccioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Linterseccioinf[p];
  end if;
end function;

unioinf:=function(Lconjunts,Lunioinf,llista)
  p:=Position(Lconjunts,llista);
  if p eq 0 then return -1;
  else return Lunioinf[p];
  end if;
end function;
*/

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;

actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]
+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lmcinf:=actualitzamcinf(Lmcinf,llista);
  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lmcinf:=actualitzamcinf(Lmcinf,llista);
    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;

joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/

/*
unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 

Output: Magma V2.10-6     Wed Dec 24 2003 08:28:37 on modular  [Seed = 937532626]
   -------------------------------------

Klein quartic[
    [ 2, 2, 2, 2, 4, 4, 5, 6 ],
    [ 3, 3, 4, 5, 6, 7, 8, 9 ],
    [ 4, 5, 5, 6, 7, 8, 9, 11 ],
    [ 5, 6, 7, 8, 9, 10, 11, -1 ],
    [ 6, 7, 8, 9, 10, 11, -1, -1 ],
    [ 7, 8, 9, 10, 11, -1, -1, -1 ],
    [ 8, 9, 10, 11, -1, -1, -1, -1 ]
]

Total time: 5.949 seconds, Total memory usage: 2.42MB


************** MAGMA *****************
Host p14196-adsau12honb1-acca.tokyo.ocn.ne.jp. (219.161.161.196)
Time: Wed Dec 24 09:11:27 2003

Input: g:=Group<a,b|(a*b)^3=(a*b*a)^4=a^3*b*a*(b*a*b^3)^3=1>;
comm:=CommutatorSubgroup(g);
ReduceGenerators(comm);

Output: Magma V2.10-6     Wed Dec 24 2003 09:11:24 on modular  [Seed = 2024724907]
   -------------------------------------

Finitely presented group on 3 generators
Generators as words in group g
    $.1 = g.2 * g.1^-1
    $.2 = g.1^2
    $.3 = g.1 * g.2
Relations
    $.3^3 = Id($)
    ($.1 * $.2)^3 = Id($)
    $.3^-1 * $.1 * $.3 * $.2 * $.3 * $.1^-1 * $.3^-1 * $.2^-1 = Id($)
    ($.1 * $.2 * $.3 * $.2)^2 = Id($)
    $.3 * $.1 * $.2 * $.3 * $.1 * $.3^-1 * $.1 * $.3 * $.1 * $.2 * $.1 = Id($)

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:27:38 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
//Lmcinf:=[[0]];
//Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

/*
actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;
*/

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

/*
actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;
*/

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lmcinf:=actualitzamcinf(Lmcinf,llista);
//  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lmcinf:=actualitzamcinf(Lmcinf,llista);
//    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/
Lunioinf;



/*
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/


/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:27:35 on modular  [Seed = 4264067036]
   -------------------------------------

Klein quartic
>>   Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
                                           ^
User error: Identifier 'Linterseccioinf' has not been declared or assigned
[ 1 ]

Total time: 3.279 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:29:14 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
//Lmcinf:=[[0]];
//Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

/*
actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;
*/

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

/*
actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;
*/

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lmcinf:=actualitzamcinf(Lmcinf,llista);
//  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lmcinf:=actualitzamcinf(Lmcinf,llista);
//    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/
Lunioinf;



/*
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/


/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:29:11 on modular  [Seed = 3239526466]
   -------------------------------------

Klein quartic
>>   Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
                                           ^
User error: Identifier 'Linterseccioinf' has not been declared or assigned
[ 1 ]

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:29:17 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
//Lmcinf:=[[0]];
//Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

/*
actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;
*/

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

/*
actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;
*/

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lmcinf:=actualitzamcinf(Lmcinf,llista);
//  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lmcinf:=actualitzamcinf(Lmcinf,llista);
//    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/
Lunioinf;



/*
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/


/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:29:14 on modular  [Seed = 3424275778]
   -------------------------------------

Klein quartic
>>   Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista);
                                           ^
User error: Identifier 'Linterseccioinf' has not been declared or assigned
[ 1 ]

Total time: 3.179 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:29:26 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;




Lconjunts:=[[0]];
//Lmcinf:=[[0]];
//Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

/*
actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;
*/

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

/*
actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;
*/

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lmcinf:=actualitzamcinf(Lmcinf,llista);
//  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lmcinf:=actualitzamcinf(Lmcinf,llista);
//    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
Lunioinf;
*/



joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];



/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:29:21 on modular  [Seed = 3996675931]
   -------------------------------------

Klein quarticVEREDICTE:=[]

Total time: 4.889 seconds, Total memory usage: 2.22MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:35:17 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
//Lmcinf:=[[0]];
//Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

/*
actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;
*/

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

/*
actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;
*/

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lmcinf:=actualitzamcinf(Lmcinf,llista);
//  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lmcinf:=actualitzamcinf(Lmcinf,llista);
//    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



/* 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 
*/


/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:35:12 on modular  [Seed = 2024703848]
   -------------------------------------

Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5,
5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5,
5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ]

Total time: 4.379 seconds, Total memory usage: 2.22MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:36:24 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


/* 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
//Lmcinf:=[[0]];
//Linterseccioinf:=[1];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

/*
actualitzamcinf:=function(Lmcinf,llista)
  maxc:=llista[1];
  if (maxc eq 0) then
    return (Append(Lmcinf,[0]));
  end if;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,llista[1]) do
      maxc:=maxc-1;
    end while;
    j:=2;
    while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while;
    if j eq #llista+1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  mcinfllista:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 then
      j:=1;
      while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while;
      if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if;
    end if;
  end for;
  return(Append(Lmcinf,mcinfllista));
end function;
*/

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

/*
actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista)
  if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1]));
  else return 
    Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]);
  end if;
end function;
*/

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lmcinf:=actualitzamcinf(Lmcinf,llista);
//  Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lmcinf:=actualitzamcinf(Lmcinf,llista);
//    Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME
*/


 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];


*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:36:21 on modular  [Seed = 2605540430]
   -------------------------------------

Klein quartic
>>   return(index(ret));
            ^
User error: Identifier 'index' has not been declared or assigned

>>  Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lun
             ^
User error: Identifier 'index' has not been declared or assigned

>>   conjuntsaux:=Lconjunts;
                  ^
User error: Identifier 'Lconjunts' has not been declared or assigned

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

>> */
   ^
User error: bad syntax

>> unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
                                                      ^
User error: Identifier 'Lconjunts' has not been declared or assigned

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

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:40:24 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



/* 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 
*/


/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:40:20 on modular  [Seed = 2058126403]
   -------------------------------------

Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5,
5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5,
5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ]

Total time: 4.329 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:41:55 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

//Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:41:51 on modular  [Seed = 2992917552]
   -------------------------------------

Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5,
5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5,
5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ]

Total time: 4.119 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:43:18 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=20;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

//Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Wed Dec 24 2003 11:42:55 on modular  [Seed = 533324380]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29523 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:43:55 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=15;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

//Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Wed Dec 24 2003 11:43:32 on modular  [Seed = 3778485401]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29613 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:44:26 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=15;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

//Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Wed Dec 24 2003 11:44:03 on modular  [Seed = 3076606632]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29691 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:44:58 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=12;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

//Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;

unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Wed Dec 24 2003 11:44:35 on modular  [Seed = 148829488]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29763 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:46:20 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=12;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



/* 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 
*/


/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Wed Dec 24 2003 11:45:57 on modular  [Seed = 1451273177]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29980 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:46:36 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



/* 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 
*/


/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:46:32 on modular  [Seed = 619895174]
   -------------------------------------

Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5,
5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5,
5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ]

Total time: 4.319 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42)
Time: Wed Dec 24 11:47:40 2003

Input: 	/* Klein quartic */


printf "Klein quartic";
MAX:=10;
c:=5;
g:=3;
semi:=[0,3];



	/* Hermitian curve */

/* 
printf "hermitian curve";
MAX:=10;
c:=12;
g:=6;
semi:=[0,4,5,8,9,10];
*/

	/* basic del semigrup */

i_cond:=c-g;
pertany:=func<i|i ge c select true else i in semi>;
gaps:=[i:i in [1..c-1]|not pertany(i)];
lambda:=func<i|i lt i_cond select semi[i+1] else i+g >;
lambdainv:=func<i|pertany(i) select i lt c select Position(semi,i)-1 else i-g  else -1>;


	/* oplus, leq, nu */

oplus:=func<i,j|lambdainv(lambda(i)+lambda(j))>;
inferior:=func<i,j|pertany(lambda(j)-lambda(i))>;
ominus:=func<j,i|inferior(i,j) select lambdainv(lambda(j)-lambda(i)) else -1>;
N:=func<i|{j:j in [0..i]|inferior(j,i)}>;
nu:=func<i|#N(i)>;


	/* order bound */
dORD:=func<i|i lt 2*c-1-g select Minimum([nu(j):j in [i+1..2*c-1-g]]) else nu(i+1)>;


 
//PROVA NOU ALGORITME
//-----------------------


Lconjunts:=[[0]];
Lunioinf:=[1];

index:=function(llista)
  i:=0;
  for j in llista do i:=i+2^j; end for;
  return(i);
end function;

actualitzaconjunts:=function (Lconjunts,llista)
  return(Append(Lconjunts,llista));
end function;

interseccio_ultim_unio_dels_altres:=function(llista)
  ultim:=llista[#llista];
  maxc:=ultim-1;
  trobat:=false;
  while not trobat do
    while not inferior(maxc,ultim) do
      maxc:=maxc-1;
    end while;
    j:=1;
    while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while;
    if j le #llista-1 then trobat:=true; end if;
    maxc:=maxc-1;
  end while;
  maxc:=maxc+1;
  ret:=[maxc];
  for h in gaps do
    candidat:=lambdainv(lambda(maxc)-h);
    if candidat gt 0 and inferior(candidat,ultim) then
      j:=1;
      while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while;
      if j le #llista-1 then ret:=Append(ret,candidat); end if;
    end if;
  end for;
  return(index(ret));
end function;

actualitzaunioinf:=function(Lconjunts,Lunioinf,llista)
  if #llista eq 1 then 
    return Append(Lunioinf,nu(llista[1]));
  else 
    return Append(Lunioinf,
 Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]);
  end if;
end function;

for i in [1..MAX] do
  conjuntsaux:=Lconjunts;
  llista:=[i];
  Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//  Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  for conj in conjuntsaux do
    llista:=Append(conj,i);
    Lconjunts:=actualitzaconjunts(Lconjunts,llista);
//    Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista);
  end for;
end for;


/*
l:=#Lconjunts;
print "CONJUNTS=";
<Lconjunts[i]: i in [1..l]>;
print "MCINF=";
<Lmcinf[i]: i in [1..l]>;
print "INTERSECCIOINF=";
Linterseccioinf;
print "UNIOINF=";
*/

Lunioinf;
//----------------------- 
//PROVA NOU ALGORITME



 
//PROVA ALGORITME SIMPLE
//-----------------------
joinsets:=function(llista)
unio:={};
for conj in llista do unio:=unio join conj; end for;
return unio;
end function;


unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts];
unioasac;
//----------------------
//PROVA ALGORITME SIMPLE 



/*
// COMPROVACIO

errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]];
printf "VEREDICTE:=";
[Lconjunts[i]:i in [1..#errors]|errors[i] ne 0];
*/

/*
conj_r_elements:=func<r|[index(llista): llista in Lconjunts|#llista eq r]>;
//[Lconjunts[i]: i in conj_r_elements(3)];
max_index:=index([1..MAX]);
conj_r_elements_ge_i:=func<ri|[k:k in [2^(ri[2])*j:j in conj_r_elements(ri[1])]|k le max_index]>;
//[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])];
unioinf_conj_r_elements_ge_i:=func<ri|[Lunioinf[j]:j in conj_r_elements_ge_i([ri[1],ri[2]+1])]>;
gen_ham_weight:=func<ri|#unioinf_conj_r_elements_ge_i(ri) eq 0 select -1 else Minimum(unioinf_conj_r_elements_ge_i(ri))>;
[[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; 
*/

Output: Magma V2.10-6     Wed Dec 24 2003 11:47:36 on modular  [Seed = 1519167035]
   -------------------------------------

Klein quartic[ 1 ]
[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 
4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5,
5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5,
5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ]

Total time: 4.159 seconds, Total memory usage: 2.12MB


************** MAGMA *****************
Host d66-183-120-209.bchsia.telus.net. (66.183.120.209)
Time: Thu Dec 25 21:51:01 2003

Input: 1+1;

Output: Magma V2.10-6     Thu Dec 25 2003 21:50:58 on modular  [Seed = 182359833]
   -------------------------------------

2

Total time: 2.879 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host d66-183-120-209.bchsia.telus.net. (66.183.120.209)
Time: Thu Dec 25 21:51:40 2003

Input: 12*12;

Output: Magma V2.10-6     Thu Dec 25 2003 21:51:37 on modular  [Seed = 365004845]
   -------------------------------------

144

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host d66-183-120-209.bchsia.telus.net. (66.183.120.209)
Time: Thu Dec 25 21:52:06 2003

Input: 13*13;

Output: Magma V2.10-6     Thu Dec 25 2003 21:52:03 on modular  [Seed = 482902350]
   -------------------------------------

169

Total time: 2.879 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host d66-183-120-209.bchsia.telus.net. (66.183.120.209)
Time: Thu Dec 25 23:44:33 2003

Input: 11*10;

Output: Magma V2.10-6     Thu Dec 25 2003 23:44:30 on modular  [Seed = 3812057164]
   -------------------------------------

110

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host node04.co.st-johns.fl.us. (205.138.150.5)
Time: Sat Dec 27 13:02:40 2003

Input: expand((x^5-7)^50)

Output: Magma V2.10-6     Sat Dec 27 2003 13:02:37 on modular  [Seed = 1401005368]
   -------------------------------------


>> expand((x^5-7)^50);
           ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host core-dr00.proxy.nacamar.net. (194.162.162.68)
Time: Mon Dec 29 07:53:01 2003

Input: H:=HammingCode(GF(8),2);
H;

Output: Magma V2.10-6     Mon Dec 29 2003 07:52:56 on modular  [Seed = 1072702418]
   -------------------------------------

[9, 7, 3] Hamming code (r = 2) over GF(2^3)
Generator matrix:
[    1     0     0     0     0     0     0     1   $.1]
[    0     1     0     0     0     0     0   $.1 $.1^6]
[    0     0     1     0     0     0     0 $.1^6 $.1^3]
[    0     0     0     1     0     0     0 $.1^3 $.1^3]
[    0     0     0     0     1     0     0 $.1^3 $.1^6]
[    0     0     0     0     0     1     0 $.1^6   $.1]
[    0     0     0     0     0     0     1   $.1     1]

Total time: 3.109 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ctb-cache1-vif1.saix.net. (198.54.202.2)
Time: Mon Dec 29 17:04:30 2003

Input: 234234324+238479234793;

Output: Magma V2.10-6     Mon Dec 29 2003 17:04:27 on modular  [Seed = 3828055869]
   -------------------------------------

238713469117

Total time: 3.239 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ctb-cache1-vif1.saix.net. (198.54.202.2)
Time: Mon Dec 29 17:04:33 2003

Input: 234234324+238479234793;

Output: Magma V2.10-6     Mon Dec 29 2003 17:04:29 on modular  [Seed = 3945033780]
   -------------------------------------

238713469117

Total time: 3.089 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (61.150.43.30)
Time: Tue Dec 30 03:51:30 2003

Input: 1+2

Output: Magma V2.10-6     Tue Dec 30 2003 03:51:26 on modular  [Seed = 3195059564]
   -------------------------------------

3

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host c207.134.75-245.clta.telus.com. (207.134.75.245)
Time: Tue Dec 30 16:24:33 2003

Input: mc(t2-f)=(m+mc)(t-t1)

Output: Magma V2.10-6     Tue Dec 30 2003 16:24:30 on modular  [Seed = 366724936]
   -------------------------------------


>> mc(t2-f)=(m+mc)(t-t1);
                   ^
User error: Identifier 't' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host c207.134.75-245.clta.telus.com. (207.134.75.245)
Time: Tue Dec 30 16:26:26 2003

Input: mc(t2-f)=(m+mc)(m-t1)

Output: Magma V2.10-6     Tue Dec 30 2003 16:26:23 on modular  [Seed = 130667819]
   -------------------------------------


>> mc(t2-f)=(m+mc)(m-t1);
                   ^
User error: Identifier 'm' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.161)
Time: Wed Dec 31 15:41:02 2003

Input: PrintBinaryPrimitiveTrinomials(521,0);

Output: Magma V2.10-6     Wed Dec 31 2003 15:40:59 on modular  [Seed = 3742618817]
   -------------------------------------


>> PrintBinaryPrimitiveTrinomials(521,0);;
   ^
User error: Identifier 'PrintBinaryPrimitiveTrinomials' has not been declared or
assigned

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.161)
Time: Wed Dec 31 15:41:35 2003

Input: PrintBinaryPrimitivePentanomials(521,0);

Output: Magma V2.10-6     Wed Dec 31 2003 15:41:32 on modular  [Seed = 3777882840]
   -------------------------------------


>> PrintBinaryPrimitivePentanomials(521,0);;
   ^
User error: Identifier 'PrintBinaryPrimitivePentanomials' has not been declared 
or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.161)
Time: Wed Dec 31 15:46:40 2003

Input: trinomial 31

Output: Magma V2.10-6     Wed Dec 31 2003 15:46:37 on modular  [Seed = 2455672954]
   -------------------------------------


>> trinomial 31;
             ^
User error: bad syntax

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.161)
Time: Wed Dec 31 15:47:07 2003

Input: trinomial 31

Output: Magma V2.10-6     Wed Dec 31 2003 15:47:04 on modular  [Seed = 2808851754]
   -------------------------------------


>> trinomial 31;
             ^
User error: bad syntax

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:04:50 2004

Input: PrintBinaryPrimitivePentanomials(21,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:04:47 on modular  [Seed = 2269941682]
   -------------------------------------


>> PrintBinaryPrimitivePentanomials(21,0);;
   ^
User error: Identifier 'PrintBinaryPrimitivePentanomials' has not been declared 
or assigned

Total time: 3.109 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:08:19 2004

Input: ?


Output: Magma V2.10-6     Thu Jan  1 2004 10:08:16 on modular  [Seed = 4047173931]
   -------------------------------------

===============================================================================
PATH: /
KIND: Overview
===============================================================================

You are reading about the Magma online help system.  This system 
gives you information about Magma while you are at the computer. 
To see this help page at any time, all you have to do is to type  

        ?

                  ----------

The online help system comes in two modes: the single request
mode and the Magma Help Browser.  To enter the Browser, type

        ??

The Browser is useful if you intend to read several related
help nodes, because you can exploit the tree structure of the
online help.  Once you are in the Browser, you can type

        help

again to find out how to use the Browser, and for a more
detailed explanation of the whole online help system.

                  ----------

Single help requests begin with the ? character.
Examples are:

?print
?magma
?ring
?example

If your help request is ambiguous, Magma will return a numbered 
list of matches.  To see the contents of one of them, 
type  ?  followed by its number.

Some help pages suggest other pages that you might like to look at 
as well.  They are prefixed by a code such as   +3  or  +5 .  
To read one of them, type  ?  followed by the code.

You can also supply the full pathname of a help node, if you know it.
For example:

?/system/quit
?/magma/module/homomorphism 

                  ----------

The online help system offers tab completion. If you type a few letters 
of your help request and then press the tab key, Magma will "complete" 
the request if there is a unique completion.  Otherwise, it will 
complete the request as far as possible, and then emit a beep.  
Press the tab key again to see all the possibilities.
ALWAYS PRESS TAB BEFORE THE END OF THE LINE, 
SO AS TO SEE EVERY RELEVANT HELP PAGE.
(On a few operating systems, the tab completion feature 
cannot be made available.)

                  ----------

The content of the online help system comes from two sources:
the "Handbook of Magma Functions" (Bosma and Cannon)
and specially-written overview nodes.
You may also wish to consult the books
"An Introduction to Algebraic Programming in Magma"
(Cannon and Playoust) and "Solving Problems with Magma"
(Bosma, Cannon, Playoust and Steel).

                  ----------

The online help system is also available in an HTML form
suitable for Internet browsers.  To use this,
move to a shell prompt (outside Magma) and type

    magmahelp

                  ----------

To leave Magma, type 

    quit;

or <Ctrl>-D.
===============================================================================

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:09:19 2004

Input: ?example


Output: Magma V2.10-6     Thu Jan  1 2004 10:09:15 on modular  [Seed = 3995462095]
   -------------------------------------

1320 matches:
     1   O   /browser/example
     2   O   /browser/example/example-intrinsic
     3   O   /browser/example/example-intrinsic-restrict
     4   O   /browser/example/example-search
     5   O   /browser/example/example-walk
     6   O   /example
     7   E   /language/function-procedure-package/attribute/examples/\
             Example-InteractiveUserAttributes
     8   E   /language/function-procedure-package/attribute/examples/\
             Example-PackageUserAttributes
     9   E   /language/function-procedure-package/attribute/examples/\
             Example-SystemAttributes
    10   E   /language/function-procedure-package/function-procedure/forward/\
             Example-forward
    11   E   /language/function-procedure-package/function-procedure/function/\
             Example-Parameters
    12   E   /language/function-procedure-package/function-procedure/function/\
             Example-Recursion
    13   E   /language/function-procedure-package/function-procedure/function/\
             Example-Underscore
    14   E   /language/function-procedure-package/function-procedure/\
             procedure/Example-Procedures
    15   E   /language/function-procedure-package/package/import/Example-import
    16   E   /language/function-procedure-package/package/intrinsic/\
             Example-intrinsic
    17   E   /language/function-procedure-package/package/require/\
             Example-require
    18   E   /language/function-procedure-package/package/spec/Example-spec
    19   E   /language/function-procedure-package/package/startup-spec/\
             Example-startup-spec
    20   E   /language/IO/file/operations/Example-GetTime
    21   E   /language/IO/file/operations/Example-LineCount
    22   E   /language/IO/file/reading-file/Example-Read
    23   E   /language/IO/print/auto-print/Example-auto-print
    24   E   /language/IO/print/printf/Example-printf
    25   E   /language/IO/print/printf/Example-printf
    26   E   /language/IO/print/printf/Example-printf2
    27   E   /language/IO/print/sprint/Example-Sprintf
    28   E   /language/IO/string/Boolean/Example-Strings
    29   E   /language/IO/string/parsing/Example-Regexp
    30   E   /language/IO/string/parsing/Example-Split
    31   E   /language/statement-expressions/assignment/generator-assignment/\
             Example-GeneratorNaming
    32   E   /language/statement-expressions/assignment/generator-assignment/\
             Example-GeneratorNamingSequence
    33   E   /language/statement-expressions/assignment/indexed-assignment/\
             Example-Indexing
    34   E   /language/statement-expressions/assignment/mutation/\
             Example-MutationAssignment
    35   E   /language/statement-expressions/assignment/simple-assignment/\
             Example-Identifiers
    36   E   /language/statement-expressions/assignment/simple-assignment/\
             Example-MultipleReturns
    37   E   /language/statement-expressions/boolean/equality-operators/\
             Example-Equality
    38   E   /language/statement-expressions/boolean/iteration/Example-Booleans
    39   E   /language/statement-expressions/comment-continuation/\
             Example-Various
    40   E   /language/statement-expressions/conditional/case-statement/\
             Example-case
    41   E   /language/statement-expressions/conditional/\
             conditional-expression/Example-InLineConditional
    42   E   /language/statement-expressions/conditional/\
             conditional-statement/Example-if
    43   E   /language/statement-expressions/iteration/continue-break/\
             Example-break
    44   E   /language/statement-expressions/iteration/repeat-statement/\
             Example-repeat
    45   E   /language/statement-expressions/iteration/repeat-statement/\
             Example-while
    46   E   /language/statement-expressions/misc/Example-IsIntrinsic
    47   E   /language/statement-expressions/random/Example-IsIntrinsic
    48   E   /language/statement-expressions/timing/Example-Time
    49   E   /language/statement-expressions/type/Example-TypeStructures
    50   E   /language/statement-expressions/where-is/Example-where
    51   E   /magma/aggregate/coproduct/retrieve/Example-cop
    52   E   /magma/aggregate/record-format/access-modification/\
             Example-RecordAccess
    53   E   /magma/aggregate/record-format/creation-format/\
             Example-RecordFormat
    54   E   /magma/aggregate/record-format/creation-record/Example-Record
    55   E   /magma/aggregate/sequence/detail/creation/arithmetic-progression/\
             Example-Progression
    56   E   /magma/aggregate/sequence/detail/iteration/Example-NestedIteration
    57   E   /magma/aggregate/sequence/detail/operation/modification/\
             Example-Farey
    58   E   /magma/aggregate/sequence/detail/operation/other/\
             Example-EgyptianFractions
    59   E   /magma/aggregate/sequence/detail/power-sequence/\
             Example-PowerSequence
    60   E   /magma/aggregate/sequence/detail/recursion-reduction-iteration/\
             recursion/Example-Self
    61   E   /magma/aggregate/set/detail/access-modification/access/\
             Example-Miscellaneous
    62   E   /magma/aggregate/set/detail/access-modification/element/\
             Example-ExtractRep
    63   E   /magma/aggregate/set/detail/access-modification/element/\
             Example-Random
    64   E   /magma/aggregate/set/detail/access-modification/modification/\
             Example-Include
    65   E   /magma/aggregate/set/detail/creation/arithmetic-progression/\
             Example-Progression
    66   E   /magma/aggregate/set/detail/creation/enumerated/\
             Example-AlmostFermat
    67   E   /magma/aggregate/set/detail/creation/enumerated/Example-Universe
    68   E   /magma/aggregate/set/detail/creation/indexed/\
             Example-AlmostFermatIndexed
    69   E   /magma/aggregate/set/detail/creation/multiset/Example-Multiset
    70   E   /magma/aggregate/set/detail/operation/binary/Example-Join
    71   E   /magma/aggregate/set/detail/power-set/Example-PowerSet
    72   E   /magma/aggregate/set/detail/quantifier/Example-Exists
    73   E   /magma/aggregate/set/detail/quantifier/Example-NestedExists
    74   E   /magma/aggregate/set/detail/reduction-iteration/Example-Reduction
    75   E   /magma/aggregate/tuple-cartesian-product/creation/\
             Example-CartesianProduct
    76   E   /magma/aggregate/tuple-cartesian-product/tuple-access/\
             Example-TupleAccess
    77   E   /magma/aggregate/tuple-cartesian-product/tuple/Example-Tuple
    78   E   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:brandt-modules/Associated-Structures/\
             Example-ModBrdt:Module-Creation
    79   E   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:brandt-modules/Example-ModBrdt:Constructors
    80   E   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:brandt-modules/Verbose-Output/\
             Example-ModBrdt:Verbose-Output
    81   E   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:dimension-formulas/Example-ModBrdt:Dimension
    82   E   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:Subspaces/Example-ModBrdt:Decomposition
    83   E   /magma/combinatorial-geometrical-incidence/brandt-modules/\
             ModBrdt:Subspaces/ModBrdt:Subspaces-Tests/\
             Example-ModBrdt:EisensteinSubspace
    84   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/creation-change_ring/Example-BaseExtend
    85   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/creation-curve/Example-Creation
    86   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/creation-curve/Example-CreationFromCurve
    87   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/creation-curve/Example-CreationFromCurve2
    88   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/creation-model-predicates/Example-Models
    89   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/creation-predicates/Example-CreationTest
    90   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/twists/Example-NonquadraticTwists
    91   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             creation/twists/Example-QuadraticTwists
    92   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             database/Example-ecdb1
    93   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             database/Example-ecdb2
    94   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             ff_curves/abelian_group/Example-AbelianGroup
    95   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             ff_curves/discrete_logs/Example-ECDL
    96   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             ff_curves/ff_curves-point_counting/Example-Invariants to Read
    97   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             ff_curves/ff_curves-point_counting/Example-Order
    98   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             ff_curves/ff_curves-point_counting/Example-SEA
    99   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             ff_curves/ff_curves-point_counting/Example-Twists
   100   E   /magma/combinatorial-geometrical-incidence/elliptic-curve/\
             function_field/function_field-torsion_polynomials/\
             Example-DivisionPolynomial
   101   E   /magma/combinatorial-geometrical-incidence/ellipt
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:10:19 2004

Input: x^31+x^3+1

Output: Magma V2.10-6     Thu Jan  1 2004 10:10:16 on modular  [Seed = 3725973948]
   -------------------------------------


>> x^31+x^3+1;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:11:03 2004

Input: list (31,3);

Output: Magma V2.10-6     Thu Jan  1 2004 10:11:00 on modular  [Seed = 3608989801]
   -------------------------------------


>> list (31,3);;
   ^
User error: Identifier 'list' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:11:22 2004

Input: print

Output: Magma V2.10-6     Thu Jan  1 2004 10:11:19 on modular  [Seed = 3439774304]
   -------------------------------------


>> print;
        ^
User error: bad syntax

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:11:57 2004

Input: print Binary Primitive Pentanomials(16,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:11:54 on modular  [Seed = 972177082]
   -------------------------------------


>> print Binary Primitive Pentanomials(16,0);;
                ^
User error: bad syntax

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:12:16 2004

Input: print Binary Pentanomials(16,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:12:13 on modular  [Seed = 821770180]
   -------------------------------------


>> print Binary Pentanomials(16,0);;
                ^
User error: bad syntax

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:12:40 2004

Input: print Binary(16,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:12:37 on modular  [Seed = 736111863]
   -------------------------------------


>> print Binary(16,0);;
         ^
User error: Identifier 'Binary' has not been declared or assigned

Total time: 3.089 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:12:57 2004

Input: print Binary (16,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:12:53 on modular  [Seed = 500570833]
   -------------------------------------


>> print Binary (16,0);;
         ^
User error: Identifier 'Binary' has not been declared or assigned

Total time: 3.269 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:13:22 2004

Input: print PrimitivePentanomials(521,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:13:19 on modular  [Seed = 350163490]
   -------------------------------------


>> print PrimitivePentanomials(521,0);;
         ^
User error: Identifier 'PrimitivePentanomials' has not been declared or assigned

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:13:40 2004

Input: print Pentanomials(521,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:13:37 on modular  [Seed = 264505623]
   -------------------------------------


>> print Pentanomials(521,0);;
         ^
User error: Identifier 'Pentanomials' has not been declared or assigned

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:14:01 2004

Input: print(521,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:13:57 on modular  [Seed = 114098186]
   -------------------------------------


>> print(521,0);;
        ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:14:18 2004

Input: print (21,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:14:15 on modular  [Seed = 1908045583]
   -------------------------------------


>> print (21,0);;
         ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.156)
Time: Thu Jan  1 10:14:37 2004

Input: print(21,0);

Output: Magma V2.10-6     Thu Jan  1 2004 10:14:34 on modular  [Seed = 1755541003]
   -------------------------------------


>> print(21,0);;
        ^
Runtime error in elt< ... >: No permutation group context in which to create 
cycle

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ds10.internetdsl.tpnet.pl. (80.53.254.10)
Time: Fri Jan  2 06:20:48 2004

Input: http://www.frenchfries.net/paul/factoring/theory/index.html


Output: Magma V2.10-6     Fri Jan  2 2004 06:20:44 on modular  [Seed = 619597574]
   -------------------------------------


>> ;
   ^
User error: bad syntax

Total time: 3.119 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 20:40:52 2004

Input: isprime(2);

Output: Magma V2.10-6     Fri Jan  2 2004 20:40:48 on modular  [Seed = 3491361364]
   -------------------------------------


>> isprime(2);;
   ^
User error: Identifier 'isprime' has not been declared or assigned

Total time: 3.279 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 20:41:23 2004

Input: 3^2;

Output: Magma V2.10-6     Fri Jan  2 2004 20:41:20 on modular  [Seed = 3641768765]
   -------------------------------------

9

Total time: 3.269 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 20:48:26 2004

Input: 3^2;

2^7;

Output: Magma V2.10-6     Fri Jan  2 2004 20:48:23 on modular  [Seed = 922687090]
   -------------------------------------

9
128

Total time: 3.269 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 20:55:42 2004

Input: ZetaFunction(R,4);


Output: Magma V2.10-6     Fri Jan  2 2004 20:55:39 on modular  [Seed = 214241844]
   -------------------------------------


>> ZetaFunction(R,4);
                ^
User error: Identifier 'R' has not been declared or assigned

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 20:58:03 2004

Input: print Factorization(20);


Output: Magma V2.10-6     Fri Jan  2 2004 20:58:00 on modular  [Seed = 450036881]
   -------------------------------------

[ <2, 2>, <5, 1> ]

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:01:11 2004

Input: isPrime(51);


Output: Magma V2.10-6     Fri Jan  2 2004 21:01:08 on modular  [Seed = 2024891711]
   -------------------------------------


>> isPrime(51);
   ^
User error: Identifier 'isPrime' has not been declared or assigned

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:02:27 2004

Input: NextPrime(12);


Output: Magma V2.10-6     Fri Jan  2 2004 21:02:24 on modular  [Seed = 1419594183]
   -------------------------------------

13

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:03:15 2004

Input: zetaFunction(2);


Output: Magma V2.10-6     Fri Jan  2 2004 21:03:12 on modular  [Seed = 2741681760]
   -------------------------------------


>> zetaFunction(2);
   ^
User error: Identifier 'zetaFunction' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:03:38 2004

Input: ZetaFunction(2);


Output: Magma V2.10-6     Fri Jan  2 2004 21:03:35 on modular  [Seed = 2858661758]
   -------------------------------------

1.64493406684822643647241516657

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:03:51 2004

Input: ZetaFunction(3);


Output: Magma V2.10-6     Fri Jan  2 2004 21:03:48 on modular  [Seed = 2977475990]
   -------------------------------------

1.202056903159594285399738161386

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:05:07 2004

Input: k :=3;
zta := ZetaFunction(k);
	ztainv :=1.0/zta;



Output: Magma V2.10-6     Fri Jan  2 2004 21:05:04 on modular  [Seed = 3161825487]
   -------------------------------------


Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:05:18 2004

Input: k :=3;
//zta := ZetaFunction(k);
//	ztainv :=1.0/zta;



Output: Magma V2.10-6     Fri Jan  2 2004 21:05:15 on modular  [Seed = 2336397299]
   -------------------------------------


Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host h68-147-114-138.cg.shawcable.net. (68.147.114.138)
Time: Fri Jan  2 21:05:41 2004

Input: k :=3;
zta := ZetaFunction(k);
	ztainv :=1.0/zta;
print ztainv;



Output: Magma V2.10-6     Fri Jan  2 2004 21:05:38 on modular  [Seed = 2455473859]
   -------------------------------------

0.83190737258070746868312627890

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ppp-62-10-141-79.dialup.tiscali.it. (62.10.141.79)
Time: Fri Jan  2 21:07:41 2004

Input: 100+10

Output: Magma V2.10-6     Fri Jan  2 2004 21:07:38 on modular  [Seed = 2555479121]
   -------------------------------------

110

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ppp-62-10-141-79.dialup.tiscali.it. (62.10.141.79)
Time: Fri Jan  2 21:08:10 2004

Input: (100+10)/10

Output: Magma V2.10-6     Fri Jan  2 2004 21:08:07 on modular  [Seed = 3878616259]
   -------------------------------------

11

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ppp-62-10-141-79.dialup.tiscali.it. (62.10.141.79)
Time: Fri Jan  2 21:08:43 2004

Input: ((100+10)/10)*2

Output: Magma V2.10-6     Fri Jan  2 2004 21:08:40 on modular  [Seed = 4114411262]
   -------------------------------------

22

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host px3so.cg.shawcable.net. (24.71.223.142)
Time: Sat Jan  3 00:15:53 2004

Input: pp := func<p,n,s | &*[(1-p(i)^(-s))^(-1): i in [1..n]]>;
	
procedure prime(s,n);
      ztainv :=1.0/ZetaFunction(s);

	q :=1-ztainv*pp(p,s,n);
      q := q^{1/s};

      print "p, s, n and p_{n+1} are: ",p,s,n,q;	 
end procedure;

procedure pp();
 
	k :=100;
      s := 100;
	prime(p,s,n);
end procedure;

Output: Magma V2.10-6     Sat Jan  3 2004 00:15:50 on modular  [Seed = 2875376781]
   -------------------------------------


>>         q :=1-ztainv*pp(p,s,n);
                           ^
User error: Identifier 'p' has not been declared or assigned

>>         prime(p,s,n);
                 ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host px3so.cg.shawcable.net. (24.71.223.142)
Time: Sat Jan  3 00:21:31 2004

Input: pr := func<p,n,s | &*[(1-p(i)^(-s))^(-1): i in [1..n]]>;

procedure primecal();

	s :=100;
      n := 100;
	prime(s,n);

end procedure;
	
procedure prime(s,n);
    
	q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s};

      print "s, n and p_{n+1} are: ", s,n,q;	 
end procedure;

Output: Magma V2.10-6     Sat Jan  3 2004 00:21:28 on modular  [Seed = 3161838277]
   -------------------------------------


>>         prime(s,n);
           ^
User error: Identifier 'prime' has not been declared or assigned

>>         q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s};
                                         ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.859 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host px3so.cg.shawcable.net. (24.71.223.142)
Time: Sat Jan  3 00:22:19 2004

Input: pr := func<p,n,s | &*[(1-p(i)^(-s))^(-1): i in [1..n]]>;

procedure primecal();

	s :=100;
      n := 100;
	primeca(s,n);

end procedure;
	
procedure primeca(s,n);
    
	q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s};

      print "s, n and p_{n+1} are: ", s,n,q;	 
end procedure;

Output: Magma V2.10-6     Sat Jan  3 2004 00:22:16 on modular  [Seed = 2253383727]
   -------------------------------------


>>         primeca(s,n);
           ^
User error: Identifier 'primeca' has not been declared or assigned

>>         q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s};
                                         ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host px3so.cg.shawcable.net. (24.71.223.142)
Time: Sat Jan  3 00:23:04 2004

Input: pr := func<p,n,s | &*[(1-p(i)^(-s))^(-1): i in [1..n]]>;

	
procedure primeca(s,n);
    
	q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s};

      print "s, n and p_{n+1} are: ", s,n,q;	 
end procedure;

procedure primecal();

	s :=100;
      n := 100;
	primeca(s,n);

end procedure;

Output: Magma V2.10-6     Sat Jan  3 2004 00:23:01 on modular  [Seed = 2438528773]
   -------------------------------------


>>         q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s};
                                         ^
User error: Identifier 'p' has not been declared or assigned

>>         primeca(s,n);
           ^
User error: Identifier 'primeca' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 06:22:57 2004

Input: R<x> := FunctionField(GF(5));
P<y> := PolynomialRing(R);
F<alpha> := FunctionField(y^2 - 1/x);
F;


Output: Magma V2.10-6     Sat Jan  3 2004 06:22:53 on modular  [Seed = 2125981545]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y^2 + 4/x

Total time: 3.459 seconds, Total memory usage: 6.52MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 06:24:43 2004

Input: R<x> := FunctionField(GF(5));
P<y> := PolynomialRing(R);
F<alpha> := FunctionField(1/x);
F;


Output: Magma V2.10-6     Sat Jan  3 2004 06:24:40 on modular  [Seed = 2009001493]
   -------------------------------------


>> F<alpha> := FunctionField(1/x);
                            ^
Runtime error in 'FunctionField': Bad argument types
Argument types given: FldFunRatUElt

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

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 06:24:59 2004

Input: R<x> := FunctionField(GF(5));
F<alpha> := FunctionField(1/x);
F;


Output: Magma V2.10-6     Sat Jan  3 2004 06:24:56 on modular  [Seed = 1822815742]
   -------------------------------------


>> F<alpha> := FunctionField(1/x);
                            ^
Runtime error in 'FunctionField': Bad argument types
Argument types given: FldFunRatUElt

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

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 06:25:31 2004

Input: R<x> := FunctionField(GF(5));
F;


Output: Magma V2.10-6     Sat Jan  3 2004 06:25:28 on modular  [Seed = 2572156971]
   -------------------------------------


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

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 06:25:36 2004

Input: R<x> := FunctionField(GF(5));
F;


Output: Magma V2.10-6     Sat Jan  3 2004 06:25:33 on modular  [Seed = 2522812193]
   -------------------------------------


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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 06:25:46 2004

Input: R<x> := FunctionField(GF(5));


Output: Magma V2.10-6     Sat Jan  3 2004 06:25:43 on modular  [Seed = 2403735074]
   -------------------------------------


Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:00:58 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y^4+y+x^5;
F<y> := FunctionField(f);
F;

Output: Magma V2.10-6     Sat Jan  3 2004 07:00:55 on modular  [Seed = 3339605546]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y^4 + y + x^5

Total time: 3.019 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:01:39 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y^4+y+x^5;
F<y> := FunctionField(f);
F;
Genus(F);


Output: Magma V2.10-6     Sat Jan  3 2004 07:01:36 on modular  [Seed = 3794498264]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y^4 + y + x^5
6

Total time: 3.159 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:03:24 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y^4+y+x^5;
F<y> := FunctionField(f);
F;
Genus(F);
Decomposition(Oinf);


Output: Magma V2.10-6     Sat Jan  3 2004 07:03:21 on modular  [Seed = 466783115]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y^4 + y + x^5
6

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

Total time: 3.159 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:03:34 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y^4+y+x^5;
F<y> := FunctionField(f);
F;
Genus(F);
Decomposition(0inf);


Output: Magma V2.10-6     Sat Jan  3 2004 07:03:31 on modular  [Seed = 316375704]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y^4 + y + x^5
6

>> Decomposition(0inf);
                  ^
User error: bad syntax

Total time: 3.099 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:07:12 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y^4+y+x^5;
F<y> := FunctionField(f);
F;
Genus(F);


Output: Magma V2.10-6     Sat Jan  3 2004 07:07:08 on modular  [Seed = 13209461]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y^4 + y + x^5
6

Total time: 3.099 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:07:51 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y;
F<y> := FunctionField(f);
F;
Genus(F);


Output: Magma V2.10-6     Sat Jan  3 2004 07:07:47 on modular  [Seed = 1005761713]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y
0

Total time: 3.039 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:21:42 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y;
F<y> := FunctionField(f);
F;
Genus(F);
print(F);


Output: Magma V2.10-6     Sat Jan  3 2004 07:21:39 on modular  [Seed = 1485952146]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y
0
Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y

Total time: 3.039 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:23:04 2004

Input: K<k> := GF(2, 4);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y;
F<y> := FunctionField(f);
F;
Genus(F);
list(F);


Output: Magma V2.10-6     Sat Jan  3 2004 07:23:00 on modular  [Seed = 1385945455]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(2^4) by
y
0

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

Total time: 2.929 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:26:37 2004

Input: K<k> := GF(5);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y;
F<y> := FunctionField(f);
F;
Genus(F);
Basis(F);

Output: Magma V2.10-6     Sat Jan  3 2004 07:26:34 on modular  [Seed = 1082772387]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y
0
[
    1
]

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:26:51 2004

Input: K<k> := GF(5);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := x;
F<y> := FunctionField(f);
F;
Genus(F);
Basis(F);

Output: Magma V2.10-6     Sat Jan  3 2004 07:26:48 on modular  [Seed = 2058612843]
   -------------------------------------


>> F<y> := FunctionField(f);
                        ^
Runtime error in 'FunctionField': Bad argument types
Argument types given: FldFunRatUElt

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

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

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

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:27:01 2004

Input: K<k> := GF(5);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := y;
F<y> := FunctionField(f);
F;
Genus(F);
Basis(F);

Output: Magma V2.10-6     Sat Jan  3 2004 07:26:58 on modular  [Seed = 1975320446]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y
0
[
    1
]

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:28:02 2004

Input: K<k> := GF(5);
X<x> := FunctionField(K);
Y<y> := PolynomialRing(X);
f := x*y^2 - 1;
F<y> := FunctionField(f);
F;
Genus(F);
Basis(F);

Output: Magma V2.10-6     Sat Jan  3 2004 07:27:58 on modular  [Seed = 1822811707]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
x*y^2 + 4
0
[
    1,
    y
]

Total time: 3.309 seconds, Total memory usage: 6.52MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:30:18 2004

Input: > P<x,y,z> := ProjectiveSpace(Rationals(),2);
> C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3);
> F<a,b> := FunctionField(C);
> F;


Output: Magma V2.10-6     Sat Jan  3 2004 07:30:15 on modular  [Seed = 2622821970]
   -------------------------------------

Algebraic function field defined over Rational Field by
$.1^4 + 2*$.1*$.2^2 + 5*$.2

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:30:35 2004

Input: > P<x,y,z> := ProjectiveSpace(Rationals(),2);
> C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3);
> F<a,b> := FunctionField(C);
> F;
Basis(F);



Output: Magma V2.10-6     Sat Jan  3 2004 07:30:32 on modular  [Seed = 2539527526]
   -------------------------------------

Algebraic function field defined over Rational Field by
$.1^4 + 2*$.1*$.2^2 + 5*$.2

>> Basis(F);
        ^
Runtime error in 'Basis': Function field is not a finite extension

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:30:52 2004

Input: P<x,y,z> := ProjectiveSpace(Rationals(),2);
C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3);
F<a,b> := FunctionField(C);
F;
Basis(F);



Output: Magma V2.10-6     Sat Jan  3 2004 07:30:49 on modular  [Seed = 2387018862]
   -------------------------------------

Algebraic function field defined over Rational Field by
$.1^4 + 2*$.1*$.2^2 + 5*$.2

>> Basis(F);
        ^
Runtime error in 'Basis': Function field is not a finite extension

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:31:29 2004

Input: P<x,y,z> := ProjectiveSpace(Rationals(),2);
C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3);
F<a,b> := FunctionField(C);
F;
Genus(F);


Output: Magma V2.10-6     Sat Jan  3 2004 07:31:26 on modular  [Seed = 3111137470]
   -------------------------------------

Algebraic function field defined over Rational Field by
$.1^4 + 2*$.1*$.2^2 + 5*$.2
2

Total time: 3.089 seconds, Total memory usage: 1.99MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Sat Jan  3 07:32:05 2004

Input: P<x,y,z> := ProjectiveSpace(Rationals(),2);
C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3);
F<a,b> := FunctionField(C);
F;
Genus(F);
Basis(C);


Output: Magma V2.10-6     Sat Jan  3 2004 07:32:02 on modular  [Seed = 3011132136]
   -------------------------------------

Algebraic function field defined over Rational Field by
$.1^4 + 2*$.1*$.2^2 + 5*$.2
2

>> Basis(C);
        ^
Runtime error in 'Basis': Bad argument types
Argument types given: Crv

Total time: 2.969 seconds, Total memory usage: 1.99MB


************** MAGMA *****************
Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94)
Time: Sat Jan  3 08:18:59 2004

Input: 2 + 3

Output: Magma V2.10-6     Sat Jan  3 2004 08:18:56 on modular  [Seed = 80607836]
   -------------------------------------

5

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94)
Time: Sat Jan  3 08:19:21 2004

Input: 2 + 3

Output: Magma V2.10-6     Sat Jan  3 2004 08:19:18 on modular  [Seed = 922732664]
   -------------------------------------

5

Total time: 2.980 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host px3so.cg.shawcable.net. (24.71.223.142)
Time: Sat Jan  3 21:24:18 2004

Input: pi^3;

Output: Magma V2.10-6     Sat Jan  3 2004 21:24:15 on modular  [Seed = 1133184263]
   -------------------------------------


>> pi^3;;
   ^
User error: Identifier 'pi' has not been declared or assigned

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host px3so.cg.shawcable.net. (24.71.223.142)
Time: Sat Jan  3 21:24:32 2004

Input: p^3;

Output: Magma V2.10-6     Sat Jan  3 2004 21:24:29 on modular  [Seed = 1519524876]
   -------------------------------------


>> p^3;;
   ^
User error: Identifier 'p' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 202-63-173-18.exatt.com. (202.63.173.18)
Time: Sun Jan  4 02:02:56 2004

Input: 1234

Output: Magma V2.10-6     Sun Jan  4 2004 02:02:53 on modular  [Seed = 1873275642]
   -------------------------------------

1234

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 202-63-173-18.exatt.com. (202.63.173.18)
Time: Sun Jan  4 02:03:32 2004

Input: 1234+120

Output: Magma V2.10-6     Sun Jan  4 2004 02:03:29 on modular  [Seed = 2024865201]
   -------------------------------------

1354

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host dialup-67.72.215.69.Dial1.Detroit1.Level3.net. (67.72.215.69)
Time: Sun Jan  4 03:55:34 2004

Input: 10!

Output: Magma V2.10-6     Sun Jan  4 2004 03:55:31 on modular  [Seed = 3609148883]
   -------------------------------------


>> 10!;
      ^
User error: bad syntax

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ar10-1i.dial-up.arnes.si. (194.249.4.65)
Time: Sun Jan  4 07:50:38 2004

Input: N:=439; q:=2; n:=Factorization(N);
A:=SortDecomposition(NewformDecomposition
(NewSubspace(CuspidalSubspace
(ModularSymbols(N,2,+1))))); for i in [1..#A] do
cg:=[]; cgo:=[]; tam:=[]; mde:=[];
Include(~cg,[N,i,1]);
for j in [1..#n] do
cgo[j]:=ComponentGroupOrder(A[i],n[j][1]);
tam[j]:=TamagawaNumber(A[i],n[j][1]);
mde[j]:=cgo[j]/tam[j];
if Dimension(A[i]) eq 1 then
cm:=GCD(tam[j],
Order(TorsionSubgroup(EllipticCurve(A[i]))) );
mde[j]:= Numerator(cgo[j]/cm); end if;
if Dimension(A[i]) ge 2 then
s:=Factorization(Numerator(Evaluate
(CharacteristicPolynomial(
DualHeckeOperator(A[i],q)),q+1)));
fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for;
cm:=GCD(tam[j],fs);
mde[j]:= Numerator(cgo[j]/cm); end if;
Include(~cg,[n[j][1],tam[j],mde[j]]); end for;
for k in [1..#cg] do printf "%o",cg[k]; end for;
print []; end for;

Output: Magma V2.10-6     Sun Jan  4 2004 07:50:33 on modular  [Seed = 1957906209]
   -------------------------------------

[ 439, 1, 1 ][]
[ 439, 2, 1 ][ 439, 1, 1 ][]
[ 439, 3, 1 ][ 439, 73, 1 ][]

Total time: 4.409 seconds, Total memory usage: 5.56MB


************** MAGMA *****************
Host ar10-1i.dial-up.arnes.si. (194.249.4.65)
Time: Sun Jan  4 07:51:44 2004

Input: N:=1001; q:=2; n:=Factorization(N);
A:=SortDecomposition(NewformDecomposition
(NewSubspace(CuspidalSubspace
(ModularSymbols(N,2,+1))))); for i in [1..#A] do
cg:=[]; cgo:=[]; tam:=[]; mde:=[];
Include(~cg,[N,i,1]);
for j in [1..#n] do
cgo[j]:=ComponentGroupOrder(A[i],n[j][1]);
tam[j]:=TamagawaNumber(A[i],n[j][1]);
mde[j]:=cgo[j]/tam[j];
if Dimension(A[i]) eq 1 then
cm:=GCD(tam[j],
Order(TorsionSubgroup(EllipticCurve(A[i]))) );
mde[j]:= Numerator(cgo[j]/cm); end if;
if Dimension(A[i]) ge 2 then
s:=Factorization(Numerator(Evaluate
(CharacteristicPolynomial(
DualHeckeOperator(A[i],q)),q+1)));
fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for;
cm:=GCD(tam[j],fs);
mde[j]:= Numerator(cgo[j]/cm); end if;
Include(~cg,[n[j][1],tam[j],mde[j]]); end for;
for k in [1..#cg] do printf "%o",cg[k]; end for;
print []; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Sun Jan  4 2004 07:51:21 on modular  [Seed = 231357960]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29505 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host ar10-1i.dial-up.arnes.si. (194.249.4.65)
Time: Sun Jan  4 07:52:14 2004

Input: N:=823; q:=2; n:=Factorization(N);
A:=SortDecomposition(NewformDecomposition
(NewSubspace(CuspidalSubspace
(ModularSymbols(N,2,+1))))); for i in [1..#A] do
cg:=[]; cgo:=[]; tam:=[]; mde:=[];
Include(~cg,[N,i,1]);
for j in [1..#n] do
cgo[j]:=ComponentGroupOrder(A[i],n[j][1]);
tam[j]:=TamagawaNumber(A[i],n[j][1]);
mde[j]:=cgo[j]/tam[j];
if Dimension(A[i]) eq 1 then
cm:=GCD(tam[j],
Order(TorsionSubgroup(EllipticCurve(A[i]))) );
mde[j]:= Numerator(cgo[j]/cm); end if;
if Dimension(A[i]) ge 2 then
s:=Factorization(Numerator(Evaluate
(CharacteristicPolynomial(
DualHeckeOperator(A[i],q)),q+1)));
fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for;
cm:=GCD(tam[j],fs);
mde[j]:= Numerator(cgo[j]/cm); end if;
Include(~cg,[n[j][1],tam[j],mde[j]]); end for;
for k in [1..#cg] do printf "%o",cg[k]; end for;
print []; end for;

Output: Magma V2.10-6     Sun Jan  4 2004 07:52:06 on modular  [Seed = 113325372]
   -------------------------------------

[ 823, 1, 1 ][]
[ 823, 2, 1 ][ 823, 137, 1 ][]

Total time: 7.729 seconds, Total memory usage: 12.31MB


************** MAGMA *****************
Host ar10-1i.dial-up.arnes.si. (194.249.4.65)
Time: Sun Jan  4 07:52:56 2004

Input: N:=2000; q:=2; n:=Factorization(N);
A:=SortDecomposition(NewformDecomposition
(NewSubspace(CuspidalSubspace
(ModularSymbols(N,2,+1))))); for i in [1..#A] do
cg:=[]; cgo:=[]; tam:=[]; mde:=[];
Include(~cg,[N,i,1]);
for j in [1..#n] do
cgo[j]:=ComponentGroupOrder(A[i],n[j][1]);
tam[j]:=TamagawaNumber(A[i],n[j][1]);
mde[j]:=cgo[j]/tam[j];
if Dimension(A[i]) eq 1 then
cm:=GCD(tam[j],
Order(TorsionSubgroup(EllipticCurve(A[i]))) );
mde[j]:= Numerator(cgo[j]/cm); end if;
if Dimension(A[i]) ge 2 then
s:=Factorization(Numerator(Evaluate
(CharacteristicPolynomial(
DualHeckeOperator(A[i],q)),q+1)));
fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for;
cm:=GCD(tam[j],fs);
mde[j]:= Numerator(cgo[j]/cm); end if;
Include(~cg,[n[j][1],tam[j],mde[j]]); end for;
for k in [1..#cg] do printf "%o",cg[k]; end for;
print []; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Sun Jan  4 2004 07:52:33 on modular  [Seed = 417278917]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 29524 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host ar10-1i.dial-up.arnes.si. (194.249.4.65)
Time: Sun Jan  4 07:53:29 2004

Input: N:=456; q:=2; n:=Factorization(N);
A:=SortDecomposition(NewformDecomposition
(NewSubspace(CuspidalSubspace
(ModularSymbols(N,2,+1))))); for i in [1..#A] do
cg:=[]; cgo:=[]; tam:=[]; mde:=[];
Include(~cg,[N,i,1]);
for j in [1..#n] do
cgo[j]:=ComponentGroupOrder(A[i],n[j][1]);
tam[j]:=TamagawaNumber(A[i],n[j][1]);
mde[j]:=cgo[j]/tam[j];
if Dimension(A[i]) eq 1 then
cm:=GCD(tam[j],
Order(TorsionSubgroup(EllipticCurve(A[i]))) );
mde[j]:= Numerator(cgo[j]/cm); end if;
if Dimension(A[i]) ge 2 then
s:=Factorization(Numerator(Evaluate
(CharacteristicPolynomial(
DualHeckeOperator(A[i],q)),q+1)));
fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for;
cm:=GCD(tam[j],fs);
mde[j]:= Numerator(cgo[j]/cm); end if;
Include(~cg,[n[j][1],tam[j],mde[j]]); end for;
for k in [1..#cg] do printf "%o",cg[k]; end for;
print []; end for;

Output: Magma V2.10-6     Sun Jan  4 2004 07:53:19 on modular  [Seed = 299246306]
   -------------------------------------

Do not know how to compute component group at  2

Total time: 9.979 seconds, Total memory usage: 4.86MB


************** MAGMA *****************
Host ar10-1i.dial-up.arnes.si. (194.249.4.65)
Time: Sun Jan  4 08:03:42 2004

Input: N:=688; q:=2; n:=Factorization(N);
A:=SortDecomposition(NewformDecomposition
(NewSubspace(CuspidalSubspace
(ModularSymbols(N,2,+1))))); for i in [1..#A] do
cg:=[]; cgo:=[]; tam:=[]; mde:=[];
Include(~cg,[N,i,1]);
for j in [1..#n] do
cgo[j]:=ComponentGroupOrder(A[i],n[j][1]);
tam[j]:=TamagawaNumber(A[i],n[j][1]);
mde[j]:=cgo[j]/tam[j];
if Dimension(A[i]) eq 1 then
cm:=GCD(tam[j],
Order(TorsionSubgroup(EllipticCurve(A[i]))) );
mde[j]:= Numerator(cgo[j]/cm); end if;
if Dimension(A[i]) ge 2 then
s:=Factorization(Numerator(Evaluate
(CharacteristicPolynomial(
DualHeckeOperator(A[i],q)),q+1)));
fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for;
cm:=GCD(tam[j],fs);
mde[j]:= Numerator(cgo[j]/cm); end if;
Include(~cg,[n[j][1],tam[j],mde[j]]); end for;
for k in [1..#cg] do printf "%o",cg[k]; end for;
print []; end for;

Output: Magma V2.10-6     Sun Jan  4 2004 08:03:33 on modular  [Seed = 3406625698]
   -------------------------------------

Do not know how to compute component group at  2

Total time: 8.789 seconds, Total memory usage: 4.85MB


************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Jan  4 17:13:28 2004

Input: R<x>:=PolynomialRing(IntegerRing());
CP:=CharacteristicPolynomial; DH:=DualHeckeOperator;
for N in [11..11] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3)); C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; 

for N in [560..560] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [7..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3)); C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; 


Output: Magma V2.10-6     Sun Jan  4 2004 17:13:16 on modular  [Seed = 3221713016]
   -------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
560,7,2,x^2,3,x^2 - x - 8,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 7*x + 
4,13,x^2 - 3*x - 6[]
560,8,2,x^2,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - x - 4,13,x^2 
- x - 38[]
560,9,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 
- 5*x + 2[]

Total time: 11.380 seconds, Total memory usage: 5.45MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Mon Jan  5 05:22:34 2004

Input: > D:=2*P1[2]+2*P1[3];
> D0:=Div!D;
> D0;
Divisor on Curve over GF(5) defined by
x^3*y + x + y^3
> RiemannRochSpace(D0);
KModule of dimension 2 over GF(5)
Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field
defined over GF(5) by
x^3*y + x + y^3
> B0:=Basis(D0);
> B0;
[ 1, 1/$.2 ]
> D:=2*P1[4]+2*P1[5];
> D0:=Div!D;
> D0;
Divisor on Curve over GF(5) defined by
x^3*y + x + y^3
> RiemannRochSpace(D0);
KModule of dimension 2 over GF(5)
Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field
defined over GF(5) by
x^3*y + x + y^3
> B0:=Basis(D0);
> B0;
[ $.2/($.2 + 3), 1/($.2 + 3) ]


Output: Magma V2.10-6     Mon Jan  5 2004 05:22:31 on modular  [Seed = 2724505461]
   -------------------------------------


>>   D:=2*P1[2]+2*P1[3];
          ^
User error: Identifier 'P1' has not been declared or assigned

>>   D0:=Div!D;
         ^
User error: Identifier 'Div' has not been declared or assigned

>>   D0;
     ^
User error: Identifier 'D0' has not been declared or assigned

>> Divisor on Curve over GF(5) defined by
           ^
User error: bad syntax

>>   RiemannRochSpace(D0);
     ^
User error: bad syntax

>> KModule of dimension 2 over GF(5)
           ^
User error: bad syntax

>> Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field
           ^
User error: bad syntax

>> defined over GF(5) by
           ^
User error: bad syntax

>>   B0:=Basis(D0);
     ^
User error: bad syntax

>>   B0;
     ^
User error: Identifier 'B0' has not been declared or assigned

>>   D:=2*P1[4]+2*P1[5];
     ^
User error: bad syntax

>>   D0:=Div!D;
         ^
User error: Identifier 'Div' has not been declared or assigned

>>   D0;
     ^
User error: Identifier 'D0' has not been declared or assigned

>> Divisor on Curve over GF(5) defined by
           ^
User error: bad syntax

>>   RiemannRochSpace(D0);
     ^
User error: bad syntax

>> KModule of dimension 2 over GF(5)
           ^
User error: bad syntax

>> Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field
           ^
User error: bad syntax

>> defined over GF(5) by
           ^
User error: bad syntax

>>   B0:=Basis(D0);
     ^
User error: bad syntax

>>   B0;
     ^
User error: Identifier 'B0' has not been declared or assigned

>> [ $.2/($.2 + 3), 1/($.2 + 3) ]
     ^
Runtime error: Bad dollar structure

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Mon Jan  5 05:58:32 2004

Input: > A<x,y> := AffineSpace(FiniteField(5),2);
> f:=x^3*y+y^3+x;
> C:=Curve(A,f);
> C;
Curve over GF(5) defined by
x^3*y + x + y^3
> D<X,Y,Z> := ProjectiveClosure(C);
>
> D;
Curve over GF(5) defined by
X^3*Y + X*Z^3 + Y^3*Z



Output: Magma V2.10-6     Mon Jan  5 2004 05:58:29 on modular  [Seed = 3777469828]
   -------------------------------------

Curve over GF(5) defined by
x^3*y + x + y^3

>> Curve over GF(5) defined by
         ^
User error: bad syntax

>>   D<X,Y,Z> := ProjectiveClosure(C);
     ^
User error: bad syntax

>> >
   ^
User error: bad syntax

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

>> Curve over GF(5) defined by
         ^
User error: bad syntax

>> X^3*Y + X*Z^3 + Y^3*Z
   ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.879 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Mon Jan  5 05:58:51 2004

Input: A<x,y> := AffineSpace(FiniteField(5),2);
f:=x^3*y+y^3+x;
C:=Curve(A,f);
C;
Curve over GF(5) defined by
x^3*y + x + y^3
D<X,Y,Z> := ProjectiveClosure(C);
D;
Curve over GF(5) defined by
X^3*Y + X*Z^3 + Y^3*Z



Output: Magma V2.10-6     Mon Jan  5 2004 05:58:48 on modular  [Seed = 3945633715]
   -------------------------------------

Curve over GF(5) defined by
x^3*y + x + y^3

>> Curve over GF(5) defined by
         ^
User error: bad syntax

>> D<X,Y,Z> := ProjectiveClosure(C);
   ^
User error: bad syntax

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

>> Curve over GF(5) defined by
         ^
User error: bad syntax

>> X^3*Y + X*Z^3 + Y^3*Z
   ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Mon Jan  5 05:59:22 2004

Input: A<x,y> := AffineSpace(FiniteField(5),2);
f:=x^3*y+y^3+x;
C:=Curve(A,f);
C;

x^3*y + x + y^3
D<X,Y,Z> := ProjectiveClosure(C);
D;
Curve over GF(5) defined by
X^3*Y + X*Z^3 + Y^3*Z



Output: Magma V2.10-6     Mon Jan  5 2004 05:59:19 on modular  [Seed = 3557992547]
   -------------------------------------

Curve over GF(5) defined by
x^3*y + x + y^3

>> D<X,Y,Z> := ProjectiveClosure(C);
   ^
User error: bad syntax

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

>> Curve over GF(5) defined by
         ^
User error: bad syntax

>> X^3*Y + X*Z^3 + Y^3*Z
   ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host R1.softjoys.com. (212.113.101.45)
Time: Mon Jan  5 07:50:02 2004

Input: A<x,y> := AffineSpace(FiniteField(5),2);
f:=x^3*y+y^3+x;
C:=Curve(A,f);
C;



Output: Magma V2.10-6     Mon Jan  5 2004 07:49:57 on modular  [Seed = 2488465102]
   -------------------------------------

Curve over GF(5) defined by
x^3*y + x + y^3

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host reached (144.122.136.201)
Time: Mon Jan  5 10:06:28 2004

Input: 2^32;


Output: Magma V2.10-6     Mon Jan  5 2004 10:06:11 on modular  [Seed = 282481246]
   -------------------------------------

4294967296

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host m201.math.metu.edu.tr. (144.122.136.201)
Time: Mon Jan  5 10:07:03 2004

Input: 2^24;


Output: Magma V2.10-6     Mon Jan  5 2004 10:06:59 on modular  [Seed = 1806510549]
   -------------------------------------

16777216

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host m201.math.metu.edu.tr. (144.122.136.201)
Time: Mon Jan  5 10:08:27 2004

Input: 2^32;


Output: Magma V2.10-6     Mon Jan  5 2004 10:08:24 on modular  [Seed = 2109423544]
   -------------------------------------

4294967296

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host m201.math.metu.edu.tr. (144.122.136.201)
Time: Mon Jan  5 10:08:57 2004

Input: 2^32;



Output: Magma V2.10-6     Mon Jan  5 2004 10:08:54 on modular  [Seed = 2008102492]
   -------------------------------------

4294967296

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (199.111.119.60)
Time: Mon Jan  5 12:04:52 2004

Input: EllipticCurve[1,2,3,1,1];

Output: Magma V2.10-6     Mon Jan  5 2004 12:04:48 on modular  [Seed = 517519365]
   -------------------------------------


>> EllipticCurve[1,2,3,1,1];;
                ^
Runtime error in '[]': Bad argument types

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (199.111.119.60)
Time: Mon Jan  5 12:06:26 2004

Input: EllipticCurve(1,2,3,1,1);

Output: Magma V2.10-6     Mon Jan  5 2004 12:06:23 on modular  [Seed = 1773129677]
   -------------------------------------


>> EllipticCurve(1,2,3,1,1);;
                ^
Runtime error in 'EllipticCurve': Bad argument types
Argument types given: RngIntElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ip-64-139-40-66.dsl.sjc.megapath.net. (64.139.40.66)
Time: Mon Jan  5 13:39:15 2004

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

Output: Magma V2.10-6     Mon Jan  5 2004 13:39:12 on modular  [Seed = 1839987991]
   -------------------------------------

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

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (213.40.3.65)
Time: Mon Jan  5 14:12:09 2004

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

Output: Magma V2.10-6     Mon Jan  5 2004 14:12:05 on modular  [Seed = 3777456590]
   -------------------------------------

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

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host aybabtu.matrox.com. (138.11.254.204)
Time: Tue Jan  6 10:24:15 2004

Input: f(x) = x^2
f(2)


Output: Magma V2.10-6     Tue Jan  6 2004 10:24:12 on modular  [Seed = 1839759735]
   -------------------------------------


>> f(2)
   ^
User error: bad syntax

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:06:35 2004

Input: e=EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000]);
Rank(e)


Output: Magma V2.10-6     Tue Jan  6 2004 17:06:32 on modular  [Seed = 1924562022]
   -------------------------------------


>> e=EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729
   ^
User error: Identifier 'e' has not been declared or assigned

>> Rank(e)
        ^
User error: Identifier 'e' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:07:06 2004

Input: Rank(EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:07:02 on modular  [Seed = 1806656913]
   -------------------------------------

Warning: rank computed (0) is only a  lower bound
(It may still be correct, though)
Warning: rank computed (0) is only a  lower bound
(It may still be correct, though)
0

Total time: 3.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:07:45 2004

Input: MordellWeilRank(EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:07:41 on modular  [Seed = 1553486477]
   -------------------------------------

Warning: rank computed (0) is only a  lower bound
(It may still be correct, though)
Warning: rank computed (0) is only a  lower bound
(It may still be correct, though)
0

Total time: 3.529 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:08:09 2004

Input: MordellWeilRankBounds(EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:08:06 on modular  [Seed = 1452431596]
   -------------------------------------

0 3

Total time: 3.599 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:08:54 2004

Input: MordellWeilRankBounds(EllipticCurve([0,0,0,-82,0]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:08:51 on modular  [Seed = 1334526400]
   -------------------------------------

3 3

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:09:38 2004

Input: MordellWeilRankBounds(EllipticCurve([0,-1,0,-24649,1355209]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:09:35 on modular  [Seed = 1022898527]
   -------------------------------------

4 4

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:10:40 2004

Input: MordellWeilRankBounds(EllipticCurve([0,0,1,-6349808647,193146346911036 ]))


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan  6 2004 17:10:17 on modular  [Seed = 753410329]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 17232 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:11:56 2004

Input: MordellWeilRankBounds(EllipticCurve([1,-1,1,-1608154463,25555312501831]))


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan  6 2004 17:11:33 on modular  [Seed = 635513036]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 17241 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:12:48 2004

Input: MordellWeilRankBounds(EllipticCurve([0,-1,0,-1485019900716,658252007072023716]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:12:35 on modular  [Seed = 517608369]
   -------------------------------------

7 9

Total time: 12.429 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:13:48 2004

Input: MordellWeilRankBounds(EllipticCurve([1,0,0,-2060795223235870670,1037860392073475481628988676]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:13:43 on modular  [Seed = 4265276053]
   -------------------------------------

10 10

Total time: 4.189 seconds, Total memory usage: 3.00MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:14:48 2004

Input: MordellWeilRankBounds(EllipticCurve([1,0,1,34318214642441646362435632562579908747,3184376895814127197244886284686214848599453811643486936756]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:14:34 on modular  [Seed = 4046847431]
   -------------------------------------

12 15

Total time: 14.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:16:01 2004

Input: MordellWeilGroup(EllipticCurve([0,0,1,-6349808647,193146346911036 ]))


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan  6 2004 17:15:37 on modular  [Seed = 3574716704]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 17321 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:16:29 2004

Input: MordellWeilRankBound(EllipticCurve([0,0,0,0,708291392738196762720225 ]))


Output: Magma V2.10-6     Tue Jan  6 2004 17:16:25 on modular  [Seed = 3322071555]
   -------------------------------------


>> MordellWeilRankBound(EllipticCurve([0,0,0,0,708291392738196762720225 ]))
   ^
User error: Identifier 'MordellWeilRankBound' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:17:12 2004

Input: MordellWeilRankBounds(EllipticCurve([0,0,0,0,708291392738196762720225 ]))


Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-6     Tue Jan  6 2004 17:17:00 on modular  [Seed = 3212555039]
   -------------------------------------


Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB

Errors: Magma: Fatal Error: not enough memory to even recover


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:18:40 2004

Input: MordellWeilRankBounds(ElliticCurve([0,0,0,0,708291392738196762720225]))

Output: Magma V2.10-6     Tue Jan  6 2004 17:18:37 on modular  [Seed = 2977282800]
   -------------------------------------


>> MordellWeilRankBounds(ElliticCurve([0,0,0,0,708291392738196762720225]));
                         ^
User error: Identifier 'ElliticCurve' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:18:56 2004

Input: MordellWeilRankBounds(EllipticCurve([0,0,0,0,708291392738196762720225]))

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-6     Tue Jan  6 2004 17:18:46 on modular  [Seed = 2842534547]
   -------------------------------------


Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Current total memory usage: 95.4MB, failed memory request: 0.0MB
System Error: User memory limit has been reached

Total time: 10.299 seconds, Total memory usage: 100.00MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:20:43 2004

Input: MordellWeilRankBounds(EllipticCurve([0,0,0,0,7]))

Output: Magma V2.10-6     Tue Jan  6 2004 17:20:39 on modular  [Seed = 2286715715]
   -------------------------------------

0 0

Total time: 2.969 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host ad14-m35.net.hinet.hr. (195.29.49.35)
Time: Tue Jan  6 17:21:20 2004

Input: MordellWeilGroup(EllipticCurve([0,0,0,-36,0]))

Output: Magma V2.10-6     Tue Jan  6 2004 17:21:16 on modular  [Seed = 2126149081]
   -------------------------------------

Abelian Group isomorphic to Z/2 + Z/2 + Z
Defined on 3 generators
Relations:
    2*$.1 = 0
    2*$.2 = 0

Total time: 3.099 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host business.mysantanarow.com. (65.122.201.5)
Time: Tue Jan  6 22:20:28 2004

Input: hello

Output: Magma V2.10-6     Tue Jan  6 2004 22:20:25 on modular  [Seed = 4063672189]
   -------------------------------------


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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host mcmail.muzo.com. (194.228.69.30)
Time: Wed Jan  7 04:28:09 2004

Input: 321654*54654


Output: Magma V2.10-6     Wed Jan  7 2004 04:28:05 on modular  [Seed = 2218814157]
   -------------------------------------

17579677716

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host host194-236.pool80207.interbusiness.it. (80.207.236.194)
Time: Wed Jan  7 06:12:13 2004

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

Output: Magma V2.10-6     Wed Jan  7 2004 06:12:09 on modular  [Seed = 3743091005]
   -------------------------------------

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

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host host194-236.pool80207.interbusiness.it. (80.207.236.194)
Time: Wed Jan  7 06:12:30 2004

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

Output: Magma V2.10-6     Wed Jan  7 2004 06:12:27 on modular  [Seed = 2909371229]
   -------------------------------------

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

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (144.122.136.202)
Time: Wed Jan  7 06:35:11 2004

Input: a:=4;
a*5;


Output: Magma V2.10-6     Wed Jan  7 2004 06:35:00 on modular  [Seed = 1638248687]
   -------------------------------------

20

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (68.222.35.14)
Time: Wed Jan  7 06:38:30 2004

Input: (x/y+y/x)^3*(x/y-y/x)^3

Output: Magma V2.10-6     Wed Jan  7 2004 06:38:27 on modular  [Seed = 1587187335]
   -------------------------------------


>> (x/y+y/x)^3*(x/y-y/x)^3;
    ^
User error: Identifier 'x' has not been declared or assigned

Total time: 3.179 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:13:03 2004

Input: [ x^2 : x in [1..5] ];
 

Output: Magma V2.10-6     Wed Jan  7 2004 11:13:00 on modular  [Seed = 3212619995]
   -------------------------------------

[ 1, 4, 9, 16, 25 ]

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:13:22 2004

Input: Maximum ([ x^2 : x in [1..5] ]);
 

Output: Magma V2.10-6     Wed Jan  7 2004 11:13:18 on modular  [Seed = 2354021370]
   -------------------------------------

25 5

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:18:10 2004

Input: F2 := FiniteField (2, 10);


Output: Magma V2.10-6     Wed Jan  7 2004 11:18:07 on modular  [Seed = 2656932041]
   -------------------------------------


Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:19:19 2004

Input: F2[i] := FiniteField (2, 10);
#F2;
E := EllipticCurve(F, 1, 1, 1, 1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:19:16 on modular  [Seed = 1638035330]
   -------------------------------------


>> F2[i] := FiniteField (2, 10);
     ^
User error: Identifier 'F2' has not been declared or assigned

>> #F2;
    ^
User error: Identifier 'F2' has not been declared or assigned

>> E := EllipticCurve(F, 1, 1, 1, 1);
                      ^
User error: Identifier 'F' has not been declared or assigned

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:19:45 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
E := EllipticCurve(F, 1, 1, 1, 1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:19:42 on modular  [Seed = 1958181517]
   -------------------------------------

1024

>> E := EllipticCurve(F, 1, 1, 1, 1);
                      ^
User error: Identifier 'F' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:20:05 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
EllipticCurve;
E := EllipticCurve(F2, 1, 1, 1, 1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:20:02 on modular  [Seed = 1317879963]
   -------------------------------------

1024
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S must be of length
        2 or 5.

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

        The J-th elliptic curve in the I-th isogeny class of conductor N found 
        in the elliptic curve database D.

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic 
        curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. "A") in the 
        elliptic curve database D.

    (<RngUPolElt> f, <RngUPolElt> h) -> CrvEll

        Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must 
        be of degree at most 1 and f must be monic of degree 3.

    (<RngUPolElt> f) -> CrvEll

        Creates the elliptic curve defined by y^2 = f(x), where f must be monic 
        of degree 3.

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j. This version is deprecated
        and will be removed in a future release -- use 
        EllipticCurveFromjInvariant() instead.

    (<Crv> C) -> CrvEll, Map

        Returns an elliptic curve from certain genus 1 curves with an easily 
        recognised rational point.

    (<Crv> C, <Pt> Point) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a point and also the
        map from C to that model. The point should be nonsingular.

    (<Crv> C, <PlcCrvElt> Place) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a degree 1 place and
        also the map from C to that model.

    (<ModFrmElt> f) -> CrvEll

        An elliptic curve with associated modular form f.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in the isogeny 
        class of elliptic curves associated to M.



>> E := EllipticCurve(F2, 1, 1, 1, 1);
                     ^
Runtime error in 'EllipticCurve': Bad argument types
Argument types given: FldFin, RngIntElt, RngIntElt, RngIntElt, RngIntElt

Total time: 2.989 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:22:27 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
EllipticCurve;
// E := EllipticCurve(i, );


Output: Magma V2.10-6     Wed Jan  7 2004 11:22:24 on modular  [Seed = 1368546422]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S must be of length
        2 or 5.

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

        The J-th elliptic curve in the I-th isogeny class of conductor N found 
        in the elliptic curve database D.

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic 
        curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. "A") in the 
        elliptic curve database D.

    (<RngUPolElt> f, <RngUPolElt> h) -> CrvEll

        Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must 
        be of degree at most 1 and f must be monic of degree 3.

    (<RngUPolElt> f) -> CrvEll

        Creates the elliptic curve defined by y^2 = f(x), where f must be monic 
        of degree 3.

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j. This version is deprecated
        and will be removed in a future release -- use 
        EllipticCurveFromjInvariant() instead.

    (<Crv> C) -> CrvEll, Map

        Returns an elliptic curve from certain genus 1 curves with an easily 
        recognised rational point.

    (<Crv> C, <Pt> Point) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a point and also the
        map from C to that model. The point should be nonsingular.

    (<Crv> C, <PlcCrvElt> Place) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a degree 1 place and
        also the map from C to that model.

    (<ModFrmElt> f) -> CrvEll

        An elliptic curve with associated modular form f.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in the isogeny 
        class of elliptic curves associated to M.



Total time: 3.009 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:23:01 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
EllipticCurve;
E := EllipticCurve(i, x^3+x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:22:58 on modular  [Seed = 619129121]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S must be of length
        2 or 5.

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

        The J-th elliptic curve in the I-th isogeny class of conductor N found 
        in the elliptic curve database D.

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic 
        curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. "A") in the 
        elliptic curve database D.

    (<RngUPolElt> f, <RngUPolElt> h) -> CrvEll

        Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must 
        be of degree at most 1 and f must be monic of degree 3.

    (<RngUPolElt> f) -> CrvEll

        Creates the elliptic curve defined by y^2 = f(x), where f must be monic 
        of degree 3.

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j. This version is deprecated
        and will be removed in a future release -- use 
        EllipticCurveFromjInvariant() instead.

    (<Crv> C) -> CrvEll, Map

        Returns an elliptic curve from certain genus 1 curves with an easily 
        recognised rational point.

    (<Crv> C, <Pt> Point) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a point and also the
        map from C to that model. The point should be nonsingular.

    (<Crv> C, <PlcCrvElt> Place) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a degree 1 place and
        also the map from C to that model.

    (<ModFrmElt> f) -> CrvEll

        An elliptic curve with associated modular form f.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in the isogeny 
        class of elliptic curves associated to M.



>> E := EllipticCurve(i, x^3+x+1);
                     ^
Runtime error in 'EllipticCurve': Bad argument types
Argument types given: FldFinElt, RngUPolElt

Total time: 2.949 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:24:09 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
F2X;
EllipticCurve;
// E := EllipticCurve(i, x^3+x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:24:06 on modular  [Seed = 922041335]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
Univariate Polynomial Ring in x over GF(2^10)
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S must be of length
        2 or 5.

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

        The J-th elliptic curve in the I-th isogeny class of conductor N found 
        in the elliptic curve database D.

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic 
        curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. "A") in the 
        elliptic curve database D.

    (<RngUPolElt> f, <RngUPolElt> h) -> CrvEll

        Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must 
        be of degree at most 1 and f must be monic of degree 3.

    (<RngUPolElt> f) -> CrvEll

        Creates the elliptic curve defined by y^2 = f(x), where f must be monic 
        of degree 3.

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j. This version is deprecated
        and will be removed in a future release -- use 
        EllipticCurveFromjInvariant() instead.

    (<Crv> C) -> CrvEll, Map

        Returns an elliptic curve from certain genus 1 curves with an easily 
        recognised rational point.

    (<Crv> C, <Pt> Point) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a point and also the
        map from C to that model. The point should be nonsingular.

    (<Crv> C, <PlcCrvElt> Place) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a degree 1 place and
        also the map from C to that model.

    (<ModFrmElt> f) -> CrvEll

        An elliptic curve with associated modular form f.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in the isogeny 
        class of elliptic curves associated to M.



Total time: 2.959 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:25:31 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
// F2X;
// EllipticCurve;
E := EllipticCurve(x, x^3+x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:25:28 on modular  [Seed = 96864410]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3

>> E := EllipticCurve(x, x^3+x+1);
                     ^
Runtime error in 'EllipticCurve': h polynomial must have degree at most 1

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:26:02 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
// F2X;
// EllipticCurve;
Degree (x+1);
E := EllipticCurve(x+1, x^3+x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:25:59 on modular  [Seed = 147522680]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
1

>> E := EllipticCurve(x+1, x^3+x+1);
                     ^
Runtime error in 'EllipticCurve': h polynomial must have degree at most 1

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:26:26 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
// F2X;
// EllipticCurve;
Degree (x+1);
E := EllipticCurve(x^2+1, x^3+x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:26:22 on modular  [Seed = 467146578]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
1

>> E := EllipticCurve(x^2+1, x^3+x+1);
                     ^
Runtime error in 'EllipticCurve': h polynomial must have degree at most 1

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:26:43 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
// F2X;
EllipticCurve;
Degree (x+1);
E := EllipticCurve(x^2+1, x^3+x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:26:40 on modular  [Seed = 3995984585]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S must be of length
        2 or 5.

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

        The J-th elliptic curve in the I-th isogeny class of conductor N found 
        in the elliptic curve database D.

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic 
        curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. "A") in the 
        elliptic curve database D.

    (<RngUPolElt> f, <RngUPolElt> h) -> CrvEll

        Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must 
        be of degree at most 1 and f must be monic of degree 3.

    (<RngUPolElt> f) -> CrvEll

        Creates the elliptic curve defined by y^2 = f(x), where f must be monic 
        of degree 3.

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j. This version is deprecated
        and will be removed in a future release -- use 
        EllipticCurveFromjInvariant() instead.

    (<Crv> C) -> CrvEll, Map

        Returns an elliptic curve from certain genus 1 curves with an easily 
        recognised rational point.

    (<Crv> C, <Pt> Point) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a point and also the
        map from C to that model. The point should be nonsingular.

    (<Crv> C, <PlcCrvElt> Place) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a degree 1 place and
        also the map from C to that model.

    (<ModFrmElt> f) -> CrvEll

        An elliptic curve with associated modular form f.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in the isogeny 
        class of elliptic curves associated to M.


1

>> E := EllipticCurve(x^2+1, x^3+x+1);
                     ^
Runtime error in 'EllipticCurve': h polynomial must have degree at most 1

Total time: 2.999 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:27:24 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
// F2X;
EllipticCurve;
Degree (x+1);
E := EllipticCurve(x^3+x+1, x+1);


Output: Magma V2.10-6     Wed Jan  7 2004 11:27:21 on modular  [Seed = 4046650879]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S must be of length
        2 or 5.

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

        The J-th elliptic curve in the I-th isogeny class of conductor N found 
        in the elliptic curve database D.

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic 
        curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. "A") in the 
        elliptic curve database D.

    (<RngUPolElt> f, <RngUPolElt> h) -> CrvEll

        Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must 
        be of degree at most 1 and f must be monic of degree 3.

    (<RngUPolElt> f) -> CrvEll

        Creates the elliptic curve defined by y^2 = f(x), where f must be monic 
        of degree 3.

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j. This version is deprecated
        and will be removed in a future release -- use 
        EllipticCurveFromjInvariant() instead.

    (<Crv> C) -> CrvEll, Map

        Returns an elliptic curve from certain genus 1 curves with an easily 
        recognised rational point.

    (<Crv> C, <Pt> Point) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a point and also the
        map from C to that model. The point should be nonsingular.

    (<Crv> C, <PlcCrvElt> Place) -> CrvEll, MapSch

        Returns a Weierstrass model of a genus 1 curve with a degree 1 place and
        also the map from C to that model.

    (<ModFrmElt> f) -> CrvEll

        An elliptic curve with associated modular form f.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in the isogeny 
        class of elliptic curves associated to M.


1

Total time: 2.949 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:27:57 2004

Input: F2<i> := FiniteField (2, 10);
#F2;
F2X<x> := PolynomialRing(F2);
(x+i)^3;
// F2X;
// EllipticCurve;
E := EllipticCurve(x^3+x+1, x+1);
time #E;


Output: Magma V2.10-6     Wed Jan  7 2004 11:27:54 on modular  [Seed = 3288844329]
   -------------------------------------

1024
x^3 + i*x^2 + i^2*x + i^3
968
Time: 0.030

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:28:54 2004

Input: F2<i> := FiniteField (2, 10); #F2;
F2X<x> := PolynomialRing(F2);
// F2X;
// EllipticCurve;
E := EllipticCurve(x^3+x+1, x+1);
time #E;
Isogeny;


Output: Magma V2.10-6     Wed Jan  7 2004 11:28:51 on modular  [Seed = 3591756402]
   -------------------------------------

1024
968
Time: 0.020
Intrinsic 'Isogeny'

Signatures:

    (<CrvEll> E, <CrvEll> F, <RngMPolElt> s, <RngMPolElt> h, <RngMPolElt> o) -> 
    Map

        Returns the isogeny E -> F defined by the polynomials psi, phi, omega, 
        taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be 
        univariate (although elements of a multivariate polynomial ring) and the
        polynomials need not be coprime.

    (<CrvEll> E, <Pt> P) -> Map

        Returns the isogeny E -> F corresponding to the point P on the modular 
        curve X_0(N).



Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:30:15 2004

Input: F2<i> := FiniteField (2, 10); #F2;
F2X<x> := PolynomialRing(F2);
// F2X;
// EllipticCurve;
E := EllipticCurve(x^3+x+1, x+1);
time #E;
// Isogeny;
P := Random (E);
P;  Order(P);



Output: Magma V2.10-6     Wed Jan  7 2004 11:30:12 on modular  [Seed = 2724309457]
   -------------------------------------

1024
968
Time: 0.020
(i^648 : i^1012 : 1)
11

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:30:40 2004

Input: F2<i> := FiniteField (2, 10); #F2;
F2X<x> := PolynomialRing(F2);
// F2X;
// EllipticCurve;
E := EllipticCurve(x^3+x+1, x+1);
time #E;
Isogeny;
P := Random (E);
P;  Order(P);
Isogeny (E, P);




Output: Magma V2.10-6     Wed Jan  7 2004 11:30:37 on modular  [Seed = 3044458239]
   -------------------------------------

1024
968
Time: 0.020
Intrinsic 'Isogeny'

Signatures:

    (<CrvEll> E, <CrvEll> F, <RngMPolElt> s, <RngMPolElt> h, <RngMPolElt> o) -> 
    Map

        Returns the isogeny E -> F defined by the polynomials psi, phi, omega, 
        taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be 
        univariate (although elements of a multivariate polynomial ring) and the
        polynomials need not be coprime.

    (<CrvEll> E, <Pt> P) -> Map

        Returns the isogeny E -> F corresponding to the point P on the modular 
        curve X_0(N).


(i^185 : i^1003 : 1)
88

Isogeny(
    E: E,
    P: (i^185 : i^1003 : 1)
)
In file "/usr/local/magma/package/Geometry/CrvMod/modular_isogenies.m", line 84,
column 28:
>>     model_type := ModelType(X0);
                              ^
Runtime error in 'ModelType': Bad argument types
Argument types given: CrvEll

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lon-igate.mckinsey.com. (213.86.15.25)
Time: Wed Jan  7 11:31:28 2004

Input: F2<i> := FiniteField (2, 10); #F2;
F2X<x> := PolynomialRing(F2);
// F2X;
// EllipticCurve;
E := EllipticCurve(x^3+x+1, x+1);
time #E;
// Isogeny;
P := Random (E);
P;  Order(P);




Output: Magma V2.10-6     Wed Jan  7 2004 11:31:25 on modular  [Seed = 3095114626]
   -------------------------------------

1024
968
Time: 0.020
(i^991 : i^969 : 1)
88

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host user-vc8frgq.biz.mindspring.com. (216.135.238.26)
Time: Wed Jan  7 18:30:19 2004

Input: P(n)=n(3n-1)

P(P(n))

Output: Magma V2.10-6     Wed Jan  7 2004 18:30:16 on modular  [Seed = 2471508602]
   -------------------------------------


>> P(n)=n(3n-1)
           ^
User error: bad syntax

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

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host user-vc8frgq.biz.mindspring.com. (216.135.238.26)
Time: Wed Jan  7 18:30:36 2004

Input: P(n)=n*(3*n-1)

P(P(n))

Output: Magma V2.10-6     Wed Jan  7 2004 18:30:33 on modular  [Seed = 2589537122]
   -------------------------------------


>> P(P(n));
   ^
User error: bad syntax

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host user-vc8frgq.biz.mindspring.com. (216.135.238.26)
Time: Wed Jan  7 18:31:22 2004

Input: (n*(3*n-1))*(3*(n*(3*n-1))-1)


Output: Magma V2.10-6     Wed Jan  7 2004 18:31:19 on modular  [Seed = 1688718787]
   -------------------------------------


>> (n*(3*n-1))*(3*(n*(3*n-1))-1)
    ^
User error: Identifier 'n' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host user-vc8frgq.biz.mindspring.com. (216.135.238.26)
Time: Wed Jan  7 18:31:55 2004

Input: P=n*(3*n-1)

Output: Magma V2.10-6     Wed Jan  7 2004 18:31:52 on modular  [Seed = 1840170213]
   -------------------------------------


>> P=n*(3*n-1);
     ^
User error: Identifier 'n' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host user-vc8frgq.biz.mindspring.com. (216.135.238.26)
Time: Wed Jan  7 18:33:38 2004

Input: n=integer

P=n*(3*n-1)

Output: Magma V2.10-6     Wed Jan  7 2004 18:33:35 on modular  [Seed = 1991630425]
   -------------------------------------


>> P=n*(3*n-1);
   ^
User error: bad syntax

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (156.143.48.248)
Time: Wed Jan  7 19:31:45 2004

Input: ploth(n=1, 1000, pi(n))

Output: Magma V2.10-6     Wed Jan  7 2004 19:31:42 on modular  [Seed = 399805606]
   -------------------------------------


>> ploth(n=1, 1000, pi(n));
         ^
User error: Identifier 'n' has not been declared or assigned

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host durian.math.sci.kobe-u.ac.jp. (133.30.64.173)
Time: Wed Jan  7 20:38:25 2004

Input: Q := RationalField();
> P<x, y, z, t, u, v> := PolynomialRing(Q, 6);I := ideal<P | + y + z + t + u + v,
>     x*y + y*z + z*t + t*u + u*v + v*x,
>     x*y*z + y*z*t + z*t*u + t*u*v + u*v*x + v*x*y,
>     x*y*z*t + y*z*t*u + z*t*u*v + t*u*v*x + u*v*x*y + v*x*y*z,
>     x*y*z*t*u + y*z*t*u*v + z*t*u*v*x + t*u*v*x*y + u*v*x*y*z + v*x*y*z*t,
>     x*y*z*t*u*v - 1>;
> time B := GroebnerBasis(I);

Output: Magma V2.10-6     Wed Jan  7 2004 20:38:13 on modular  [Seed = 3675803651]
   -------------------------------------

Time: 1.010

Total time: 3.979 seconds, Total memory usage: 2.84MB


************** MAGMA *****************
Host durian.math.sci.kobe-u.ac.jp. (133.30.64.173)
Time: Wed Jan  7 20:39:08 2004

Input: B;

Output: Magma V2.10-6     Wed Jan  7 2004 20:39:05 on modular  [Seed = 3507640886]
   -------------------------------------


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

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host durian.math.sci.kobe-u.ac.jp. (133.30.64.173)
Time: Wed Jan  7 20:40:03 2004

Input: Q := RationalField();
> P<x, y, z, t, u, v> := PolynomialRing(Q, 6);
> I := ideal<P |
>     x + y + z + t + u + v,
>     x*y + y*z + z*t + t*u + u*v + v*x,
>     x*y*z + y*z*t + z*t*u + t*u*v + u*v*x + v*x*y,
>     x*y*z*t + y*z*t*u + z*t*u*v + t*u*v*x + u*v*x*y + v*x*y*z,
>     x*y*z*t*u + y*z*t*u*v + z*t*u*v*x + t*u*v*x*y + u*v*x*y*z + v*x*y*z*t,
>     x*y*z*t*u*v - 1>;
B:=GroebnerBasis(I);


Output: Magma V2.10-6     Wed Jan  7 2004 20:39:59 on modular  [Seed = 3221441393]
   -------------------------------------


Total time: 3.519 seconds, Total memory usage: 3.41MB


************** MAGMA *****************
Host banjo.cs.iitm.ernet.in. (202.141.24.2)
Time: Thu Jan  8 03:09:30 2004

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

Output: Magma V2.10-6     Thu Jan  8 2004 03:09:27 on modular  [Seed = 3423527842]
   -------------------------------------

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

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (80.90.160.162)
Time: Thu Jan  8 04:52:46 2004

Input: /*
 *  An implementation of the Number Field Sieve as described in
 *  "Factoring Integers with the Number Field Sieve" by J.P. Buhler,
 *  H.W. Lenstra, and Carl Pomerance.  (Algorithm 11.1)
 *
 *  This code is not at all optimized - it is demonstration of the
 *  Magma computer algebra package, and to for people who want to
 *  learn the Number Field Sieve algorithm or how to code it.  Note
 *  that the algebraic square root code is available only for the
 *  most recent release of Magma.
 *
 *  This code is best demonstrated for numbers around 20-digits.
 *  Larger numbers will cause the program to take up too much memory,
 *  and numbers that are too small do not work well with this algorithm.
 *
 *  "print" statements that can be ommitted are left justified.
 *
 *  by Contini - Fri March 3rd, 2000.
 */

function SelectPolynomial(n);
    /* select a degree according to the asymptotic formula */
    d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) );
print "degree ", d;

    m := Iroot( n, d );
print "m := ", m, ";";

    coeffs := [];
    for i := d to 0 by -1 do
	temp2 := m^i;
	coeff := n div temp2;
	/* Append (~coeffs, coeff); */
	coeffs[i+1] := coeff;
	n -:= coeff*temp2;
    end for;

    P<X> := PolynomialRing( IntegerRing() );
    f := P!coeffs;
    return f, m, d;

end function;


procedure RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots,
  m_mod_p, sieve_len);
    /*  
     *  RATIONAL SIEVE
     */
    sieve_array := [0 : i in [1..sieve_len]];

    for i in [1..#FB] do
	p := FB[i];
	logp := log_primes[i];
	/*
	 *  Compute  loc  - the first location in the sieve array
	 *  where  p  divides the corresponding residue
	 */
	loc := prev_roots[i] - m_mod_p[i];
	if loc lt 0 then
	    loc +:= p;
	end if;
	prev_roots[i] := loc;
	/*  sieve begins at location 1, so skip location 0 */
	if loc eq 0 then
	    loc := p;
	end if;

	/*  MAIN SIEVE LOOP  */
	while loc le sieve_len do
	    sieve_array[loc] +:= logp;
	    loc +:= p;
	end while;

    end for;

end procedure;


procedure AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes,
  R_p_set, sieve_len );
    /*  
     *  NUMBER FIELD SIEVE
     */
    nf_sieve_array := [0 : i in [1..sieve_len]];
    for i in [1..#R_p_set] do
	R_p := R_p_set[i];
	p := R_p[1];
	r := R_p[2];
	logp := R_p[3];

	loc := nf_prev_roots[i] - r;
	if loc lt 0 then
	    loc +:= p;
	end if;
	nf_prev_roots[i] := loc;
	if loc eq 0 then
	    loc := p;
	end if;

	/*  MAIN SIEVE LOOP  */
	while loc le sieve_len do
	    nf_sieve_array[loc] +:= logp;
	    loc +:= p;
	end while;

    end for;
end procedure;


procedure ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array,
  error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots,
  R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset );
	/*  scan sieve array
	 */
    threshold := Round( Log( bm ) ) - error_term;
    zero := [0: i in [1..d]];
    x := zero;
    x[1] := 1; x[2] := b;
    nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) ) - error_term;
    for a in [1..sieve_len] do
	if sieve_array[a] ge threshold then
	    /*  rational side appears to be smooth */
	    if nf_sieve_array[a] ge nf_threshold then
		/*  number field side appears to be smooth */
		if Gcd(b, a) ne 1 then
		    /*  relation is redundant */
		    continue;
		end if;

		/*  see if it really is smooth */
		relation := [];
		rational_side := a + bm;
		for i in [1..#FB] do
		    p := FB[i];
		    if a mod p eq prev_roots[i] then
			e := 0;
			quot, rem := Quotrem( rational_side, p );
			repeat
			    rational_side := quot;
			    e +:= 1;
			    quot, rem := Quotrem( rational_side, p );
			until rem ne 0;
			Append( ~relation, [i, e] );
		    end if;
		end for;
		if Abs(rational_side) ne 1 then
		    /*  rational side is not smooth :-( */
		    continue;
		end if;

		/*  try algebraic side */
		x := zero;
		x[1] := a; x[2] := b;
		alg_elt := J!x;
		norm := IntegerRing()!Norm(alg_elt);

		for i in [1..#R_p_set] do
		    R_p := R_p_set[i];
		    p := R_p[1];
		    if a mod p eq nf_prev_roots[i] then
			e := 0;
			quot, rem := Quotrem( norm, p );
			repeat
			    norm := quot;
			    e +:= 1;
			    quot, rem := Quotrem( norm, p );
			until rem ne 0;
			Append( ~relation, [i+#FB, e] );
		    end if;
		end for;
		if Abs(norm) ne 1 then
		    /*  algebraic side is not smooth :-( */
		    continue;
		end if;

		/*  The relation is a keeper! */
print "a := ", a, "; b:= ", b,";";
		num_rels +:= 1;

		/*  Compute the character columns corresponding to
		    alg_elt  */
		for i in [1..#char_cols] do
		    p := char_cols[i][1];
		    r := char_cols[i][2];
		    if LegendreSymbol( (a + b*r) mod p, p ) eq -1 then
			M[num_rels, i + char_offset] := 1;
		    end if;
		end for;

		/*  store the algebraic element */
		Append( ~smooth_alg_elts, alg_elt );

		/*  store relation in matrix */
		for j in [1..#relation] do
		    M[num_rels, relation[j, 1]] := relation[j, 2];
		end for;

		if num_rels eq enough_rels then
		    break;
		end if;

		/*  update the  nf_threshold  - since the norms
		    grow somewhat quickly, we waste a lot of time
		    on false reports if this update is not made */
		x := zero;
		x[1] := a; x[2] := b;
		nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) );
		nf_threshold -:= error_term;
	    end if;
	end if;
    end for;
end procedure;


function NFS( n )

    f, m, d := SelectPolynomial(n);
    fprime := Derivative( f );

    J<alpha> := NumberField( f );

    /*  choose  y  - the bound for smoothness  */
    dlogd := d*Log(d);
    temp := 1.0/d * Log( n );
    e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) );
    y := Round( Exp( 0.5*e ) );
    print "smoothness bound is ", y;

    /*  prepare data for rational sieve */
    FB := [p : p in [2..y] | IsPrime( p ) ];
    log_primes := [Round(Log(p)) : p in FB];
    prev_roots := [0: p in FB];
    m_mod_p := [m mod p: p in FB];

    /*  prepare data for the algebraic sieve */
    cols := #FB;
    R_p_set := [];
    nf_prev_roots := [];
    for p in FB do
	K := GF(p);
	roots_mod_p := Roots( f, K );
	for i in [1..#roots_mod_p] do
	    r := IntegerRing()!roots_mod_p[i][1];
	    /*  also include the rounded logarithm of  p  in the storage */
	    Append( ~R_p_set, [p, r, Round(Log(p))] );
	    Append( ~nf_prev_roots, 0 );
	    cols +:= 1;
	end for;
    end for;
    smooth_alg_elts := [];

    /*  create the character columns */
    char_offset := cols;
    num_char_cols := 3 * Ilog2( n );
    char_cols := [];
    p := NextPrime( y );
    i := 0;
    repeat
	K := GF(p);
	roots_mod_p := Roots( f, K );
	for j in [1..#roots_mod_p] do
	    r := IntegerRing()!roots_mod_p[j][1];
	    Append( ~char_cols, [p, r] );
	    i +:= 1;
	    if i eq num_char_cols then
		break;
	    end if;
	end for;

	p := NextPrime( p );
    until i eq num_char_cols;
    cols +:= num_char_cols;

    enough_rels := cols+50;
print "will quit after", enough_rels," relations";

    /*  allow for an error in the sieve threshold */
    error_term := 3;

    /*  set up matrix */
    M := RMatrixSpace (IntegerRing(), enough_rels, cols)!0;

    num_rels := 0;
    b := 1;
    /*  bm = b*m */
    bm := m;
    sieve_len := y * 25;

    while true do
	RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots,
	  m_mod_p, sieve_len );

	AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes,
	  R_p_set, sieve_len );

	ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array,
	  error_term, ~num_rels, sieve_len, ~M, FB, prev_roots,
	  nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts,
	  char_cols, char_offset );

	bm +:= m;
	b +:= 1;
print "Number of relations: ", num_rels;

	if num_rels ge enough_rels then
	    break;
	end if;
    end while;


print "matrix size: ",num_rels," by ", cols;
print "finding null space";

    gf2 := GF(2);
    Mprime := RMatrixSpace (gf2, num_rels, cols)!M;
    time null_space := NullSpace( Mprime );

    /*  "free" Mprime */
    Mprime := 0;

    for j in  [1..Dimension(null_space)] do
print "trying null space vector #",j;

	/*  get the first element of the solution vector */
	soln := ChangeUniverse (Eltseq (null_space.j), IntegerRing());

	/*  compute the exponents of a relation that involves an
	    algebraic square and an integer square
	 */

	exps := RSpace(IntegerRing(), cols)!0;
	for i in [1..num_rels] do
	    if soln[i] eq 1 then
		exps +:= M[i];
	    end if;
	end for;

	/*  compute the square root  x  of the integer element of the relation
	 */
	x := 1;
	for i in [1..#FB] do
	    e := exps[i];
	    if e gt 0 then
		x := (x * ( FB[i]^(e div 2) ) ) mod n;
	    end if;
	end for;
	x := ( x * Evaluate( fprime, m ) ) mod n;
print x,"^2 mod n = ", x^2 mod n;

	list := [];
	for i in [1..num_rels] do
	    if soln[i] eq 1 then
		Append( ~list, smooth_alg_elts[i] );
	    end if;
	end for;
	Append( ~list, Evaluate( fprime, alpha )^2 );

	/*  Compute the square root  beta  of the algebraic element */
	ok, l := Root(2, list, []);
        if ok eq false then
            print "Element is not a square... continuing!";
            continue;
        end if;

	/*  map the sqrt to an integer  v  modulo  n  */
	v := 1;
	for i in [1..#l] do
	    list := l[i];
	    prod_list := 1;
	    for j in [1..#list] do
		seq := Eltseq( list[j] );
		elt := 0;
		for k in [0..d-1] do
		    num := Numerator( seq[k+1] ) mod n;
		    den := Denominator( seq[k+1] ) mod n;
		    elt +:= ( ( num * Modinv( den, n ) mod n) *
		      Modexp( m, k, n ) ) mod n;
		end for;
		prod_list := (prod_list * elt) mod n;
	    end for;
	    v := v * Modexp( Modinv( prod_list, n ), 2^(i-1), n ) mod n;
	end for;
	
print v,"^2 mod n = ", v^2 mod n;

	gcd := Gcd(x-v, n);
print "Gcd of ",x-v," and ",v," is ", gcd;
	if gcd ne 1 and gcd ne n then
	    print "FACTOR: ", gcd;
	    return gcd;
	end if;
    end for;

print "no factor found :-( ";
    return 0;

end function;

















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

************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:24:37 2004

Input: p := NextPrime(10^9);
p;
K := GF(p);
E := EllipticCurve([K | -1, 1]);
time SEA(E : MaxSmooth := 1);


Output: Magma V2.10-6     Thu Jan  8 2004 17:24:34 on modular  [Seed = 3575067192]
   -------------------------------------

1000000007
0
Time: 0.090

Total time: 3.059 seconds, Total memory usage: 2.75MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:27:40 2004

Input: p := 31648573662208007208411279340972174081655191771220726603117102285639562723584318781472781870749438532939445789762497;
p;


Output: Magma V2.10-6     Thu Jan  8 2004 17:27:37 on modular  [Seed = 3895070462]
   -------------------------------------

3164857366220800720841127934097217408165519177122072660311710228563956272358431\
8781472781870749438532939445789762497

Total time: 3.089 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:29:04 2004

Input: p := 31648573662208007208411279340972174081655191771220726603117102285639562723584318781472781870749438532939445789762497;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);

Output: Magma V2.10-6     Thu Jan  8 2004 17:29:00 on modular  [Seed = 4282194204]
   -------------------------------------

3164857366220800720841127934097217408165519177122072660310671542798638878133954\
6528939270299746635961126958582050640

Total time: 3.599 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:32:39 2004

Input: p := 31648573662208007208411279340972174081655191771220726603117102285639562723584318781472781870749438532939445789762497;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);
Factorization($1);


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Thu Jan  8 2004 17:32:16 on modular  [Seed = 2387372977]
   -------------------------------------

3164857366220800720841127934097217408165519177122072660310671542798638878133954\
6528939270299746635961126958582050640

Errors: /home/mfd/gomagma: line 2: 28865 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:33:38 2004

Input: p := 279731234232179;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);


Output: Magma V2.10-6     Thu Jan  8 2004 17:33:35 on modular  [Seed = 2236047477]
   -------------------------------------

279731234232180

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:35:06 2004

Input: p := 279731234232179;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);
Factorization($1);



Output: Magma V2.10-6     Thu Jan  8 2004 17:35:02 on modular  [Seed = 2538959823]
   -------------------------------------

279731234232180
[ <2, 2>, <3, 2>, <5, 1>, <823, 1>, <1123, 1>, <1681469, 1> ]

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:35:50 2004

Input: p := 1009;
K := GF(p);
E := EllipticCurve([K | 71, 602]);
SEA(E : MaxSmooth := 1);
Factorization($1);



Output: Magma V2.10-6     Thu Jan  8 2004 17:35:46 on modular  [Seed = 2926332579]
   -------------------------------------

1060
[ <2, 2>, <5, 1>, <53, 1> ]

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:36:30 2004

Input: p := 279731234232179;
K := GF(p);
E := EllipticCurve([K | 1, 2]);
SEA(E : MaxSmooth := 1);
Factorization($1);



Output: Magma V2.10-6     Thu Jan  8 2004 17:36:26 on modular  [Seed = 2775007616]
   -------------------------------------

0

>> Factorization($1);
                ^
Runtime error in 'Factorization': Argument 1 is not non-zero

Total time: 3.169 seconds, Total memory usage: 2.75MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:36:57 2004

Input: p := 279731234232179;
K := GF(p);
E := EllipticCurve([K | 1, 2]);
SEA(E : MaxSmooth := 1);




Output: Magma V2.10-6     Thu Jan  8 2004 17:36:54 on modular  [Seed = 3162396789]
   -------------------------------------

0

Total time: 2.989 seconds, Total memory usage: 2.75MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:37:28 2004

Input: p := 2797312367;
K := GF(p);
E := EllipticCurve([K | 1, 2]);
SEA(E : MaxSmooth := 1);




Output: Magma V2.10-6     Thu Jan  8 2004 17:37:25 on modular  [Seed = 3010549593]
   -------------------------------------

0

Total time: 3.039 seconds, Total memory usage: 2.75MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:54:04 2004

Input: p := 22771656396649042914677651938348976006738044330885828909690000917475479649330897416453073715484777125675617411561753;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);




Output: Magma V2.10-6     Thu Jan  8 2004 17:54:00 on modular  [Seed = 1351790742]
   -------------------------------------

2277165639664904291467765193834897600673804433088582890968087619490985411965451\
9076304824198934082753513693882127520

Total time: 3.589 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 17:59:28 2004

Input: p := 34434335923751399698518505516722285557281631663360135021571830978812886664047949565106992641249608613800031755822209;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);


Output: Magma V2.10-6     Thu Jan  8 2004 17:59:25 on modular  [Seed = 1654701537]
   -------------------------------------

3443433592375139969851850551672228555728163166336013502156054198056930829719069\
4068389128882706321764053054021911760

Total time: 3.619 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 18:09:16 2004

Input: p := 21690482571471944131858536333908058782272452491831771308020961342630740764170913541267450561542337158596383516743897;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);

Output: Magma V2.10-6     Thu Jan  8 2004 18:09:13 on modular  [Seed = 450414157]
   -------------------------------------

2169048257147194413185853633390805878227245249183177130801288304892016253318338\
1513845564003262104587338680209387280

Total time: 3.499 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530B26.dip.t-dialin.net. (217.83.11.38)
Time: Thu Jan  8 18:14:46 2004

Input: p := 27935674986520266205325579045503384555589668080548467527362175072470197761098090571694173551976792685114398933033353;
K := GF(p);
E := EllipticCurve([K | 1, 0]);
SEA(E : MaxSmooth := 1);

Output: Magma V2.10-6     Thu Jan  8 2004 18:14:43 on modular  [Seed = 955966229]
   -------------------------------------

2793567498652026620532557904550338455558966808054846752735212790270242752181874\
3878157138687189351173894399046846240

Total time: 3.569 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host pD9530E68.dip.t-dialin.net. (217.83.14.104)
Time: Fri Jan  9 10:38:33 2004

Input: p := 2797312367;
K := GF(p);
E := EllipticCurve([K | 1, 2]);
SEA(E : MaxSmooth := 1);

Output: Magma V2.10-6     Fri Jan  9 2004 10:38:29 on modular  [Seed = 96792757]
   -------------------------------------

0

Total time: 3.209 seconds, Total memory usage: 2.75MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:19:20 2004

Input: IntegralQuarticPoints([6,24,34,24,9]) : [ RngIntElt ] -> [ SeqEnum ]

Output: Magma V2.10-6     Fri Jan  9 2004 14:19:17 on modular  [Seed = 1082229174]
   -------------------------------------


>> IntegralQuarticPoints([6,24,34,24,9]) : [ RngIntElt ] -> [ SeqEnum ];
                                           ^
User error: bad syntax

Total time: 3.189 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:20:14 2004

Input: IntegralQuarticPoints([6,24,34,24,9]);

Output: Magma V2.10-6     Fri Jan  9 2004 14:20:10 on modular  [Seed = 1671602890]
   -------------------------------------


IntegralQuarticPoints(
    Q: Full Matrix Algebra of degree 2 over Integer Ring
)
In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 2003, 
column 20:
>>         M:= Ceiling(M^(1/2));
                      ^
Runtime error in 'Ceiling': Argument 1 should be real

Total time: 3.959 seconds, Total memory usage: 2.33MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:21:25 2004

Input: IntegralQuarticPoints([1, 0, -8, 8, 1]);

Output: Magma V2.10-6     Fri Jan  9 2004 14:21:16 on modular  [Seed = 1873719040]
   -------------------------------------

[
    [ 2, -1 ],
    [ -6, -31 ],
    [ 0, 1 ]
]

Total time: 9.069 seconds, Total memory usage: 2.33MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:22:22 2004

Input: IntegralQuarticPoints([27, 0, -180, 0, 324]);

Output: Magma V2.10-6     Fri Jan  9 2004 14:22:18 on modular  [Seed = 1991751263]
   -------------------------------------

[
    [ 0, 18 ],
    [ 2, 6 ],
    [ -2, 6 ],
    [ 4, -66 ],
    [ -4, -66 ]
]

Total time: 3.569 seconds, Total memory usage: 2.23MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:23:57 2004

Input: IntegralQuarticPoints([6, 24, 34, 24, 9]);

Output: Magma V2.10-6     Fri Jan  9 2004 14:23:53 on modular  [Seed = 130467725]
   -------------------------------------


IntegralQuarticPoints(
    Q: Full Matrix Algebra of degree 2 over Integer Ring
)
In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 2003, 
column 20:
>>         M:= Ceiling(M^(1/2));
                      ^
Runtime error in 'Ceiling': Argument 1 should be real

Total time: 3.919 seconds, Total memory usage: 2.33MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:25:27 2004

Input: IntegralQuarticPoints([6, 0, -2, 4, 1]);

Output: Magma V2.10-6     Fri Jan  9 2004 14:25:23 on modular  [Seed = 298921585]
   -------------------------------------


IntegralQuarticPoints(
    Q: Full Matrix Algebra of degree 2 over Integer Ring
)
In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 2003, 
column 20:
>>         M:= Ceiling(M^(1/2));
                      ^
Runtime error in 'Ceiling': Argument 1 should be real

Total time: 3.939 seconds, Total memory usage: 2.33MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 14:28:03 2004

Input: IntegralQuarticPoints([1,0,-12,144,216]);

Output: Magma V2.10-6     Fri Jan  9 2004 14:28:00 on modular  [Seed = 669456548]
   -------------------------------------

[]

Total time: 3.329 seconds, Total memory usage: 2.33MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:17:40 2004

Input: ?



Output: Magma V2.10-6     Fri Jan  9 2004 16:17:37 on modular  [Seed = 2673851052]
   -------------------------------------

===============================================================================
PATH: /
KIND: Overview
===============================================================================

You are reading about the Magma online help system.  This system 
gives you information about Magma while you are at the computer. 
To see this help page at any time, all you have to do is to type  

        ?

                  ----------

The online help system comes in two modes: the single request
mode and the Magma Help Browser.  To enter the Browser, type

        ??

The Browser is useful if you intend to read several related
help nodes, because you can exploit the tree structure of the
online help.  Once you are in the Browser, you can type

        help

again to find out how to use the Browser, and for a more
detailed explanation of the whole online help system.

                  ----------

Single help requests begin with the ? character.
Examples are:

?print
?magma
?ring
?example

If your help request is ambiguous, Magma will return a numbered 
list of matches.  To see the contents of one of them, 
type  ?  followed by its number.

Some help pages suggest other pages that you might like to look at 
as well.  They are prefixed by a code such as   +3  or  +5 .  
To read one of them, type  ?  followed by the code.

You can also supply the full pathname of a help node, if you know it.
For example:

?/system/quit
?/magma/module/homomorphism 

                  ----------

The online help system offers tab completion. If you type a few letters 
of your help request and then press the tab key, Magma will "complete" 
the request if there is a unique completion.  Otherwise, it will 
complete the request as far as possible, and then emit a beep.  
Press the tab key again to see all the possibilities.
ALWAYS PRESS TAB BEFORE THE END OF THE LINE, 
SO AS TO SEE EVERY RELEVANT HELP PAGE.
(On a few operating systems, the tab completion feature 
cannot be made available.)

                  ----------

The content of the online help system comes from two sources:
the "Handbook of Magma Functions" (Bosma and Cannon)
and specially-written overview nodes.
You may also wish to consult the books
"An Introduction to Algebraic Programming in Magma"
(Cannon and Playoust) and "Solving Problems with Magma"
(Bosma, Cannon, Playoust and Steel).

                  ----------

The online help system is also available in an HTML form
suitable for Internet browsers.  To use this,
move to a shell prompt (outside Magma) and type

    magmahelp

                  ----------

To leave Magma, type 

    quit;

or <Ctrl>-D.
===============================================================================

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:19:51 2004

Input: S6:=SymGrp(6);

Output: Magma V2.10-6     Fri Jan  9 2004 16:19:48 on modular  [Seed = 2825424158]
   -------------------------------------


>> S6:=SymGrp(6);;
       ^
User error: Identifier 'SymGrp' has not been declared or assigned

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:20:19 2004

Input: S6:=SymmetricGroup(6);

Output: Magma V2.10-6     Fri Jan  9 2004 16:20:16 on modular  [Seed = 3111755243]
   -------------------------------------


Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:20:58 2004

Input: S6:=SymmetricGroup(6);MaximalSubgroups(S6);


Output: Magma V2.10-6     Fri Jan  9 2004 16:20:54 on modular  [Seed = 1166369074]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (3, 6)(4, 5)
            (1, 6, 3)(2, 5, 4)
            (5, 6)
            (3, 4)
            (1, 2)
[2]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (2, 3)
            (2, 3, 4)
            (1, 2)(3, 4)
            (1, 4)(2, 3)
            (5, 6)
[3]     Order 72           Length 10
        Permutation group acting on a set of cardinality 6
        Order = 72 = 2^3 * 3^2
            (1, 4)
            (1, 5)(2, 4)(3, 6)
            (1, 4)(2, 6)
            (1, 4, 3)
            (2, 5, 6)
[4]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (5, 6)
            (2, 6)(3, 4, 5)
[5]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (1, 2)(3, 4)(5, 6)
            (1, 3, 2, 4, 6, 5)
[6]     Order 360          Length 1
        Permutation group acting on a set of cardinality 6
        Order = 360 = 2^3 * 3^2 * 5
            (3, 4)(5, 6)
            (1, 5)(2, 6, 3, 4)

Total time: 2.969 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:21:56 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);m6[1]


Output: Magma V2.10-6     Fri Jan  9 2004 16:21:53 on modular  [Seed = 1284270204]
   -------------------------------------


>> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);m6[1]
                                                  ^
User error: Identifier 'm6' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:22:16 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1]


Output: Magma V2.10-6     Fri Jan  9 2004 16:22:13 on modular  [Seed = 1469543315]
   -------------------------------------

rec<recformat<order, length, subgroup, presentation> | 
    order := 48,
    length := 15,
    subgroup := Permutation group acting on a set of cardinality 6
    Order = 48 = 2^4 * 3
        (1, 2)(3, 6)
        (3, 6, 4)
        (1, 2)(3, 5)(4, 6)
        (1, 2)(3, 4)(5, 6)
        (1, 2)(3, 6)(4, 5)
    >

Total time: 2.939 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:23:29 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses(M61);


Output: Magma V2.10-6     Fri Jan  9 2004 16:23:26 on modular  [Seed = 1587444433]
   -------------------------------------


>> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses(
                                                                             ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: Rec

Total time: 2.979 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:23:37 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses(M61);


Output: Magma V2.10-6     Fri Jan  9 2004 16:23:34 on modular  [Seed = 1772703230]
   -------------------------------------


>> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses(
                                                                             ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: Rec

Total time: 3.019 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:24:00 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];
ConjugacyClasses(M61);

Output: Magma V2.10-6     Fri Jan  9 2004 16:23:57 on modular  [Seed = 1890604252]
   -------------------------------------


>> ConjugacyClasses(M61);;
                   ^
Runtime error in 'ConjugacyClasses': Bad argument types
Argument types given: Rec

Total time: 2.959 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:24:34 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];
Nclasses(M61);

Output: Magma V2.10-6     Fri Jan  9 2004 16:24:31 on modular  [Seed = 2075875381]
   -------------------------------------


>> Nclasses(M61);;
           ^
Runtime error in 'Nclasses': Bad argument types
Argument types given: Rec

Total time: 2.919 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:25:10 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);
Nclasses(M6[1]);

Output: Magma V2.10-6     Fri Jan  9 2004 16:25:07 on modular  [Seed = 164178555]
   -------------------------------------


>> Nclasses(M6[1]);;
           ^
Runtime error in 'Nclasses': Bad argument types
Argument types given: Rec

Total time: 2.919 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:25:24 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Nclasses(M6[1]);

Output: Magma V2.10-6     Fri Jan  9 2004 16:25:21 on modular  [Seed = 282080016]
   -------------------------------------


>> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Nclasses(M6[1]);;
                                                          ^
Runtime error in 'Nclasses': Bad argument types
Argument types given: Rec

Total time: 2.959 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:26:04 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Classes(M6[1]);

Output: Magma V2.10-6     Fri Jan  9 2004 16:26:01 on modular  [Seed = 467351603]
   -------------------------------------


>> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Classes(M6[1]);;
                                                         ^
Runtime error in 'Classes': Bad argument types
Argument types given: Rec

Total time: 2.959 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:26:27 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);


Output: Magma V2.10-6     Fri Jan  9 2004 16:26:24 on modular  [Seed = 585236963]
   -------------------------------------


Total time: 2.939 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:27:02 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);G:=M6[1];


Output: Magma V2.10-6     Fri Jan  9 2004 16:26:58 on modular  [Seed = 770510542]
   -------------------------------------


Total time: 2.979 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:27:13 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1];


Output: Magma V2.10-6     Fri Jan  9 2004 16:27:10 on modular  [Seed = 888412122]
   -------------------------------------

rec<recformat<order, length, subgroup, presentation> | 
    order := 48,
    length := 15,
    subgroup := Permutation group acting on a set of cardinality 6
    Order = 48 = 2^4 * 3
        (1, 6)(2, 3)
        (1, 4, 6)(2, 5, 3)
        (3, 6)
        (1, 2)
        (4, 5)
    >

Total time: 2.919 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host dirichlet.math.umass.edu. (128.119.47.126)
Time: Fri Jan  9 16:28:04 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1];
G:=sub<Sym(6) | (1,6)(2,3), (1,4,6)(2,5,3), (3,6), (1,2), (4,5)>;
Classes(G);

Output: Magma V2.10-6     Fri Jan  9 2004 16:28:00 on modular  [Seed = 1073683614]
   -------------------------------------

rec<recformat<order, length, subgroup, presentation> | 
    order := 48,
    length := 15,
    subgroup := Permutation group acting on a set of cardinality 6
    Order = 48 = 2^4 * 3
        (1, 2)(5, 6)
        (1, 4, 2)(3, 6, 5)
        (2, 6)
        (1, 5)
        (3, 4)
    >
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1      
        Rep (1, 2)(3, 6)(4, 5)

[3]     Order 2       Length 3      
        Rep (3, 6)(4, 5)

[4]     Order 2       Length 3      
        Rep (4, 5)

[5]     Order 2       Length 6      
        Rep (1, 6)(2, 3)

[6]     Order 2       Length 6      
        Rep (1, 6)(2, 3)(4, 5)

[7]     Order 3       Length 8      
        Rep (1, 4, 6)(2, 5, 3)

[8]     Order 4       Length 6      
        Rep (3, 5, 6, 4)

[9]     Order 4       Length 6      
        Rep (1, 3, 2, 6)(4, 5)

[10]    Order 6       Length 8      
        Rep (1, 4, 3, 2, 5, 6)



Total time: 2.939 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:32:26 2004

Input: ?magma



Output: Magma V2.10-6     Fri Jan  9 2004 16:32:22 on modular  [Seed = 3524456565]
   -------------------------------------

24 matches:
     1   O   /magma
     2   O   /system/Magma
     3   O   /system/Magma/update
     4   S   /magma/combinatorial-geometrical-incidence/plane/introduction/\
             planes-in-magma
     5   S   /magma/group/automatic/creation/magma
     6   S   /magma/group/group-overview/creation-general/magma
     7   S   /magma/group/matrix/creation-general-linear-group/magma
     8   S   /magma/group/permutation/creation-symmetric/magma
     9   S   /magma/group/polycyclic/polycyclic-groups/magma
    10   S   /magma/group/rewrite-system/creation/magma
    11   S   /magma/module-lattice/vector-space-linear-transformation/\
             creation-arithmetic/creation-magma
    12   S   /magma/ring-field-algebra/abelian-extension/introduction/magma
    13   S   /magma/ring-field-algebra/alg_grp/creation/complete-magma
    14   S   /magma/ring-field-algebra/algebraic-field/creation/magma
    15   S   /magma/ring-field-algebra/integer/nfs/nfs-data-files-formats/\
             nfs-magma-native
    16   S   /magma/ring-field-algebra/matrix/creation/complete-magma
    17   S   /magma/ring-field-algebra/matrix/creation/general-magma
    18   S   /magma/ring-field-algebra/rational-function-field/operation/magma
    19   S   /magma/ring-field-algebra/rational/creation/magma
    20   S   /magma/ring-field-algebra/real-complex/creation/magma
    21   S   /magma/ring-field-algebra/univariate-polynomial/creation/magma
    22   S   /magma/semigroup/finitely-presented/presentation/general-magma
    23   I   /language/IO/print/printing-file/PrintFileMagma
    24   I   /magma/ring-field-algebra/detail/generic/predicate/\
             IsMagmaEuclideanRing
To view an entry, type ? followed by the number next to it

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:33:58 2004

Input: ? 2




Output: Magma V2.10-6     Fri Jan  9 2004 16:33:55 on modular  [Seed = 3709730015]
   -------------------------------------

No numbers are defined

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:34:19 2004

Input: ?magma 1





Output: Magma V2.10-6     Fri Jan  9 2004 16:34:16 on modular  [Seed = 3827615229]
   -------------------------------------

24 matches:
     1   O   /magma
     2   O   /system/Magma
     3   O   /system/Magma/update
     4   S   /magma/combinatorial-geometrical-incidence/plane/introduction/\
             planes-in-magma
     5   S   /magma/group/automatic/creation/magma
     6   S   /magma/group/group-overview/creation-general/magma
     7   S   /magma/group/matrix/creation-general-linear-group/magma
     8   S   /magma/group/permutation/creation-symmetric/magma
     9   S   /magma/group/polycyclic/polycyclic-groups/magma
    10   S   /magma/group/rewrite-system/creation/magma
    11   S   /magma/module-lattice/vector-space-linear-transformation/\
             creation-arithmetic/creation-magma
    12   S   /magma/ring-field-algebra/abelian-extension/introduction/magma
    13   S   /magma/ring-field-algebra/alg_grp/creation/complete-magma
    14   S   /magma/ring-field-algebra/algebraic-field/creation/magma
    15   S   /magma/ring-field-algebra/integer/nfs/nfs-data-files-formats/\
             nfs-magma-native
    16   S   /magma/ring-field-algebra/matrix/creation/complete-magma
    17   S   /magma/ring-field-algebra/matrix/creation/general-magma
    18   S   /magma/ring-field-algebra/rational-function-field/operation/magma
    19   S   /magma/ring-field-algebra/rational/creation/magma
    20   S   /magma/ring-field-algebra/real-complex/creation/magma
    21   S   /magma/ring-field-algebra/univariate-polynomial/creation/magma
    22   S   /magma/semigroup/finitely-presented/presentation/general-magma
    23   I   /language/IO/print/printing-file/PrintFileMagma
    24   I   /magma/ring-field-algebra/detail/generic/predicate/\
             IsMagmaEuclideanRing
To view an entry, type ? followed by the number next to it

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:35:00 2004

Input: 1+2





Output: Magma V2.10-6     Fri Jan  9 2004 16:34:57 on modular  [Seed = 3996045102]
   -------------------------------------

3

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:35:24 2004

Input: ?prime





Output: Magma V2.10-6     Fri Jan  9 2004 16:35:20 on modular  [Seed = 4248689700]
   -------------------------------------

45 matches:
     1   S   /magma/ring-field-algebra/function-field/ideals/boolean/\
             pred-ideal-prime
     2   S   /magma/ring-field-algebra/function-field/ideals/\
             ideal-ops-further/ideals-prime
     3   S   /magma/ring-field-algebra/integer/prime
     4   I   /magma/geometry/schemes/schemes-global/PrimeComponents
     5   I   /magma/geometry/supersingular-divisors-on-module-curves/\
             properties/Prime
     6   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/tools-soluble-quotient-process/\
             tools-specific-normal-series/KeepPrimePower
     7   I   /magma/module-lattice/lattice/genus/local_genus_invariants/Prime
     8   I   /magma/module-lattice/quadratic/creation/creation/PrimeForm
     9   I   /magma/ring-field-algebra/affine-algebra/operations/IsPrime
    10   I   /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\
             PrimeIdeal
    11   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             DegreeOnePrimeIdeals
    12   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\
             IsPrime
    13   I   /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime
    14   I   /magma/ring-field-algebra/detail/generic/related/PrimeField
    15   I   /magma/ring-field-algebra/detail/generic/related/PrimeRing
    16   I   /magma/ring-field-algebra/finite-Galois-field/creation/structure/\
             PrimeField
    17   I   /magma/ring-field-algebra/function-field/elements/elt-other/\
             DifferentiationSequence
    18   I   /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime
    19   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    20   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    21   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    22   I   /magma/ring-field-algebra/ideal-groebner/ideal-operation/\
             predicate/IsPrime
    23   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    24   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    25   I   /magma/ring-field-algebra/integer/operation-element/\
             element-Boolean/IsPrime
    26   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    27   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    28   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    29   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    30   I   /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis
    31   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    32   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    33   I   /magma/ring-field-algebra/integer/prime/primality/IsPrime
    34   I   /magma/ring-field-algebra/integer/prime/primality/IsPrimePower
    35   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    36   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    37   I   /magma/ring-field-algebra/integer/random/RandomPrime
    38   I   /magma/ring-field-algebra/integer/random/RandomPrime
    39   I   /magma/ring-field-algebra/local/invariants/Prime
    40   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    41   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    42   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    43   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             NumberOfPrimePolynomials
    44   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             PrimePolynomials
    45   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             RandomPrimePolynomial
To view an entry, type ? followed by the number next to it

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:36:44 2004

Input: ?prime 23





Output: Magma V2.10-6     Fri Jan  9 2004 16:36:41 on modular  [Seed = 2219091244]
   -------------------------------------

45 matches:
     1   S   /magma/ring-field-algebra/function-field/ideals/boolean/\
             pred-ideal-prime
     2   S   /magma/ring-field-algebra/function-field/ideals/\
             ideal-ops-further/ideals-prime
     3   S   /magma/ring-field-algebra/integer/prime
     4   I   /magma/geometry/schemes/schemes-global/PrimeComponents
     5   I   /magma/geometry/supersingular-divisors-on-module-curves/\
             properties/Prime
     6   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/tools-soluble-quotient-process/\
             tools-specific-normal-series/KeepPrimePower
     7   I   /magma/module-lattice/lattice/genus/local_genus_invariants/Prime
     8   I   /magma/module-lattice/quadratic/creation/creation/PrimeForm
     9   I   /magma/ring-field-algebra/affine-algebra/operations/IsPrime
    10   I   /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\
             PrimeIdeal
    11   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             DegreeOnePrimeIdeals
    12   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\
             IsPrime
    13   I   /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime
    14   I   /magma/ring-field-algebra/detail/generic/related/PrimeField
    15   I   /magma/ring-field-algebra/detail/generic/related/PrimeRing
    16   I   /magma/ring-field-algebra/finite-Galois-field/creation/structure/\
             PrimeField
    17   I   /magma/ring-field-algebra/function-field/elements/elt-other/\
             DifferentiationSequence
    18   I   /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime
    19   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    20   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    21   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    22   I   /magma/ring-field-algebra/ideal-groebner/ideal-operation/\
             predicate/IsPrime
    23   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    24   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    25   I   /magma/ring-field-algebra/integer/operation-element/\
             element-Boolean/IsPrime
    26   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    27   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    28   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    29   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    30   I   /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis
    31   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    32   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    33   I   /magma/ring-field-algebra/integer/prime/primality/IsPrime
    34   I   /magma/ring-field-algebra/integer/prime/primality/IsPrimePower
    35   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    36   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    37   I   /magma/ring-field-algebra/integer/random/RandomPrime
    38   I   /magma/ring-field-algebra/integer/random/RandomPrime
    39   I   /magma/ring-field-algebra/local/invariants/Prime
    40   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    41   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    42   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    43   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             NumberOfPrimePolynomials
    44   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             PrimePolynomials
    45   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             RandomPrimePolynomial
To view an entry, type ? followed by the number next to it

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:37:07 2004

Input: ? 23





Output: Magma V2.10-6     Fri Jan  9 2004 16:37:04 on modular  [Seed = 2404364238]
   -------------------------------------

No numbers are defined

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:37:27 2004

Input: ? prime ? 23





Output: Magma V2.10-6     Fri Jan  9 2004 16:37:24 on modular  [Seed = 2522265283]
   -------------------------------------

45 matches:
     1   S   /magma/ring-field-algebra/function-field/ideals/boolean/\
             pred-ideal-prime
     2   S   /magma/ring-field-algebra/function-field/ideals/\
             ideal-ops-further/ideals-prime
     3   S   /magma/ring-field-algebra/integer/prime
     4   I   /magma/geometry/schemes/schemes-global/PrimeComponents
     5   I   /magma/geometry/supersingular-divisors-on-module-curves/\
             properties/Prime
     6   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/tools-soluble-quotient-process/\
             tools-specific-normal-series/KeepPrimePower
     7   I   /magma/module-lattice/lattice/genus/local_genus_invariants/Prime
     8   I   /magma/module-lattice/quadratic/creation/creation/PrimeForm
     9   I   /magma/ring-field-algebra/affine-algebra/operations/IsPrime
    10   I   /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\
             PrimeIdeal
    11   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             DegreeOnePrimeIdeals
    12   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\
             IsPrime
    13   I   /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime
    14   I   /magma/ring-field-algebra/detail/generic/related/PrimeField
    15   I   /magma/ring-field-algebra/detail/generic/related/PrimeRing
    16   I   /magma/ring-field-algebra/finite-Galois-field/creation/structure/\
             PrimeField
    17   I   /magma/ring-field-algebra/function-field/elements/elt-other/\
             DifferentiationSequence
    18   I   /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime
    19   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    20   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    21   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    22   I   /magma/ring-field-algebra/ideal-groebner/ideal-operation/\
             predicate/IsPrime
    23   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    24   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    25   I   /magma/ring-field-algebra/integer/operation-element/\
             element-Boolean/IsPrime
    26   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    27   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    28   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    29   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    30   I   /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis
    31   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    32   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    33   I   /magma/ring-field-algebra/integer/prime/primality/IsPrime
    34   I   /magma/ring-field-algebra/integer/prime/primality/IsPrimePower
    35   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    36   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    37   I   /magma/ring-field-algebra/integer/random/RandomPrime
    38   I   /magma/ring-field-algebra/integer/random/RandomPrime
    39   I   /magma/ring-field-algebra/local/invariants/Prime
    40   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    41   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    42   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    43   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             NumberOfPrimePolynomials
    44   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             PrimePolynomials
    45   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             RandomPrimePolynomial
To view an entry, type ? followed by the number next to it

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:37:56 2004

Input: factor ?





Output: Magma V2.10-6     Fri Jan  9 2004 16:37:53 on modular  [Seed = 2707522001]
   -------------------------------------


>> factor ?
          ^
User error: bad syntax

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:38:16 2004

Input:  ? factor 





Output: Magma V2.10-6     Fri Jan  9 2004 16:38:13 on modular  [Seed = 2825423020]
   -------------------------------------

11 matches:
     1   S   /magma/ring-field-algebra/integer/factor
     2   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     3   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     4   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactorModChar
     5   I   /magma/group/braid/braid-groups-elements/\
             braid-groups-elements-access/CanonicalFactorRepresentation
     6   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/socle/SocleFactor
     7   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             ClassGroupCyclicFactorGenerators
     8   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
     9   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
    10   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
    11   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
To view an entry, type ? followed by the number next to it

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:38:53 2004

Input:  ? factor 
? 1





Output: Magma V2.10-6     Fri Jan  9 2004 16:38:50 on modular  [Seed = 3010696088]
   -------------------------------------

11 matches:
     1   S   /magma/ring-field-algebra/integer/factor
     2   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     3   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactor
     4   I   /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\
             point_structures_jacobian/counting_jacobian/EulerFactorModChar
     5   I   /magma/group/braid/braid-groups-elements/\
             braid-groups-elements-access/CanonicalFactorRepresentation
     6   I   /magma/group/permutation/\
             characteristic-subgroup-normal-structure/socle/SocleFactor
     7   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             ClassGroupCyclicFactorGenerators
     8   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
     9   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             FactorBasis
    10   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
    11   I   /magma/ring-field-algebra/integer/nfs/nfs-process/\
             nfs-factorization-stage/Factor
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/ring-field-algebra/integer/factor
KIND: Section
===============================================================================
Factorization.

This section contains a description of most of the machinery provided in
Magma for the factorization of integers.  An account of the Number Field
Sieve is deferred until later in the chapter.

In the first subsection the general-purpose Factorization function is
described.  It employs a combination of methods in an attempt to find the
complete prime factorization of a given integer.  Some control is possible
over each of the methods, but in general default choices for the parameters
would give good results for a wide range of arguments.

In the second subsection we decribe functions that enable access to each of
the factorization methods available in Magma.  The user has control over
parameters for these methods.

Factorization functions in Magma return a factorization sequence.  This is a
sequence of two-element tuples [ <p_1, k_1>, ..., <p_r, k_r>], with p_1<p_2<
... <p_r distinct prime numbers and k_i positive, which is used to represent
integers in factored form: n is the product over i of p_i^(k_i).  Although
such sequences are printed like ordinary sequences, they form a separate
category RngIntEltfact.  Operations on such factorization sequences are
described in the next online help node.

Subsections:

    [+1] factorization-general
    [+2] factorization-specific
    [+3] factorization-related
===============================================================================

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:40:09 2004

Input: factor(22)





Output: Magma V2.10-6     Fri Jan  9 2004 16:40:06 on modular  [Seed = 1132684213]
   -------------------------------------

[ <2, 1>, <11, 1> ]
1

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:40:40 2004

Input: prime(22)






Output: Magma V2.10-6     Fri Jan  9 2004 16:40:37 on modular  [Seed = 1284271321]
   -------------------------------------


>> prime(22)
   ^
User error: Identifier 'prime' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:41:03 2004

Input: prime ?






Output: Magma V2.10-6     Fri Jan  9 2004 16:41:00 on modular  [Seed = 1435858425]
   -------------------------------------


>> prime ?
         ^
User error: bad syntax

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:41:22 2004

Input: ? prime 






Output: Magma V2.10-6     Fri Jan  9 2004 16:41:19 on modular  [Seed = 1587445473]
   -------------------------------------

45 matches:
     1   S   /magma/ring-field-algebra/function-field/ideals/boolean/\
             pred-ideal-prime
     2   S   /magma/ring-field-algebra/function-field/ideals/\
             ideal-ops-further/ideals-prime
     3   S   /magma/ring-field-algebra/integer/prime
     4   I   /magma/geometry/schemes/schemes-global/PrimeComponents
     5   I   /magma/geometry/supersingular-divisors-on-module-curves/\
             properties/Prime
     6   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/tools-soluble-quotient-process/\
             tools-specific-normal-series/KeepPrimePower
     7   I   /magma/module-lattice/lattice/genus/local_genus_invariants/Prime
     8   I   /magma/module-lattice/quadratic/creation/creation/PrimeForm
     9   I   /magma/ring-field-algebra/affine-algebra/operations/IsPrime
    10   I   /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\
             PrimeIdeal
    11   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             DegreeOnePrimeIdeals
    12   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\
             IsPrime
    13   I   /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime
    14   I   /magma/ring-field-algebra/detail/generic/related/PrimeField
    15   I   /magma/ring-field-algebra/detail/generic/related/PrimeRing
    16   I   /magma/ring-field-algebra/finite-Galois-field/creation/structure/\
             PrimeField
    17   I   /magma/ring-field-algebra/function-field/elements/elt-other/\
             DifferentiationSequence
    18   I   /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime
    19   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    20   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    21   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    22   I   /magma/ring-field-algebra/ideal-groebner/ideal-operation/\
             predicate/IsPrime
    23   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    24   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    25   I   /magma/ring-field-algebra/integer/operation-element/\
             element-Boolean/IsPrime
    26   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    27   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    28   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    29   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    30   I   /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis
    31   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    32   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    33   I   /magma/ring-field-algebra/integer/prime/primality/IsPrime
    34   I   /magma/ring-field-algebra/integer/prime/primality/IsPrimePower
    35   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    36   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    37   I   /magma/ring-field-algebra/integer/random/RandomPrime
    38   I   /magma/ring-field-algebra/integer/random/RandomPrime
    39   I   /magma/ring-field-algebra/local/invariants/Prime
    40   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    41   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    42   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    43   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             NumberOfPrimePolynomials
    44   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             PrimePolynomials
    45   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             RandomPrimePolynomial
To view an entry, type ? followed by the number next to it

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:42:32 2004

Input: ? ?






Output: Magma V2.10-6     Fri Jan  9 2004 16:42:28 on modular  [Seed = 1739028579]
   -------------------------------------

2 matches:
     1   O   /
     2   O   /browser
To view an entry, type ? followed by the number next to it

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:42:52 2004

Input: ? ? 2






Output: Magma V2.10-6     Fri Jan  9 2004 16:42:49 on modular  [Seed = 1890611049]
   -------------------------------------

2 matches:
     1   O   /
     2   O   /browser
To view an entry, type ? followed by the number next to it

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:43:11 2004

Input: ?






Output: Magma V2.10-6     Fri Jan  9 2004 16:43:07 on modular  [Seed = 2042193493]
   -------------------------------------

===============================================================================
PATH: /
KIND: Overview
===============================================================================

You are reading about the Magma online help system.  This system 
gives you information about Magma while you are at the computer. 
To see this help page at any time, all you have to do is to type  

        ?

                  ----------

The online help system comes in two modes: the single request
mode and the Magma Help Browser.  To enter the Browser, type

        ??

The Browser is useful if you intend to read several related
help nodes, because you can exploit the tree structure of the
online help.  Once you are in the Browser, you can type

        help

again to find out how to use the Browser, and for a more
detailed explanation of the whole online help system.

                  ----------

Single help requests begin with the ? character.
Examples are:

?print
?magma
?ring
?example

If your help request is ambiguous, Magma will return a numbered 
list of matches.  To see the contents of one of them, 
type  ?  followed by its number.

Some help pages suggest other pages that you might like to look at 
as well.  They are prefixed by a code such as   +3  or  +5 .  
To read one of them, type  ?  followed by the code.

You can also supply the full pathname of a help node, if you know it.
For example:

?/system/quit
?/magma/module/homomorphism 

                  ----------

The online help system offers tab completion. If you type a few letters 
of your help request and then press the tab key, Magma will "complete" 
the request if there is a unique completion.  Otherwise, it will 
complete the request as far as possible, and then emit a beep.  
Press the tab key again to see all the possibilities.
ALWAYS PRESS TAB BEFORE THE END OF THE LINE, 
SO AS TO SEE EVERY RELEVANT HELP PAGE.
(On a few operating systems, the tab completion feature 
cannot be made available.)

                  ----------

The content of the online help system comes from two sources:
the "Handbook of Magma Functions" (Bosma and Cannon)
and specially-written overview nodes.
You may also wish to consult the books
"An Introduction to Algebraic Programming in Magma"
(Cannon and Playoust) and "Solving Problems with Magma"
(Bosma, Cannon, Playoust and Steel).

                  ----------

The online help system is also available in an HTML form
suitable for Internet browsers.  To use this,
move to a shell prompt (outside Magma) and type

    magmahelp

                  ----------

To leave Magma, type 

    quit;

or <Ctrl>-D.
===============================================================================

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:44:39 2004

Input: ??






Output: Magma V2.10-6     Fri Jan  9 2004 16:44:36 on modular  [Seed = 46275974]
   -------------------------------------

Magma Help Browser
Type help for more information
Unknown command ";"
Unknown command "quit;"

Total time: 2.879 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:45:05 2004

Input: ??






Output: Magma V2.10-6     Fri Jan  9 2004 16:45:02 on modular  [Seed = 282070926]
   -------------------------------------

Magma Help Browser
Type help for more information
Unknown command ";"
Unknown command "quit;"

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 16:45:20 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);


Output: Magma V2.10-6     Fri Jan  9 2004 16:45:17 on modular  [Seed = 433653428]
   -------------------------------------


Total time: 2.989 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:45:23 2004

Input: ?? help






Output: Magma V2.10-6     Fri Jan  9 2004 16:45:20 on modular  [Seed = 568409745]
   -------------------------------------

2 matches:
     1   O   /
     2   O   /browser
To view an entry, type ? followed by the number next to it

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 16:45:35 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);
M6;

Output: Magma V2.10-6     Fri Jan  9 2004 16:45:31 on modular  [Seed = 736834704]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (1, 6)(2, 3)
            (1, 4, 6)(2, 5, 3)
            (3, 6)
            (1, 2)
            (4, 5)
[2]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (1, 5)
            (1, 2, 5)
            (1, 2)(4, 5)
            (1, 5)(2, 4)
            (3, 6)
[3]     Order 72           Length 10
        Permutation group acting on a set of cardinality 6
        Order = 72 = 2^3 * 3^2
            (2, 4)
            (1, 6)(2, 5)(3, 4)
            (2, 4)(5, 6)
            (1, 4, 2)
            (3, 6, 5)
[4]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (3, 6)
            (1, 2, 3)(5, 6)
[5]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (1, 2)(3, 6)(4, 5)
            (1, 5, 2, 6, 3, 4)
[6]     Order 360          Length 1
        Permutation group acting on a set of cardinality 6
        Order = 360 = 2^3 * 3^2 * 5
            (1, 2)(3, 6)
            (1, 2, 5, 6)(3, 4)

Total time: 2.989 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:45:42 2004

Input: ?? help
?2





Output: Magma V2.10-6     Fri Jan  9 2004 16:45:39 on modular  [Seed = 888416887]
   -------------------------------------

2 matches:
     1   O   /
     2   O   /browser
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /browser
KIND: Overview
===============================================================================
Introduction
------------

You are reading about the Magma Help Browser. 
To read this help page when you are in the Browser, type

        help

The Browser is entered by typing

        ??

and it lets you browse through the Magma Help tree.  
When you are in the Browser, the prompt is  ??> .
To get from the Browser back to Magma, type

        quit

or

        <Ctrl>-D

at the Browser prompt.

Magma has a simpler help system, which you can access without entering 
the Browser.  To find out about it, leave the Browser (as explained
above) and then type

        ? 

While you are still in the Browser, you can type the single word
"walk" (without the quotes) followed by <Return> to view the next
help screen.  Keep typing "walk" (or "w") to see further screens.

[If you are in the Browser, type the single word "w" (without the quotes)
followed by <Return> to view the next help screen.]
===============================================================================

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:46:28 2004

Input: ?? help
?2 walk






Output: Magma V2.10-6     Fri Jan  9 2004 16:46:25 on modular  [Seed = 1039999820]
   -------------------------------------

2 matches:
     1   O   /
     2   O   /browser
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /browser
KIND: Overview
===============================================================================
Introduction
------------

You are reading about the Magma Help Browser. 
To read this help page when you are in the Browser, type

        help

The Browser is entered by typing

        ??

and it lets you browse through the Magma Help tree.  
When you are in the Browser, the prompt is  ??> .
To get from the Browser back to Magma, type

        quit

or

        <Ctrl>-D

at the Browser prompt.

Magma has a simpler help system, which you can access without entering 
the Browser.  To find out about it, leave the Browser (as explained
above) and then type

        ? 

While you are still in the Browser, you can type the single word
"walk" (without the quotes) followed by <Return> to view the next
help screen.  Keep typing "walk" (or "w") to see further screens.

[If you are in the Browser, type the single word "w" (without the quotes)
followed by <Return> to view the next help screen.]
===============================================================================

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:47:10 2004

Input: w






Output: Magma V2.10-6     Fri Jan  9 2004 16:47:07 on modular  [Seed = 3322337501]
   -------------------------------------


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

Total time: 2.879 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:47:26 2004

Input: ?






Output: Magma V2.10-6     Fri Jan  9 2004 16:47:23 on modular  [Seed = 3490762491]
   -------------------------------------

===============================================================================
PATH: /
KIND: Overview
===============================================================================

You are reading about the Magma online help system.  This system 
gives you information about Magma while you are at the computer. 
To see this help page at any time, all you have to do is to type  

        ?

                  ----------

The online help system comes in two modes: the single request
mode and the Magma Help Browser.  To enter the Browser, type

        ??

The Browser is useful if you intend to read several related
help nodes, because you can exploit the tree structure of the
online help.  Once you are in the Browser, you can type

        help

again to find out how to use the Browser, and for a more
detailed explanation of the whole online help system.

                  ----------

Single help requests begin with the ? character.
Examples are:

?print
?magma
?ring
?example

If your help request is ambiguous, Magma will return a numbered 
list of matches.  To see the contents of one of them, 
type  ?  followed by its number.

Some help pages suggest other pages that you might like to look at 
as well.  They are prefixed by a code such as   +3  or  +5 .  
To read one of them, type  ?  followed by the code.

You can also supply the full pathname of a help node, if you know it.
For example:

?/system/quit
?/magma/module/homomorphism 

                  ----------

The online help system offers tab completion. If you type a few letters 
of your help request and then press the tab key, Magma will "complete" 
the request if there is a unique completion.  Otherwise, it will 
complete the request as far as possible, and then emit a beep.  
Press the tab key again to see all the possibilities.
ALWAYS PRESS TAB BEFORE THE END OF THE LINE, 
SO AS TO SEE EVERY RELEVANT HELP PAGE.
(On a few operating systems, the tab completion feature 
cannot be made available.)

                  ----------

The content of the online help system comes from two sources:
the "Handbook of Magma Functions" (Bosma and Cannon)
and specially-written overview nodes.
You may also wish to consult the books
"An Introduction to Algebraic Programming in Magma"
(Cannon and Playoust) and "Solving Problems with Magma"
(Bosma, Cannon, Playoust and Steel).

                  ----------

The online help system is also available in an HTML form
suitable for Internet browsers.  To use this,
move to a shell prompt (outside Magma) and type

    magmahelp

                  ----------

To leave Magma, type 

    quit;

or <Ctrl>-D.
===============================================================================

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 16:47:48 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1];

Output: Magma V2.10-6     Fri Jan  9 2004 16:47:44 on modular  [Seed = 3642345241]
   -------------------------------------

rec<recformat<order, length, subgroup, presentation> | 
    order := 48,
    length := 15,
    subgroup := Permutation group acting on a set of cardinality 6
    Order = 48 = 2^4 * 3
        (1, 2)(3, 6)
        (3, 6, 4)
        (1, 2)(3, 5)(4, 6)
        (1, 2)(3, 4)(5, 6)
        (1, 2)(3, 6)(4, 5)
    >

Total time: 2.919 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 16:48:01 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6;

Output: Magma V2.10-6     Fri Jan  9 2004 16:47:58 on modular  [Seed = 3777101615]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (1, 5)(4, 6)
            (1, 5, 3)(2, 6, 4)
            (1, 6)
            (4, 5)
            (2, 3)
[2]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (3, 4)
            (3, 4, 5)
            (2, 3)(4, 5)
            (2, 5)(3, 4)
            (1, 6)
[3]     Order 72           Length 10
        Permutation group acting on a set of cardinality 6
        Order = 72 = 2^3 * 3^2
            (2, 5)
            (1, 2)(3, 5)(4, 6)
            (2, 5)(3, 6)
            (2, 5, 4)
            (1, 6, 3)
[4]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (1, 6)
            (1, 4, 5)(3, 6)
[5]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (1, 6)(2, 3)(4, 5)
            (1, 2, 4, 3, 5, 6)
[6]     Order 360          Length 1
        Permutation group acting on a set of cardinality 6
        Order = 360 = 2^3 * 3^2 * 5
            (1, 6)(4, 5)
            (1, 2)(3, 6, 4, 5)

Total time: 2.929 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:48:11 2004

Input: ?prime






Output: Magma V2.10-6     Fri Jan  9 2004 16:48:08 on modular  [Seed = 3911841585]
   -------------------------------------

45 matches:
     1   S   /magma/ring-field-algebra/function-field/ideals/boolean/\
             pred-ideal-prime
     2   S   /magma/ring-field-algebra/function-field/ideals/\
             ideal-ops-further/ideals-prime
     3   S   /magma/ring-field-algebra/integer/prime
     4   I   /magma/geometry/schemes/schemes-global/PrimeComponents
     5   I   /magma/geometry/supersingular-divisors-on-module-curves/\
             properties/Prime
     6   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/tools-soluble-quotient-process/\
             tools-specific-normal-series/KeepPrimePower
     7   I   /magma/module-lattice/lattice/genus/local_genus_invariants/Prime
     8   I   /magma/module-lattice/quadratic/creation/creation/PrimeForm
     9   I   /magma/ring-field-algebra/affine-algebra/operations/IsPrime
    10   I   /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\
             PrimeIdeal
    11   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             DegreeOnePrimeIdeals
    12   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\
             IsPrime
    13   I   /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime
    14   I   /magma/ring-field-algebra/detail/generic/related/PrimeField
    15   I   /magma/ring-field-algebra/detail/generic/related/PrimeRing
    16   I   /magma/ring-field-algebra/finite-Galois-field/creation/structure/\
             PrimeField
    17   I   /magma/ring-field-algebra/function-field/elements/elt-other/\
             DifferentiationSequence
    18   I   /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime
    19   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    20   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    21   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    22   I   /magma/ring-field-algebra/ideal-groebner/ideal-operation/\
             predicate/IsPrime
    23   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    24   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    25   I   /magma/ring-field-algebra/integer/operation-element/\
             element-Boolean/IsPrime
    26   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    27   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    28   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    29   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    30   I   /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis
    31   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    32   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    33   I   /magma/ring-field-algebra/integer/prime/primality/IsPrime
    34   I   /magma/ring-field-algebra/integer/prime/primality/IsPrimePower
    35   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    36   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    37   I   /magma/ring-field-algebra/integer/random/RandomPrime
    38   I   /magma/ring-field-algebra/integer/random/RandomPrime
    39   I   /magma/ring-field-algebra/local/invariants/Prime
    40   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    41   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    42   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    43   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             NumberOfPrimePolynomials
    44   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             PrimePolynomials
    45   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             RandomPrimePolynomial
To view an entry, type ? followed by the number next to it

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 16:48:34 2004

Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);
M6;

Output: Magma V2.10-6     Fri Jan  9 2004 16:48:31 on modular  [Seed = 4063423517]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (1, 2)(5, 6)
            (1, 4, 2)(3, 6, 5)
            (2, 6)
            (1, 5)
            (3, 4)
[2]     Order 48           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 48 = 2^4 * 3
            (4, 5)
            (1, 4, 5)
            (1, 5)(3, 4)
            (1, 3)(4, 5)
            (2, 6)
[3]     Order 72           Length 10
        Permutation group acting on a set of cardinality 6
        Order = 72 = 2^3 * 3^2
            (1, 3)
            (1, 4)(2, 3)(5, 6)
            (1, 3)(4, 6)
            (1, 5, 3)
            (2, 6, 4)
[4]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (2, 6)
            (1, 2, 5)(4, 6)
[5]     Order 120          Length 6
        Permutation group acting on a set of cardinality 6
        Order = 120 = 2^3 * 3 * 5
            (1, 5)(2, 6)(3, 4)
            (1, 6, 2, 3, 5, 4)
[6]     Order 360          Length 1
        Permutation group acting on a set of cardinality 6
        Order = 360 = 2^3 * 3^2 * 5
            (1, 5)(2, 6)
            (1, 4, 6, 5)(2, 3)

Total time: 2.899 seconds, Total memory usage: 1.94MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:48:41 2004

Input: ?prime
?3






Output: Magma V2.10-6     Fri Jan  9 2004 16:48:38 on modular  [Seed = 4215006477]
   -------------------------------------

45 matches:
     1   S   /magma/ring-field-algebra/function-field/ideals/boolean/\
             pred-ideal-prime
     2   S   /magma/ring-field-algebra/function-field/ideals/\
             ideal-ops-further/ideals-prime
     3   S   /magma/ring-field-algebra/integer/prime
     4   I   /magma/geometry/schemes/schemes-global/PrimeComponents
     5   I   /magma/geometry/supersingular-divisors-on-module-curves/\
             properties/Prime
     6   I   /magma/group/finitely-presented-groups-advanced/\
             soluble-quotients/tools-soluble-quotient-process/\
             tools-specific-normal-series/KeepPrimePower
     7   I   /magma/module-lattice/lattice/genus/local_genus_invariants/Prime
     8   I   /magma/module-lattice/quadratic/creation/creation/PrimeForm
     9   I   /magma/ring-field-algebra/affine-algebra/operations/IsPrime
    10   I   /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\
             PrimeIdeal
    11   I   /magma/ring-field-algebra/algebraic-field/ideal-class-group/\
             DegreeOnePrimeIdeals
    12   I   /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\
             IsPrime
    13   I   /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime
    14   I   /magma/ring-field-algebra/detail/generic/related/PrimeField
    15   I   /magma/ring-field-algebra/detail/generic/related/PrimeRing
    16   I   /magma/ring-field-algebra/finite-Galois-field/creation/structure/\
             PrimeField
    17   I   /magma/ring-field-algebra/function-field/elements/elt-other/\
             DifferentiationSequence
    18   I   /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime
    19   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    20   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    21   I   /magma/ring-field-algebra/function-field/structure-related/\
             structure-related-other/PrimeRing
    22   I   /magma/ring-field-algebra/ideal-groebner/ideal-operation/\
             predicate/IsPrime
    23   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    24   I   /magma/ring-field-algebra/integer/factor/factorization-related/\
             PrimeBasis
    25   I   /magma/ring-field-algebra/integer/operation-element/\
             element-Boolean/IsPrime
    26   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    27   I   /magma/ring-field-algebra/integer/prime/next-previous/NextPrime
    28   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    29   I   /magma/ring-field-algebra/integer/prime/next-previous/\
             PreviousPrime
    30   I   /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis
    31   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    32   I   /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime
    33   I   /magma/ring-field-algebra/integer/prime/primality/IsPrime
    34   I   /magma/ring-field-algebra/integer/prime/primality/IsPrimePower
    35   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    36   I   /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime
    37   I   /magma/ring-field-algebra/integer/random/RandomPrime
    38   I   /magma/ring-field-algebra/integer/random/RandomPrime
    39   I   /magma/ring-field-algebra/local/invariants/Prime
    40   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    41   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    42   I   /magma/ring-field-algebra/local/invariants/PrimeRing
    43   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             NumberOfPrimePolynomials
    44   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             PrimePolynomials
    45   I   /magma/ring-field-algebra/univariate-polynomial/finitefields/\
             RandomPrimePolynomial
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/ring-field-algebra/integer/prime
KIND: Section
===============================================================================
Primes and Primality Testing.

Primality testing algorithms enable the user to certify the primality of
prime integers.  Proving the primality of very big integers can be time
consuming and therefore in some of the algorithms using primes and
factorization of integers the user can speed up the algorithm by explicitly
allowing Magma to use probable primes rather than certified primes.

A probable prime is an integer that has failed some compositeness test; if
an integer passes a compositeness test it will be composite, but there is a
(small) probability that a composite number will fail the test and is hence
called a probable prime.  Each Miller-Rabin test for instance, has a
probability of less than 1/4 of declaring a composite number probably prime;
in practice that means that numbers that fail several such cheap independent
Miller-Rabin compositeness tests will be prime.

Unless specifically asked otherwise, Magma will use rigorous primality
proofs.

Subsections:

    [+1] primality
    [+2] next-previous
===============================================================================

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:49:39 2004

Input: ?PI







Output: Magma V2.10-6     Fri Jan  9 2004 16:49:36 on modular  [Seed = 2219088436]
   -------------------------------------

2 matches:
     1   S   /magma/group/soluble/subgroups/Hall-pi-Sylow
     2   I   /magma/ring-field-algebra/real-complex/operation-element/\
             constant/Pi
To view an entry, type ? followed by the number next to it

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:50:03 2004

Input: ?pi







Output: Magma V2.10-6     Fri Jan  9 2004 16:49:59 on modular  [Seed = 2387514313]
   -------------------------------------

2 matches:
     1   S   /magma/group/soluble/subgroups/Hall-pi-Sylow
     2   I   /magma/ring-field-algebra/real-complex/operation-element/\
             constant/Pi
To view an entry, type ? followed by the number next to it

Total time: 3.169 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:50:28 2004

Input: ?PI







Output: Magma V2.10-6     Fri Jan  9 2004 16:50:24 on modular  [Seed = 2656994302]
   -------------------------------------

2 matches:
     1   S   /magma/group/soluble/subgroups/Hall-pi-Sylow
     2   I   /magma/ring-field-algebra/real-complex/operation-element/\
             constant/Pi
To view an entry, type ? followed by the number next to it

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 16:50:47 2004

Input: ?PI
?2







Output: Magma V2.10-6     Fri Jan  9 2004 16:50:44 on modular  [Seed = 2808593107]
   -------------------------------------

2 matches:
     1   S   /magma/group/soluble/subgroups/Hall-pi-Sylow
     2   I   /magma/ring-field-algebra/real-complex/operation-element/\
             constant/Pi
To view an entry, type ? followed by the number next to it
===============================================================================
PATH: /magma/ring-field-algebra/real-complex/operation-element/constant/Pi
KIND: Intrinsic
===============================================================================
Pi(R) : FldPr -> FldPrElt
Pi(R) : FldRe -> FldReElt
Pi(R) : FldCom -> FldComElt
Pi(R, p) : FldPr, RngIntElt -> FldPrElt

    The value of pi computed to the accuracy associated with R if R is a
    field of fixed precision, and to the default precision if R is the
    free real field.  To allow the calculation of the constant to a
    precision different from the default in the latter case, a version
    of this function with the precision as a second argument is
    available.
===============================================================================

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29)
Time: Fri Jan  9 17:43:11 2004

Input: ?list







Output: Magma V2.10-6     Fri Jan  9 2004 17:43:08 on modular  [Seed = 3179130111]
   -------------------------------------

11 matches:
     1   S   /magma/aggregate/list
     2   S   /magma/ring-field-algebra/ideal-groebner/order/elim-list
     3   I   /language/function-procedure-package/attribute/access/\
             ListAttributes
     4   I   /magma/aggregate/list/creation/SequenceToList
     5   I   /magma/aggregate/list/creation/TupleToList
     6   I   /magma/aggregate/tuple-cartesian-product/tuple-access/TupleToList
     7   I   /magma/geometry/grd-rng/gr-lists/gr-searching/K3ListCodimensions
     8   I   /system/environment-options/info/ListCategories
     9   I   /system/environment-options/info/ListCategories
    10   I   /system/environment-options/info/ListSignatures
    11   I   /system/environment-options/verbose/ListVerbose
To view an entry, type ? followed by the number next to it

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 18:51:56 2004

Input: A6:=Alt(6);M6:=MaximalSubgroups(A6);
M6;

Output: Magma V2.10-6     Fri Jan  9 2004 18:51:53 on modular  [Seed = 349443504]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 24           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 24 = 2^3 * 3
            (1, 3)(2, 4)
            (3, 6, 5)
            (1, 6)(3, 5)
            (1, 3)(5, 6)
[2]     Order 24           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 24 = 2^3 * 3
            (1, 3)(5, 6)
            (1, 4, 3)(2, 5, 6)
            (1, 6)(3, 5)
            (1, 6)(2, 4)
[3]     Order 36           Length 10
        Permutation group acting on a set of cardinality 6
        Order = 36 = 2^2 * 3^2
            (1, 3)(2, 5, 4, 6)
            (2, 4)(5, 6)
            (1, 2, 4)(3, 6, 5)
            (1, 4, 2)(3, 6, 5)
[4]     Order 60           Length 6
        Permutation group acting on a set of cardinality 6
        Order = 60 = 2^2 * 3 * 5
            (1, 5)(3, 4)
            (1, 6, 3)
[5]     Order 60           Length 6
        Permutation group acting on a set of cardinality 6
        Order = 60 = 2^2 * 3 * 5
            (3, 5)(4, 6)
            (1, 4, 2)(3, 5, 6)

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 18:53:33 2004

Input: A6:=Alt(6);M6:=MaximalSubgroups(A6);
M6;
G:=sub<Sym(6)|(1,3)(2,5,4,6),(2,4)(5,6),(1,2,4)(3,6,5),(1,4,2)(3,6,5)>;
Classes(G);


Output: Magma V2.10-6     Fri Jan  9 2004 18:53:30 on modular  [Seed = 265227976]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 24           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 24 = 2^3 * 3
            (3, 4)(5, 6)
            (1, 4, 5)(2, 6, 3)
            (1, 2)(3, 5)
            (3, 5)(4, 6)
[2]     Order 24           Length 15
        Permutation group acting on a set of cardinality 6
        Order = 24 = 2^3 * 3
            (3, 5)(4, 6)
            (1, 5, 3)
            (1, 2)(3, 5)
            (1, 3)(2, 5)
[3]     Order 36           Length 10
        Permutation group acting on a set of cardinality 6
        Order = 36 = 2^2 * 3^2
            (1, 2)(3, 5, 6, 4)
            (3, 6)(4, 5)
            (1, 5, 4)
            (2, 3, 6)
[4]     Order 60           Length 6
        Permutation group acting on a set of cardinality 6
        Order = 60 = 2^2 * 3 * 5
            (2, 5)(3, 6)
            (1, 4, 3)(2, 6, 5)
[5]     Order 60           Length 6
        Permutation group acting on a set of cardinality 6
        Order = 60 = 2^2 * 3 * 5
            (2, 4)(5, 6)
            (1, 4, 5)
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 9      
        Rep (2, 4)(5, 6)

[3]     Order 3       Length 4      
        Rep (1, 2, 4)(3, 6, 5)

[4]     Order 3       Length 4      
        Rep (3, 6, 5)

[5]     Order 4       Length 9      
        Rep (1, 3)(2, 6, 4, 5)

[6]     Order 4       Length 9      
        Rep (1, 3)(2, 5, 4, 6)



Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 19:03:51 2004

Input: A8:=Alt(8);M8:=MaximalSubgroups(A8);
M8;
G:=sub<Sym(8)|(1,3)(2,5,4,6),(2,4)(5,6),(1,2,4)(3,6,5),(1,4,2)(3,6,5)>;
Classes(G);


Output: Magma V2.10-6     Fri Jan  9 2004 19:03:48 on modular  [Seed = 1536894210]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 360          Length 56
        Permutation group acting on a set of cardinality 8
        Order = 360 = 2^3 * 3^2 * 5
            (2, 6)(7, 8)
            (1, 7)(2, 3, 5)(4, 6)
            (1, 8, 7)
[2]     Order 720          Length 28
        Permutation group acting on a set of cardinality 8
        Order = 720 = 2^4 * 3^2 * 5
            (1, 4, 3, 7, 5)
            (2, 6)(7, 8)
[3]     Order 2520         Length 8
        Permutation group acting on a set of cardinality 8
        Order = 2520 = 2^3 * 3^2 * 5 * 7
            (1, 6, 7)
            (1, 4)(3, 7)(5, 8, 6)
[4]     Order 576          Length 35
        Permutation group acting on a set of cardinality 8
        Order = 576 = 2^6 * 3^2
            (2, 8)(6, 7)
            (1, 4, 3, 5)(2, 6, 8, 7)
            (5, 6, 7)
            (1, 2, 8)
            (4, 6)(5, 7)
            (4, 5)(6, 7)
            (1, 8)(2, 3)
            (1, 2)(3, 8)
[5]     Order 1344         Length 15
        Permutation group acting on a set of cardinality 8
        Order = 1344 = 2^6 * 3 * 7
            (1, 8, 4, 6)(2, 7, 5, 3)
            (1, 8, 3, 4)(2, 5, 7, 6)
            (1, 2)(3, 8)(4, 5)(6, 7)
            (1, 6)(2, 7)(3, 5)(4, 8)
            (1, 8)(2, 3)(4, 6)(5, 7)
[6]     Order 1344         Length 15
        Permutation group acting on a set of cardinality 8
        Order = 1344 = 2^6 * 3 * 7
            (1, 6)(2, 3)(4, 7)(5, 8)
            (1, 6, 2, 8)(3, 7, 5, 4)
            (1, 6)(2, 4)(3, 7)(5, 8)
            (1, 3)(2, 5)(4, 8)(6, 7)
            (1, 2)(3, 5)(4, 6)(7, 8)
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 9      
        Rep (2, 4)(5, 6)

[3]     Order 3       Length 4      
        Rep (1, 2, 4)(3, 6, 5)

[4]     Order 3       Length 4      
        Rep (3, 6, 5)

[5]     Order 4       Length 9      
        Rep (1, 3)(2, 6, 4, 5)

[6]     Order 4       Length 9      
        Rep (1, 3)(2, 5, 4, 6)



Total time: 3.009 seconds, Total memory usage: 2.24MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 19:07:56 2004

Input: A8:=Alt(8);M8:=MaximalSubgroups(A8);
M8;
G:=sub<Sym(8)|(2,8)(6,7),(1,4,3,5)(2,6,8,7),(5,6,7),(1,2,8),(4,6)(5,7),(4,6)(5,7),(1,8)(2,3),(1,2)(3,8)
>;
Classes(G);

H:=sub<Sym(8)|(1,8,4,6)(2,7,5,3),(1,8,3,4)(2,5,7,6),(1,2)(3,8)(4,5)(6,7),(1,6)(2,7)(3,5)(4,8),(1,8)(2,3)(4,6)(5,7)>;
Classes(H);


Output: Magma V2.10-6     Fri Jan  9 2004 19:07:53 on modular  [Seed = 3078081235]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 360          Length 56
        Permutation group acting on a set of cardinality 8
        Order = 360 = 2^3 * 3^2 * 5
            (2, 6)(3, 4)
            (1, 6, 7)(2, 8)(3, 5)
            (3, 5, 4)
[2]     Order 720          Length 28
        Permutation group acting on a set of cardinality 8
        Order = 720 = 2^4 * 3^2 * 5
            (1, 5, 8, 7, 3)
            (2, 6)(3, 4)
[3]     Order 2520         Length 8
        Permutation group acting on a set of cardinality 8
        Order = 2520 = 2^3 * 3^2 * 5 * 7
            (2, 3, 5)
            (1, 4, 2)(3, 7)(5, 8)
[4]     Order 576          Length 35
        Permutation group acting on a set of cardinality 8
        Order = 576 = 2^6 * 3^2
            (2, 3)(4, 6)
            (1, 5, 8, 7)(2, 4, 3, 6)
            (1, 2, 3)
            (4, 5, 6)
            (1, 3)(2, 8)
            (1, 8)(2, 3)
            (4, 5)(6, 7)
            (4, 7)(5, 6)
[5]     Order 1344         Length 15
        Permutation group acting on a set of cardinality 8
        Order = 1344 = 2^6 * 3 * 7
            (1, 7, 6, 3)(2, 5, 4, 8)
            (1, 3, 2, 6)(4, 7, 8, 5)
            (1, 8)(2, 3)(4, 7)(5, 6)
            (1, 7)(2, 5)(3, 6)(4, 8)
            (1, 3)(2, 8)(4, 5)(6, 7)
[6]     Order 1344         Length 15
        Permutation group acting on a set of cardinality 8
        Order = 1344 = 2^6 * 3 * 7
            (1, 4)(2, 5)(3, 8)(6, 7)
            (1, 8, 7, 3)(2, 6, 4, 5)
            (1, 4)(2, 5)(3, 7)(6, 8)
            (1, 6)(2, 3)(4, 8)(5, 7)
            (1, 7)(2, 8)(3, 4)(5, 6)

>>  ;
    ^
User error: bad syntax

>> Classes(G);
           ^
User error: Identifier 'G' has not been declared or assigned
Conjugacy Classes of group H
----------------------------
[1]     Order 1       Length 1      
        Rep Id(H)

[2]     Order 2       Length 7      
        Rep (1, 4)(2, 5)(3, 7)(6, 8)

[3]     Order 2       Length 42     
        Rep (1, 3)(2, 7)(4, 8)(5, 6)

[4]     Order 2       Length 42     
        Rep (2, 4)(7, 8)

[5]     Order 3       Length 224    
        Rep (1, 5, 8)(3, 4, 6)

[6]     Order 4       Length 84     
        Rep (1, 8, 4, 6)(2, 7, 5, 3)

[7]     Order 4       Length 168    
        Rep (1, 4, 3, 8)(2, 6, 7, 5)

[8]     Order 4       Length 168    
        Rep (1, 5)(2, 8, 4, 7)

[9]     Order 6       Length 224    
        Rep (1, 4)(2, 7, 8, 5, 3, 6)

[10]    Order 7       Length 192    
        Rep (1, 3, 5, 4, 2, 6, 8)

[11]    Order 7       Length 192    
        Rep (1, 4, 8, 5, 6, 3, 2)



Total time: 3.009 seconds, Total memory usage: 2.24MB


************** MAGMA *****************
Host weil.math.umass.edu. (128.119.47.164)
Time: Fri Jan  9 19:08:19 2004

Input: A8:=Alt(8);M8:=MaximalSubgroups(A8);
M8;
G:=sub<Sym(8)|(2,8)(6,7),(1,4,3,5)(2,6,8,7),(5,6,7),(1,2,8),(4,6)(5,7),(4,6)(5,7),(1,8)(2,3),(1,2)(3,8)>;
Classes(G);

H:=sub<Sym(8)|(1,8,4,6)(2,7,5,3),(1,8,3,4)(2,5,7,6),(1,2)(3,8)(4,5)(6,7),(1,6)(2,7)(3,5)(4,8),(1,8)(2,3)(4,6)(5,7)>;
Classes(H);


Output: Magma V2.10-6     Fri Jan  9 2004 19:08:15 on modular  [Seed = 2842285284]
   -------------------------------------

Conjugacy classes of subgroups
------------------------------

[1]     Order 360          Length 56
        Permutation group acting on a set of cardinality 8
        Order = 360 = 2^3 * 3^2 * 5
            (1, 2)(3, 7)
            (2, 8)(3, 6)(4, 7, 5)
            (1, 2, 8)
[2]     Order 720          Length 28
        Permutation group acting on a set of cardinality 8
        Order = 720 = 2^4 * 3^2 * 5
            (2, 4, 8, 6, 5)
            (1, 2)(3, 7)
[3]     Order 2520         Length 8
        Permutation group acting on a set of cardinality 8
        Order = 2520 = 2^3 * 3^2 * 5 * 7
            (2, 8, 3)
            (1, 3, 4)(2, 5)(6, 8)
[4]     Order 576          Length 35
        Permutation group acting on a set of cardinality 8
        Order = 576 = 2^6 * 3^2
            (1, 7)(2, 3)
            (1, 2, 7, 3)(4, 8, 6, 5)
            (2, 4, 3)
            (1, 8, 7)
            (2, 4)(3, 6)
            (2, 3)(4, 6)
            (1, 8)(5, 7)
            (1, 5)(7, 8)
[5]     Order 1344         Length 15
        Permutation group acting on a set of cardinality 8
        Order = 1344 = 2^6 * 3 * 7
            (1, 6, 3, 8)(2, 4, 5, 7)
            (1, 5, 6, 8)(2, 3, 7, 4)
            (1, 5)(2, 3)(4, 6)(7, 8)
            (1, 6)(2, 7)(3, 8)(4, 5)
            (1, 8)(2, 4)(3, 6)(5, 7)
[6]     Order 1344         Length 15
        Permutation group acting on a set of cardinality 8
        Order = 1344 = 2^6 * 3 * 7
            (1, 4)(2, 6)(3, 8)(5, 7)
            (1, 8, 3, 7)(2, 4, 6, 5)
            (1, 4)(2, 5)(3, 8)(6, 7)
            (1, 6)(2, 3)(4, 7)(5, 8)
            (1, 2)(3, 6)(4, 5)(7, 8)
Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 6      
        Rep (4, 6)(5, 7)

[3]     Order 2       Length 9      
        Rep (1, 3)(2, 8)(4, 5)(6, 7)

[4]     Order 2       Length 12     
        Rep (1, 5)(2, 6)(3, 7)(4, 8)

[5]     Order 2       Length 12     
        Rep (1, 5)(2, 7)(3, 6)(4, 8)

[6]     Order 2       Length 36     
        Rep (2, 8)(4, 7)

[7]     Order 3       Length 16     
        Rep (5, 6, 7)

[8]     Order 3       Length 32     
        Rep (1, 3, 8)(4, 5, 7)

[9]     Order 3       Length 32     
        Rep (1, 3, 8)(4, 5, 6)

[10]    Order 4       Length 36     
        Rep (1, 2, 3, 8)(4, 7, 5, 6)

[11]    Order 4       Length 36     
        Rep (1, 4, 3, 5)(2, 6, 8, 7)

[12]    Order 4       Length 36     
        Rep (1, 4, 3, 5)(2, 7, 8, 6)

[13]    Order 4       Length 72     
        Rep (2, 8)(4, 7, 5, 6)

[14]    Order 6       Length 48     
        Rep (1, 3)(2, 8)(4, 5, 7)

[15]    Order 6       Length 96     
        Rep (1, 4, 3, 5, 8, 6)(2, 7)

[16]    Order 6       Length 96     
        Rep (1, 4, 3, 5, 8, 7)(2, 6)


Conjugacy Classes of group H
----------------------------
[1]     Order 1       Length 1      
        Rep Id(H)

[2]     Order 2       Length 7      
        Rep (1, 4)(2, 5)(3, 7)(6, 8)

[3]     Order 2       Length 42     
        Rep (1, 3)(2, 7)(4, 8)(5, 6)

[4]     Order 2       Length 42     
        Rep (2, 4)(7, 8)

[5]     Order 3       Length 224    
        Rep (1, 5, 8)(3, 4, 6)

[6]     Order 4       Length 84     
        Rep (1, 8, 4, 6)(2, 7, 5, 3)

[7]     Order 4       Length 168    
        Rep (1, 4, 3, 8)(2, 6, 7, 5)

[8]     Order 4       Length 168    
        Rep (1, 5)(2, 8, 4, 7)

[9]     Order 6       Length 224    
        Rep (1, 4)(2, 7, 8, 5, 3, 6)

[10]    Order 7       Length 192    
        Rep (1, 3, 5, 4, 2, 6, 8)

[11]    Order 7       Length 192    
        Rep (1, 4, 8, 5, 6, 3, 2)



Total time: 3.029 seconds, Total memory usage: 2.24MB


************** MAGMA *****************
Host host-65-199-137-206.link.com.eg. (65.199.137.206)
Time: Sat Jan 10 02:05:27 2004

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

Output: Magma V2.10-6     Sat Jan 10 2004 02:05:24 on modular  [Seed = 4097077241]
   -------------------------------------

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

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host host-65-199-137-206.link.com.eg. (65.199.137.206)
Time: Sat Jan 10 02:06:00 2004

Input: x^2

Output: Magma V2.10-6     Sat Jan 10 2004 02:05:57 on modular  [Seed = 4012864643]
   -------------------------------------


>> x^2;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host f03v-10-160.d1.club-internet.fr. (212.194.45.160)
Time: Sat Jan 10 08:31:40 2004

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

Output: Magma V2.10-6     Sat Jan 10 2004 08:31:37 on modular  [Seed = 1132692174]
   -------------------------------------

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

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30)
Time: Sat Jan 10 14:28:35 2004

Input: x�+2x�+7x+3

Output: Magma V2.10-6     Sat Jan 10 2004 14:28:32 on modular  [Seed = 290521919]
   -------------------------------------


>> x^�+2x^�+7x+3;
    ^
User error: Unknown character (ascii value -77)

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30)
Time: Sat Jan 10 14:29:42 2004

Input: 2*x^2=3 + 6*x^2 + 22*x + 12

Output: Magma V2.10-6     Sat Jan 10 2004 14:29:39 on modular  [Seed = 1065299410]
   -------------------------------------


>> 2*x^2=3 + 6*x^2 + 22*x + 12;
               ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30)
Time: Sat Jan 10 14:44:46 2004

Input: solve 2*x^2=3 + 6*x^2 + 22*x + 12

Output: Magma V2.10-6     Sat Jan 10 2004 14:44:43 on modular  [Seed = 4004444299]
   -------------------------------------


>> solve 2*x^2=3 + 6*x^2 + 22*x + 12;
         ^
User error: bad syntax

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30)
Time: Sat Jan 10 14:49:06 2004

Input: solve( 2*x^2=3 + 6*x^2 + 22*x + 12=0)

Output: Magma V2.10-6     Sat Jan 10 2004 14:49:03 on modular  [Seed = 2395904495]
   -------------------------------------


>> solve( 2*x^2=3 + 6*x^2 + 22*x + 12=0);
            ^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30)
Time: Sat Jan 10 14:50:16 2004

Input: polroots(2*x^3+ 6*x^2 + 22*x + 12 = 0)

Output: Magma V2.10-6     Sat Jan 10 2004 14:50:12 on modular  [Seed = 2732766616]
   -------------------------------------


>> polroots(2*x^3+ 6*x^2 + 22*x + 12 = 0);
              ^
User error: Identifier 'x' has not been declared or assigned

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host lns-vlq-1-82-65-162-47.adsl.proxad.net. (82.65.162.47)
Time: Sat Jan 10 16:15:06 2004

Input: 6941372044925487738675387152189111745732039847701504273612536130666996402409750124783895966530170647511075085147439137214921516137540516588371707169957057

Output: Magma V2.10-6     Sat Jan 10 2004 16:15:03 on modular  [Seed = 2918024885]
   -------------------------------------

6941372044925487738675387152189111745732039847701504273612536130666996402409750\
124783895966530170647511075085147439137214921516137540516588371707169957057

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host p508F5134.dip0.t-ipconnect.de. (80.143.81.52)
Time: Sun Jan 11 06:12:18 2004

Input: 123

Output: Magma V2.10-6     Sun Jan 11 2004 06:12:14 on modular  [Seed = 526282880]
   -------------------------------------

123

Total time: 3.149 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host p508F5134.dip0.t-ipconnect.de. (80.143.81.52)
Time: Sun Jan 11 06:12:33 2004

Input: 123*4

Output: Magma V2.10-6     Sun Jan 11 2004 06:12:30 on modular  [Seed = 105343369]
   -------------------------------------

492

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host cw178.neoplus.adsl.tpnet.pl. (80.54.219.178)
Time: Sun Jan 11 08:06:15 2004

Input: 2+2

Output: Magma V2.10-6     Sun Jan 11 2004 08:06:12 on modular  [Seed = 4071880871]
   -------------------------------------

4

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host cw178.neoplus.adsl.tpnet.pl. (80.54.219.178)
Time: Sun Jan 11 08:06:34 2004

Input: 2+2+2

Output: Magma V2.10-6     Sun Jan 11 2004 08:06:31 on modular  [Seed = 4257019835]
   -------------------------------------

6

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host cw178.neoplus.adsl.tpnet.pl. (80.54.219.178)
Time: Sun Jan 11 08:07:05 2004

Input: G := [1 2 3];
IsPlanar(G);

Output: Magma V2.10-6     Sun Jan 11 2004 08:07:02 on modular  [Seed = 3836079747]
   -------------------------------------


>> G := [1 2 3];
           ^
User error: bad syntax

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

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host bln2-t2-2.mcbone.net. (62.104.208.83)
Time: Sun Jan 11 11:59:57 2004

Input: g:=Sl(2,3);

Output: Magma V2.10-6     Sun Jan 11 2004 11:59:53 on modular  [Seed = 1865330293]
   -------------------------------------


>> g:=Sl(2,3);;
      ^
User error: Identifier 'Sl' has not been declared or assigned

Total time: 3.210 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host wbar11.tampa1-4-4-132-114.tampa1.dsl-verizon.net. (4.4.132.114)
Time: Sun Jan 11 16:09:55 2004

Input: 1+1

Output: Magma V2.10-6     Sun Jan 11 2004 16:09:52 on modular  [Seed = 1646500311]
   -------------------------------------

2

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:33:43 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);

Output: Magma V2.10-6     Mon Jan 12 2004 11:33:39 on modular  [Seed = 358062421]
   -------------------------------------


Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:33:56 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);

Output: Magma V2.10-6     Mon Jan 12 2004 11:33:52 on modular  [Seed = 1629744434]
   -------------------------------------


Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:34:10 2004

Input: 2+2;

Output: Magma V2.10-6     Mon Jan 12 2004 11:34:07 on modular  [Seed = 1747641396]
   -------------------------------------

4

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:34:22 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);

Output: Magma V2.10-6     Mon Jan 12 2004 11:34:19 on modular  [Seed = 2000026591]
   -------------------------------------


Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:34:34 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);


Output: Magma V2.10-6     Mon Jan 12 2004 11:34:31 on modular  [Seed = 2117923530]
   -------------------------------------

false

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:35:44 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));


Output: Magma V2.10-6     Mon Jan 12 2004 11:35:41 on modular  [Seed = 1208665270]
   -------------------------------------

false

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:35:54 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
fac;


Output: Magma V2.10-6     Mon Jan 12 2004 11:35:51 on modular  [Seed = 1461050259]
   -------------------------------------

false
[ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ]

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:36:39 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
fac;
NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 


Output: Magma V2.10-6     Mon Jan 12 2004 11:36:36 on modular  [Seed = 2816813712]
   -------------------------------------

false
[ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ]

>> NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
                                         ^
User error: bad syntax

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:37:11 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
fac;
[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 


Output: Magma V2.10-6     Mon Jan 12 2004 11:37:08 on modular  [Seed = 2934711225]
   -------------------------------------

false
[ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ]
[ -1, 1, 1, -1, 1 ]

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:37:21 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
fac;
&*[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 


Output: Magma V2.10-6     Mon Jan 12 2004 11:37:18 on modular  [Seed = 3221041826]
   -------------------------------------

false
[ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ]
1

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:37:38 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
fac;
&*[<NormResidueSymbol(-a/c,-b/c,p[1]),p> : p in fac ]; 


Output: Magma V2.10-6     Mon Jan 12 2004 11:37:35 on modular  [Seed = 2260995050]
   -------------------------------------

false
[ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ]

&*(
    S: [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <...
)
reduct(
    S: [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <...,
    op: Intrinsic '*' ,
    allow_empty: true,
    id: 1,
    ids: one
)
In file "/usr/local/magma/package/Aggregate/SeqEnum/eseq_misc.m", line 45, 
column 20:
>>             s := op(s, x);
                      ^
Runtime error in '*': Bad argument types
Argument types given: Tup, Tup

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:37:46 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
fac;
[<NormResidueSymbol(-a/c,-b/c,p[1]),p> : p in fac ]; 


Output: Magma V2.10-6     Mon Jan 12 2004 11:37:43 on modular  [Seed = 2379153657]
   -------------------------------------

false
[ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ]
[ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ]

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:37:58 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[<NormResidueSymbol(-a/c,-b/c,p[1]),p> : p in fac ]; 


Output: Magma V2.10-6     Mon Jan 12 2004 11:37:55 on modular  [Seed = 2497059284]
   -------------------------------------

false
[ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ]

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 11:38:10 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[<NormResidueSymbol(-a/c,-b/c,p[1]),p> : p in fac ]; 
BadPrimes(C);


Output: Magma V2.10-6     Mon Jan 12 2004 11:38:07 on modular  [Seed = 3819007663]
   -------------------------------------

false
[ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ]
[ 2, 127 ]

Total time: 3.289 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:23:14 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 234; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[<NormResidueSymbol(-a/c,-b/c,p[1]),p> : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:23:11 on modular  [Seed = 4038223659]
   -------------------------------------

false
[ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ]
[ 2, 127 ]
false

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:23:25 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[<NormResidueSymbol(-a/c,-b/c,p[1]),p> : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:23:22 on modular  [Seed = 4189807063]
   -------------------------------------

false
[ <-1, <2, 2>>, <1, <13, 1>>, <-1, <41, 1>>, <1, <127, 1>>, <-1, <2593, 1>>, 
<-1, <571303, 1>> ]
[ 2, 41, 2593, 571303 ]
false

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:23:55 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
&*[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:23:52 on modular  [Seed = 3263191758]
   -------------------------------------

false
1
[ 2, 41, 2593, 571303 ]
false

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:24:26 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -33709; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:24:23 on modular  [Seed = 3414774696]
   -------------------------------------

false
[ -1, 1, -1, 1, -1, -1 ]
[ 2, 41, 2593, 571303 ]
false

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:24:43 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -337034234249; c := 127;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:24:40 on modular  [Seed = 3701359776]
   -------------------------------------

false
[ -1, 1, -1, 1, -1, -1 ]
[ 2, 127, 571303, 849203 ]
false

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:24:57 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -337034234249; c := 12452342347;
C := Conic(P2,a*x^2 + b*y^2 + c*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:24:53 on modular  [Seed = 610712676]
   -------------------------------------

false
[ -1, -1, 1, 1, -1, -1, 1 ]
[ 2, 23, 571303, 849203 ]
false

Total time: 3.619 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:35:30 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -337034234249; c := 12452342347;
C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x-5);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:35:26 on modular  [Seed = 492799974]
   -------------------------------------


>> C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x-5);
             ^
Runtime error in 'Conic': The polynomial is not homogeneous

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

>> fac := Factorization(Integers()!Discriminant(C));
                                                ^
User error: Identifier 'C' has not been declared or assigned

>> [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
                                             ^
User error: Identifier 'fac' has not been declared or assigned

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

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Mon Jan 12 12:36:01 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
a := 23423423; b := -337034234249; c := 12452342347;
C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x*z-5*z^2);
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
BadPrimes(C);
HasSolubilityCertificate(C);


Output: Magma V2.10-6     Mon Jan 12 2004 12:35:58 on modular  [Seed = 1730543036]
   -------------------------------------


>> C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x*z-5*z^2);
             ^
Runtime error in 'Conic': The polynomial is not homogeneous

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

>> fac := Factorization(Integers()!Discriminant(C));
                                                ^
User error: Identifier 'C' has not been declared or assigned

>> [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
                                             ^
User error: Identifier 'fac' has not been declared or assigned

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

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host PCjmedina.upct.es. (212.128.22.131)
Time: Mon Jan 12 13:43:13 2004

Input: #g:=GL(2,3);

Output: Magma V2.10-6     Mon Jan 12 2004 13:43:09 on modular  [Seed = 3246615385]
   -------------------------------------


>> #g:=GL(2,3);;
     ^
User error: Illegal left hand side of an assignment statement

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host PCjmedina.upct.es. (212.128.22.131)
Time: Mon Jan 12 13:43:27 2004

Input: #GL(2,3);

Output: Magma V2.10-6     Mon Jan 12 2004 13:43:24 on modular  [Seed = 3583475516]
   -------------------------------------

48

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host PCjmedina.upct.es. (212.128.22.131)
Time: Mon Jan 12 13:44:02 2004

Input: g:=GL(2,3);
for x in g do;
print x;
end for;


Output: Magma V2.10-6     Mon Jan 12 2004 13:43:58 on modular  [Seed = 3701372439]
   -------------------------------------

[1 0]
[0 1]
[2 1]
[2 0]
[1 1]
[1 0]
[0 2]
[1 2]
[2 0]
[0 1]
[1 2]
[2 0]
[2 2]
[1 0]
[0 1]
[1 2]
[1 0]
[1 1]
[2 1]
[1 1]
[1 1]
[2 1]
[0 2]
[1 1]
[2 0]
[2 1]
[1 2]
[0 2]
[2 2]
[0 2]
[0 1]
[1 0]
[1 0]
[2 1]
[2 1]
[0 2]
[1 1]
[0 2]
[0 2]
[1 0]
[2 0]
[1 1]
[1 2]
[1 1]
[2 2]
[2 1]
[0 1]
[1 1]
[1 0]
[0 2]
[2 1]
[1 0]
[1 1]
[2 0]
[0 2]
[2 1]
[2 0]
[0 2]
[1 2]
[1 0]
[2 2]
[2 0]
[0 1]
[2 1]
[1 0]
[2 2]
[2 1]
[2 2]
[1 1]
[1 2]
[0 2]
[2 2]
[2 0]
[1 2]
[1 2]
[0 1]
[2 2]
[0 1]
[0 1]
[2 0]
[1 0]
[1 2]
[2 1]
[0 1]
[1 1]
[0 1]
[0 2]
[2 0]
[2 0]
[2 2]
[1 2]
[2 2]
[2 2]
[1 2]
[0 1]
[2 2]

Total time: 2.929 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host 2(SERVFAIL) (209.234.160.76)
Time: Mon Jan 12 14:29:28 2004

Input: p := 1000000000000000000000000000057;
F := POpen("sort -n", "w");
for i := 100 to 110 do
   fprintf F, "%30o (2^%o mod p)n", 2^i mod p, i;
end for;
delete F;


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

************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:35:49 2004

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

Output: Magma V2.10-6     Tue Jan 13 2004 01:35:46 on modular  [Seed = 1815068059]
   -------------------------------------

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:36:35 2004

Input: print 2+4 ;

Output: Magma V2.10-6     Tue Jan 13 2004 01:36:32 on modular  [Seed = 1444251539]
   -------------------------------------

6

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:44:05 2004

Input: print 2+4 ;
2/3-4/5;

Output: Magma V2.10-6     Tue Jan 13 2004 01:44:02 on modular  [Seed = 3002163509]
   -------------------------------------

6
-2/15

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:46:28 2004

Input: 1/7 + 1/8;

Output: Magma V2.10-6     Tue Jan 13 2004 01:46:25 on modular  [Seed = 2479900647]
   -------------------------------------

15/56

Total time: 2.869 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:47:20 2004

Input: 1/2+1/7 + 1/8;

Output: Magma V2.10-6     Tue Jan 13 2004 01:47:17 on modular  [Seed = 2244366789]
   -------------------------------------

43/56

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:48:12 2004

Input: 1/2+1/3;

Output: Magma V2.10-6     Tue Jan 13 2004 01:48:08 on modular  [Seed = 2362398737]
   -------------------------------------

5/6

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:49:03 2004

Input: 1.0/7.0;

Output: Magma V2.10-6     Tue Jan 13 2004 01:49:00 on modular  [Seed = 4155777822]
   -------------------------------------

0.142857142857142857142857142855

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:51:13 2004

Input: Factorial(19);

Output: Magma V2.10-6     Tue Jan 13 2004 01:51:10 on modular  [Seed = 3886297740]
   -------------------------------------

121645100408832000

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:51:33 2004

Input: Factorial(50);

Output: Magma V2.10-6     Tue Jan 13 2004 01:51:30 on modular  [Seed = 4004330409]
   -------------------------------------

30414093201713378043612608166064768844377641568960512000000000000

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:51:51 2004

Input: Factorial(150);

Output: Magma V2.10-6     Tue Jan 13 2004 01:51:48 on modular  [Seed = 3499296097]
   -------------------------------------

5713383956445854590478932865261054003189553578601126418254837583317982912484539\
8393126574488675311145377107878746854204162666250198684504466355949195922066574\
9425920957357789293253572904449624724054167907221184454371222696755200000000000\
00000000000000000000000000

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:52:20 2004

Input: Factorial(1500);

Output: Magma V2.10-6     Tue Jan 13 2004 01:52:17 on modular  [Seed = 3684175439]
   -------------------------------------

4811997796779774860166990093581379781834808040672613808130855941163057518900109\
5591292230585206733851868464009619343585194052091124618166270271481881393331431\
6279628102998441493337890446893955104871678797693253036994704678292343992633265\
4565286074860507574636692832360664549227754112008343808672736937788767600021140\
5318480244354207419604864176969950581435222198851194568984095705945549589054568\
3217923389191494429859199577347929594024990968456430204018693811756039644243332\
2211412597437481780424263330976980429395287003461935412501421004564766406324016\
2007560108665290568646128342557147350985358724154623253371867470765120422073867\
9639357752586921097530417620943435690504974703535317644815031747509118582309069\
9836106608478775831611058573601336537743186073857226132573823365683527194735269\
5180865573043834027955539012765489372645042504406597752357481931532872356635411\
2245783340405222947464028295854584787087783463794318623688248190091770914440348\
8594139431934391022316865586976179966907505952760850246559318139856621478680121\
1651657222004123456498258513120359126022843038535083709796101565934859483203933\
4433086014758131083630741185624044124201919471275854829191721730459611221227014\
3429787069193215408298694595474825110578218158639727582034210147045730063359013\
9512919549474113721711616912519714191760699935509810254849967087635936181176363\
9542241860313466829288784928722494854566901388316101353779163279405037014002901\
2550913214078261464049573351804867098336013409786036476263865889487317449987013\
3559364805443430831459505987809215393353387232078177562975021460595422358573128\
0854171623360302351386527354380530345319626208115660198968792752571639883520908\
7493034611551833120292726370844672939438187988883954973187697868224932062859963\
1628662375508826209854754631984276392670919216923002770077734756077549035942976\
2091594162115814394614845095493703574867702768076875445801643146475950313689484\
9028289717332801351843575870005642592263841188949652797584605271795804481373708\
6806600171993703579485864029383208714528950303253881360812631162134750100307772\
6343374670128204707156508107146899051214322595285054830539304022174006860616124\
7165963019243486409453982808567746538302612835377107115230419754979887070613989\
3609140045659756285435787771636258253666592102151236142132724425850991205720020\
4936605808966008918885946596129277243578662659345176158412987891544622491696888\
6009264028475638243174612035776793311958928046868734806178807298636278858222701\
9465263474828590646048451070702923434422714349595857654843699542321849363652767\
7719783146810135894429552198797020080689340966246506257697052333334628260138600\
9869815518033114536565245348295549797991558643847468734567787445111770225044171\
1504844638414485210092261397271970571029038581873069951161330495772310508760528\
2497065142383842698086395070804182983183113613736285120417164151968683342541191\
3713958914959721003215354594111466653049890652924079816480400739477592783604566\
8573993316428972539932745757171947402454257142633700815922407278403640595355142\
0755994460563379867172123162232577634121641808995327220393832444625114103466461\
4886339723709627682265615756119466554575701742984240484030975892561865050792104\
3007241637877939825811059339138925526124514467627126548126795078784022672860886\
2519745813621417827864074028963096780089096632639870185381070508861934890124974\
0500582072727123273372814177513272201386059116962069278929045679469840980855744\
7756701311883266010859016027592252397754508251628808293537776536569608111330584\
7971606948478989231967439702444518427022664033263173190921171511439716795000425\
9026925509313021598441809741843547430046728194979822710252987373274902799207970\
0287275900856241172902880909546551703263202853584498085358955307673717177961902\
0810986187290463488490602496000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000000000000\
0000000

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 01:54:06 2004

Input: GCD(512,68);

Output: Magma V2.10-6     Tue Jan 13 2004 01:54:03 on modular  [Seed = 3448642547]
   -------------------------------------

4

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:01:56 2004

Input: Sqrt(19);

Output: Magma V2.10-6     Tue Jan 13 2004 02:01:53 on modular  [Seed = 139190239]
   -------------------------------------

4.358898943540673552236981983816

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:21:57 2004

Input: Z:=
BraidGroup(6);


Output: Magma V2.10-6     Tue Jan 13 2004 02:21:54 on modular  [Seed = 1073978596]
   -------------------------------------


Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:22:10 2004

Input: Z:=
BraidGroup(6);
Z

Output: Magma V2.10-6     Tue Jan 13 2004 02:22:07 on modular  [Seed = 1225430496]
   -------------------------------------

GrpBrd : Z on 6 strings

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:23:14 2004

Input: Z:=
BraidGroup(6);
Z
z=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2

Output: Magma V2.10-6     Tue Jan 13 2004 02:23:11 on modular  [Seed = 3204276823]
   -------------------------------------


>> z=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2;
   ^
User error: bad syntax

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:23:27 2004

Input: Z:=
BraidGroup(6);
Z
z:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2

Output: Magma V2.10-6     Tue Jan 13 2004 02:23:24 on modular  [Seed = 2816768893]
   -------------------------------------


>> z:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2;
   ^
User error: bad syntax

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:23:47 2004

Input: Z:=
BraidGroup(6);
Z
u:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2

Output: Magma V2.10-6     Tue Jan 13 2004 02:23:43 on modular  [Seed = 2901373029]
   -------------------------------------


>> u:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2;
   ^
User error: bad syntax

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:24:18 2004

Input: Z:=
BraidGroup(6);
Z
Z.1*Z.2*Z.1*Z.2*Z.1*Z.2

Output: Magma V2.10-6     Tue Jan 13 2004 02:24:15 on modular  [Seed = 2513848508]
   -------------------------------------


>> Z.1*Z.2*Z.1*Z.2*Z.1*Z.2;
   ^
User error: bad syntax

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:27:23 2004

Input: Z:=BraidGroup(6);
u:=Z.1;


Output: Magma V2.10-6     Tue Jan 13 2004 02:27:20 on modular  [Seed = 4054985759]
   -------------------------------------


Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:27:42 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;

Output: Magma V2.10-6     Tue Jan 13 2004 02:27:39 on modular  [Seed = 3869588283]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:28:21 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
v:=Z.1*Z.2;

Output: Magma V2.10-6     Tue Jan 13 2004 02:28:18 on modular  [Seed = 4021039563]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:29:26 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
v:=Z.1*Z.2;
U:=Z.1*Z.2*Z.1;
V=Z.2*Z.1*Z.2;

Output: Magma V2.10-6     Tue Jan 13 2004 02:29:23 on modular  [Seed = 3718120376]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>

>> V=Z.2*Z.1*Z.2;;
   ^
User error: Identifier 'V' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:29:53 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;

Output: Magma V2.10-6     Tue Jan 13 2004 02:29:50 on modular  [Seed = 3246530457]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:31:03 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;
NormalForm(u*v);


Output: Magma V2.10-6     Tue Jan 13 2004 02:31:00 on modular  [Seed = 1031726014]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>
Z.2 * Z.1 * Z.2^2 * Z.1 * Z.2
<Artin, 0, [
    (1, 3),
    (1, 3)
], 0>

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:31:33 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;
y:=NormalForm(u*v);


Output: Magma V2.10-6     Tue Jan 13 2004 02:31:30 on modular  [Seed = 307350775]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:31:56 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;
y:=NormalForm(u*v^(-1));


Output: Magma V2.10-6     Tue Jan 13 2004 02:31:53 on modular  [Seed = 256692689]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:32:12 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;
y:=NormalForm(u*v^(-1));
y;

Output: Magma V2.10-6     Tue Jan 13 2004 02:32:09 on modular  [Seed = 1932570045]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>
Id(Z)
<Artin, 0, [], 0>

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:32:57 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;
y:=NormalForm(u*v^(-1));
y;
A:=Z.1;


Output: Magma V2.10-6     Tue Jan 13 2004 02:32:54 on modular  [Seed = 2050598251]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>
Id(Z)
<Artin, 0, [], 0>

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 02:33:19 2004

Input: Z:=BraidGroup(6);
u:=Z.1;
u;
u:=Z.1*Z.2;
u:=Z.1*Z.2*Z.1;
v:=Z.2*Z.1*Z.2;
y:=NormalForm(u*v^(-1));
y;
A:=Z.1;
A;


Output: Magma V2.10-6     Tue Jan 13 2004 02:33:16 on modular  [Seed = 1747695459]
   -------------------------------------

Z.1
<Artin, 0, [
    (1, 2)
], 0>
Id(Z)
<Artin, 0, [], 0>
Z.1
<Artin, 0, [
    (1, 2)
], 0>

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:42:59 2004

Input: 1/0.;

Output: Magma V2.10-6     Tue Jan 13 2004 02:42:56 on modular  [Seed = 4122350658]
   -------------------------------------


>> 1/0.;;
       ^
User error: Real literal has no digits after decimal point

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:43:20 2004

Input: 1.0/0.0;

Output: Magma V2.10-6     Tue Jan 13 2004 02:43:17 on modular  [Seed = 4240383326]
   -------------------------------------


>> 1.0/0.0;;
      ^
Runtime error in '/': Division by zero

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:44:35 2004

Input: Sqrt(-1);

Output: Magma V2.10-6     Tue Jan 13 2004 02:44:32 on modular  [Seed = 3936947005]
   -------------------------------------

1.0000000000000000000000000000*i

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:55:54 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(100);

Output: Magma V2.10-6     Tue Jan 13 2004 02:55:51 on modular  [Seed = 3381276025]
   -------------------------------------

[ 0, 1/100, 1/99, 1/98, 1/97, 1/96, 1/95, 1/94, 1/93, 1/92, 1/91, 1/90, 1/89, 
1/88, 1/87, 1/86, 1/85, 1/84, 1/83, 1/82, 1/81, 1/80, 1/79, 1/78, 1/77, 1/76, 
1/75, 1/74, 1/73, 1/72, 1/71, 1/70, 1/69, 1/68, 1/67, 1/66, 1/65, 1/64, 1/63, 
1/62, 1/61, 1/60, 1/59, 1/58, 1/57, 1/56, 1/55, 1/54, 1/53, 1/52, 1/51, 1/50, 
2/99, 1/49, 2/97, 1/48, 2/95, 1/47, 2/93, 1/46, 2/91, 1/45, 2/89, 1/44, 2/87, 
1/43, 2/85, 1/42, 2/83, 1/41, 2/81, 1/40, 2/79, 1/39, 2/77, 1/38, 2/75, 1/37, 
2/73, 1/36, 2/71, 1/35, 2/69, 1/34, 2/67, 3/100, 1/33, 3/98, 2/65, 3/97, 1/32, 
3/95, 2/63, 3/94, 1/31, 3/92, 2/61, 3/91, 1/30, 3/89, 2/59, 3/88, 1/29, 3/86, 
2/57, 3/85, 1/28, 3/83, 2/55, 3/82, 1/27, 3/80, 2/53, 3/79, 1/26, 3/77, 2/51, 
3/76, 1/25, 4/99, 3/74, 2/49, 3/73, 4/97, 1/24, 4/95, 3/71, 2/47, 3/70, 4/93, 
1/23, 4/91, 3/68, 2/45, 3/67, 4/89, 1/22, 4/87, 3/65, 2/43, 3/64, 4/85, 1/21, 
4/83, 3/62, 2/41, 3/61, 4/81, 1/20, 5/99, 4/79, 3/59, 5/98, 2/39, 5/97, 3/58, 
4/77, 5/96, 1/19, 5/94, 4/75, 3/56, 5/93, 2/37, 5/92, 3/55, 4/73, 5/91, 1/18, 
5/89, 4/71, 3/53, 5/88, 2/35, 5/87, 3/52, 4/69, 5/86, 1/17, 5/84, 4/67, 3/50, 
5/83, 2/33, 5/82, 3/49, 4/65, 5/81, 6/97, 1/16, 6/95, 5/79, 4/63, 3/47, 5/78, 
2/31, 5/77, 3/46, 4/61, 5/76, 6/91, 1/15, 6/89, 5/74, 4/59, 3/44, 5/73, 2/29, 
5/72, 3/43, 7/100, 4/57, 5/71, 6/85, 7/99, 1/14, 7/97, 6/83, 5/69, 4/55, 7/96, 
3/41, 5/68, 7/95, 2/27, 7/94, 5/67, 3/40, 7/93, 4/53, 5/66, 6/79, 7/92, 1/13, 
7/90, 6/77, 5/64, 4/51, 7/89, 3/38, 5/63, 7/88, 2/25, 7/87, 5/62, 8/99, 3/37, 
7/86, 4/49, 5/61, 6/73, 7/85, 8/97, 1/12, 8/95, 7/83, 6/71, 5/59, 4/47, 7/82, 
3/35, 8/93, 5/58, 7/81, 2/23, 7/80, 5/57, 8/91, 3/34, 7/79, 4/45, 5/56, 6/67, 
7/78, 8/89, 9/100, 1/11, 9/98, 8/87, 7/76, 6/65, 5/54, 9/97, 4/43, 7/75, 3/32, 
8/85, 5/53, 7/74, 9/95, 2/21, 9/94, 7/73, 5/52, 8/83, 3/31, 7/72, 4/41, 9/92, 
5/51, 6/61, 7/71, 8/81, 9/91, 1/10, 10/99, 9/89, 8/79, 7/69, 6/59, 5/49, 9/88, 
4/39, 7/68, 10/97, 3/29, 8/77, 5/48, 7/67, 9/86, 2/19, 9/85, 7/66, 5/47, 8/75, 
3/28, 10/93, 7/65, 4/37, 9/83, 5/46, 6/55, 7/64, 8/73, 9/82, 10/91, 11/100, 1/9,
11/98, 10/89, 9/80, 8/71, 7/62, 6/53, 11/97, 5/44, 9/79, 4/35, 11/96, 7/61, 
10/87, 3/26, 11/95, 8/69, 5/43, 7/60, 9/77, 11/94, 2/17, 11/93, 9/76, 7/59, 
5/42, 8/67, 11/92, 3/25, 10/83, 7/58, 11/91, 4/33, 9/74, 5/41, 11/90, 6/49, 
7/57, 8/65, 9/73, 10/81, 11/89, 12/97, 1/8, 12/95, 11/87, 10/79, 9/71, 8/63, 
7/55, 6/47, 11/86, 5/39, 9/70, 4/31, 11/85, 7/54, 10/77, 13/100, 3/23, 11/84, 
8/61, 13/99, 5/38, 12/91, 7/53, 9/68, 11/83, 13/98, 2/15, 13/97, 11/82, 9/67, 
7/52, 12/89, 5/37, 13/96, 8/59, 11/81, 3/22, 13/95, 10/73, 7/51, 11/80, 4/29, 
13/94, 9/65, 5/36, 11/79, 6/43, 13/93, 7/50, 8/57, 9/64, 10/71, 11/78, 12/85, 
13/92, 14/99, 1/7, 14/97, 13/90, 12/83, 11/76, 10/69, 9/62, 8/55, 7/48, 13/89, 
6/41, 11/75, 5/34, 14/95, 9/61, 13/88, 4/27, 11/74, 7/47, 10/67, 13/87, 3/20, 
14/93, 11/73, 8/53, 13/86, 5/33, 12/79, 7/46, 9/59, 11/72, 13/85, 15/98, 2/13, 
15/97, 13/84, 11/71, 9/58, 7/45, 12/77, 5/32, 13/83, 8/51, 11/70, 14/89, 3/19, 
13/82, 10/63, 7/44, 11/69, 15/94, 4/25, 13/81, 9/56, 14/87, 5/31, 16/99, 11/68, 
6/37, 13/80, 7/43, 15/92, 8/49, 9/55, 10/61, 11/67, 12/73, 13/79, 14/85, 15/91, 
16/97, 1/6, 16/95, 15/89, 14/83, 13/77, 12/71, 11/65, 10/59, 9/53, 17/100, 8/47,
15/88, 7/41, 13/76, 6/35, 17/99, 11/64, 16/93, 5/29, 14/81, 9/52, 13/75, 17/98, 
4/23, 15/86, 11/63, 7/40, 17/97, 10/57, 13/74, 16/91, 3/17, 17/96, 14/79, 11/62,
8/45, 13/73, 5/28, 17/95, 12/67, 7/39, 16/89, 9/50, 11/61, 13/72, 15/83, 17/94, 
2/11, 17/93, 15/82, 13/71, 11/60, 9/49, 16/87, 7/38, 12/65, 17/92, 5/27, 18/97, 
13/70, 8/43, 11/59, 14/75, 17/91, 3/16, 16/85, 13/69, 10/53, 17/90, 7/37, 18/95,
11/58, 15/79, 19/100, 4/21, 17/89, 13/68, 9/47, 14/73, 19/99, 5/26, 16/83, 
11/57, 17/88, 6/31, 19/98, 13/67, 7/36, 15/77, 8/41, 17/87, 9/46, 19/97, 10/51, 
11/56, 12/61, 13/66, 14/71, 15/76, 16/81, 17/86, 18/91, 19/96, 1/5, 20/99, 
19/94, 18/89, 17/84, 16/79, 15/74, 14/69, 13/64, 12/59, 11/54, 10/49, 19/93, 
9/44, 17/83, 8/39, 15/73, 7/34, 20/97, 13/63, 19/92, 6/29, 17/82, 11/53, 16/77, 
5/24, 19/91, 14/67, 9/43, 13/62, 17/81, 21/100, 4/19, 19/90, 15/71, 11/52, 
18/85, 7/33, 17/80, 10/47, 13/61, 16/75, 19/89, 3/14, 20/93, 17/79, 14/65, 
11/51, 19/88, 8/37, 21/97, 13/60, 18/83, 5/23, 17/78, 12/55, 19/87, 7/32, 16/73,
9/41, 20/91, 11/50, 13/59, 15/68, 17/77, 19/86, 21/95, 2/9, 21/94, 19/85, 17/76,
15/67, 13/58, 11/49, 20/89, 9/40, 16/71, 7/31, 19/84, 12/53, 17/75, 22/97, 5/22,
18/79, 13/57, 21/92, 8/35, 19/83, 11/48, 14/61, 17/74, 20/87, 23/100, 3/13, 
22/95, 19/82, 16/69, 13/56, 23/99, 10/43, 17/73, 7/30, 18/77, 11/47, 15/64, 
19/81, 23/98, 4/17, 21/89, 17/72, 13/55, 22/93, 9/38, 23/97, 14/59, 19/80, 5/21,
21/88, 16/67, 11/46, 17/71, 23/96, 6/25, 19/79, 13/54, 20/83, 7/29, 22/91, 
15/62, 23/95, 8/33, 17/70, 9/37, 19/78, 10/41, 21/86, 11/45, 23/94, 12/49, 
13/53, 14/57, 15/61, 16/65, 17/69, 18/73, 19/77, 20/81, 21/85, 22/89, 23/93, 
24/97, 1/4, 25/99, 24/95, 23/91, 22/87, 21/83, 20/79, 19/75, 18/71, 17/67, 
16/63, 15/59, 14/55, 13/51, 25/98, 12/47, 23/90, 11/43, 21/82, 10/39, 19/74, 
9/35, 17/66, 25/97, 8/31, 23/89, 15/58, 22/85, 7/27, 20/77, 13/50, 19/73, 25/96,
6/23, 23/88, 17/65, 11/42, 16/61, 21/80, 26/99, 5/19, 24/91, 19/72, 14/53, 
23/87, 9/34, 22/83, 13/49, 17/64, 21/79, 25/94, 4/15, 23/86, 19/71, 15/56, 
26/97, 11/41, 18/67, 25/93, 7/26, 24/89, 17/63, 27/100, 10/37, 23/85, 13/48, 
16/59, 19/70, 22/81, 25/92, 3/11, 26/95, 23/84, 20/73, 17/62, 14/51, 25/91, 
11/40, 19/69, 27/98, 8/29, 21/76, 13/47, 18/65, 23/83, 5/18, 27/97, 22/79, 
17/61, 12/43, 19/68, 26/93, 7/25, 23/82, 16/57, 25/89, 9/32, 20/71, 11/39, 
24/85, 13/46, 28/99, 15/53, 17/60, 19/67, 21/74, 23/81, 25/88, 27/95, 2/7, 
27/94, 25/87, 23/80, 21/73, 19/66, 17/59, 15/52, 28/97, 13/45, 24/83, 11/38, 
20/69, 29/100, 9/31, 25/86, 16/55, 23/79, 7/24, 26/89, 19/65, 12/41, 29/99, 
17/58, 22/75, 27/92, 5/17, 28/95, 23/78, 18/61, 13/44, 21/71, 29/98, 8/27, 
27/91, 19/64, 11/37, 25/84, 14/47, 17/57, 20/67, 23/77, 26/87, 29/97, 3/10, 
28/93, 25/83, 22/73, 19/63, 16/53, 29/96, 13/43, 23/76, 10/33, 27/89, 17/56, 
24/79, 7/23, 25/82, 18/59, 29/95, 11/36, 26/85, 15/49, 19/62, 23/75, 27/88, 
4/13, 29/94, 25/81, 21/68, 17/55, 30/97, 13/42, 22/71, 31/100, 9/29, 23/74, 
14/45, 19/61, 24/77, 29/93, 5/16, 31/99, 26/83, 21/67, 16/51, 27/86, 11/35, 
28/89, 17/54, 23/73, 29/92, 6/19, 31/98, 25/79, 19/60, 13/41, 20/63, 27/85, 
7/22, 29/91, 22/69, 15/47, 23/72, 31/97, 8/25, 25/78, 17/53, 26/81, 9/28, 28/87,
19/59, 29/90, 10/31, 31/96, 21/65, 32/99, 11/34, 23/71, 12/37, 25/77, 13/40, 
27/83, 14/43, 29/89, 15/46, 31/95, 16/49, 17/52, 18/55, 19/58, 20/61, 21/64, 
22/67, 23/70, 24/73, 25/76, 26/79, 27/82, 28/85, 29/88, 30/91, 31/94, 32/97, 
33/100, 1/3, 33/98, 32/95, 31/92, 30/89, 29/86, 28/83, 27/80, 26/77, 25/74, 
24/71, 23/68, 22/65, 21/62, 20/59, 19/56, 18/53, 17/50, 33/97, 16/47, 31/91, 
15/44, 29/85, 14/41, 27/79, 13/38, 25/73, 12/35, 23/67, 34/99, 11/32, 32/93, 
21/61, 31/90, 10/29, 29/84, 19/55, 28/81, 9/26, 26/75, 17/49, 25/72, 33/95, 
8/23, 31/89, 23/66, 15/43, 22/63, 29/83, 7/20, 34/97, 27/77, 20/57, 33/94, 
13/37, 32/91, 19/54, 25/71, 31/88, 6/17, 35/99, 29/82, 23/65, 17/48, 28/79, 
11/31, 27/76, 16/45, 21/59, 26/73, 31/87, 5/14, 34/95, 29/81, 24/67, 19/53, 
33/92, 14/39, 23/64, 32/89, 9/25, 31/86, 22/61, 35/97, 13/36, 30/83, 17/47, 
21/58, 25/69, 29/80, 33/91, 4/11, 35/96, 31/85, 27/74, 23/63, 19/52, 34/93, 
15/41, 26/71, 11/30, 29/79, 18/49, 25/68, 32/87, 7/19, 31/84, 24/65, 17/46, 
27/73, 37/100, 10/27, 33/89, 23/62, 36/97, 13/35, 29/78, 16/43, 35/94, 19/51, 
22/59, 25/67, 28/75, 31/83, 34/91, 37/99, 3/8, 35/93, 32/85, 29/77, 26/69, 
23/61, 20/53, 37/98, 17/45, 31/82, 14/37, 25/66, 36/95, 11/29, 30/79, 19/50, 
27/71, 35/92, 8/21, 37/97, 29/76, 21/55, 34/89, 13/34, 31/81, 18/47, 23/60, 
28/73, 33/86, 38/99, 5/13, 37/96, 32/83, 27/70, 22/57, 17/44, 29/75, 12/31, 
31/80, 19/49, 26/67, 33/85, 7/18, 37/95, 30/77, 23/59, 39/100, 16/41, 25/64, 
34/87, 9/23, 38/97, 29/74, 20/51, 31/79, 11/28, 35/89, 24/61, 37/94, 13/33, 
28/71, 15/38, 32/81, 17/43, 36/91, 19/48, 21/53, 23/58, 25/63, 27/68, 29/73, 
31/78, 33/83, 35/88, 37/93, 39/98, 2/5, 39/97, 37/92, 35/87, 33/82, 31/77, 
29/72, 27/67, 25/62, 23/57, 21/52, 40/99, 19/47, 36/89, 17/42, 32/79, 15/37, 
28/69, 13/32, 37/91, 24/59, 35/86, 11/27, 31/76, 20/49, 29/71, 38/93, 9/22, 
34/83, 25/61, 41/100, 16/39, 39/95, 23/56, 30/73, 37/90, 7/17, 40/97, 33/80, 
26/63, 19/46, 31/75, 12/29, 41/99, 29/70, 17/41, 39/94, 22/53, 27/65, 32/77, 
37/89, 5/12, 38/91, 33/79, 28/67, 23/55, 41/98, 18/43, 31/74, 13/31, 34/81, 
21/50, 29/69, 37/88, 8/19, 35/83, 27/64, 19/45, 30/71, 41/97, 11/26, 36/85, 
25/59, 39/92, 14/33, 31/73, 17/40, 37/87, 20/47, 23/54, 26/61, 29/68, 32/75, 
35/82, 38/89, 41/96, 3/7, 43/100, 40/93, 37/86, 34/79, 31/72, 28/65, 25/58, 
22/51, 41/95, 19/44, 35/81, 16/37, 29/67, 42/97, 13/30, 36/83, 23/53, 33/76, 
43/99, 10/23, 37/85, 27/62, 17/39, 41/94, 24/55, 31/71, 38/87, 7/16, 39/89, 
32/73, 25/57, 43/98, 18/41, 29/66, 40/91, 11/25, 37/84, 26/59, 41/93, 15/34, 
34/77, 19/43, 42/95, 23/52, 27/61, 31/70, 35/79, 39/88, 43/97, 4/9, 41/92, 
37/83, 33/74, 29/65, 25/56, 21/47, 38/85, 17/38, 30/67, 43/96, 13/29, 35/78, 
22/49, 31/69, 40/89, 9/20, 41/91, 32/71, 23/51, 37/82, 14/31, 33/73, 19/42, 
43/95, 24/53, 29/64, 34/75, 39/86, 44/97, 5/11, 41/90, 36/79, 31/68, 26/57, 
21/46, 37/81, 16/35, 43/94, 27/59, 38/83, 11/24, 39/85, 28/61, 45/98, 17/37, 
40/87, 23/50, 29/63, 35/76, 41/89, 6/13, 43/93, 37/80, 31/67, 25/54, 44/95, 
19/41, 32/69, 45/97, 13/28, 46/99, 33/71, 20/43, 27/58, 34/73, 41/88, 7/15, 
43/92, 36/77, 29/62, 22/47, 37/79, 15/32, 38/81, 23/49, 31/66, 39/83, 47/100, 
8/17, 41/87, 33/70, 25/53, 42/89, 17/36, 43/91, 26/55, 35/74, 44/93, 9/19, 
46/97, 37/78, 28/59, 47/99, 19/40, 29/61, 39/82, 10/21, 41/86, 31/65, 21/44, 
32/67, 43/90, 11/23, 45/94, 34/71, 23/48, 35/73, 47/98, 12/25, 37/77, 25/52, 
38/79, 13/27, 40/83, 27/56, 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:57:04 2004

Input: > farey(3);

Output: Magma V2.10-6     Tue Jan 13 2004 02:57:01 on modular  [Seed = 812897477]
   -------------------------------------


>>   farey(3);;
     ^
User error: Identifier 'farey' has not been declared or assigned

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:57:59 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))farey(3);

Output: Magma V2.10-6     Tue Jan 13 2004 02:57:56 on modular  [Seed = 711577366]
   -------------------------------------


>> n {1..n} | a le b }))farey(3);;
                        ^
User error: bad syntax

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:58:59 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(3);

Output: Magma V2.10-6     Tue Jan 13 2004 02:58:56 on modular  [Seed = 610779484]
   -------------------------------------

[ 0, 1/3, 1/2, 2/3, 1 ]

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:59:16 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(2);

Output: Magma V2.10-6     Tue Jan 13 2004 02:59:13 on modular  [Seed = 492763252]
   -------------------------------------

[ 0, 1/2, 1 ]

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:59:29 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(1);

Output: Magma V2.10-6     Tue Jan 13 2004 02:59:26 on modular  [Seed = 374731632]
   -------------------------------------

[ 0, 1 ]

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 02:59:41 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(0);

Output: Magma V2.10-6     Tue Jan 13 2004 02:59:38 on modular  [Seed = 256698973]
   -------------------------------------

[]

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:00:17 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(-3);

Output: Magma V2.10-6     Tue Jan 13 2004 03:00:14 on modular  [Seed = 2134678217]
   -------------------------------------

[]

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:00:39 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(4);

Output: Magma V2.10-6     Tue Jan 13 2004 03:00:36 on modular  [Seed = 1747684852]
   -------------------------------------

[ 0, 1/4, 1/3, 1/2, 2/3, 3/4, 1 ]

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:01:29 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>;
farey(5);

Output: Magma V2.10-6     Tue Jan 13 2004 03:01:26 on modular  [Seed = 1393604285]
   -------------------------------------

[ 0, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1 ]

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:03:46 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {-n..n}, b in {-n..n} | a le b }))>;
farey(5);

Output: Magma V2.10-6     Tue Jan 13 2004 03:03:43 on modular  [Seed = 1292806954]
   -------------------------------------


[<main>:3](
    n: 5
)
>> farey := func< n | Sort(Setseq({ a/b : a in {-n..n}, b in {-n..n} | a le b 
                                     ^
Runtime error in '/': Division by zero

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:05:35 2004

Input: farey := func< n | Sort(Setseq({ a/b : a in {-n..n}, b in {1..n} | a le b  }))>;
farey(5);

Output: Magma V2.10-6     Tue Jan 13 2004 03:05:32 on modular  [Seed = 3136904270]
   -------------------------------------

[ -5, -4, -3, -5/2, -2, -5/3, -3/2, -4/3, -5/4, -1, -4/5, -3/4, -2/3, -3/5, 
-1/2, -2/5, -1/3, -1/4, -1/5, 0, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1 
]

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:29:36 2004

Input: Xgcd(12, 15);

Output: Magma V2.10-6     Tue Jan 13 2004 03:29:33 on modular  [Seed = 2463203015]
   -------------------------------------

3 -1 1

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:35:56 2004

Input: m,n:=12,5
d,x,m:=Xgcd(m, n);
d;"=";x;"*";m;" + ";y;"*";n;

Output: Magma V2.10-6     Tue Jan 13 2004 03:35:53 on modular  [Seed = 4206434091]
   -------------------------------------


>> m,n:=12,5
          ^
User error: bad syntax

>> d,x,m:=Xgcd(m, n);
               ^
User error: Identifier 'm' has not been declared or assigned

>> d;"=";x;"*";m;" + ";y;"*";n;;
   ^
User error: Identifier 'd' has not been declared or assigned
=

>> d;"=";x;"*";m;" + ";y;"*";n;;
         ^
User error: Identifier 'x' has not been declared or assigned
*

>> d;"=";x;"*";m;" + ";y;"*";n;;
               ^
User error: Identifier 'm' has not been declared or assigned
 + 

>> d;"=";x;"*";m;" + ";y;"*";n;;
                       ^
User error: Identifier 'y' has not been declared or assigned
*

>> d;"=";x;"*";m;" + ";y;"*";n;;
                             ^
User error: Identifier 'n' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:39:29 2004

Input: m := 12;
n := 5;
d, x, y := Xgcd(m, n);
d;"=";x;"*";m;" + ";y;"*";n;

Output: Magma V2.10-6     Tue Jan 13 2004 03:39:26 on modular  [Seed = 4105640562]
   -------------------------------------

1
=
-2
*
12
 + 
5
*
5

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:41:36 2004

Input: m := 12;
n := 5;
d, x, y := Xgcd(m, n);
print d, "=", x, "*", m, " + ", y, "*", n;

Output: Magma V2.10-6     Tue Jan 13 2004 03:41:33 on modular  [Seed = 3836152801]
   -------------------------------------

1 = -2 * 12  +  5 * 5

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:42:25 2004

Input: m := 12;
n := 4;
d, x, y := Xgcd(m, n);
print d, "=", x, "*", m, " + ", y, "*", n;

Output: Magma V2.10-6     Tue Jan 13 2004 03:42:22 on modular  [Seed = 3734843784]
   -------------------------------------

4 = 0 * 12  +  1 * 4

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:43:18 2004

Input: m := 120;
n := 36;
d, x, y := Xgcd(m, n);
print d, "=", x, "*", m, " + ", y, "*", n;

Output: Magma V2.10-6     Tue Jan 13 2004 03:43:15 on modular  [Seed = 3616815180]
   -------------------------------------

12 = 1 * 120  +  -3 * 36

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.205.76.74)
Time: Tue Jan 13 03:44:01 2004

Input: m, n := 120, 36;
d, x, y := Xgcd(m, n);
print d, "=", x, "*", m, " + ", y, "*", n;

Output: Magma V2.10-6     Tue Jan 13 2004 03:43:58 on modular  [Seed = 3229822774]
   -------------------------------------


>> m, n := 120, 36;
              ^
User error: bad syntax

>> d, x, y := Xgcd(m, n);
                   ^
User error: Identifier 'm' has not been declared or assigned

>> print d, "=", x, "*", m, " + ", y, "*", n;;
         ^
User error: Identifier 'd' has not been declared or assigned

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:56:57 2004

Input: Br:=BraidGroup(6);

Output: Magma V2.10-6     Tue Jan 13 2004 05:56:53 on modular  [Seed = 3229830670]
   -------------------------------------


Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:57:12 2004

Input: Br:=BraidGroup(6);
Br;

Output: Magma V2.10-6     Tue Jan 13 2004 05:57:08 on modular  [Seed = 947631872]
   -------------------------------------

GrpBrd : Br on 6 strings

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:58:01 2004

Input: Br:=BraidGroup(6);
Br;
Br<a,b,c,d,e>:=BraidGroup(6);

Output: Magma V2.10-6     Tue Jan 13 2004 05:57:58 on modular  [Seed = 829603387]
   -------------------------------------

GrpBrd : Br on 6 strings

Total time: 3.189 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:58:17 2004

Input: Br:=BraidGroup(6);
Br;
Br<a,b,c,d,e>:=BraidGroup(6);
Br;

Output: Magma V2.10-6     Tue Jan 13 2004 05:58:14 on modular  [Seed = 593538137]
   -------------------------------------

GrpBrd : Br on 6 strings
GrpBrd : Br on 6 strings

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:59:08 2004

Input: Br:=BraidGroup(6);
Br;
Br<a,b,c,d,e>:=BraidGroup(6);
Br;
v=a*b*a*(b*a*b)^-1;

Output: Magma V2.10-6     Tue Jan 13 2004 05:59:05 on modular  [Seed = 139167565]
   -------------------------------------

GrpBrd : Br on 6 strings
GrpBrd : Br on 6 strings

>> v=a*b*a*(b*a*b)^-1;;
   ^
User error: Identifier 'v' has not been declared or assigned

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 05:59:21 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));


Output: Magma V2.10-6     Tue Jan 13 2004 05:59:17 on modular  [Seed = 21139128]
   -------------------------------------

true (13/21 : 4/7 : 1)

Total time: 3.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:59:22 2004

Input: Br:=BraidGroup(6);
Br;
Br<a,b,c,d,e>:=BraidGroup(6);
Br;
v:=a*b*a*(b*a*b)^-1;

Output: Magma V2.10-6     Tue Jan 13 2004 05:59:18 on modular  [Seed = 2084565958]
   -------------------------------------

GrpBrd : Br on 6 strings
GrpBrd : Br on 6 strings

Total time: 3.539 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 05:59:53 2004

Input: Br:=BraidGroup(6);
Br;
Br<a,b,c,d,e>:=BraidGroup(6);
Br;
v:=a*b*a*(b*a*b)^-1;
v;


Output: Magma V2.10-6     Tue Jan 13 2004 05:59:50 on modular  [Seed = 1932590313]
   -------------------------------------

GrpBrd : Br on 6 strings
GrpBrd : Br on 6 strings
e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d 
* c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * 
e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e
<Artin, -3, [
    (5, 6),
    (4, 5),
    (5, 6),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 6)(2, 4, 3, 5)
], 0>

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:01:03 2004

Input: Br:=BraidGroup(6);
Br;
Br<a,b,c,d,e>:=BraidGroup(6);
Br;
v:=a*b*a*(b*a*b)^-1;
v;
NormalForm(v);

Output: Magma V2.10-6     Tue Jan 13 2004 06:00:57 on modular  [Seed = 1595723914]
   -------------------------------------

GrpBrd : Br on 6 strings
GrpBrd : Br on 6 strings
e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d 
* c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * 
e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e
<Artin, -3, [
    (5, 6),
    (4, 5),
    (5, 6),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 6)(2, 4, 3, 5)
], 0>
Id(Br)
<Artin, 0, [], 0>

Total time: 3.719 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:03:56 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
[ NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 


Output: Magma V2.10-6     Tue Jan 13 2004 06:03:48 on modular  [Seed = 2884123395]
   -------------------------------------

true (13/21 : 4/7 : 1)

>> [ NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; 
                        ^
User error: Identifier 'a' has not been declared or assigned

Total time: 4.779 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:04:42 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
NormResidueSymbol;

Output: Magma V2.10-6     Tue Jan 13 2004 06:04:39 on modular  [Seed = 2311723378]
   -------------------------------------

true (13/21 : 4/7 : 1)
Intrinsic 'NormResidueSymbol'

Signatures:

    (<FldRatElt> a, <FldRatElt> b, <RngIntElt> p) -> RngIntElt
    (<RngIntElt> a, <RngIntElt> b, <RngIntElt> p) -> RngIntElt

        Returns 1 if ax^2 + by^2 represents a p-adic nonzero square, and 
        otherwise returns -1.



Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:05:51 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);


Output: Magma V2.10-6     Tue Jan 13 2004 06:05:47 on modular  [Seed = 3667479530]
   -------------------------------------


Total time: 3.689 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:05:57 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);


Output: Magma V2.10-6     Tue Jan 13 2004 06:05:54 on modular  [Seed = 3549446909]
   -------------------------------------


Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:06:08 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
Br;

Output: Magma V2.10-6     Tue Jan 13 2004 06:06:05 on modular  [Seed = 3297203685]
   -------------------------------------

GrpBrd : Br on 6 strings

Total time: 3.409 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:06:10 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
LegendreModel(C);

Output: Magma V2.10-6     Tue Jan 13 2004 06:06:06 on modular  [Seed = 3347338981]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2
Mapping from: CrvCon: C to Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2
with equations : 
-7*x - 14/3*y + 28/3*z
7/3*y - 2/3*z
z
and inverse
-1/7*x - 2/7*y + 8/7*z
3/7*y + 2/7*z
z

Total time: 3.489 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:06:26 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
Br;
v:=ab;

Output: Magma V2.10-6     Tue Jan 13 2004 06:06:23 on modular  [Seed = 930391589]
   -------------------------------------

GrpBrd : Br on 6 strings

>> v:=ab;;
      ^
User error: Identifier 'ab' has not been declared or assigned

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:06:53 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
c,m:=LegendreModel(C);
c;

Output: Magma V2.10-6     Tue Jan 13 2004 06:06:49 on modular  [Seed = 560115797]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:07:15 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
c,m:=LegendreModel(C);
c;
Coeffcients(c);

Output: Magma V2.10-6     Tue Jan 13 2004 06:07:11 on modular  [Seed = 307331952]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2

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

Total time: 3.399 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:11:31 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
c,m:=LegendreModel(C);
c;
Coefficients(c);

Output: Magma V2.10-6     Tue Jan 13 2004 06:11:27 on modular  [Seed = 1410844214]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2

>> Coefficients(c);;
               ^
Runtime error in 'Coefficients': Bad argument types
Argument types given: CrvCon

Total time: 3.759 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:16:20 2004

Input: Br<a,b,c,d,e,f>:=BraidGroup(6);


Output: Magma V2.10-6     Tue Jan 13 2004 06:16:16 on modular  [Seed = 3364576117]
   -------------------------------------


>> Br<a,b,c,d,e,f>:=BraidGroup(6);
     ^
Runtime error in 'AssignNames': Too many names given for this object

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:16:40 2004

Input: Br<a,b,c,d,e,A>:=BraidGroup(6);


Output: Magma V2.10-6     Tue Jan 13 2004 06:16:37 on modular  [Seed = 3279966315]
   -------------------------------------


>> Br<a,b,c,d,e,A>:=BraidGroup(6);
     ^
Runtime error in 'AssignNames': Too many names given for this object

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:16:56 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);


Output: Magma V2.10-6     Tue Jan 13 2004 06:16:53 on modular  [Seed = 964340386]
   -------------------------------------


Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:17:11 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
u:=a*b*a;

Output: Magma V2.10-6     Tue Jan 13 2004 06:17:08 on modular  [Seed = 795655333]
   -------------------------------------


Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:17:51 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
u:=a*b*a;
v:=b*a*b;
f:=u*v^-1;


Output: Magma V2.10-6     Tue Jan 13 2004 06:17:48 on modular  [Seed = 610777030]
   -------------------------------------


Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:18:05 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
u:=a*b*a;
v:=b*a*b;
f:=u*v^-1;
f;


Output: Magma V2.10-6     Tue Jan 13 2004 06:18:02 on modular  [Seed = 492736201]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d 
* c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * 
e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e
<Artin, -3, [
    (5, 6),
    (4, 5),
    (5, 6),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 6)(2, 4, 3, 5)
], 0>

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:18:44 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
u:=a*b*a;
v:=b*a*b;
f:=u*v^-1;
f;
NormalForm(f);


Output: Magma V2.10-6     Tue Jan 13 2004 06:18:41 on modular  [Seed = 88510762]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d 
* c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * 
e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e
<Artin, -3, [
    (5, 6),
    (4, 5),
    (5, 6),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 6)(2, 4, 3, 5)
], 0>
Id(Br)
<Artin, 0, [], 0>

Total time: 3.109 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:24:37 2004

Input: S:="aba";


Output: Magma V2.10-6     Tue Jan 13 2004 06:24:34 on modular  [Seed = 1815083296]
   -------------------------------------


Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host proxy1.cc.biu.ac.il. (132.70.9.117)
Time: Tue Jan 13 06:24:51 2004

Input: S:="aba";
S[2]

Output: Magma V2.10-6     Tue Jan 13 2004 06:24:48 on modular  [Seed = 1697050843]
   -------------------------------------

b

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:55:01 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
c,m:=LegendreModel(C);
c;
ReducedLegendreModel(C);

Output: Magma V2.10-6     Tue Jan 13 2004 06:54:57 on modular  [Seed = 3018862364]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2
Mapping from: CrvCon: C to Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2
with equations : 
-3*x - 2*y + 4*z
7*y - 2*z
z
and inverse
-1/3*x - 2/21*y + 8/7*z
1/7*y + 2/7*z
z

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:55:16 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
c,m:=LegendreModel(C);
c;
cc,mm:=ReducedLegendreModel(C);

Output: Magma V2.10-6     Tue Jan 13 2004 06:55:13 on modular  [Seed = 2766616635]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 06:55:34 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
fac := Factorization(Integers()!Discriminant(C));
c,m:=LegendreModel(C);
c;
cc,mm:=ReducedLegendreModel(C);
cc;

Output: Magma V2.10-6     Tue Jan 13 2004 06:55:31 on modular  [Seed = 2648572176]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-3*x^2 + 21*y^2 + 7*z^2
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 07:59:30 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
cc,mm:=ReducedLegendreModel(C);
cc;
RationalPoints(cc); 

Output: Magma V2.10-6     Tue Jan 13 2004 07:59:27 on modular  [Seed = 678134712]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2

>> RationalPoints(cc); ;
                 ^
Runtime error in 'RationalPoints': A positive naive height bound must be given

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 07:59:46 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
cc,mm:=ReducedLegendreModel(C);
cc;
RationalPoints(cc,10); 

Output: Magma V2.10-6     Tue Jan 13 2004 07:59:43 on modular  [Seed = 526169247]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2

>> RationalPoints(cc,10); ;
                 ^
Runtime error in 'RationalPoints': Bad argument types
Argument types given: CrvCon, RngIntElt

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 08:00:19 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
cc,mm:=ReducedLegendreModel(C);
cc;
RationalPoints(cc : Bound := 32);

Output: Magma V2.10-6     Tue Jan 13 2004 08:00:16 on modular  [Seed = 223258322]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2
{@ (-31 : 82 : 1), (-31 : -82 : 1), (-14 : 37 : 1), (-14 : -37 : 1), (-2 : 5 : 
1), (-2 : -5 : 1), (-1 : 2 : 1), (-1 : -2 : 1), (1 : 2 : 1), (1 : -2 : 1), (2 : 
5 : 1), (2 : -5 : 1), (14 : 37 : 1), (14 : -37 : 1), (31 : 82 : 1), (31 : -82 : 
1), (-19/3 : 50/3 : 1), (-19/3 : -50/3 : 1), (-13/3 : 34/3 : 1), (-13/3 : -34/3 
: 1), (-2/3 : 1/3 : 1), (-2/3 : -1/3 : 1), (2/3 : 1/3 : 1), (2/3 : -1/3 : 1), 
(13/3 : 34/3 : 1), (13/3 : -34/3 : 1), (19/3 : 50/3 : 1), (19/3 : -50/3 : 1), 
(-26/9 : 67/9 : 1), (-26/9 : -67/9 : 1), (-7/9 : 10/9 : 1), (-7/9 : -10/9 : 1), 
(7/9 : 10/9 : 1), (7/9 : -10/9 : 1), (26/9 : 67/9 : 1), (26/9 : -67/9 : 1), 
(-14/19 : 17/19 : 1), (-14/19 : -17/19 : 1), (-13/19 : 10/19 : 1), (-13/19 : 
-10/19 : 1), (13/19 : 10/19 : 1), (13/19 : -10/19 : 1), (14/19 : 17/19 : 1), 
(14/19 : -17/19 : 1), (-26/29 : 47/29 : 1), (-26/29 : -47/29 : 1), (-19/29 : 
2/29 : 1), (-19/29 : -2/29 : 1), (19/29 : 2/29 : 1), (19/29 : -2/29 : 1), (26/29
: 47/29 : 1), (26/29 : -47/29 : 1), (-26/31 : 43/31 : 1), (-26/31 : -43/31 : 1),
(26/31 : 43/31 : 1), (26/31 : -43/31 : 1) @}

Total time: 2.969 seconds, Total memory usage: 29.50MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 08:01:21 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
cc,mm:=ReducedLegendreModel(C);
cc;
Parametrization(cc);

Output: Magma V2.10-6     Tue Jan 13 2004 08:01:18 on modular  [Seed = 1915870803]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2
Mapping from: Projective Space of dimension 1
Variables : $.1, $.2 to CrvCon: cc
with equations : 
-$.1^2 - 3*$.2^2
-2*$.1^2 - 6*$.1*$.2 + 6*$.2^2
$.1^2 - 4*$.1*$.2 - 3*$.2^2
and inverse
7*x + 2*y - 3*z
y + 2*z
and alternative inverse equations :
3/7*y + 6/7*z
x - 2/7*y + 3/7*z

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 08:03:09 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
cc,mm:=ReducedLegendreModel(C);
cc;
?Parametrization;

Output: Magma V2.10-6     Tue Jan 13 2004 08:03:06 on modular  [Seed = 1747698909]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2
No references for word "Parametrization;"

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (212.128.18.14)
Time: Tue Jan 13 08:03:28 2004

Input: P2<x,y,z> := ProjectiveSpace(RationalField(),2);
C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2);  
HasRationalPoint(C);
cc,mm:=ReducedLegendreModel(C);
cc;
Parametrization;

Output: Magma V2.10-6     Tue Jan 13 2004 08:03:24 on modular  [Seed = 1595732989]
   -------------------------------------

true (13/21 : 4/7 : 1)
Conic over Rational Field defined by
-7*x^2 + y^2 + 3*z^2
Intrinsic 'Parametrization'

Signatures:

    (<Crv> C, <Pt> p) -> MapSch
    (<Prj> P, <Crv> C, <Pt> p) -> MapSch

        Parametrization of the rational curve C given a rational point p on C. 
        The the affine or projective line P will be set as the domain of this 
        map if included as an argument.

    (<CrvCon> C) -> MapSch
    (<Prj> P, <CrvCon> C) -> MapSch

        Parametrization of the conic curve C; if provided, the projective line P
        will be used as the domain of this map.

    (<FldFun> F, <DivFunElt> D) -> FldFunElt, SeqEnum

        Parametrization for the algebraic function field F defined by the 
        divisor D of degree one.



Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host slip-12-65-174-130.mis.prserv.net. (12.65.174.130)
Time: Tue Jan 13 08:39:49 2004

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

Output: Magma V2.10-6     Tue Jan 13 2004 08:39:46 on modular  [Seed = 2665294723]
   -------------------------------------

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

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host slip-12-65-174-130.mis.prserv.net. (12.65.174.130)
Time: Tue Jan 13 08:40:40 2004

Input: 4a.b2-4.-b3

Output: Magma V2.10-6     Tue Jan 13 2004 08:40:37 on modular  [Seed = 2395814884]
   -------------------------------------


>> 4a.b2-4.-b3;
    ^
User error: bad syntax

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 08:43:38 2004

Input: trinomial(8)

Output: Magma V2.10-6     Tue Jan 13 2004 08:43:35 on modular  [Seed = 4257106885]
   -------------------------------------


>> trinomial(8);
   ^
User error: Identifier 'trinomial' has not been declared or assigned

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 08:43:55 2004

Input: printtrinomial(8)

Output: Magma V2.10-6     Tue Jan 13 2004 08:43:52 on modular  [Seed = 4105650899]
   -------------------------------------


>> printtrinomial(8);
   ^
User error: Identifier 'printtrinomial' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:03:02 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,2);
C;



Output: Magma V2.10-6     Tue Jan 13 2004 09:02:59 on modular  [Seed = 896962535]
   -------------------------------------

D^2 + D + 1

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:03:55 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,8);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:03:52 on modular  [Seed = 1014990517]
   -------------------------------------

D^8 + D^4 + D^3 + D^2 + 1

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:04:21 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,521);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:04:18 on modular  [Seed = 3347348836]
   -------------------------------------

D^521 + D^32 + 1

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:06:46 2004

Input: K :=GF(2);
C<D> := PrimitiveTrinomial(K,521);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:06:43 on modular  [Seed = 3583405799]
   -------------------------------------


>> C<D> := PrimitiveTrinomial(K,521);
           ^
User error: Identifier 'PrimitiveTrinomial' has not been declared or assigned

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:07:43 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,521);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:07:40 on modular  [Seed = 3751568434]
   -------------------------------------

D^521 + D^32 + 1

Total time: 3.229 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:08:11 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(521,0);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:08:08 on modular  [Seed = 3869597039]
   -------------------------------------


>> C<D> := PrimitivePolynomial(521,0);
                              ^
Runtime error in 'PrimitivePolynomial': Bad argument types
Argument types given: RngIntElt, RngIntElt

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

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:08:46 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,521);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:08:43 on modular  [Seed = 4054993499]
   -------------------------------------

D^521 + D^32 + 1

Total time: 3.199 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:10:55 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomialRing(K,521);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:10:52 on modular  [Seed = 2176990636]
   -------------------------------------


>> C<D> := PrimitivePolynomialRing(K,521);
           ^
User error: Identifier 'PrimitivePolynomialRing' has not been declared or 
assigned

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

Total time: 3.129 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:11:22 2004

Input: K :=GF(2);
C<D> := PolynomialRing(521);
C;




Output: Magma V2.10-6     Tue Jan 13 2004 09:11:19 on modular  [Seed = 2295018574]
   -------------------------------------


>> C<D> := PolynomialRing(521);
                         ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: RngIntElt

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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:13:42 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:13:39 on modular  [Seed = 2463182784]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.169 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:16:06 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := MinimalPolynomial(521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:16:03 on modular  [Seed = 2783320135]
   -------------------------------------

D - 521
D - 521
D - 521
D - 521
D - 521
D - 521
D - 521
D - 521
D - 521
D - 521

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:16:27 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := MaximalPolynomial(521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:16:24 on modular  [Seed = 2901348693]
   -------------------------------------


>> C<D> := MaximalPolynomial(521);
           ^
User error: Identifier 'MaximalPolynomial' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:16:55 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := BinomialPolynomial(521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:16:52 on modular  [Seed = 3086223906]
   -------------------------------------


>> C<D> := BinomialPolynomial(521);
                             ^
Runtime error in 'BinomialPolynomial': Bad argument types
Argument types given: RngIntElt

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:17:12 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := BinomialPolynomial(K,521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:17:09 on modular  [Seed = 1107427301]
   -------------------------------------


>> C<D> := BinomialPolynomial(K,521);
                             ^
Runtime error in 'BinomialPolynomial': Bad argument types
Argument types given: FldFin, RngIntElt

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:17:50 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:17:47 on modular  [Seed = 1258878210]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.149 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:18:11 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrintBinaryPrimitivePolynomial(K,521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:18:08 on modular  [Seed = 1343483442]
   -------------------------------------


>> C<D> := PrintBinaryPrimitivePolynomial(K,521);
           ^
User error: Identifier 'PrintBinaryPrimitivePolynomial' has not been declared or
assigned

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:18:26 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := BinaryPrimitivePolynomial(K,521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:18:23 on modular  [Seed = 1579016243]
   -------------------------------------


>> C<D> := BinaryPrimitivePolynomial(K,521);
           ^
User error: Identifier 'BinaryPrimitivePolynomial' has not been declared or 
assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:18:44 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(2,521);
C;
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:18:41 on modular  [Seed = 1730468196]
   -------------------------------------


>> C<D> := PrimitivePolynomial(2,521);
                              ^
Runtime error in 'PrimitivePolynomial': Bad argument types
Argument types given: RngIntElt, RngIntElt

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:19:23 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
K :=GF(2);
end for;





Output: Magma V2.10-6     Tue Jan 13 2004 09:19:20 on modular  [Seed = 1815073350]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.219 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:25:32 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitiveTrinomials(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:25:29 on modular  [Seed = 155891346]
   -------------------------------------


>> C<D> := PrimitiveTrinomials(K,521);
           ^
User error: Identifier 'PrimitiveTrinomials' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:25:53 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomials(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:25:49 on modular  [Seed = 374712762]
   -------------------------------------


>> C<D> := PrimitivePolynomials(K,521);
           ^
User error: Identifier 'PrimitivePolynomials' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:26:21 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:26:18 on modular  [Seed = 475552852]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.159 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:26:39 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitiveTrinomial(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:26:36 on modular  [Seed = 627139963]
   -------------------------------------


>> C<D> := PrimitiveTrinomial(K,521);
           ^
User error: Identifier 'PrimitiveTrinomial' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:26:59 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:26:56 on modular  [Seed = 846623296]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.129 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:27:30 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitiveTrinomial(521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:27:27 on modular  [Seed = 947681333]
   -------------------------------------


>> C<D> := PrimitiveTrinomial(521);
           ^
User error: Identifier 'PrimitiveTrinomial' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:28:02 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomials(521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:27:59 on modular  [Seed = 3246752236]
   -------------------------------------


>> C<D> := PrimitivePolynomials(521);
           ^
User error: Identifier 'PrimitivePolynomials' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:28:24 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:28:21 on modular  [Seed = 3431500811]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.129 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:28:53 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:28:50 on modular  [Seed = 3819414275]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.139 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:32:45 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PolynomialRing(521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:32:42 on modular  [Seed = 4105221436]
   -------------------------------------


>> C<D> := PolynomialRing(521);
                         ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: RngIntElt

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:33:07 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PolynomialRing(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:33:04 on modular  [Seed = 4256807967]
   -------------------------------------

Polynomial ring of rank 521 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, 
$.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, 
$.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, 
$.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, 
$.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, 
$.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, 
$.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, 
$.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, 
$.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, 
$.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, 
$.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, 
$.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, 
$.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, 
$.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, 
$.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, 
$.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, 
$.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, 
$.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, 
$.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, 
$.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, 
$.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, 
$.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, 
$.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, 
$.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, 
$.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, 
$.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, 
$.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, 
$.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, 
$.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, 
$.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, 
$.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, 
$.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, 
$.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, 
$.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, 
$.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, 
$.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, 
$.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, 
$.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, 
$.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, 
$.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, 
$.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, 
$.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, 
$.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, 
$.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, 
$.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, 
$.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521
Polynomial ring of rank 521 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, 
$.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, 
$.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, 
$.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, 
$.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, 
$.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, 
$.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, 
$.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, 
$.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, 
$.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, 
$.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, 
$.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, 
$.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, 
$.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, 
$.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, 
$.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, 
$.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, 
$.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, 
$.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, 
$.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, 
$.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, 
$.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, 
$.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, 
$.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, 
$.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, 
$.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, 
$.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, 
$.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, 
$.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, 
$.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, 
$.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, 
$.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, 
$.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, 
$.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, 
$.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, 
$.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, 
$.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, 
$.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, 
$.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, 
$.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, 
$.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, 
$.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, 
$.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, 
$.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, 
$.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, 
$.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521
Polynomial ring of rank 521 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, 
$.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, 
$.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, 
$.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, 
$.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, 
$.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, 
$.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, 
$.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, 
$.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, 
$.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, 
$.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, 
$.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, 
$.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, 
$.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, 
$.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, 
$.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, 
$.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, 
$.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, 
$.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, 
$.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, 
$.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, 
$.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, 
$.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, 
$.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, 
$.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, 
$.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, 
$.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, 
$.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, 
$.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, 
$.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, 
$.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, 
$.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, 
$.368, $.369, 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:34:37 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomial(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:34:34 on modular  [Seed = 2295122224]
   -------------------------------------

D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1
D^521 + D^32 + 1

Total time: 3.159 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:38:01 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PrimitivePolynomialRing(521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:37:58 on modular  [Seed = 2615138591]
   -------------------------------------


>> C<D> := PrimitivePolynomialRing(521);
           ^
User error: Identifier 'PrimitivePolynomialRing' has not been declared or 
assigned

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:38:18 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PolynomialRing(521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:38:15 on modular  [Seed = 2699354677]
   -------------------------------------


>> C<D> := PolynomialRing(521);
                         ^
Runtime error in 'PolynomialRing': Bad argument types
Argument types given: RngIntElt

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:38:35 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PolynomialRing(K,521);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:38:31 on modular  [Seed = 2850941708]
   -------------------------------------

Polynomial ring of rank 521 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, 
$.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, 
$.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, 
$.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, 
$.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, 
$.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, 
$.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, 
$.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, 
$.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, 
$.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, 
$.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, 
$.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, 
$.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, 
$.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, 
$.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, 
$.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, 
$.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, 
$.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, 
$.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, 
$.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, 
$.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, 
$.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, 
$.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, 
$.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, 
$.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, 
$.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, 
$.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, 
$.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, 
$.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, 
$.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, 
$.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, 
$.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, 
$.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, 
$.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, 
$.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, 
$.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, 
$.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, 
$.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, 
$.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, 
$.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, 
$.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, 
$.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, 
$.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, 
$.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, 
$.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, 
$.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521
Polynomial ring of rank 521 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, 
$.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, 
$.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, 
$.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, 
$.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, 
$.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, 
$.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, 
$.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, 
$.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, 
$.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, 
$.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, 
$.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, 
$.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, 
$.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, 
$.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, 
$.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, 
$.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, 
$.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, 
$.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, 
$.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, 
$.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, 
$.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, 
$.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, 
$.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, 
$.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, 
$.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, 
$.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, 
$.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, 
$.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, 
$.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, 
$.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, 
$.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, 
$.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, 
$.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, 
$.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, 
$.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, 
$.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, 
$.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, 
$.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, 
$.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, 
$.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, 
$.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, 
$.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, 
$.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, 
$.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, 
$.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521
Polynomial ring of rank 521 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, 
$.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, 
$.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, 
$.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, 
$.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, 
$.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, 
$.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, 
$.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, 
$.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, 
$.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, 
$.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, 
$.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, 
$.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, 
$.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, 
$.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, 
$.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, 
$.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, 
$.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, 
$.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, 
$.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, 
$.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, 
$.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, 
$.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, 
$.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, 
$.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, 
$.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, 
$.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, 
$.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, 
$.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, 
$.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, 
$.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, 
$.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, 
$.368, $.369, 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:39:00 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := PolynomialRing(K,8);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:38:57 on modular  [Seed = 3069375989]
   -------------------------------------

Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8
Polynomial ring of rank 8 over GF(2)
Lexicographical Order
Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:39:42 2004

Input: K :=GF(2);
for i in [1 .. 10] do
C<D> := TrinomialRing(K,8);
C;
end for;






Output: Magma V2.10-6     Tue Jan 13 2004 09:39:39 on modular  [Seed = 3220962518]
   -------------------------------------


>> C<D> := TrinomialRing(K,8);
           ^
User error: Identifier 'TrinomialRing' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:40:08 2004

Input: K :=GF(2);
C<D> := TrinomialRing(K,8);








Output: Magma V2.10-6     Tue Jan 13 2004 09:40:05 on modular  [Seed = 1309281608]
   -------------------------------------


>> C<D> := TrinomialRing(K,8);
           ^
User error: Identifier 'TrinomialRing' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:40:32 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,8);








Output: Magma V2.10-6     Tue Jan 13 2004 09:40:29 on modular  [Seed = 1427183179]
   -------------------------------------


Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:40:52 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,8);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:40:49 on modular  [Seed = 1545084782]
   -------------------------------------

D^8 + D^4 + D^3 + D^2 + 1

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:41:14 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,8);
C;
C<D> := PrimitivePolynomial(K,8);
C;
C<D> := PrimitivePolynomial(K,8);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:41:11 on modular  [Seed = 1781410222]
   -------------------------------------

D^8 + D^4 + D^3 + D^2 + 1
D^8 + D^4 + D^3 + D^2 + 1
D^8 + D^4 + D^3 + D^2 + 1

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:41:36 2004

Input: K :=GF(2);
C<D> := PrimitivePolynomial(K,8);
C;
C<E> := PrimitivePolynomial(K,8);
C;
C<F> := PrimitivePolynomial(K,8);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:41:33 on modular  [Seed = 1882469294]
   -------------------------------------

D^8 + D^4 + D^3 + D^2 + 1
E^8 + E^4 + E^3 + E^2 + 1
F^8 + F^4 + F^3 + F^2 + 1

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:42:06 2004

Input: K :=GF(2);
C<X> := PrimitivePolynomial(K,8);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:42:03 on modular  [Seed = 2117746054]
   -------------------------------------

X^8 + X^4 + X^3 + X^2 + 1

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:42:48 2004

Input: K :=GF(2);
C<X> := PrimitivePolynomial(K,10000);
C;








Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 09:42:25 on modular  [Seed = 71321494]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2:   839 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:43:07 2004

Input: K :=GF(2);
C<X> := PrimitivePolynomial(K,1000);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:43:03 on modular  [Seed = 324489383]
   -------------------------------------

X^1000 + X^992 + X^968 + X^960 + X^936 + X^928 + X^904 + X^896 + X^872 + X^864 +
    X^840 + X^832 + X^808 + X^800 + X^776 + X^768 + X^744 + X^736 + X^712 + 
    X^704 + X^680 + X^672 + X^648 + X^640 + X^616 + X^608 + X^584 + X^576 + 
    X^552 + X^544 + X^520 + X^512 + X^488 + X^480 + X^456 + X^448 + X^424 + 
    X^416 + X^392 + X^384 + X^360 + X^352 + X^328 + X^320 + X^296 + X^288 + 
    X^264 + X^256 + X^232 + X^224 + X^200 + X^192 + X^168 + X^160 + X^136 + 
    X^128 + X^104 + X^96 + X^72 + X^64 + X^40 + X^32 + X^8 + X^5 + X^3 + X^2 + 1

Total time: 4.479 seconds, Total memory usage: 1.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:54:00 2004

Input: K :=GF(2);
P := x^8 + x^2 +1;
C<X> := IsPrimitive(P);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:53:56 on modular  [Seed = 3347284224]
   -------------------------------------


>> P := x^8 + x^2 +1;
        ^
User error: Identifier 'x' has not been declared or assigned

>> C<X> := IsPrimitive(P);
                       ^
User error: Identifier 'P' has not been declared or assigned

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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:57:15 2004

Input: K :=GF(2);
P := x^8 + x^2 +1;
C<X> := IsPrimitive(101);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:57:12 on modular  [Seed = 3583087326]
   -------------------------------------


>> P := x^8 + x^2 +1;
        ^
User error: Identifier 'x' has not been declared or assigned

>> C<X> := IsPrimitive(101);
                      ^
Runtime error in 'IsPrimitive': Bad argument types
Argument types given: RngIntElt

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:57:28 2004

Input: K :=GF(2);
C<X> := IsPrimitive(101);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:57:24 on modular  [Seed = 3700988875]
   -------------------------------------


>> C<X> := IsPrimitive(101);
                      ^
Runtime error in 'IsPrimitive': Bad argument types
Argument types given: RngIntElt

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

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 09:59:11 2004

Input: K :=GF(2);
B := B * Coefficient(B, 2)^-1;
B;
C<X> := IsPrimitive(B);
C;








Output: Magma V2.10-6     Tue Jan 13 2004 09:59:08 on modular  [Seed = 3954158612]
   -------------------------------------


>> B := B * Coefficient(B, 2)^-1;
        ^
User error: Identifier 'B' has not been declared or assigned

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

>> C<X> := IsPrimitive(B);
                       ^
User error: Identifier 'B' has not been declared or assigned

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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:07:52 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..1000] do
for> print MinimalPolynomial(PrimitiveElement(GF(2^m)));
for> 
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:07:48 on modular  [Seed = 2816732704]
   -------------------------------------


>> for> print MinimalPolynomial(PrimitiveElement(GF(2^m)));
      ^
User error: bad syntax

>> for> 
      ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:08:29 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..100] do
print MinimalPolynomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:08:18 on modular  [Seed = 2934630159]
   -------------------------------------

x^2 + x + 1
x^3 + x + 1
x^4 + x + 1
x^5 + x^2 + 1
x^6 + x^4 + x^3 + x + 1
x^7 + x + 1
x^8 + x^4 + x^3 + x^2 + 1
x^9 + x^4 + 1
x^10 + x^6 + x^5 + x^3 + x^2 + x + 1
x^11 + x^2 + 1
x^12 + x^7 + x^6 + x^5 + x^3 + x + 1
x^13 + x^4 + x^3 + x + 1
x^14 + x^7 + x^5 + x^3 + 1
x^15 + x^5 + x^4 + x^2 + 1
x^16 + x^5 + x^3 + x^2 + 1
x^17 + x^3 + 1
x^18 + x^12 + x^10 + x + 1
x^19 + x^5 + x^2 + x + 1
x^20 + x^10 + x^9 + x^7 + x^6 + x^5 + x^4 + x + 1
x^21 + x^6 + x^5 + x^2 + 1
x^22 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5 + 1
x^23 + x^5 + 1
x^24 + x^16 + x^15 + x^14 + x^13 + x^10 + x^9 + x^7 + x^5 + x^3 + 1
x^25 + x^8 + x^6 + x^2 + 1
x^26 + x^14 + x^10 + x^8 + x^7 + x^6 + x^4 + x + 1
x^27 + x^12 + x^10 + x^9 + x^7 + x^5 + x^3 + x^2 + 1
x^28 + x^13 + x^7 + x^6 + x^5 + x^2 + 1
x^29 + x^2 + 1
x^30 + x^17 + x^16 + x^13 + x^11 + x^7 + x^5 + x^3 + x^2 + x + 1
x^31 + x^3 + 1
x^32 + x^15 + x^9 + x^7 + x^4 + x^3 + 1
x^33 + x^13 + x^12 + x^11 + x^10 + x^8 + x^6 + x^3 + 1
x^34 + x^16 + x^15 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + x + 1
x^35 + x^11 + x^10 + x^7 + x^5 + x^2 + 1
x^36 + x^23 + x^22 + x^20 + x^19 + x^17 + x^14 + x^13 + x^8 + x^6 + x^5 + x + 1
x^37 + x^5 + x^4 + x^3 + x^2 + x + 1
x^38 + x^14 + x^10 + x^9 + x^8 + x^5 + x^2 + x + 1
x^39 + x^15 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^2 + 1
x^40 + x^23 + x^21 + x^18 + x^16 + x^15 + x^13 + x^12 + x^8 + x^5 + x^3 + x + 1
x^41 + x^3 + 1
x^42 + x^30 + x^26 + x^25 + x^24 + x^20 + x^18 + x^12 + x^11 + x^9 + x^6 + x^5 +
    x^2 + x + 1
x^43 + x^6 + x^4 + x^3 + 1
x^44 + x^24 + x^19 + x^17 + x^16 + x^4 + x^3 + x + 1
x^45 + x^20 + x^17 + x^15 + x^14 + x^12 + x^11 + x^6 + 1
x^46 + x^44 + x^41 + x^40 + x^39 + x^38 + x^32 + x^31 + x^30 + x^27 + x^26 + 
    x^24 + x^23 + x^21 + x^20 + x^17 + x^12 + x^5 + x^4 + x^3 + x^2 + x + 1
x^47 + x^5 + 1
x^48 + x^25 + x^23 + x^17 + x^12 + x^11 + x^10 + x^8 + x^7 + x^3 + 1
x^49 + x^10 + x^8 + x^6 + x^4 + x^3 + x^2 + x + 1
x^50 + x^4 + x^3 + x^2 + 1
x^51 + x^16 + x^15 + x^12 + x^9 + x^6 + 1
x^52 + x^3 + 1
x^53 + x^6 + x^2 + x + 1
x^54 + x^34 + x^32 + x^31 + x^30 + x^29 + x^27 + x^25 + x^21 + x^18 + x^17 + 
    x^16 + x^15 + x^13 + x^7 + x^4 + x^2 + x + 1
x^55 + x^11 + x^10 + x^9 + x^7 + x^4 + 1
x^56 + x^7 + x^4 + x^2 + 1
x^57 + x^21 + x^19 + x^16 + x^13 + x^11 + x^10 + x^8 + x^6 + x^5 + x^4 + x^3 + 
    x^2 + x + 1
x^58 + x^19 + 1
x^59 + x^6 + x^5 + x^4 + x^3 + x + 1
x^60 + x + 1
x^61 + x^5 + x^2 + x + 1
x^62 + x^61 + x^60 + x^57 + x^55 + x^54 + x^52 + x^51 + x^47 + x^44 + x^42 + 
    x^38 + x^37 + x^34 + x^33 + x^32 + x^31 + x^27 + x^26 + x^25 + x^24 + x^22 +
    x^20 + x^16 + x^15 + x^14 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^2 + x +
    1
x^63 + x + 1
x^64 + x^4 + x^3 + x + 1
x^65 + x^15 + x^14 + x^13 + x^12 + x^10 + x^9 + x^7 + x^5 + x + 1
x^66 + x^63 + x^62 + x^59 + x^58 + x^57 + x^56 + x^53 + x^51 + x^49 + x^45 + 
    x^44 + x^43 + x^40 + x^37 + x^35 + x^34 + x^33 + x^32 + x^27 + x^23 + x^22 +
    x^19 + x^16 + x^15 + x^11 + x^10 + x^8 + x^7 + x^6 + x^5 + x^4 + 1
x^67 + x^5 + x^2 + x + 1
x^68 + x^9 + 1
x^69 + x^6 + x^5 + x^2 + 1
x^70 + x^5 + x^3 + x + 1
x^71 + x^5 + x^3 + x + 1
x^72 + x^10 + x^9 + x^3 + 1
x^73 + x^4 + x^3 + x^2 + 1
x^74 + x^73 + x^71 + x^70 + x^64 + x^60 + x^59 + x^58 + x^55 + x^52 + x^48 + 
    x^47 + x^46 + x^43 + x^40 + x^38 + x^37 + x^34 + x^32 + x^30 + x^29 + x^27 +
    x^25 + x^20 + x^18 + x^17 + x^15 + x^13 + x^8 + x^5 + x^2 + x + 1
x^75 + x^6 + x^3 + x + 1
x^76 + x^75 + x^73 + x^72 + x^69 + x^64 + x^58 + x^57 + x^56 + x^55 + x^54 + 
    x^53 + x^52 + x^51 + x^50 + x^47 + x^44 + x^37 + x^35 + x^32 + x^30 + x^27 +
    x^26 + x^25 + x^23 + x^20 + x^19 + x^18 + x^17 + x^10 + x^9 + x^8 + x^7 + 
    x^6 + x^3 + x + 1
x^77 + x^6 + x^5 + x^2 + 1
x^78 + x^76 + x^75 + x^71 + x^69 + x^67 + x^65 + x^64 + x^60 + x^58 + x^56 + 
    x^55 + x^54 + x^53 + x^52 + x^48 + x^47 + x^46 + x^45 + x^42 + x^39 + x^35 +
    x^32 + x^30 + x^29 + x^27 + x^24 + x^23 + x^20 + x^18 + x^16 + x^15 + x^9 + 
    x^8 + x^7 + x^5 + x^4 + x^3 + 1
x^79 + x^4 + x^3 + x^2 + 1
x^80 + x^9 + x^4 + x^2 + 1
x^81 + x^4 + 1
x^82 + x^81 + x^80 + x^76 + x^75 + x^73 + x^69 + x^68 + x^67 + x^66 + x^65 + 
    x^63 + x^62 + x^61 + x^60 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^51 +
    x^50 + x^48 + x^47 + x^45 + x^43 + x^39 + x^38 + x^36 + x^35 + x^32 + x^28 +
    x^27 + x^23 + x^20 + x^19 + x^16 + x^14 + x^13 + x^11 + x^10 + x^9 + x^4 + 
    x^2 + x + 1
x^83 + x^7 + x^4 + x^2 + 1
x^84 + x^83 + x^82 + x^80 + x^79 + x^78 + x^76 + x^75 + x^74 + x^73 + x^72 + 
    x^71 + x^69 + x^66 + x^61 + x^60 + x^57 + x^54 + x^52 + x^46 + x^45 + x^44 +
    x^42 + x^41 + x^39 + x^33 + x^31 + x^29 + x^25 + x^23 + x^22 + x^19 + x^17 +
    x^15 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^4 + x^3 + x + 1
x^85 + x^8 + x^2 + x + 1
x^86 + x^81 + x^79 + x^75 + x^74 + x^73 + x^71 + x^70 + x^69 + x^67 + x^65 + 
    x^62 + x^61 + x^59 + x^56 + x^54 + x^51 + x^49 + x^48 + x^45 + x^44 + x^43 +
    x^42 + x^41 + x^38 + x^35 + x^34 + x^32 + x^29 + x^28 + x^26 + x^25 + x^20 +
    x^14 + x^13 + x^12 + x^10 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x + 1
x^87 + x^13 + 1
x^88 + x^86 + x^85 + x^84 + x^83 + x^78 + x^77 + x^76 + x^75 + x^74 + x^71 + 
    x^67 + x^64 + x^60 + x^59 + x^58 + x^57 + x^55 + x^53 + x^50 + x^48 + x^47 +
    x^44 + x^42 + x^41 + x^40 + x^38 + x^37 + x^36 + x^34 + x^33 + x^31 + x^27 +
    x^26 + x^22 + x^20 + x^17 + x^15 + x^14 + x^11 + x^5 + x^4 + 1
x^89 + x^6 + x^5 + x^3 + 1
x^90 + x^88 + x^86 + x^85 + x^84 + x^82 + x^79 + x^78 + x^75 + x^74 + x^72 + 
    x^71 + x^70 + x^63 + x^60 + x^59 + x^56 + x^55 + x^53 + x^51 + x^50 + x^48 +
    x^44 + x^41 + x^38 + x^34 + x^32 + x^31 + x^30 + x^22 + x^21 + x^18 + x^17 +
    x^14 + x^12 + x^9 + x^8 + x^5 + x^2 + x + 1
x^91 + x^8 + x^5 + x + 1
x^92 + x^90 + x^89 + x^87 + x^84 + x^82 + x^81 + x^79 + x^77 + x^76 + x^75 + 
    x^72 + x^70 + x^69 + x^65 + x^64 + x^63 + x^62 + x^60 + x^59 + x^58 + x^57 +
    x^55 + x^49 + x^47 + x^43 + x^39 + x^36 + x^32 + x^30 + x^28 + x^21 + x^16 +
    x^15 + x^14 + x^12 + x^10 + x^9 + x^5 + x + 1
x^93 + x^2 + 1
x^94 + x^21 + 1
x^95 + x^11 + 1
x^96 + x^10 + x^9 + x^6 + 1
x^97 + x^6 + 1
x^98 + x^11 + 1
x^99 + x^95 + x^90 + x^88 + x^85 + x^82 + x^80 + x^77 + x^75 + x^74 + x^70 + 
    x^69 + x^68 + x^67 + x^65 + x^64 + x^60 + x^59 + x^58 + x^55 + x^54 + x^50 +
    x^49 + x^41 + x^40 + x^39 + x^38 + x^35 + x^33 + x^31 + x^30 + x^28 + x^27 +
    x^26 + x^23 + x^21 + x^20 + x^19 + x^15 + x^14 + x^8 + x^7 + x^4 + x^3 + x^2
    + x + 1
x^100 + x^96 + x^68 + x^64 + x^36 + x^32 + x^15 + x^14 + x^13 + x^12 + x^11 + 
    x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + x^2 + x + 1

Total time: 11.000 seconds, Total memory usage: 14.37MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:09:39 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..100] do
print MinimalTrinomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:09:36 on modular  [Seed = 3052535750]
   -------------------------------------


>> print MinimalTrinomial(PrimitiveElement(GF(2^m)));
         ^
User error: Identifier 'MinimalTrinomial' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:10:03 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..100] do
print Trinomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:10:00 on modular  [Seed = 3170432695]
   -------------------------------------


>> print Trinomial(PrimitiveElement(GF(2^m)));
         ^
User error: Identifier 'Trinomial' has not been declared or assigned

Total time: 3.149 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:10:28 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..10] do
print Polynomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:10:25 on modular  [Seed = 1259274606]
   -------------------------------------


>> print Polynomial(PrimitiveElement(GF(2^m)));
                   ^
Runtime error in 'Polynomial': Bad argument types
Argument types given: FldFinElt

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:11:05 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..10] do
print minimalPolynomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:11:02 on modular  [Seed = 1495077787]
   -------------------------------------


>> print minimalPolynomial(PrimitiveElement(GF(2^m)));
         ^
User error: Identifier 'minimalPolynomial' has not been declared or assigned

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:11:22 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [2..10] do
print MinimalPolynomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:11:19 on modular  [Seed = 1646667953]
   -------------------------------------

x^2 + x + 1
x^3 + x + 1
x^4 + x + 1
x^5 + x^2 + 1
x^6 + x^4 + x^3 + x + 1
x^7 + x + 1
x^8 + x^4 + x^3 + x^2 + 1
x^9 + x^4 + 1
x^10 + x^6 + x^5 + x^3 + x^2 + x + 1

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:12:01 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print MinimalPolynomial(PrimitiveElement(GF(2^m)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:11:55 on modular  [Seed = 1798250900]
   -------------------------------------

x^520 + x^512 + x^15 + x^14 + x^13 + x^12 + x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 
    1
x^521 + x^32 + 1
x^522 + x^361 + x^359 + x^348 + x^339 + x^336 + x^332 + x^331 + x^315 + x^307 + 
    x^304 + x^300 + x^299 + x^297 + x^295 + x^284 + x^275 + x^272 + x^268 + 
    x^267 + x^200 + x^187 + x^185 + x^179 + x^178 + x^174 + x^171 + x^168 + 
    x^167 + x^163 + x^162 + x^159 + x^156 + x^153 + x^149 + x^147 + x^146 + 
    x^145 + x^144 + x^142 + x^140 + x^139 + x^138 + x^137 + x^133 + x^130 + 
    x^129 + x^114 + x^112 + x^108 + x^106 + x^105 + x^104 + x^103 + x^101 + x^99
    + x^97 + x^95 + x^92 + x^89 + x^85 + x^83 + x^82 + x^81 + x^80 + x^78 + x^76
    + x^75 + x^74 + x^73 + x^72 + x^69 + x^66 + x^65 + x^59 + x^57 + x^51 + x^50
    + x^46 + x^43 + x^40 + x^35 + x^34 + x^31 + x^28 + x^26 + x^25 + x^24 + x^21
    + x^18 + x^17 + x^16 + x^14 + x^13 + x^12 + x^8 + x^7 + x^5 + 1
x^523 + x^13 + x^6 + x^2 + 1
x^524 + x^167 + 1
x^525 + x^6 + x^4 + x + 1

Total time: 5.439 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:14:05 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print MinimalPolynomial(PrimitiveElement(GF(2)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:14:00 on modular  [Seed = 2067738630]
   -------------------------------------

x + 1
x + 1
x + 1
x + 1
x + 1
x + 1

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:14:34 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print MinimalPolynomial(PrimitiveElement(GF(521)));
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:14:31 on modular  [Seed = 222905886]
   -------------------------------------

$.1 + 518
$.1 + 518
$.1 + 518
$.1 + 518
$.1 + 518
$.1 + 518

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:17:09 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print PrintBinaryPrimitiveTrinomials(329);
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:17:06 on modular  [Seed = 324491429]
   -------------------------------------


>> print PrintBinaryPrimitiveTrinomials(329);
         ^
User error: Identifier 'PrintBinaryPrimitiveTrinomials' has not been declared or
assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:17:30 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print BinaryPrimitiveTrinomials(329);
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:17:27 on modular  [Seed = 610297959]
   -------------------------------------


>> print BinaryPrimitiveTrinomials(329);
         ^
User error: Identifier 'BinaryPrimitiveTrinomials' has not been declared or 
assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:17:48 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print PrimitiveTrinomials(329);
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:17:45 on modular  [Seed = 761880944]
   -------------------------------------


>> print PrimitiveTrinomials(329);
         ^
User error: Identifier 'PrimitiveTrinomials' has not been declared or assigned

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:18:11 2004

Input: P<x> := PolynomialAlgebra(GF(2));
for m in [520..525] do
print PrimitivePolynomials(329);
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:18:07 on modular  [Seed = 913472093]
   -------------------------------------


>> print PrimitivePolynomials(329);
         ^
User error: Identifier 'PrimitivePolynomials' has not been declared or assigned

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:18:44 2004

Input: P<x> := PolynomialAlgebra(GF(2));
K := GF(2)
for m in [520..525] do
print PrimitivePolynomial(K,329);
end for;







Output: Magma V2.10-6     Tue Jan 13 2004 10:18:41 on modular  [Seed = 1065055018]
   -------------------------------------


>> for m in [520..525] do
   ^
User error: bad syntax

>> print PrimitivePolynomial(K,329);
                             ^
User error: Identifier 'K' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:19:10 2004

Input: P<x> := PolynomialAlgebra(GF(2));
K := GF(2)
print PrimitivePolynomial(K,329);








Output: Magma V2.10-6     Tue Jan 13 2004 10:19:07 on modular  [Seed = 3229912303]
   -------------------------------------


>> print PrimitivePolynomial(K,329);
   ^
User error: bad syntax

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 10:20:24 2004

Input: P<x> := PolynomialAlgebra(GF(2));
K := GF(2)
for m in [1 .. 5] do
print PrimitivePolynomial(K,329);
end for;








Output: Magma V2.10-6     Tue Jan 13 2004 10:20:20 on modular  [Seed = 3499400225]
   -------------------------------------


>> for m in [1 .. 5] do
   ^
User error: bad syntax

>> print PrimitivePolynomial(K,329);
                             ^
User error: Identifier 'K' has not been declared or assigned

>> end for;
   ^
User error: bad syntax

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host fenfak84063.fenfak.ege.edu.tr. (155.223.84.63)
Time: Tue Jan 13 11:38:06 2004

Input: 2^10000

Output: Magma V2.10-6     Tue Jan 13 2004 11:38:03 on modular  [Seed = 3296762474]
   -------------------------------------

1995063116880758384883742162683585083823496831886192454852008949852943883022194\
6631919961684036194597899331129423209124271556491349413781117593785932096323957\
8557300467937945267652465512660598955205500869181933115425086084606181046855090\
7486608962488809048989483800925394163325785062156830947390255691238806522509664\
3874441046759871626985453222868538161694315775629640762836880760732228535091641\
4761839563814589694638994108409605362678210646214273333940365255656495306031426\
8023496940033593431665145929777327966577560617258203140799419817960737824568376\
2280037302885487251900834464581454650557929601414833921615734588139257095379769\
1192778008269577356744441230620187578363255027283237892707103738028663930314281\
3324140162419567169057406141965434232463880124885614730520743199225961179625013\
0992860241708340807605932320161268492288496255841312844061536738951487114256315\
1110897455142033138202029316409575964647560104058458415660720449628670165150619\
2063100418642227590867090057460641785695191145605506825125040600751984226189805\
9237118054444788072906395242548339221982707404473162376760846613033778706039803\
4131971334936546227005631699374555082417809728109832913144035718775247685098572\
7693792643322159939987688666080836883783802764328277517227365757274478411229438\
9733810861607423253291974813120197604178281965697475898164531258434135959862784\
1301281854062834766490886905210475808826158239619857701224070443305830758690393\
1960460340497315658320867210591330090375282341553974539439771525745529051021231\
0947321610753474825740775273986348298498340756937955646638621874569499279016572\
1037013644331358172143117913982229838458473344402709641828510050729277483645505\
7863450110085298781238947392869954083434615880704395911898581514577917714361969\
8728131459483783202081474982171858011389071228250905826817436220577475921417653\
7156877256149045829049924610286300815355833081301019876758562343435389554091756\
2340084488752616264356864883351946372037729324009445624692325435040067802727383\
7755376406726898636241037491410966718557050759098100246789880178271925953381282\
4219540283027594084489550146766683896979968862416363133763939033734558014076367\
4187771105538422573949911018646821969658165148513049422236994771476306915546821\
7682876200362777257723781365331611196811280792669481887201298643660768551639860\
5346022978715575179473852463694469230878942659482170080511203223654962881690357\
3912136833839359175641873385051097027161391543959099159815465441733631165693603\
1122249937969999226781732358023111862644575299135758175008199839236284615249881\
0889602322443621737716180863570154684840586223297928538756234865564405369626220\
1896357102881236156751254333830327002909766865056855715750551672751889919412971\
1337690149916181315171544007728650573189557450920330185304847113818315407324053\
3190384620840364217637039115506397890007428536721962809034779745333204683687958\
6858023795221862912008074281955131794815762444829851846150970488802727472157468\
8131594750409732115080498190455803416826949787141316063210686391511681774304792\
596709376

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (128.164.140.228)
Time: Tue Jan 13 12:07:49 2004

Input: 2^49988585

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 12:07:26 on modular  [Seed = 2463561497]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2:  1495 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:08:18 2004

Input: S:="abc";
S;

Output: Magma V2.10-6     Tue Jan 13 2004 13:08:15 on modular  [Seed = 459239250]
   -------------------------------------

abc

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:08:49 2004

Input: S:="abc";
S;
S[1];


Output: Magma V2.10-6     Tue Jan 13 2004 13:08:46 on modular  [Seed = 543446088]
   -------------------------------------

abc
a

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:09:40 2004

Input: S:="abc";
S;
S[1];
Br<a,b,c,d,e>:=BraidGroup;

Output: Magma V2.10-6     Tue Jan 13 2004 13:09:37 on modular  [Seed = 695033102]
   -------------------------------------

abc
a

>> Br<a,b,c,d,e>:=BraidGroup;;
     ^
Runtime error in 'AssignNames': Bad argument types
Argument types given: Intrinsic ~, SeqEnum[MonStgElt]

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host vhe-370047.sshn.net. (195.169.221.8)
Time: Tue Jan 13 13:10:28 2004

Input: Q<x> := PolynomialRing(Integers());
f := x^4 - 8*x^2 +8;
K := NumberField(f);

Output: Magma V2.10-6     Tue Jan 13 2004 13:10:24 on modular  [Seed = 964513263]
   -------------------------------------


Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:11:16 2004

Input: S:="abc";
S;
S[1];
Br<<a,b,c,d,e>>:=BraidGroup;
T:="ab";
T[1]*T[1]^(-1);


Output: Magma V2.10-6     Tue Jan 13 2004 13:11:13 on modular  [Seed = 3465198153]
   -------------------------------------

abc
a

>> Br<<a,b,c,d,e>>:=BraidGroup;
      ^
User error: bad syntax

>> T[1]*T[1]^(-1);
            ^
Runtime error in '^': Argument 2 (-1) should be >= 0

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host vhe-370047.sshn.net. (195.169.221.8)
Time: Tue Jan 13 13:11:41 2004

Input: Q<x> := PolynomialRing(Integers());
f := x^4 - 8*x^2 +8;
K := NumberField(f);
Discriminant(f);



Output: Magma V2.10-6     Tue Jan 13 2004 13:11:38 on modular  [Seed = 3616777035]
   -------------------------------------

131072

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host vhe-370047.sshn.net. (195.169.221.8)
Time: Tue Jan 13 13:12:16 2004

Input: Q<x> := PolynomialRing(Integers());
f := x^4 - 8*x^2 +8;
K := NumberField(f);
Discriminant(f);
M := MaximumOrder(K);
Discriminant(M);




Output: Magma V2.10-6     Tue Jan 13 2004 13:12:13 on modular  [Seed = 3700992103]
   -------------------------------------

131072

>> M := MaximumOrder(K);
        ^
User error: Identifier 'MaximumOrder' has not been declared or assigned

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:12:25 2004

Input: S:="abc";
S;
S[1];
Br<a,b,c,d,e>:=BraidGroup(6);
T:="ab";
T[1]*T[1]^(-1);


Output: Magma V2.10-6     Tue Jan 13 2004 13:12:22 on modular  [Seed = 3802568610]
   -------------------------------------

abc
a

>> T[1]*T[1]^(-1);
            ^
Runtime error in '^': Argument 2 (-1) should be >= 0

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:18:02 2004

Input: S:="abc";
S;
S[1];
Br<a,b,c,d,e>:=BraidGroup(6);
T:="ab";
T[1]*T[1]^(-1);
read T[1];


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

************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:21:44 2004

Input: S:="abc";
S;
S[1];
Br<a,b,c,d,e>:=BraidGroup(6);
T:="ab";


StringToCode(T) 


Output: Magma V2.10-6     Tue Jan 13 2004 13:21:41 on modular  [Seed = 2260922869]
   -------------------------------------

abc
a
97

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:57:57 2004

Input: length("abcd");


Output: Magma V2.10-6     Tue Jan 13 2004 13:57:54 on modular  [Seed = 1031357128]
   -------------------------------------


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

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:58:19 2004

Input: Length("abcd");


Output: Magma V2.10-6     Tue Jan 13 2004 13:58:16 on modular  [Seed = 3296770891]
   -------------------------------------


>> Length("abcd");
         ^
Runtime error in 'Length': Bad argument types
Argument types given: MonStgElt

Total time: 3.149 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:59:43 2004

Input: A:="abcd";



Output: Magma V2.10-6     Tue Jan 13 2004 13:59:40 on modular  [Seed = 3415198608]
   -------------------------------------


Total time: 3.199 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 13:59:58 2004

Input: A:="abcd";
#A;


Output: Magma V2.10-6     Tue Jan 13 2004 13:59:54 on modular  [Seed = 3533099711]
   -------------------------------------

4

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 14:11:58 2004

Input: A:="abcd";
#A;
A[1];
f:=function(s)
n:=
 

Output: Magma V2.10-6     Tue Jan 13 2004 14:11:55 on modular  [Seed = 2361953840]
   -------------------------------------

4
a

>>  ;
    ^
User error: bad syntax

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227)
Time: Tue Jan 13 14:12:19 2004

Input: A:="abcd";
#A;
A[1];

 

Output: Magma V2.10-6     Tue Jan 13 2004 14:12:16 on modular  [Seed = 2480378052]
   -------------------------------------

4
a

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:32:58 2004

Input: p := 2^331;
p;


Output: Magma V2.10-6     Tue Jan 13 2004 14:32:55 on modular  [Seed = 1208766439]
   -------------------------------------

4374501449566023848745004454235242730706338861786424872851541212819905998398751\
846447026354046107648

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:33:35 2004

Input: p := 2^331;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:33:32 on modular  [Seed = 1124551431]
   -------------------------------------

[ <2, 331> ]

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:34:05 2004

Input: p := 2^273;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:34:02 on modular  [Seed = 1545098302]
   -------------------------------------

[ <2, 273> ]

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:34:37 2004

Input: p := (2^273)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:34:33 on modular  [Seed = 1427201364]
   -------------------------------------

[ <7, 2>, <79, 1>, <127, 1>, <337, 1>, <911, 1>, <8191, 1>, <121369, 1>, 
<108749551, 1>, <112901153, 1>, <23140471537, 1>, <4093204977277417, 1>, 
<86977595801949844993, 1> ]

Total time: 3.739 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:35:09 2004

Input: p := (2^8)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:35:06 on modular  [Seed = 1679846470]
   -------------------------------------

[ <3, 1>, <5, 1>, <17, 1> ]

Total time: 2.959 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:35:28 2004

Input: p := (2^6)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:35:25 on modular  [Seed = 2100917576]
   -------------------------------------

[ <3, 2>, <7, 1> ]

Total time: 2.899 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:35:50 2004

Input: p := (2^273)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:35:46 on modular  [Seed = 1983020716]
   -------------------------------------

[ <7, 2>, <79, 1>, <127, 1>, <337, 1>, <911, 1>, <8191, 1>, <121369, 1>, 
<108749551, 1>, <112901153, 1>, <23140471537, 1>, <4093204977277417, 1>, 
<86977595801949844993, 1> ]

Total time: 3.449 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:37:16 2004

Input: p := (2^521)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:37:12 on modular  [Seed = 21301665]
   -------------------------------------

[ <6864797660130609714981900799081393217269435300143305409394463459185543183397\
6560521225596406614545549772963113914808580371219879997166438125740282911150571\
51, 1> ]

Total time: 3.569 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:37:58 2004

Input: p := (2^493)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:37:46 on modular  [Seed = 459215449]
   -------------------------------------

[ <233, 1>, <1103, 1>, <2089, 1>, <131071, 1>, <3616649, 1>, <10353001, 1>, 
<970596583005459173652432922101781006420152100417834935620226828285267019891114\
1357299732185324536769414538999508070197039, 1> ]

Total time: 11.319 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:41:12 2004

Input: p := (2^471)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:41:06 on modular  [Seed = 745022902]
   -------------------------------------

[ <7, 1>, <852133201, 1>, <60726444167, 1>, <1654058017289, 1>, 
<2134387368610417, 1>, <4767828205180602862488887736985607398666751166000769605\
012698283856806259916006281652253453751, 1> ]

Total time: 4.699 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:41:40 2004

Input: p := (2^41)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:41:37 on modular  [Seed = 643968927]
   -------------------------------------

[ <13367, 1>, <164511353, 1> ]

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:41:56 2004

Input: p := (2^471)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:41:51 on modular  [Seed = 1065039496]
   -------------------------------------

[ <7, 1>, <852133201, 1>, <60726444167, 1>, <1654058017289, 1>, 
<2134387368610417, 1>, <4767828205180602862488887736985607398666751166000769605\
012698283856806259916006281652253453751, 1> ]

Total time: 4.789 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:43:04 2004

Input: p := (2^331)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:43:00 on modular  [Seed = 3415196103]
   -------------------------------------

[ <16937389168607, 1>, <865118802936559, 1>, 
<298542624980197463613767215333569428005686468835821253721796682625551919, 1> ]

Total time: 3.529 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:43:38 2004

Input: p := (2^317)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:43:35 on modular  [Seed = 3296775915]
   -------------------------------------

[ <9511, 1>, <587492521482839879, 1>, <4868122671322098041565641, 1>, 
<9815639231755686605031317440031161584572466128599, 1> ]

Total time: 3.089 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:43:56 2004

Input: p := (2^311)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:43:52 on modular  [Seed = 3734689006]
   -------------------------------------

[ <5344847, 1>, <2647649373910205158468946067671, 1>, 
<294803681348959296477194164064643062187559537539328375831, 1> ]

Total time: 3.579 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:44:11 2004

Input: p := (2^293)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:44:08 on modular  [Seed = 3616791831]
   -------------------------------------

[ <40122362455616221971122353, 1>, <3966452270281388904156112207107579216439107\
43103031701971222447, 1> ]

Total time: 3.289 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:44:30 2004

Input: p := (2^417)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:44:26 on modular  [Seed = 3768904242]
   -------------------------------------

[ <7, 1>, <5625767248687, 1>, <7606017793609, 1>, 
<123876132205208335762278423601, 1>, <91218603148026315357293387146275367218703\
08627534265066967795115502591, 1> ]

Total time: 3.719 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:46:11 2004

Input: p := (2^457)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:45:55 on modular  [Seed = 4256823110]
   -------------------------------------

[ <150327409, 1>, <247553941968992978493531934444940989829116509732371457865094\
3035813830300993611462717419801770460539016610145009605554380104535919, 1> ]

Total time: 16.410 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:46:58 2004

Input: p := (2^419)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:46:55 on modular  [Seed = 4138925457]
   -------------------------------------

[ <839, 1>, <903780021613921, 1>, <5800422716722833271214743, 1>, 
<10287968884341772230096159036619433593, 1>, 
<29919490848598531825060153417921002916701815927, 1> ]

Total time: 3.159 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:48:09 2004

Input: p := (2^317)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:48:06 on modular  [Seed = 2160364478]
   -------------------------------------

[ <9511, 1>, <587492521482839879, 1>, <4868122671322098041565641, 1>, 
<9815639231755686605031317440031161584572466128599, 1> ]

Total time: 3.169 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:48:36 2004

Input: p := (2^311)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:48:32 on modular  [Seed = 2581434945]
   -------------------------------------

[ <5344847, 1>, <2647649373910205158468946067671, 1>, 
<294803681348959296477194164064643062187559537539328375831, 1> ]

Total time: 3.529 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:49:11 2004

Input: p := (2^293)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:49:07 on modular  [Seed = 2463537513]
   -------------------------------------

[ <40122362455616221971122353, 1>, <3966452270281388904156112207107579216439107\
43103031701971222447, 1> ]

Total time: 3.279 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:49:47 2004

Input: p := (2^271)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:49:43 on modular  [Seed = 2900928307]
   -------------------------------------

[ <15242475217, 1>, <2489277578681318902773305415678200452563642739707732865421\
88386932989391, 1> ]

Total time: 3.819 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:50:10 2004

Input: p := (2^8)-1;
Factorization(p);


Output: Magma V2.10-6     Tue Jan 13 2004 14:50:07 on modular  [Seed = 3170416411]
   -------------------------------------

[ <3, 1>, <5, 1>, <17, 1> ]

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:51:34 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,521);
C;


Output: Magma V2.10-6     Tue Jan 13 2004 14:51:31 on modular  [Seed = 3052517822]
   -------------------------------------

X^521 + X^32 + 1

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:52:29 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,521);
C;
C := C * Coefficient(C,0)^-1;
C;


Output: Magma V2.10-6     Tue Jan 13 2004 14:52:26 on modular  [Seed = 1107709553]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^32 + 1

Total time: 3.129 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:54:05 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,521);
C;
C := C * Coefficient(C,0)^-1;
C;
S := LSFRSequence (C,[K|1,1],(2^521)-1);
S;


Output: Magma V2.10-6     Tue Jan 13 2004 14:54:02 on modular  [Seed = 1561940430]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^32 + 1

>> S := LSFRSequence (C,[K|1,1],(2^521)-1);
                         ^
User error: Identifier 'K' has not been declared or assigned

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

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:55:11 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,521);
C;
C := C * Coefficient(C,0)^-1;
C;
S := LSFRSequence (C,[K| 1,1],(2^521)-1);
S;


Output: Magma V2.10-6     Tue Jan 13 2004 14:55:08 on modular  [Seed = 1747739965]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^32 + 1

>> S := LSFRSequence (C,[K| 1,1],(2^521)-1);
                         ^
User error: Identifier 'K' has not been declared or assigned

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

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:55:55 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,521);
C;
C := C * Coefficient(C,0)^-1;
C;
S := LSFRSequence (C,[1,1],(2^521)-1);
S;


Output: Magma V2.10-6     Tue Jan 13 2004 14:55:52 on modular  [Seed = 1663528546]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^32 + 1

>> S := LSFRSequence (C,[1,1],(2^521)-1);
        ^
User error: Identifier 'LSFRSequence' has not been declared or assigned

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

Total time: 3.109 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:56:36 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
C := C * Coefficient(C,0)^-1;
C;
S := LSFRSequence (C,[K,1,1],(2^521)-1);
S;


Output: Magma V2.10-6     Tue Jan 13 2004 14:56:33 on modular  [Seed = 2050914114]
   -------------------------------------

X^7 + X + 1
X^7 + X + 1

>> S := LSFRSequence (C,[K,1,1],(2^521)-1);
                         ^
User error: Identifier 'K' has not been declared or assigned

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

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:57:43 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
C := C * Coefficient(C,0)^-1;
C;
S := LSFRSequence (C,[Kl 1,1],48);
S;


Output: Magma V2.10-6     Tue Jan 13 2004 14:57:40 on modular  [Seed = 139199989]
   -------------------------------------

X^7 + X + 1
X^7 + X + 1

>> S := LSFRSequence (C,[Kl 1,1],48);
                            ^
User error: bad syntax

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

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:58:05 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
C := C * Coefficient(C,0)^-1;
C;
S := LSFRSequence (C,[K| 1,1],48);
S;


Output: Magma V2.10-6     Tue Jan 13 2004 14:58:02 on modular  [Seed = 54988416]
   -------------------------------------

X^7 + X + 1
X^7 + X + 1

>> S := LSFRSequence (C,[K| 1,1],48);
                         ^
User error: Identifier 'K' has not been declared or assigned

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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 14:59:19 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
IsPrimitive(C);


Output: Magma V2.10-6     Tue Jan 13 2004 14:59:16 on modular  [Seed = 442373191]
   -------------------------------------

X^7 + X + 1
true

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:00:21 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
C := 1 + X^3 + X^13 + X^521;
IsPrimitive(C);


Output: Magma V2.10-6     Tue Jan 13 2004 15:00:18 on modular  [Seed = 711861297]
   -------------------------------------

X^7 + X + 1
false

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:00:45 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
C := 1 + X^32 + X^521;
IsPrimitive(C);


Output: Magma V2.10-6     Tue Jan 13 2004 15:00:42 on modular  [Seed = 627124998]
   -------------------------------------

X^7 + X + 1
true

Total time: 3.039 seconds, Total memory usage: 1.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:02:19 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for m in [32..520] do
C := 1 + X^m + X^521;
IsPrimitive(C);
for end;


Output: Magma V2.10-6     Tue Jan 13 2004 15:02:16 on modular  [Seed = 3229929025]
   -------------------------------------

X^7 + X + 1

>> for end;
       ^
User error: bad syntax

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:02:39 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for m in [32..520] do
C := 1 + X^m + X^521;
IsPrimitive(C);
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:02:36 on modular  [Seed = 3667842127]
   -------------------------------------

X^7 + X + 1
true
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
true
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false
false

Total time: 3.429 seconds, Total memory usage: 2.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:05:23 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for m in [32..520] do
C := 1 + X^m + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:05:20 on modular  [Seed = 3920487968]
   -------------------------------------

X^7 + X + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1

Total time: 3.379 seconds, Total memory usage: 2.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:08:10 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for n in [1..520]do
for m in [32..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:07:47 on modular  [Seed = 3819434937]
   -------------------------------------

X^7 + X + 1

Errors: /home/mfd/gomagma: line 2:  2474 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:08:49 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for n in [1..20]do
for m in [32..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:08:45 on modular  [Seed = 4206815998]
   -------------------------------------

X^7 + X + 1

Total time: 3.779 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:09:15 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for n in [20..50]do
for m in [32..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:09:10 on modular  [Seed = 4122076634]
   -------------------------------------

X^7 + X + 1

Total time: 4.249 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:09:53 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for n in [1..50]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:09:48 on modular  [Seed = 2361957449]
   -------------------------------------

X^7 + X + 1

Total time: 5.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:10:22 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,7);
C;
for n in [50..100]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:10:17 on modular  [Seed = 2631437436]
   -------------------------------------

X^7 + X + 1

Total time: 5.139 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:11:10 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [100..150]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:11:05 on modular  [Seed = 2547222279]
   -------------------------------------

X^9 + X^4 + 1

Total time: 5.179 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:11:37 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [150..250]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:11:29 on modular  [Seed = 2934619670]
   -------------------------------------

X^9 + X^4 + 1

Total time: 7.379 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:12:06 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [250..350]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:11:58 on modular  [Seed = 3120408830]
   -------------------------------------

X^9 + X^4 + 1

Total time: 7.639 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:12:29 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [350..450]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:12:21 on modular  [Seed = 3019350748]
   -------------------------------------

X^9 + X^4 + 1

Total time: 7.709 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:12:54 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [450..520]do
for m in [1..520] do
C := 1 + X^m + X^n + X^521;
if IsPrimitive(C) then 
C;
end if;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:12:48 on modular  [Seed = 1225611331]
   -------------------------------------

X^9 + X^4 + 1

Total time: 6.289 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:14:23 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [0..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:14:15 on modular  [Seed = 1174558619]
   -------------------------------------

X^9 + X^4 + 1

Total time: 7.309 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:15:22 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [0..100]do
    for m in [1..520] do
        C := 1 + X^m + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:14:59 on modular  [Seed = 1595625174]
   -------------------------------------

X^9 + X^4 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1

Errors: /home/mfd/gomagma: line 2:  2581 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:17:25 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [0..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^17 + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:17:02 on modular  [Seed = 1747745308]
   -------------------------------------

X^9 + X^4 + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^386 + X^17 + X^2 + 1
X^521 + X^333 + X^17 + X^3 + 1
X^521 + X^377 + X^17 + X^3 + 1
X^521 + X^416 + X^17 + X^3 + 1
X^521 + X^189 + X^17 + X^4 + 1
X^521 + X^487 + X^17 + X^4 + 1
X^521 + X^505 + X^17 + X^4 + 1
X^521 + X^75 + X^17 + X^5 + 1
X^521 + X^83 + X^17 + X^5 + 1
X^521 + X^111 + X^17 + X^5 + 1
X^521 + X^131 + X^17 + X^5 + 1
X^521 + X^143 + X^17 + X^5 + 1
X^521 + X^152 + X^17 + X^5 + 1
X^521 + X^182 + X^17 + X^5 + 1
X^521 + X^243 + X^17 + X^5 + 1
X^521 + X^261 + X^17 + X^5 + 1
X^521 + X^278 + X^17 + X^5 + 1
X^521 + X^336 + X^17 + X^5 + 1
X^521 + X^360 + X^17 + X^5 + 1
X^521 + X^378 + X^17 + X^5 + 1
X^521 + X^425 + X^17 + X^5 + 1
X^521 + X^474 + X^17 + X^5 + 1
X^521 + X^94 + X^17 + X^6 + 1
X^521 + X^146 + X^17 + X^6 + 1
X^521 + X^159 + X^17 + X^6 + 1
X^521 + X^243 + X^17 + X^6 + 1
X^521 + X^269 + X^17 + X^6 + 1
X^521 + X^286 + X^17 + X^6 + 1
X^521 + X^314 + X^17 + X^6 + 1
X^521 + X^386 + X^17 + X^6 + 1
X^521 + X^458 + X^17 + X^6 + 1
X^521 + X^37 + X^17 + X^7 + 1
X^521 + X^166 + X^17 + X^7 + 1
X^521 + X^436 + X^17 + X^7 + 1
X^521 + X^439 + X^17 + X^7 + 1
X^521 + X^451 + X^17 + X^7 + 1
X^521 + X^477 + X^17 + X^7 + 1
X^521 + X^481 + X^17 + X^7 + 1
X^521 + X^120 + X^17 + X^8 + 1
X^521 + X^272 + X^17 + X^8 + 1
X^521 + X^485 + X^17 + X^8 + 1
X^521 + X^235 + X^17 + X^9 + 1
X^521 + X^267 + X^17 + X^9 + 1
X^521 + X^287 + X^17 + X^9 + 1
X^521 + X^299 + X^17 + X^9 + 1
X^521 + X^337 + X^17 + X^9 + 1
X^521 + X^481 + X^17 + X^9 + 1
X^521 + X^63 + X^17 + X^10 + 1
X^521 + X^103 + X^17 + X^10 + 1
X^521 + X^495 + X^17 + X^10 + 1
X^521 + X^57 + X^17 + X^11 + 1
X^521 + X^60 + X^17 + X^11 + 1
X^521 + X^63 + X^17 + X^11 + 1
X^521 + X^119 + X^17 + X^11 + 1
X^521 + X^267 + X^17 + X^11 + 1
X^521 + X^477 + X^17 + X^11 + 1
X^521 + X^75 + X^17 + X^12 + 1
X^521 + X^90 + X^17 + X^12 + 1
X^521 + X^91 + X^17 + X^12 + 1
X^521 + X^261 + X^17 + X^12 + 1
X^521 + X^318 + X^17 + X^12 + 1
X^521 + X^434 + X^17 + X^12 + 1
X^521 + X^454 + X^17 + X^12 + 1
X^521 + X^36 + X^17 + X^13 + 1
X^521 + X^97 + X^17 + X^13 + 1
X^521 + X^105 + X^17 + X^13 + 1
X^521 + X^276 + X^17 + X^13 + 1
X^521 + X^280 + X^17 + X^13 + 1
X^521 + X^475 + X^17 + X^13 + 1
X^521 + X^495 + X^17 + X^13 + 1
X^521 + X^496 + X^17 + X^13 + 1
X^521 + X^516 + X^17 + X^13 + 1
X^521 + X^517 + X^17 + X^13 + 1
X^521 + X^231 + X^17 + X^14 + 1
X^521 + X^410 + X^17 + X^14 + 1
X^521 + X^480 + X^17 + X^14 + 1
X^521 + X^519 + X^17 + X^14 + 1
X^521 + X^41 + X^17 + X^15 + 1
X^521 + X^235 + X^17 + X^15 + 1
X^521 + X^347 + X^17 + X^15 + 1
X^521 + X^63 + X^17 + X^16 + 1
X^521 + X^81 + X^17 + X^16 + 1
X^521 + X^240 + X^17 + X^16 + 1
X^521 + X^301 + X^17 + X^16 + 1
X^521 + X^408 + X^17 + X^16 + 1
X^521 + X^477 + X^17 + X^16 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^77 + X^18 + X^17 + 1
X^521 + X^228 + X^18 + X^17 + 1
X^521 + X^315 + X^18 + X^17 + 1
X^521 + X^361 + X^18 + X^17 + 1
X^521 + X^393 + X^18 + X^17 + 1
X^521 + X^61 + X^19 + X^17 + 1
X^521 + X^229 + X^19 + X^17 + 1
X^521 + X^265 + X^19 + X^17 + 1
X^521 + X^406 + X^19 + X^17 + 1
X^521 + X^439 + X^19 + X^17 + 1
X^521 + X^496 + X^19 + X^17 + 1
X^521 + X^502 + X^19 + X^17 + 1
X^521 + X^517 + X^19 + X^17 + 1
X^521 + X^47 + X^20 + X^17 + 1
X^521 + X^206 + X^20 + X^17 + 1
X^521 + X^344 + X^20 + X^17 + 1
X^521 + X^395 + X^20 + X^17 + 1
X^521 + X^27 + X^21 + X^17 + 1
X^521 + X^29 + X^21 + X^17 + 1
X^521 + X^53 + X^21 + X^17 + 1
X^521 + X^196 + X^21 + X^17 + 1
X^521 + X^216 + X^21 + X^17 + 1
X^521 + X^252 + X^21 + X^17 + 1
X^521 + X^297 + X^21 + X^17 + 1
X^521 + X^354 + X^21 + X^17 + 1
X^521 + X^360 + X^21 + X^17 + 1
X^521 + X^414 + X^21 + X^17 + 1
X^521 + X^434 + X^21 + X^17 + 1
X^521 + X^435 + X^21 + X^17 + 1
X^521 + X^503 + X^21 + X^17 + 1
X^521 + X^174 + X^22 + X^17 + 1
X^521 + X^330 + X^22 + X^17 + 1
X^521 + X^483 + X^22 + X^17 + 1
X^521 + X^81 + X^23 + X^17 + 1
X^521 + X^203 + X^23 + X^17 + 1
X^521 + X^207 + X^23 + X^17 + 1
X^521 + X^228 + X^23 + X^17 + 1
X^521 + X^347 + X^23 + X^17 + 1
X^521 + X^392 + X^23 + X^17 + 1
X^521 + X^40 + X^24 + X^17 + 1
X^521 + X^126 + X^24 + X^17 + 1
X^521 + X^139 + X^24 + X^17 + 1
X^521 + X^187 + X^24 + X^17 + 1
X^521 + X^355 + X^24 + X^17 + 1
X^521 + X^385 + X^24 + X^17 + 1
X^521 + X^78 + X^25 + X^17 + 1
X^521 + X^79 + X^25 + X^17 + 1
X^521 + X^324 + X^25 + X^17 + 1
X^521 + X^86 + X^26 + X^17 + 1
X^521 + X^423 + X^26 + X^17 + 1
X^521 + X^27 + X^21 + X^17 + 1
X^521 + X^99 + X^27 + X^17 + 1
X^521 + X^271 + X^27 + X^17 + 1
X^521 + X^283 + X^27 + X^17 + 1
X^521 + X^285 + X^27 + X^17 + 1
X^521 + X^418 + X^27 + X^17 + 1
X^521 + X^430 + X^27 + X^17 + 1
X^521 + X^60 + X^28 + X^17 + 1
X^521 + X^120 + X^28 + X^17 + 1
X^521 + X^190 + X^28 + X^17 + 1
X^521 + X^232 + X^28 + X^17 + 1
X^521 + X^283 + X^28 + X^17 + 1
X^521 + X^315 + X^28 + X^17 + 1
X^521 + X^421 + X^28 + X^17 + 1
X^521 + X^492 + X^28 + X^17 + 1
X^521 + X^29 + X^21 + X^17 + 1
X^521 + X^126 + X^29 + X^17 + 1
X^521 + X^195 + X^29 + X^17 + 1
X^521 + X^246 + X^29 + X^17 + 1
X^521 + X^93 + X^30 + X^17 + 1
X^521 + X^113 + X^30 + X^17 + 1
X^521 + X^166 + X^30 + X^17 + 1
X^521 + X^190 + X^30 + X^17 + 1
X^521 + X^203 + X^30 + X^17 + 1
X^521 + X^207 + X^30 + X^17 + 1
X^521 + X^464 + X^30 + X^17 + 1
X^521 + X^66 + X^31 + X^17 + 1
X^521 + X^153 + X^31 + X^17 + 1
X^521 + X^159 + X^31 + X^17 + 1
X^521 + X^165 + X^31 + X^17 + 1
X^521 + X^168 + X^31 + X^17 + 1
X^521 + X^273 + X^31 + X^17 + 1
X^521 + X^391 + X^31 + X^17 + 1
X^521 + X^402 + X^31 + X^17 + 1
X^521 + X^424 + X^31 + X^17 + 1
X^521 + X^432 + X^31 + X^17 + 1
X^521 + X^483 + X^31 + X^17 + 1
X^521 + X^489 + X^31 + X^17 + 1
X^521 + X^32 + 1
X^521 + X^200 + X^32 + X^17 + 1
X^521 + X^221 + X^32 + X^17 + 1
X^521 + X^245 + X^32 + X^17 + 1
X^521 + X^437 + X^32 + X^17 + 1
X^521 + X^65 + X^33 + X^17 + 1
X^521 + X^87 + X^33 + X^17 + 1
X^521 + X^90 + X^33 + X^17 + 1
X^521 + X^153 + X^33 + X^17 + 1
X^521 + X^188 + X^33 + X^17 + 1
X^521 + X^191 + X^33 + X^17 + 1
X^521 + X^217 + X^33 + X^17 + 1
X^521 + X^321 + X^33 + X^17 + 1
X^521 + X^294 + X^34 + X^17 + 1
X^521 + X^489 + X^34 + X^17 + 1
X^521 + X^54 + X^35 + X^17 + 1
X^521 + X^63 + X^35 + X^17 + 1
X^521 + X^66 + X^35 + X^17 + 1
X^521 + X^156 + X^35 + X^17 + 1
X^521 + X^228 + X^35 + X^17 + 1
X^521 + X^231 + X^35 + X^17 + 1
X^521 + X^291 + X^35 + X^17 + 1
X^521 + X^294 + X^35 + X^17 + 1
X^521 + X^299 + X^35 + X^17 + 1
X^521 + X^375 + X^35 + X^17 + 1
X^521 + X^399 + X^35 + X^17 + 1
X^521 + X^407 + X^35 + X^17 + 1
X^521 + X^443 + X^35 + X^17 + 1
X^521 + X^453 + X^35 + X^17 + 1
X^521 + X^504 + X^35 + X^17 + 1
X^521 + X^36 + X^17 + X^13 + 1
X^521 + X^44 + X^36 + X^17 + 1
X^521 + X^98 + X^36 + X^17 + 1
X^521 + X^363 + X^36 + X^17 + 1
X^521 + X^387 + X^36 + X^17 + 1
X^521 + X^441 + X^36 + X^17 + 1
X^521 + X^447 + X^36 + X^17 + 1
X^521 + X^37 + X^17 + X^7 + 1
X^521 + X^112 + X^37 + X^17 + 1
X^521 + X^127 + X^37 + X^17 + 1
X^521 + X^147 + X^37 + X^17 + 1
X^521 + X^187 + X^37 + X^17 + 1
X^521 + X^495 + X^37 + X^17 + 1
X^521 + X^63 + X^38 + X^17 + 1
X^521 + X^252 + X^38 + X^17 + 1
X^521 + X^255 + X^38 + X^17 + 1
X^521 + X^258 + X^38 + X^17 + 1
X^521 + X^335 + X^38 + X^17 + 1
X^521 + X^77 + X^39 + X^17 + 1
X^521 + X^246 + X^39 + X^17 + 1
X^521 + X^256 + X^39 + X^17 + 1
X^521 + X^457 + X^39 + X^17 + 1
X^521 + X^40 + X^24 + X^17 + 1
X^521 + X^135 + X^40 + X^17 + 1
X^521 + X^195 + X^40 + X^17 + 1
X^521 + X^229 + X^40 + X^17 + 1
X^521 + X^324 + X^40 + X^17 + 1
X^521 + X^355 + X^40 + X^17 + 1
X^521 + X^450 + X^40 + X^17 + 1
X^521 + X^41 + X^17 + X^15 + 1
X^521 + X^42 + X^41 + X^17 + 1
X^521 + X^146 + X^41 + X^17 + 1
X^521 + X^297 + X^41 + X^17 + 1
X^521 + X^335 + X^41 + X^17 + 1
X^521 + X^377 + X^41 + X^17 + 1
X^521 + X^416 + X^41 + X^17 + 1
X^521 + X^510 + X^41 + X^17 + 1
X^521 + X^42 + X^41 + X^17 + 1
X^521 + X^44 + X^42 + X^17 + 1
X^521 + X^148 + X^42 + X^17 + 1
X^521 + X^181 + X^42 + X^17 + 1
X^521 + X^249 + X^42 + X^17 + 1
X^521 + X^289 + X^42 + X^17 + 1
X^521 + X^312 + X^42 + X^17 + 1
X^521 + X^382 + X^42 + X^17 + 1
X^521 + X^433 + X^42 + X^17 + 1
X^521 + X^504 + X^42 + X^17 + 1
X^521 + X^127 + X^43 + X^17 + 1
X^521 + X^357 + X^43 + X^17 + 1
X^521 + X^370 + X^43 + X^17 + 1
X^521 + X^396 + X^43 + X^17 + 1
X^521 + X^403 + X^43 + X^17 + 1
X^521 + X^471 + X^43 + X^17 + 1
X^521 + X^483 + X^43 + X^17 + 1
X^521 + X^513 + X^43 + X^17 + 1
X^521 + X^44 + X^36 + X^17 + 1
X^521 + X^44 + X^42 + X^17 + 1
X^521 + X^89 + X^44 + X^17 + 1
X^521 + X^135 + X^44 + X^17 + 1
X^521 + X^240 + X^44 + X^17 + 1
X^521 + X^446 + X^44 + X^17 + 1
X^521 + X^95 + X^45 + X^17 + 1
X^521 + X^112 + X^45 + X^17 + 1
X^521 + X^133 + X^45 + X^17 + 1
X^521 + X^180 + X^45 + X^17 + 1
X^521 + X^271 + X^45 + X^17 + 1
X^521 + X^283 + X^45 + X^17 + 1
X^521 + X^300 + X^45 + X^17 + 1
X^521 + X^320 + X^45 + X^17 + 1
X^521 + X^322 + X^45 + X^17 + 1
X^521 + X^356 + X^45 + X^17 + 1
X^521 + X^368 + X^45 + X^17 + 1
X^521 + X^378 + X^45 + X^17 + 1
X^521 + X^406 + X^45 + X^17 + 1
X^521 + X^440 + X^45 + X^17 + 1
X^521 + X^49 + X^46 + X^17 + 1
X^521 + X^189 + X^46 + X^17 + 1
X^521 + X^199 + X^46 + X^17 + 1
X^521 + X^207 + X^46 + X^17 + 1
X^521 + X^214 + X^46 + X^17 + 1
X^521 + X^253 + X^46 + X^17 + 1
X^521 + X^47 + X^20 + X^17 + 1
X^521 + X^125 + X^47 + X^17 + 1
X^521 + X^380 + X^47 + X^17 + 1
X^521 + X^381 + X^47 + X^17 + 1
X^521 + X^423 + X^47 + X^17 + 1
X^521 + X^443 + X^47 + X^17 + 1
X^521 + X^495 + X^47 + X^17 + 1
X^521 + X^506 + X^47 + X^17 + 1
X^521 + X^48 + 1
X^521 + X^146 + X^48 + X^17 + 1
X^521 + X^162 + X^48 + X^17 + 1
X^521 + X^211 + X^48 + X^17 + 1
X^521 + X^423 + X^48 + X^17 + 1
X^521 + X^451 + X^48 + X^17 + 1
X^521 + X^461 + X^48 + X^17 + 1
X^521 + X^49 + X^46 + X^17 + 1
X^521 + X^66 + X^49 + X^17 + 1
X^521 + X^112 + X^49 + X^17 + 1

Errors: /home/mfd/gomagma: line 2:  2594 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:18:50 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [0..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:18:43 on modular  [Seed = 1713534095]
   -------------------------------------

X^9 + X^4 + 1

Total time: 7.459 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:19:17 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [0..200]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:19:05 on modular  [Seed = 2134601100]
   -------------------------------------

X^9 + X^4 + 1

Total time: 11.859 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:19:46 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [0..300]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:19:29 on modular  [Seed = 1949329135]
   -------------------------------------

X^9 + X^4 + 1

Total time: 16.420 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:20:25 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for n in [300..520]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:20:11 on modular  [Seed = 408685230]
   -------------------------------------

X^9 + X^4 + 1

Total time: 13.649 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:22:43 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,9);
C;
for t in [1..10] do
for n in [1..200]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:22:20 on modular  [Seed = 374474016]
   -------------------------------------

X^9 + X^4 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
X^521 + X^169 + X^12 + X + 1
X^521 + X^205 + X^12 + X + 1
X^521 + X^398 + X^12 + X + 1
X^521 + X^415 + X^12 + X + 1
X^521 + X^457 + X^12 + X + 1
X^521 + X^464 + X^12 + X + 1
X^521 + X^80 + X^13 + X + 1
X^521 + X^179 + X^13 + X + 1
X^521 + X^225 + X^13 + X + 1
X^521 + X^312 + X^13 + X + 1
X^521 + X^353 + X^13 + X + 1
X^521 + X^401 + X^13 + X + 1
X^521 + X^432 + X^13 + X + 1
X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
X^521 + X^454 + X^14 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^242 + X^15 + X + 1
X^521 + X^293 + X^15 + X + 1
X^521 + X^307 + X^15 + X + 1
X^521 + X^403 + X^15 + X + 1
X^521 + X^413 + X^15 + X + 1
X^521 + X^84 + X^16 + X + 1
X^521 + X^234 + X^16 + X + 1
X^521 + X^273 + X^16 + X + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^215 + X^18 + X + 1
X^521 + X^341 + X^18 + X + 1
X^521 + X^231 + X^19 + X + 1
X^521 + X^372 + X^19 + X + 1
X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1
X^521 + X^513 + X^55 + X + 1
X^521 + X^148 + X^56 + X + 1
X^521 + X^309 + X^56 + X + 1
X^521 + X^405 + X^56 + X + 1
X^521 + X^442 + X^56 + X + 1

Errors: /home/mfd/gomagma: line 2:  2652 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:24:36 2004

Input: k := GF(2);
for t in [1..10] do
for n in [1..200]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:24:32 on modular  [Seed = 795556709]
   -------------------------------------


>>         C := 1 + X^m + X^n + X^t + X^521;
                    ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:25:24 2004

Input: k := GF(2);
C<X> := 1;
for t in [1..10] do
for n in [1..200]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:25:21 on modular  [Seed = 947661891]
   -------------------------------------


>> C<X> := 1;
    ^
Runtime error in 'AssignNames': Bad argument types
Argument types given: RngIntElt ~, SeqEnum[MonStgElt]

>>         C := 1 + X^m + X^n + X^t + X^521;
                    ^
User error: Identifier 'X' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:26:21 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,2);
for t in [1..10] do
for n in [1..200]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:25:58 on modular  [Seed = 829760813]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
X^521 + X^169 + X^12 + X + 1
X^521 + X^205 + X^12 + X + 1
X^521 + X^398 + X^12 + X + 1
X^521 + X^415 + X^12 + X + 1
X^521 + X^457 + X^12 + X + 1
X^521 + X^464 + X^12 + X + 1
X^521 + X^80 + X^13 + X + 1
X^521 + X^179 + X^13 + X + 1
X^521 + X^225 + X^13 + X + 1
X^521 + X^312 + X^13 + X + 1
X^521 + X^353 + X^13 + X + 1
X^521 + X^401 + X^13 + X + 1
X^521 + X^432 + X^13 + X + 1
X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
X^521 + X^454 + X^14 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^242 + X^15 + X + 1
X^521 + X^293 + X^15 + X + 1
X^521 + X^307 + X^15 + X + 1
X^521 + X^403 + X^15 + X + 1
X^521 + X^413 + X^15 + X + 1
X^521 + X^84 + X^16 + X + 1
X^521 + X^234 + X^16 + X + 1
X^521 + X^273 + X^16 + X + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^215 + X^18 + X + 1
X^521 + X^341 + X^18 + X + 1
X^521 + X^231 + X^19 + X + 1
X^521 + X^372 + X^19 + X + 1
X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1
X^521 + X^513 + X^55 + X + 1
X^521 + X^148 + X^56 + X + 1
X^521 + X^309 + X^56 + X + 1

Errors: /home/mfd/gomagma: line 2:  2683 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:27:50 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,2);
for t in [1..10] do
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:27:27 on modular  [Seed = 3482049322]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
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X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
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X^521 + X^205 + X^12 + X + 1
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X^521 + X^457 + X^12 + X + 1
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X^521 + X^80 + X^13 + X + 1
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X^521 + X^401 + X^13 + X + 1
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X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
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X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
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X^521 + X^63 + X^20 + X + 1
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X^521 + X^163 + X^21 + X + 1
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X^521 + X^472 + X^21 + X + 1
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X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
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X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
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X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
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X^521 + X^151 + X^45 + X + 1
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X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1
X^521 + X^513 + X^55 + X + 1
X^521 + X^148 + X^56 + X + 1

Errors: /home/mfd/gomagma: line 2:  2693 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:28:38 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,2);
for t in [1..5] do
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:28:15 on modular  [Seed = 3296776273]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
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X^521 + X^370 + X^3 + X + 1
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X^521 + X^213 + X^4 + X + 1
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X^521 + X^516 + X^4 + X + 1
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X^521 + X^149 + X^7 + X + 1
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X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
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X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
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X^521 + X^53 + X^9 + X + 1
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X^521 + X^205 + X^12 + X + 1
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X^521 + X^225 + X^13 + X + 1
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X^521 + X^40 + X^18 + X + 1
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X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1
X^521 + X^513 + X^55 + X + 1
X^521 + X^148 + X^56 + X + 1

Errors: /home/mfd/gomagma: line 2:  2702 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:29:30 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,2);
for t in [1..2] do
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^t + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:29:07 on modular  [Seed = 3717843076]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
X^521 + X^169 + X^12 + X + 1
X^521 + X^205 + X^12 + X + 1
X^521 + X^398 + X^12 + X + 1
X^521 + X^415 + X^12 + X + 1
X^521 + X^457 + X^12 + X + 1
X^521 + X^464 + X^12 + X + 1
X^521 + X^80 + X^13 + X + 1
X^521 + X^179 + X^13 + X + 1
X^521 + X^225 + X^13 + X + 1
X^521 + X^312 + X^13 + X + 1
X^521 + X^353 + X^13 + X + 1
X^521 + X^401 + X^13 + X + 1
X^521 + X^432 + X^13 + X + 1
X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
X^521 + X^454 + X^14 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^242 + X^15 + X + 1
X^521 + X^293 + X^15 + X + 1
X^521 + X^307 + X^15 + X + 1
X^521 + X^403 + X^15 + X + 1
X^521 + X^413 + X^15 + X + 1
X^521 + X^84 + X^16 + X + 1
X^521 + X^234 + X^16 + X + 1
X^521 + X^273 + X^16 + X + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^215 + X^18 + X + 1
X^521 + X^341 + X^18 + X + 1
X^521 + X^231 + X^19 + X + 1
X^521 + X^372 + X^19 + X + 1
X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1

Errors: /home/mfd/gomagma: line 2:  2711 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:30:21 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,2);
for t in [1..2] do
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^1 + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:29:58 on modular  [Seed = 3937337318]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
X^521 + X^169 + X^12 + X + 1
X^521 + X^205 + X^12 + X + 1
X^521 + X^398 + X^12 + X + 1
X^521 + X^415 + X^12 + X + 1
X^521 + X^457 + X^12 + X + 1
X^521 + X^464 + X^12 + X + 1
X^521 + X^80 + X^13 + X + 1
X^521 + X^179 + X^13 + X + 1
X^521 + X^225 + X^13 + X + 1
X^521 + X^312 + X^13 + X + 1
X^521 + X^353 + X^13 + X + 1
X^521 + X^401 + X^13 + X + 1
X^521 + X^432 + X^13 + X + 1
X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
X^521 + X^454 + X^14 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^242 + X^15 + X + 1
X^521 + X^293 + X^15 + X + 1
X^521 + X^307 + X^15 + X + 1
X^521 + X^403 + X^15 + X + 1
X^521 + X^413 + X^15 + X + 1
X^521 + X^84 + X^16 + X + 1
X^521 + X^234 + X^16 + X + 1
X^521 + X^273 + X^16 + X + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^215 + X^18 + X + 1
X^521 + X^341 + X^18 + X + 1
X^521 + X^231 + X^19 + X + 1
X^521 + X^372 + X^19 + X + 1
X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1
X^521 + X^513 + X^55 + X + 1
X^521 + X^148 + X^56 + X + 1

Errors: /home/mfd/gomagma: line 2:  2720 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:31:27 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,2);
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^1 + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:31:04 on modular  [Seed = 4206817080]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
X^521 + X^169 + X^12 + X + 1
X^521 + X^205 + X^12 + X + 1
X^521 + X^398 + X^12 + X + 1
X^521 + X^415 + X^12 + X + 1
X^521 + X^457 + X^12 + X + 1
X^521 + X^464 + X^12 + X + 1
X^521 + X^80 + X^13 + X + 1
X^521 + X^179 + X^13 + X + 1
X^521 + X^225 + X^13 + X + 1
X^521 + X^312 + X^13 + X + 1
X^521 + X^353 + X^13 + X + 1
X^521 + X^401 + X^13 + X + 1
X^521 + X^432 + X^13 + X + 1
X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
X^521 + X^454 + X^14 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^242 + X^15 + X + 1
X^521 + X^293 + X^15 + X + 1
X^521 + X^307 + X^15 + X + 1
X^521 + X^403 + X^15 + X + 1
X^521 + X^413 + X^15 + X + 1
X^521 + X^84 + X^16 + X + 1
X^521 + X^234 + X^16 + X + 1
X^521 + X^273 + X^16 + X + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^215 + X^18 + X + 1
X^521 + X^341 + X^18 + X + 1
X^521 + X^231 + X^19 + X + 1
X^521 + X^372 + X^19 + X + 1
X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1

Errors: /home/mfd/gomagma: line 2:  2736 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:32:30 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^1 + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:32:07 on modular  [Seed = 4088915582]
   -------------------------------------

X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^159 + X^2 + X + 1
X^521 + X^382 + X^2 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^91 + X^3 + X + 1
X^521 + X^116 + X^3 + X + 1
X^521 + X^127 + X^3 + X + 1
X^521 + X^179 + X^3 + X + 1
X^521 + X^211 + X^3 + X + 1
X^521 + X^370 + X^3 + X + 1
X^521 + X^391 + X^3 + X + 1
X^521 + X^512 + X^3 + X + 1
X^521 + X^213 + X^4 + X + 1
X^521 + X^363 + X^4 + X + 1
X^521 + X^516 + X^4 + X + 1
X^521 + X^415 + X^5 + X + 1
X^521 + X^477 + X^5 + X + 1
X^521 + X^510 + X^5 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^217 + X^6 + X + 1
X^521 + X^383 + X^6 + X + 1
X^521 + X^506 + X^6 + X + 1
X^521 + X^83 + X^7 + X + 1
X^521 + X^93 + X^7 + X + 1
X^521 + X^149 + X^7 + X + 1
X^521 + X^212 + X^7 + X + 1
X^521 + X^233 + X^7 + X + 1
X^521 + X^285 + X^7 + X + 1
X^521 + X^369 + X^7 + X + 1
X^521 + X^129 + X^8 + X + 1
X^521 + X^216 + X^8 + X + 1
X^521 + X^507 + X^8 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^89 + X^9 + X + 1
X^521 + X^124 + X^9 + X + 1
X^521 + X^157 + X^9 + X + 1
X^521 + X^334 + X^9 + X + 1
X^521 + X^353 + X^9 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^120 + X^11 + X + 1
X^521 + X^204 + X^11 + X + 1
X^521 + X^292 + X^11 + X + 1
X^521 + X^517 + X^11 + X + 1
X^521 + X^169 + X^12 + X + 1
X^521 + X^205 + X^12 + X + 1
X^521 + X^398 + X^12 + X + 1
X^521 + X^415 + X^12 + X + 1
X^521 + X^457 + X^12 + X + 1
X^521 + X^464 + X^12 + X + 1
X^521 + X^80 + X^13 + X + 1
X^521 + X^179 + X^13 + X + 1
X^521 + X^225 + X^13 + X + 1
X^521 + X^312 + X^13 + X + 1
X^521 + X^353 + X^13 + X + 1
X^521 + X^401 + X^13 + X + 1
X^521 + X^432 + X^13 + X + 1
X^521 + X^446 + X^13 + X + 1
X^521 + X^504 + X^13 + X + 1
X^521 + X^408 + X^14 + X + 1
X^521 + X^454 + X^14 + X + 1
X^521 + X^15 + X^11 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^242 + X^15 + X + 1
X^521 + X^293 + X^15 + X + 1
X^521 + X^307 + X^15 + X + 1
X^521 + X^403 + X^15 + X + 1
X^521 + X^413 + X^15 + X + 1
X^521 + X^84 + X^16 + X + 1
X^521 + X^234 + X^16 + X + 1
X^521 + X^273 + X^16 + X + 1
X^521 + X^111 + X^17 + X + 1
X^521 + X^319 + X^17 + X + 1
X^521 + X^412 + X^17 + X + 1
X^521 + X^420 + X^17 + X + 1
X^521 + X^426 + X^17 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^215 + X^18 + X + 1
X^521 + X^341 + X^18 + X + 1
X^521 + X^231 + X^19 + X + 1
X^521 + X^372 + X^19 + X + 1
X^521 + X^498 + X^19 + X + 1
X^521 + X^20 + X^3 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^63 + X^20 + X + 1
X^521 + X^156 + X^20 + X + 1
X^521 + X^175 + X^20 + X + 1
X^521 + X^357 + X^20 + X + 1
X^521 + X^445 + X^20 + X + 1
X^521 + X^513 + X^20 + X + 1
X^521 + X^142 + X^21 + X + 1
X^521 + X^163 + X^21 + X + 1
X^521 + X^212 + X^21 + X + 1
X^521 + X^241 + X^21 + X + 1
X^521 + X^310 + X^21 + X + 1
X^521 + X^370 + X^21 + X + 1
X^521 + X^437 + X^21 + X + 1
X^521 + X^470 + X^21 + X + 1
X^521 + X^472 + X^21 + X + 1
X^521 + X^505 + X^21 + X + 1
X^521 + X^520 + X^21 + X + 1
X^521 + X^203 + X^22 + X + 1
X^521 + X^207 + X^22 + X + 1
X^521 + X^224 + X^22 + X + 1
X^521 + X^300 + X^22 + X + 1
X^521 + X^444 + X^22 + X + 1
X^521 + X^70 + X^23 + X + 1
X^521 + X^76 + X^23 + X + 1
X^521 + X^102 + X^23 + X + 1
X^521 + X^249 + X^23 + X + 1
X^521 + X^399 + X^23 + X + 1
X^521 + X^412 + X^23 + X + 1
X^521 + X^480 + X^23 + X + 1
X^521 + X^88 + X^24 + X + 1
X^521 + X^148 + X^24 + X + 1
X^521 + X^296 + X^24 + X + 1
X^521 + X^478 + X^24 + X + 1
X^521 + X^155 + X^25 + X + 1
X^521 + X^225 + X^25 + X + 1
X^521 + X^248 + X^25 + X + 1
X^521 + X^311 + X^25 + X + 1
X^521 + X^356 + X^25 + X + 1
X^521 + X^240 + X^26 + X + 1
X^521 + X^336 + X^26 + X + 1
X^521 + X^426 + X^26 + X + 1
X^521 + X^468 + X^26 + X + 1
X^521 + X^194 + X^27 + X + 1
X^521 + X^220 + X^27 + X + 1
X^521 + X^515 + X^27 + X + 1
X^521 + X^261 + X^28 + X + 1
X^521 + X^302 + X^28 + X + 1
X^521 + X^320 + X^28 + X + 1
X^521 + X^359 + X^28 + X + 1
X^521 + X^112 + X^29 + X + 1
X^521 + X^129 + X^29 + X + 1
X^521 + X^159 + X^29 + X + 1
X^521 + X^193 + X^29 + X + 1
X^521 + X^208 + X^29 + X + 1
X^521 + X^229 + X^29 + X + 1
X^521 + X^273 + X^29 + X + 1
X^521 + X^328 + X^29 + X + 1
X^521 + X^403 + X^29 + X + 1
X^521 + X^74 + X^30 + X + 1
X^521 + X^140 + X^30 + X + 1
X^521 + X^266 + X^30 + X + 1
X^521 + X^430 + X^30 + X + 1
X^521 + X^195 + X^31 + X + 1
X^521 + X^225 + X^31 + X + 1
X^521 + X^497 + X^31 + X + 1
X^521 + X^32 + 1
X^521 + X^156 + X^32 + X + 1
X^521 + X^292 + X^32 + X + 1
X^521 + X^471 + X^32 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^71 + X^33 + X + 1
X^521 + X^76 + X^33 + X + 1
X^521 + X^197 + X^33 + X + 1
X^521 + X^224 + X^33 + X + 1
X^521 + X^259 + X^33 + X + 1
X^521 + X^329 + X^33 + X + 1
X^521 + X^349 + X^33 + X + 1
X^521 + X^352 + X^33 + X + 1
X^521 + X^407 + X^33 + X + 1
X^521 + X^466 + X^33 + X + 1
X^521 + X^102 + X^34 + X + 1
X^521 + X^119 + X^34 + X + 1
X^521 + X^147 + X^34 + X + 1
X^521 + X^179 + X^34 + X + 1
X^521 + X^231 + X^34 + X + 1
X^521 + X^58 + X^35 + X + 1
X^521 + X^183 + X^35 + X + 1
X^521 + X^282 + X^35 + X + 1
X^521 + X^306 + X^35 + X + 1
X^521 + X^447 + X^35 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^284 + X^36 + X + 1
X^521 + X^473 + X^36 + X + 1
X^521 + X^517 + X^36 + X + 1
X^521 + X^37 + X^33 + X + 1
X^521 + X^90 + X^37 + X + 1
X^521 + X^105 + X^37 + X + 1
X^521 + X^117 + X^37 + X + 1
X^521 + X^180 + X^37 + X + 1
X^521 + X^188 + X^37 + X + 1
X^521 + X^306 + X^37 + X + 1
X^521 + X^444 + X^37 + X + 1
X^521 + X^38 + X^15 + X + 1
X^521 + X^130 + X^38 + X + 1
X^521 + X^219 + X^38 + X + 1
X^521 + X^366 + X^38 + X + 1
X^521 + X^462 + X^38 + X + 1
X^521 + X^97 + X^39 + X + 1
X^521 + X^167 + X^39 + X + 1
X^521 + X^328 + X^39 + X + 1
X^521 + X^439 + X^39 + X + 1
X^521 + X^517 + X^39 + X + 1
X^521 + X^40 + X^18 + X + 1
X^521 + X^40 + X^36 + X + 1
X^521 + X^216 + X^40 + X + 1
X^521 + X^333 + X^40 + X + 1
X^521 + X^434 + X^40 + X + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^91 + X^41 + X + 1
X^521 + X^79 + X^42 + X + 1
X^521 + X^83 + X^42 + X + 1
X^521 + X^92 + X^42 + X + 1
X^521 + X^118 + X^42 + X + 1
X^521 + X^139 + X^42 + X + 1
X^521 + X^268 + X^42 + X + 1
X^521 + X^514 + X^42 + X + 1
X^521 + X^43 + X^20 + X + 1
X^521 + X^59 + X^43 + X + 1
X^521 + X^95 + X^43 + X + 1
X^521 + X^207 + X^43 + X + 1
X^521 + X^248 + X^43 + X + 1
X^521 + X^257 + X^43 + X + 1
X^521 + X^494 + X^43 + X + 1
X^521 + X^88 + X^44 + X + 1
X^521 + X^133 + X^44 + X + 1
X^521 + X^276 + X^44 + X + 1
X^521 + X^277 + X^44 + X + 1
X^521 + X^342 + X^44 + X + 1
X^521 + X^349 + X^44 + X + 1
X^521 + X^465 + X^44 + X + 1
X^521 + X^76 + X^45 + X + 1
X^521 + X^107 + X^45 + X + 1
X^521 + X^151 + X^45 + X + 1
X^521 + X^175 + X^45 + X + 1
X^521 + X^191 + X^45 + X + 1
X^521 + X^263 + X^45 + X + 1
X^521 + X^358 + X^45 + X + 1
X^521 + X^421 + X^45 + X + 1
X^521 + X^482 + X^45 + X + 1
X^521 + X^107 + X^46 + X + 1
X^521 + X^176 + X^46 + X + 1
X^521 + X^362 + X^46 + X + 1
X^521 + X^390 + X^46 + X + 1
X^521 + X^47 + X^9 + X + 1
X^521 + X^141 + X^47 + X + 1
X^521 + X^181 + X^47 + X + 1
X^521 + X^301 + X^47 + X + 1
X^521 + X^336 + X^47 + X + 1
X^521 + X^499 + X^47 + X + 1
X^521 + X^48 + 1
X^521 + X^154 + X^48 + X + 1
X^521 + X^197 + X^48 + X + 1
X^521 + X^280 + X^48 + X + 1
X^521 + X^382 + X^48 + X + 1
X^521 + X^445 + X^48 + X + 1
X^521 + X^476 + X^48 + X + 1
X^521 + X^49 + X^6 + X + 1
X^521 + X^135 + X^49 + X + 1
X^521 + X^197 + X^49 + X + 1
X^521 + X^423 + X^49 + X + 1
X^521 + X^440 + X^49 + X + 1
X^521 + X^474 + X^49 + X + 1
X^521 + X^76 + X^50 + X + 1
X^521 + X^342 + X^50 + X + 1
X^521 + X^370 + X^50 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^80 + X^51 + X + 1
X^521 + X^137 + X^51 + X + 1
X^521 + X^181 + X^51 + X + 1
X^521 + X^272 + X^51 + X + 1
X^521 + X^320 + X^51 + X + 1
X^521 + X^203 + X^52 + X + 1
X^521 + X^273 + X^52 + X + 1
X^521 + X^450 + X^52 + X + 1
X^521 + X^489 + X^52 + X + 1
X^521 + X^53 + X^9 + X + 1
X^521 + X^66 + X^53 + X + 1
X^521 + X^253 + X^53 + X + 1
X^521 + X^370 + X^53 + X + 1
X^521 + X^376 + X^53 + X + 1
X^521 + X^505 + X^53 + X + 1
X^521 + X^169 + X^54 + X + 1
X^521 + X^286 + X^54 + X + 1
X^521 + X^349 + X^54 + X + 1
X^521 + X^517 + X^54 + X + 1
X^521 + X^55 + X^51 + X + 1
X^521 + X^101 + X^55 + X + 1
X^521 + X^191 + X^55 + X + 1
X^521 + X^441 + X^55 + X + 1
X^521 + X^513 + X^55 + X + 1
X^521 + X^148 + X^56 + X + 1
X^521 + X^309 + X^56 + X + 1
X^521 + X^405 + X^56 + X + 1
X^521 + X^442 + X^56 + X + 1
X^521 + X^109 + X^57 + X + 1
X^521 + X^262 + X^57 + X + 1
X^521 + X^284 + X^57 + X + 1
X^521 + X^412 + X^57 + X + 1
X^521 + X^433 + X^57 + X + 1

Errors: /home/mfd/gomagma: line 2:  2745 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:33:10 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^10 + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Tue Jan 13 2004 15:32:47 on modular  [Seed = 2311953452]
   -------------------------------------

X^521 + X^41 + X^10 + X + 1
X^521 + X^321 + X^10 + X + 1
X^521 + X^389 + X^10 + X + 1
X^521 + X^114 + X^10 + X^2 + 1
X^521 + X^46 + X^10 + X^3 + 1
X^521 + X^448 + X^10 + X^3 + 1
X^521 + X^476 + X^10 + X^3 + 1
X^521 + X^45 + X^10 + X^4 + 1
X^521 + X^429 + X^10 + X^4 + 1
X^521 + X^16 + X^10 + X^5 + 1
X^521 + X^240 + X^10 + X^5 + 1
X^521 + X^276 + X^10 + X^5 + 1
X^521 + X^399 + X^10 + X^5 + 1
X^521 + X^38 + X^10 + X^6 + 1
X^521 + X^215 + X^10 + X^6 + 1
X^521 + X^220 + X^10 + X^6 + 1
X^521 + X^341 + X^10 + X^6 + 1
X^521 + X^418 + X^10 + X^6 + 1
X^521 + X^65 + X^10 + X^7 + 1
X^521 + X^191 + X^10 + X^7 + 1
X^521 + X^204 + X^10 + X^7 + 1
X^521 + X^294 + X^10 + X^7 + 1
X^521 + X^311 + X^10 + X^7 + 1
X^521 + X^387 + X^10 + X^7 + 1
X^521 + X^407 + X^10 + X^7 + 1
X^521 + X^36 + X^10 + X^8 + 1
X^521 + X^394 + X^10 + X^8 + 1
X^521 + X^412 + X^10 + X^8 + 1
X^521 + X^64 + X^10 + X^9 + 1
X^521 + X^232 + X^10 + X^9 + 1
X^521 + X^235 + X^10 + X^9 + 1
X^521 + X^274 + X^10 + X^9 + 1
X^521 + X^442 + X^10 + X^9 + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1
X^521 + X^169 + X^11 + X^10 + 1
X^521 + X^189 + X^11 + X^10 + 1
X^521 + X^309 + X^11 + X^10 + 1
X^521 + X^262 + X^12 + X^10 + 1
X^521 + X^313 + X^12 + X^10 + 1
X^521 + X^406 + X^12 + X^10 + 1
X^521 + X^440 + X^13 + X^10 + 1
X^521 + X^519 + X^13 + X^10 + 1
X^521 + X^48 + X^14 + X^10 + 1
X^521 + X^157 + X^14 + X^10 + 1
X^521 + X^171 + X^14 + X^10 + 1
X^521 + X^216 + X^14 + X^10 + 1
X^521 + X^504 + X^14 + X^10 + 1
X^521 + X^85 + X^15 + X^10 + 1
X^521 + X^125 + X^15 + X^10 + 1
X^521 + X^296 + X^15 + X^10 + 1
X^521 + X^491 + X^15 + X^10 + 1
X^521 + X^16 + X^10 + X^5 + 1
X^521 + X^57 + X^16 + X^10 + 1
X^521 + X^63 + X^17 + X^10 + 1
X^521 + X^103 + X^17 + X^10 + 1
X^521 + X^495 + X^17 + X^10 + 1
X^521 + X^25 + X^18 + X^10 + 1
X^521 + X^59 + X^18 + X^10 + 1
X^521 + X^119 + X^19 + X^10 + 1
X^521 + X^152 + X^19 + X^10 + 1
X^521 + X^168 + X^19 + X^10 + 1
X^521 + X^300 + X^19 + X^10 + 1
X^521 + X^369 + X^19 + X^10 + 1
X^521 + X^392 + X^19 + X^10 + 1
X^521 + X^355 + X^20 + X^10 + 1
X^521 + X^364 + X^20 + X^10 + 1
X^521 + X^142 + X^21 + X^10 + 1
X^521 + X^157 + X^21 + X^10 + 1
X^521 + X^436 + X^21 + X^10 + 1
X^521 + X^77 + X^24 + X^10 + 1
X^521 + X^160 + X^24 + X^10 + 1
X^521 + X^217 + X^24 + X^10 + 1
X^521 + X^440 + X^24 + X^10 + 1
X^521 + X^25 + X^18 + X^10 + 1
X^521 + X^158 + X^25 + X^10 + 1
X^521 + X^228 + X^25 + X^10 + 1
X^521 + X^414 + X^25 + X^10 + 1
X^521 + X^196 + X^26 + X^10 + 1
X^521 + X^216 + X^26 + X^10 + 1
X^521 + X^244 + X^26 + X^10 + 1
X^521 + X^279 + X^26 + X^10 + 1
X^521 + X^465 + X^26 + X^10 + 1
X^521 + X^136 + X^27 + X^10 + 1
X^521 + X^167 + X^27 + X^10 + 1
X^521 + X^371 + X^27 + X^10 + 1
X^521 + X^395 + X^27 + X^10 + 1
X^521 + X^469 + X^27 + X^10 + 1
X^521 + X^225 + X^28 + X^10 + 1
X^521 + X^269 + X^28 + X^10 + 1
X^521 + X^312 + X^28 + X^10 + 1
X^521 + X^144 + X^29 + X^10 + 1
X^521 + X^489 + X^29 + X^10 + 1
X^521 + X^496 + X^29 + X^10 + 1
X^521 + X^407 + X^30 + X^10 + 1
X^521 + X^108 + X^31 + X^10 + 1
X^521 + X^195 + X^31 + X^10 + 1
X^521 + X^284 + X^31 + X^10 + 1
X^521 + X^416 + X^31 + X^10 + 1
X^521 + X^503 + X^31 + X^10 + 1
X^521 + X^32 + 1
X^521 + X^87 + X^32 + X^10 + 1
X^521 + X^135 + X^32 + X^10 + 1
X^521 + X^214 + X^32 + X^10 + 1
X^521 + X^375 + X^32 + X^10 + 1
X^521 + X^442 + X^32 + X^10 + 1
X^521 + X^445 + X^32 + X^10 + 1
X^521 + X^133 + X^33 + X^10 + 1
X^521 + X^330 + X^34 + X^10 + 1
X^521 + X^210 + X^35 + X^10 + 1
X^521 + X^301 + X^35 + X^10 + 1
X^521 + X^348 + X^35 + X^10 + 1
X^521 + X^349 + X^35 + X^10 + 1
X^521 + X^454 + X^35 + X^10 + 1
X^521 + X^460 + X^35 + X^10 + 1
X^521 + X^36 + X^10 + X^8 + 1
X^521 + X^74 + X^36 + X^10 + 1
X^521 + X^148 + X^36 + X^10 + 1
X^521 + X^410 + X^36 + X^10 + 1
X^521 + X^413 + X^36 + X^10 + 1
X^521 + X^78 + X^37 + X^10 + 1
X^521 + X^261 + X^37 + X^10 + 1
X^521 + X^312 + X^37 + X^10 + 1
X^521 + X^320 + X^37 + X^10 + 1
X^521 + X^414 + X^37 + X^10 + 1
X^521 + X^38 + X^10 + X^6 + 1
X^521 + X^49 + X^38 + X^10 + 1
X^521 + X^91 + X^38 + X^10 + 1
X^521 + X^486 + X^38 + X^10 + 1
X^521 + X^428 + X^39 + X^10 + 1
X^521 + X^170 + X^40 + X^10 + 1
X^521 + X^240 + X^40 + X^10 + 1
X^521 + X^278 + X^40 + X^10 + 1
X^521 + X^293 + X^40 + X^10 + 1
X^521 + X^303 + X^40 + X^10 + 1
X^521 + X^416 + X^40 + X^10 + 1
X^521 + X^458 + X^40 + X^10 + 1
X^521 + X^468 + X^40 + X^10 + 1
X^521 + X^41 + X^10 + X + 1
X^521 + X^90 + X^41 + X^10 + 1
X^521 + X^181 + X^41 + X^10 + 1
X^521 + X^315 + X^41 + X^10 + 1
X^521 + X^215 + X^42 + X^10 + 1
X^521 + X^209 + X^43 + X^10 + 1
X^521 + X^249 + X^43 + X^10 + 1
X^521 + X^270 + X^43 + X^10 + 1
X^521 + X^354 + X^43 + X^10 + 1
X^521 + X^375 + X^43 + X^10 + 1
X^521 + X^378 + X^43 + X^10 + 1
X^521 + X^419 + X^43 + X^10 + 1
X^521 + X^434 + X^43 + X^10 + 1
X^521 + X^204 + X^44 + X^10 + 1
X^521 + X^382 + X^44 + X^10 + 1
X^521 + X^45 + X^10 + X^4 + 1
X^521 + X^136 + X^45 + X^10 + 1
X^521 + X^437 + X^45 + X^10 + 1
X^521 + X^46 + X^10 + X^3 + 1
X^521 + X^63 + X^46 + X^10 + 1
X^521 + X^150 + X^46 + X^10 + 1
X^521 + X^374 + X^46 + X^10 + 1
X^521 + X^410 + X^46 + X^10 + 1
X^521 + X^132 + X^47 + X^10 + 1
X^521 + X^147 + X^47 + X^10 + 1
X^521 + X^48 + 1
X^521 + X^48 + X^14 + X^10 + 1
X^521 + X^62 + X^48 + X^10 + 1
X^521 + X^136 + X^48 + X^10 + 1
X^521 + X^232 + X^48 + X^10 + 1
X^521 + X^283 + X^48 + X^10 + 1
X^521 + X^311 + X^48 + X^10 + 1
X^521 + X^374 + X^48 + X^10 + 1
X^521 + X^49 + X^38 + X^10 + 1
X^521 + X^206 + X^49 + X^10 + 1
X^521 + X^209 + X^49 + X^10 + 1
X^521 + X^275 + X^49 + X^10 + 1
X^521 + X^288 + X^49 + X^10 + 1
X^521 + X^294 + X^49 + X^10 + 1
X^521 + X^324 + X^49 + X^10 + 1
X^521 + X^341 + X^49 + X^10 + 1
X^521 + X^401 + X^49 + X^10 + 1
X^521 + X^428 + X^49 + X^10 + 1
X^521 + X^506 + X^49 + X^10 + 1
X^521 + X^512 + X^49 + X^10 + 1
X^521 + X^196 + X^50 + X^10 + 1
X^521 + X^396 + X^50 + X^10 + 1
X^521 + X^489 + X^50 + X^10 + 1
X^521 + X^110 + X^51 + X^10 + 1
X^521 + X^172 + X^51 + X^10 + 1
X^521 + X^260 + X^51 + X^10 + 1
X^521 + X^376 + X^51 + X^10 + 1
X^521 + X^434 + X^51 + X^10 + 1
X^521 + X^460 + X^51 + X^10 + 1
X^521 + X^194 + X^52 + X^10 + 1
X^521 + X^234 + X^52 + X^10 + 1
X^521 + X^299 + X^52 + X^10 + 1
X^521 + X^518 + X^52 + X^10 + 1
X^521 + X^70 + X^53 + X^10 + 1
X^521 + X^105 + X^53 + X^10 + 1
X^521 + X^175 + X^53 + X^10 + 1
X^521 + X^101 + X^54 + X^10 + 1
X^521 + X^167 + X^54 + X^10 + 1
X^521 + X^223 + X^54 + X^10 + 1
X^521 + X^245 + X^54 + X^10 + 1
X^521 + X^439 + X^54 + X^10 + 1
X^521 + X^467 + X^54 + X^10 + 1
X^521 + X^502 + X^54 + X^10 + 1
X^521 + X^161 + X^55 + X^10 + 1

Errors: /home/mfd/gomagma: line 2:  2755 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:34:03 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
for n in [1..100]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:33:55 on modular  [Seed = 2227213053]
   -------------------------------------


Total time: 7.249 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:34:37 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
C;
for n in [1..300]do
    for m in [1..520] do
        C := 1 + X^m + X^n + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;
end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:34:21 on modular  [Seed = 2648279962]
   -------------------------------------

X^12 + X^7 + X^6 + X^5 + X^3 + X + 1

Total time: 16.260 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:35:40 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
C;
    for m in [1..520] do
        C := 1 + X^m + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:35:36 on modular  [Seed = 2934618236]
   -------------------------------------

X^12 + X^7 + X^6 + X^5 + X^3 + X + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1
X^521 + X^353 + 1
X^521 + X^363 + 1
X^521 + X^473 + 1
X^521 + X^489 + 1

Total time: 3.479 seconds, Total memory usage: 2.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:36:35 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
C;
    for m in [1..331] do
        C := 1 + X^m + X^521;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:36:32 on modular  [Seed = 2816717117]
   -------------------------------------

X^12 + X^7 + X^6 + X^5 + X^3 + X + 1
X^521 + X^32 + 1
X^521 + X^48 + 1
X^521 + X^158 + 1
X^521 + X^168 + 1

Total time: 3.219 seconds, Total memory usage: 2.09MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:36:54 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
C;
    for m in [1..331] do
        C := 1 + X^m + X^331;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:36:51 on modular  [Seed = 3170413077]
   -------------------------------------

X^12 + X^7 + X^6 + X^5 + X^3 + X + 1

>>         if IsPrimitive(C) then 
                         ^
Runtime error in 'IsPrimitive': Degree of argument 1 must be >= 1

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:37:17 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,12);
C;
    for m in [1..330] do
        C := 1 + X^m + X^331;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:37:14 on modular  [Seed = 3052512005]
   -------------------------------------

X^12 + X^7 + X^6 + X^5 + X^3 + X + 1

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Tue Jan 13 15:37:43 2004

Input: k := GF(2);
C<X> := PrimitivePolynomial(k,331);
C;
    for m in [1..330] do
        C := 1 + X^m + X^331;
        if IsPrimitive(C) then 
           C;
        end if;
    end for;


Output: Magma V2.10-6     Tue Jan 13 2004 15:37:39 on modular  [Seed = 1107711258]
   -------------------------------------

X^331 + X^10 + X^6 + X^2 + 1

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 20:47:39 2004

Input: F := EllipticCurve([0, 17]);
F;

Output: Magma V2.10-6     Tue Jan 13 2004 20:47:35 on modular  [Seed = 3069339985]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 20:48:52 2004

Input: F := EllipticCurve([0, 17]);
F;

Output: Magma V2.10-6     Tue Jan 13 2004 20:48:49 on modular  [Seed = 2850900472]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field

Total time: 3.089 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 20:49:42 2004

Input: F := EllipticCurve([0, 17]);
F;

MW, f := MordellWeilGroup(F);
MW;       

a := f(MW.1);
b := f(MW.2);
a, b;

intpts := [ pt : i, j in [-4..4] |
IsIntegral(pt) where pt is i*a + j*b] ;
intpts;

#intpts;

Output: Magma V2.10-6     Tue Jan 13 2004 20:49:38 on modular  [Seed = 1394062128]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field
Abelian Group isomorphic to Z + Z
Defined on 2 generators (free)
(-2 : 3 : 1) (4 : 9 : 1)
[ (52 : -375 : 1), (8 : 23 : 1), (5234 : 378661 : 1), (-1 : 4 : 1), (-2 : -3 : 
1), (2 : -5 : 1), (43 : -282 : 1), (4 : -9 : 1), (4 : 9 : 1), (43 : 282 : 1), (2
: 5 : 1), (-2 : 3 : 1), (-1 : -4 : 1), (5234 : -378661 : 1), (8 : -23 : 1), (52 
: 375 : 1) ]
16

Total time: 3.739 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host nycmny1-ar5-4-35-085-151.nycmny1.elnk.dsl.genuity.net. (4.35.85.151)
Time: Tue Jan 13 20:53:41 2004

Input: 8*64

Output: Magma V2.10-6     Tue Jan 13 2004 20:53:38 on modular  [Seed = 1107731249]
   -------------------------------------

512

Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:34:05 2004

Input: F := EllipticCurve([0, -4]);
F;

MW, f := MordellWeilGroup(F);
MW;       

a := f(MW.1);
b := f(MW.2);
a, b;

intpts := [ pt : i, j in [-4..4] |
IsIntegral(pt) where pt is i*a + j*b] ;
intpts;

#intpts;

Output: Magma V2.10-6     Tue Jan 13 2004 21:34:02 on modular  [Seed = 1191423374]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 4 over Rational Field
Abelian Group isomorphic to Z
Defined on 1 generator (free)

>> b := f(MW.2);
            ^
Runtime error in '.': Argument 2 (2) should be in the range [-1 .. 1]

>> a, b;
      ^
User error: Identifier 'b' has not been declared or assigned

>> IsIntegral(pt) where pt is i*a + j*b] ;
                                      ^
User error: Identifier 'b' has not been declared or assigned

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

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

Total time: 3.139 seconds, Total memory usage: 1.89MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:34:41 2004

Input: F := EllipticCurve([-4, 0]);
F;

MW, f := MordellWeilGroup(F);
MW;       

a := f(MW.1);
b := f(MW.2);
a, b;

intpts := [ pt : i, j in [-4..4] |
IsIntegral(pt) where pt is i*a + j*b] ;
intpts;

#intpts;

Output: Magma V2.10-6     Tue Jan 13 2004 21:34:38 on modular  [Seed = 1309320355]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 4*x over Rational Field
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    2*MW.1 = 0
    2*MW.2 = 0
(-2 : 0 : 1) (0 : 0 : 1)
[ (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1),
(-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1),
(-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (-2 : 0 : 1), 
(2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1),
(2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), 
(-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1),
(-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), 
(0 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1),
(2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), 
(0 : 0 : 1), (0 : 0 : 1) ]
56

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:41:02 2004

Input: E := EllipticCurve([-27, 55350]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:40:59 on modular  [Seed = 1629850889]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 27*x + 55350 over Rational Field
Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 + 1 over Rational Field
[ (0 : 1 : 0), (51 : 432 : 1), (-21 : 216 : 1), (-21 : -216 : 1), (51 : -432 : 
1) ]
[ (0 : 1 : 0), (1 : 1 : 1), (-1 : 1 : 1), (-1 : -1 : 1), (1 : -3 : 1) ]

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:41:37 2004

Input: E := EllipticCurve([-4, 0]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:41:34 on modular  [Seed = 1747747941]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 4*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 4*x over Rational Field
[ (0 : 1 : 0), (-2 : 0 : 1), (0 : 0 : 1), (2 : 0 : 1) ]
[ (0 : 1 : 0), (-2 : 0 : 1), (0 : 0 : 1), (2 : 0 : 1) ]

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:42:52 2004

Input: E := EllipticCurve([-25, 0]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:42:49 on modular  [Seed = 492433895]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 25*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 25*x over Rational Field
[ (0 : 1 : 0), (5 : 0 : 1), (0 : 0 : 1), (-5 : 0 : 1) ]
[ (0 : 1 : 0), (5 : 0 : 1), (0 : 0 : 1), (-5 : 0 : 1) ]

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:43:11 2004

Input: E := EllipticCurve([-25, 32]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:43:08 on modular  [Seed = 71362795]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 25*x + 32 over Rational Field
Elliptic Curve defined by y^2 = x^3 - 25*x + 32 over Rational Field
[ (0 : 1 : 0) ]
[ (0 : 1 : 0) ]

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:43:27 2004

Input: E := EllipticCurve([-25, 128]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:43:24 on modular  [Seed = 863494060]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 25*x + 128 over Rational Field
Elliptic Curve defined by y^2 = x^3 - 25*x + 128 over Rational Field
[ (0 : 1 : 0) ]
[ (0 : 1 : 0) ]

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:43:39 2004

Input: E := EllipticCurve([-23, 128]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:43:36 on modular  [Seed = 981391025]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 23*x + 128 over Rational Field
Elliptic Curve defined by y^2 = x^3 - 23*x + 128 over Rational Field
[ (0 : 1 : 0) ]
[ (0 : 1 : 0) ]

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (210.77.19.20)
Time: Tue Jan 13 21:43:55 2004

Input: E := EllipticCurve([-23, 12]);
E;

M := MinimalModel(E);
M;


G, h := TorsionSubgroup(E);
torsion_pts_E := [ h(g) : g in G ];
torsion_pts_E;


G2, h2 := TorsionSubgroup(M);
torsion_pts_M := [ h2(g) : g in G2 ];
torsion_pts_M;


Output: Magma V2.10-6     Tue Jan 13 2004 21:43:52 on modular  [Seed = 560319898]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 - 23*x + 12 over Rational Field
Elliptic Curve defined by y^2 = x^3 - 23*x + 12 over Rational Field
[ (0 : 1 : 0) ]
[ (0 : 1 : 0) ]

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 01:28:26 2004

Input: p := 2^521;
p;


Output: Magma V2.10-6     Wed Jan 14 2004 01:28:23 on modular  [Seed = 4206779179]
   -------------------------------------

6864797660130609714981900799081393217269435300143305409394463459185543183397656\
052122559640661454554977296311391480858037121987999716643812574028291115057152

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 01:29:03 2004

Input: p := (2^521)-1;
p;


Output: Magma V2.10-6     Wed Jan 14 2004 01:29:00 on modular  [Seed = 3819389465]
   -------------------------------------

6864797660130609714981900799081393217269435300143305409394463459185543183397656\
052122559640661454554977296311391480858037121987999716643812574028291115057151

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:40:58 2004

Input: p := (2^401)-1;
Factorisation (p-1);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:40:54 on modular  [Seed = 1798298042]
   -------------------------------------

[ <2, 1>, <3, 1>, <5, 3>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 
1>, <257, 1>, <401, 1>, <601, 1>, <1601, 1>, <1801, 1>, <4051, 1>, <8101, 1>, 
<25601, 1>, <61681, 1>, <268501, 1>, <340801, 1>, <2787601, 1>, <82471201, 1>, 
<3173389601, 1>, <4278255361, 1>, <432363203127002885506543172618401, 1> ]
5164499756173817179311838344006023748659411585658447025661318713081295244033682\
389259290706560275662871806343945494986751

Total time: 4.019 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:41:30 2004

Input: p := (2^271)-1;
Factorisation (p-1);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:41:27 on modular  [Seed = 307667170]
   -------------------------------------

[ <2, 1>, <3, 4>, <7, 1>, <11, 1>, <19, 1>, <31, 1>, <73, 1>, <151, 1>, <271, 
1>, <331, 1>, <631, 1>, <811, 1>, <15121, 1>, <23311, 1>, <87211, 1>, <262657, 
1>, <348031, 1>, <18837001, 1>, <49971617830801, 1>, <385838642647891, 1> ]
3794275180128377091639574036764685364535950857523710002444946112771297432041422\
847

Total time: 3.259 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:41:52 2004

Input: p := (2^271)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:41:48 on modular  [Seed = 425569266]
   -------------------------------------

[ <15242475217, 1>, <2489277578681318902773305415678200452563642739707732865421\
88386932989391, 1> ]
3794275180128377091639574036764685364535950857523710002444946112771297432041422\
847

Total time: 3.799 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:42:29 2004

Input: p := (2^293)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:42:25 on modular  [Seed = 4502198]
   -------------------------------------

[ <40122362455616221971122353, 1>, <3966452270281388904156112207107579216439107\
43103031701971222447, 1> ]
1591434356511317254897223194069826688321459682551512695809484726058110390440106\
8017057791

Total time: 3.239 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:42:59 2004

Input: p := (2^311)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:42:55 on modular  [Seed = 913474718]
   -------------------------------------

[ <5344847, 1>, <2647649373910205158468946067671, 1>, 
<294803681348959296477194164064643062187559537539328375831, 1> ]
4171849679533027504677776769862406473833407270227837441302815640277772901915313\
574263597826047

Total time: 3.619 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:43:25 2004

Input: p := (2^317)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:43:21 on modular  [Seed = 1031376499]
   -------------------------------------

[ <9511, 1>, <587492521482839879, 1>, <4868122671322098041565641, 1>, 
<9815639231755686605031317440031161584572466128599, 1> ]
2669983794901137602993777132711940143253380652945815962433802009777774657225800\
68752870260867071

Total time: 3.249 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:43:51 2004

Input: p := (2^331)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:43:47 on modular  [Seed = 610309952]
   -------------------------------------

[ <16937389168607, 1>, <865118802936559, 1>, 
<298542624980197463613767215333569428005686468835821253721796682625551919, 1> ]
4374501449566023848745004454235242730706338861786424872851541212819905998398751\
846447026354046107647

Total time: 3.599 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:44:11 2004

Input: p := (2^347)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:44:07 on modular  [Seed = 728733755]
   -------------------------------------

[ <14143189112952632419639, 1>, <2027034530254598711604006944281449672934166611\
2096057885992643120463337596490211193, 1> ]
2866873269987589389513526119127608675995706236460351404671986049233653595110606\
01008752319138765710819327

Total time: 4.219 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:44:35 2004

Input: p := (2^401)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:44:32 on modular  [Seed = 3533070821]
   -------------------------------------

[ <856971565399, 1>, <2136958965524920285681, 1>, 
<594538100848945223169882301931953, 1>, <47433587754438046660400107045347804188\
40545962266329593, 1> ]
5164499756173817179311838344006023748659411585658447025661318713081295244033682\
389259290706560275662871806343945494986751

Total time: 3.209 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:44:51 2004

Input: p := (2^419)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:44:48 on modular  [Seed = 3650972414]
   -------------------------------------

[ <839, 1>, <903780021613921, 1>, <5800422716722833271214743, 1>, 
<10287968884341772230096159036619433593, 1>, 
<29919490848598531825060153417921002916701815927, 1> ]
1353842624082429130653522550851115089568572790710847937094960732721983060451965\
636249987502980536903367866802227247837807116287

Total time: 3.179 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:45:34 2004

Input: p := (2^457)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:45:14 on modular  [Seed = 3431497489]
   -------------------------------------

[ <150327409, 1>, <247553941968992978493531934444940989829116509732371457865094\
3035813830300993611462717419801770460539016610145009605554380104535919, 1> ]
3721414268393507279612537896386583215890643766719068468641229819804873155140597\
36743009817965446945567110411062408283101969716033850703871

Total time: 19.569 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:45:54 2004

Input: p := (2^521)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:45:50 on modular  [Seed = 4088872970]
   -------------------------------------

[ <6864797660130609714981900799081393217269435300143305409394463459185543183397\
6560521225596406614545549772963113914808580371219879997166438125740282911150571\
51, 1> ]
6864797660130609714981900799081393217269435300143305409394463459185543183397656\
052122559640661454554977296311391480858037121987999716643812574028291115057151

Total time: 3.579 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host 3(NXDOMAIN) (194.165.15.3)
Time: Wed Jan 14 02:46:49 2004

Input: p := (2^331)-1;
Factorisation (p);
p;


Output: Magma V2.10-6     Wed Jan 14 2004 02:46:46 on modular  [Seed = 4206774603]
   -------------------------------------

[ <16937389168607, 1>, <865118802936559, 1>, 
<298542624980197463613767215333569428005686468835821253721796682625551919, 1> ]
4374501449566023848745004454235242730706338861786424872851541212819905998398751\
846447026354046107647

Total time: 3.499 seconds, Total memory usage: 2.99MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:35:26 2004

Input: Br<a,b,c,d,e>:=BraidGroup;

Output: Magma V2.10-6     Wed Jan 14 2004 05:35:22 on modular  [Seed = 2362038204]
   -------------------------------------


>> Br<a,b,c,d,e>:=BraidGroup;;
     ^
Runtime error in 'AssignNames': Bad argument types
Argument types given: Intrinsic ~, SeqEnum[MonStgElt]

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:35:49 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);

Output: Magma V2.10-6     Wed Jan 14 2004 05:35:46 on modular  [Seed = 2244009565]
   -------------------------------------


Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:36:18 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
FundamentalElement(Br);


Output: Magma V2.10-6     Wed Jan 14 2004 05:36:15 on modular  [Seed = 3002591607]
   -------------------------------------

e * d * c * b * a * e * d * c * b * e * d * c * e * d * e
<Artin, 1, [], 0>

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:37:02 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);


Output: Magma V2.10-6     Wed Jan 14 2004 05:36:59 on modular  [Seed = 2884563002]
   -------------------------------------


Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:38:18 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);

Output: Magma V2.10-6     Wed Jan 14 2004 05:38:15 on modular  [Seed = 2716138988]
   -------------------------------------


Total time: 2.909 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:42:30 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s[1]:=d^3;
s[2]:=(c^d)^2;
s[3]:=c^3;
s[4]:=c^3;
s[5]:=(c^(D*c))^2;
s[6]:=b^(c*d*d*c*c);
s[7]:=(b^(c^3))^3;
s[8]:=e^(d*c*b*b*c*d*d*c*b);
s[9]:=(e^(d*c*b))^3;
s[10]:=a^(b*c*d*e*e*d*c*b);
s[11]:=a;
s[12]:=(c^D)^2;
s[13]:=s[12];
s[14]:=d^3;

Output: Magma V2.10-6     Wed Jan 14 2004 05:42:27 on modular  [Seed = 1427114013]
   -------------------------------------


>> s[1]:=d^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[2]:=(c^d)^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[3]:=c^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[4]:=c^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[5]:=(c^(D*c))^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[6]:=b^(c*d*d*c*c);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[7]:=(b^(c^3))^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[8]:=e^(d*c*b*b*c*d*d*c*b);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[9]:=(e^(d*c*b))^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[10]:=a^(b*c*d*e*e*d*c*b);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[11]:=a;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[12]:=(c^D)^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[13]:=s[12];
          ^
User error: Identifier 's' has not been declared or assigned

>> s[14]:=d^3;;
    ^
User error: Identifier 's' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:52:06 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=vector(14,Br);
s[1]:=d^3;
s[2]:=(c^d)^2;
s[3]:=c^3;
s[4]:=c^3;
s[5]:=(c^(D*c))^2;
s[6]:=b^(c*d*d*c*c);
s[7]:=(b^(c^3))^3;
s[8]:=e^(d*c*b*b*c*d*d*c*b);
s[9]:=(e^(d*c*b))^3;
s[10]:=a^(b*c*d*e*e*d*c*b);
s[11]:=a;
s[12]:=(c^D)^2;
s[13]:=s[12];
s[14]:=d^3;

Output: Magma V2.10-6     Wed Jan 14 2004 05:52:03 on modular  [Seed = 2134515831]
   -------------------------------------


>> s:=vector(14,Br);
      ^
User error: Identifier 'vector' has not been declared or assigned

>> s[1]:=d^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[2]:=(c^d)^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[3]:=c^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[4]:=c^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[5]:=(c^(D*c))^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[6]:=b^(c*d*d*c*c);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[7]:=(b^(c^3))^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[8]:=e^(d*c*b*b*c*d*d*c*b);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[9]:=(e^(d*c*b))^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[10]:=a^(b*c*d*e*e*d*c*b);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[11]:=a;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[12]:=(c^D)^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[13]:=s[12];
          ^
User error: Identifier 's' has not been declared or assigned

>> s[14]:=d^3;;
    ^
User error: Identifier 's' has not been declared or assigned

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 05:52:25 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=Vector(14,Br);
s[1]:=d^3;
s[2]:=(c^d)^2;
s[3]:=c^3;
s[4]:=c^3;
s[5]:=(c^(D*c))^2;
s[6]:=b^(c*d*d*c*c);
s[7]:=(b^(c^3))^3;
s[8]:=e^(d*c*b*b*c*d*d*c*b);
s[9]:=(e^(d*c*b))^3;
s[10]:=a^(b*c*d*e*e*d*c*b);
s[11]:=a;
s[12]:=(c^D)^2;
s[13]:=s[12];
s[14]:=d^3;

Output: Magma V2.10-6     Wed Jan 14 2004 05:52:22 on modular  [Seed = 1983064395]
   -------------------------------------


>> s:=Vector(14,Br);
            ^
Runtime error in 'Vector': Bad argument types
Argument types given: RngIntElt, GrpBrd

>> s[1]:=d^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[2]:=(c^d)^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[3]:=c^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[4]:=c^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[5]:=(c^(D*c))^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[6]:=b^(c*d*d*c*c);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[7]:=(b^(c^3))^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[8]:=e^(d*c*b*b*c*d*d*c*b);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[9]:=(e^(d*c*b))^3;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[10]:=a^(b*c*d*e*e*d*c*b);
    ^
User error: Identifier 's' has not been declared or assigned

>> s[11]:=a;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[12]:=(c^D)^2;
    ^
User error: Identifier 's' has not been declared or assigned

>> s[13]:=s[12];
          ^
User error: Identifier 's' has not been declared or assigned

>> s[14]:=d^3;;
    ^
User error: Identifier 's' has not been declared or assigned

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:08:25 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2));
Append(s,(c^D)^2));
Append(s,d^3);


Output: Magma V2.10-6     Wed Jan 14 2004 06:08:20 on modular  [Seed = 947739463]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

Total time: 3.239 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:11:19 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
n:=#s;
W:=Id(Br)
for i from 1 to n
do W*=s[i];
end for ;
normalform(W);

Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2));
Append(s,(c^D)^2));
Append(s,d^3);


Output: Magma V2.10-6     Wed Jan 14 2004 06:11:16 on modular  [Seed = 678251431]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]

>> for i from 1 to n
   ^
User error: bad syntax

>> do W*=s[i];
   ^
User error: bad syntax

>> end for ;
   ^
User error: bad syntax

>> normalform(W);
              ^
User error: Identifier 'W' has not been declared or assigned
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

Total time: 3.089 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:15:27 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
n:=#s;
W:=Id(Br)
for i from 1 to n
do W*=s[i];
end for ;
normalform(W);

Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2));
Append(s,(c^D)^2));
Append(s,d^3);


Output: Magma V2.10-6     Wed Jan 14 2004 06:15:24 on modular  [Seed = 3734747721]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]

>> for i from 1 to n
   ^
User error: bad syntax

>> do W*=s[i];
   ^
User error: bad syntax

>> end for ;
   ^
User error: bad syntax

>> normalform(W);
              ^
User error: Identifier 'W' has not been declared or assigned
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:19:24 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2));
Append(s,(c^D)^2));
Append(s,d^3);
n:=#s;
W:=Id(Br)
for i:=1 to n by 
do W*=s[i];
end for ;
normalform(W);

Output: Magma V2.10-6     Wed Jan 14 2004 06:19:21 on modular  [Seed = 3566317878]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

>> for i:=1 to n by 
   ^
User error: bad syntax

>> do W*=s[i];
   ^
User error: bad syntax

>> end for ;
   ^
User error: bad syntax

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

Total time: 2.969 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:19:54 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2));
Append(s,(c^D)^2));
Append(s,d^3);
n:=#s;
W:=Id(Br)
for i:=1 to n by 1
do W*=s[i];
end for ;
normalform(W);

Output: Magma V2.10-6     Wed Jan 14 2004 06:19:51 on modular  [Seed = 3263670094]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax

>> Append(s,(c^D)^2));
                    ^
User error: bad syntax
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

>> for i:=1 to n by 1
   ^
User error: bad syntax

>> do W*=s[i];
   ^
User error: bad syntax

>> end for ;
   ^
User error: bad syntax

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

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:21:08 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2);
Append(s,(c^D)^2);
Append(s,d^3);
n:=#s;
W:=Id(Br)
for i:=1 to n by 1
do W*=s[i];
end for ;
normalform(W);

Output: Magma V2.10-6     Wed Jan 14 2004 06:21:05 on modular  [Seed = 4055144331]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d *
c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * 
d * c * d * e
<Artin, -2, [
    (4, 5),
    (3, 4),
    (1, 6)(2, 4, 3, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d *
c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * 
d * c * d * e
<Artin, -2, [
    (4, 5),
    (3, 4),
    (1, 6)(2, 4, 3, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4)
], 0> *]
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

>> for i:=1 to n by 1
   ^
User error: bad syntax

>> do W*=s[i];
   ^
User error: b
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:23:57 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
l:=FundamentalElement(Br);
E:=e^(-1);
D:=d^(-1);
C:=c^(-1);
B:=b^(-1);
A:=a^(-1);
s:=[**];
Append(s,d^3);
Append(s,(c^d)^2);
Append(s,c^3);
Append(s,c^3);
Append(s,(c^(D*c))^2);
Append(s,b^(c*d*d*c*c));
Append(s,(b^(c^3))^3);
Append(s,e^(d*c*b*b*c*d*d*c*b));
Append(s,(e^(d*c*b))^3);
Append(s,a^(b*c*d*e*e*d*c*b));
Append(s,a);
Append(s,(c^D)^2);
Append(s,(c^D)^2);
Append(s,d^3);
n:=#s;
W:=Id(Br)
for i:=1 to n do
W*=s[i];
end for ;
normalform(W);

Output: Magma V2.10-6     Wed Jan 14 2004 06:23:54 on modular  [Seed = 3970534013]
   -------------------------------------

[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e * c * d
<Artin, -2, [
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* c^3
<Artin, 0, [
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * 
d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c
<Artin, -4, [
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b
* a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * 
d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * 
b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2
<Artin, -5, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d 
* c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3
<Artin, -9, [
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d 
* c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * 
c * b^2 * c * d^2 * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d *
c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * 
b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * 
d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b
<Artin, -9, [
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d 
* c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * 
d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c 
* b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * 
a * b * c * d * e^2 * d * c * b
<Artin, -8, [
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3)
], 0> *]
[* a
<Artin, 0, [
    (1, 2)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d *
c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * 
d * c * d * e
<Artin, -2, [
    (4, 5),
    (3, 4),
    (1, 6)(2, 4, 3, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4)
], 0> *]
[* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d *
c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * 
d * c * d * e
<Artin, -2, [
    (4, 5),
    (3, 4),
    (1, 6)(2, 4, 3, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4)
], 0> *]
[* d^3
<Artin, 0, [
    (4, 5),
    (4, 5),
    (4, 5)
], 0> *]

>> for i:=1 to n do
   ^
User error: bad syntax

>> W*=s[i];
     ^
User error: bad 
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:26:52 2004

Input: #s;

Output: Magma V2.10-6     Wed Jan 14 2004 06:26:49 on modular  [Seed = 2446653107]
   -------------------------------------


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

Total time: 3.119 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:31:10 2004

Input: Br<a,b,b,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:31:07 on modular  [Seed = 2227301540]
   -------------------------------------


>> C:=c^(-1);
      ^
User error: Identifier 'c' has not been declared or assigned

>> w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*
                   ^
User error: bad syntax

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

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:31:29 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:31:26 on modular  [Seed = 3019299686]
   -------------------------------------


>> w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*
                   ^
User error: bad syntax

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

Total time: 2.949 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:31:58 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:31:55 on modular  [Seed = 2867839578]
   -------------------------------------


>> w:=(d^3)*(c^d)^2*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c
                                          ^
User error: bad syntax

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

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:32:19 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:32:16 on modular  [Seed = 2716125498]
   -------------------------------------


>> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*
                                         ^
User error: bad syntax

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:32:28 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:32:25 on modular  [Seed = 1595553738]
   -------------------------------------


>> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*
                                         ^
User error: bad syntax

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:34:28 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:34:25 on modular  [Seed = 1393965646]
   -------------------------------------


>> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b
                                                       ^
User error: bad syntax

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

Total time: 3.039 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:34:43 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:34:40 on modular  [Seed = 1140927816]
   -------------------------------------


>> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3)*e^(d*c*b*
                                                                   ^
User error: bad syntax

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

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:35:40 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:35:36 on modular  [Seed = 2033979565]
   -------------------------------------


>> ^(c^3))^3*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D
                                  ^
User error: bad syntax

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

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:36:17 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
normalform(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:36:14 on modular  [Seed = 1916214144]
   -------------------------------------


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

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:36:36 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);

Output: Magma V2.10-6     Wed Jan 14 2004 06:36:33 on modular  [Seed = 1798177526]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>

Total time: 2.999 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:39:26 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

NormalForm(w*l^(-2))

Output: Magma V2.10-6     Wed Jan 14 2004 06:39:23 on modular  [Seed = 492336938]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c
* e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b 
* a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c 
* b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * 
c^3 * d^2
<Artin, -6, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:40:03 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

t:=NormalForm(w*l^(-2));
t;


Output: Magma V2.10-6     Wed Jan 14 2004 06:39:59 on modular  [Seed = 374570181]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c
* e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b 
* a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c 
* b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * 
c^3 * d^2
<Artin, -6, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>

Total time: 3.149 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:45:34 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

w eq l^2;



Output: Magma V2.10-6     Wed Jan 14 2004 06:45:30 on modular  [Seed = 54945924]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
false

Total time: 2.929 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:46:12 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

w eq l^2;

l


Output: Magma V2.10-6     Wed Jan 14 2004 06:46:09 on modular  [Seed = 879843433]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
false
e * d * c * b * a * e * d * c * b * e * d * c * e * d * e
<Artin, 1, [], 0>

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:53:32 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

w eq l^2;
a^b;
l


Output: Magma V2.10-6     Wed Jan 14 2004 06:53:29 on modular  [Seed = 660753090]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
false
e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b 
* e * d * c * e * d * e * a * b
<Artin, -1, [
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3)
], 0>
e * d * c * b * a * e * d * c * b * e * d * c * e * d * e
<Artin, 1, [], 0>

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:54:05 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

w eq l^2;
k:=a^b;

l


Output: Magma V2.10-6     Wed Jan 14 2004 06:54:02 on modular  [Seed = 3634214238]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
false
e * d * c * b * a * e * d * c * b * e * d * c * e * d * e
<Artin, 1, [], 0>

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:54:23 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
C:=c^(-1);
D:=d^(-1);
w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3;
NormalForm(w);
l:=FundamentalElement(Br);

w eq l^2;
k:=a^b;
k;

l


Output: Magma V2.10-6     Wed Jan 14 2004 06:54:20 on modular  [Seed = 3516185697]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>
false
e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b 
* e * d * c * e * d * e * a * b
<Artin, -1, [
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3)
], 0>
e * d * c * b * a * e * d * c * b * e * d * c * e * d * e
<Artin, 1, [], 0>

Total time: 2.979 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:55:42 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);



k:=a^b;
k;




Output: Magma V2.10-6     Wed Jan 14 2004 06:55:39 on modular  [Seed = 3330517153]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b 
* e * d * c * e * d * e * a * b
<Artin, -1, [
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3)
], 0>

Total time: 2.889 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 06:56:16 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);



a^b;





Output: Magma V2.10-6     Wed Jan 14 2004 06:56:13 on modular  [Seed = 4290417150]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b 
* e * d * c * e * d * e * a * b
<Artin, -1, [
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3)
], 0>

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 09:53:12 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*

*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*

D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d

*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c

*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ;
l:=FundamentalElement(Br);
w eq l^2; 








Output: Magma V2.10-6     Wed Jan 14 2004 09:53:09 on modular  [Seed = 1865054425]
   -------------------------------------


>> *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*
   ^
User error: bad syntax

>> D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d
   ^
User error: Identifier 'D' has not been declared or assigned

>> w eq l^2; 
   ^
User error: Identifier 'w' has not been declared or assigned

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 09:54:32 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D

*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*

D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d

*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c

*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ;
l:=FundamentalElement(Br);
w eq l^2; 








Output: Magma V2.10-6     Wed Jan 14 2004 09:54:29 on modular  [Seed = 1983082032]
   -------------------------------------

false

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 09:55:17 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D

*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*

D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d

*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c

*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ;
l:=FundamentalElement(Br);
w eq l^2; 

k:=a
*b
k;






Output: Magma V2.10-6     Wed Jan 14 2004 09:55:14 on modular  [Seed = 1528709994]
   -------------------------------------

false

>> k;
   ^
User error: bad syntax

Total time: 2.989 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 09:55:57 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D

*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*

D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d

*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c

*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ;
l:=FundamentalElement(Br);
w eq l^2; 

k:=a
*b;
k;






Output: Magma V2.10-6     Wed Jan 14 2004 09:55:54 on modular  [Seed = 577190459]
   -------------------------------------

false
a * b
<Artin, 0, [
    (1, 2),
    (2, 3)
], 0>

Total time: 3.179 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:02:09 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D

*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*

D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d

*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c

*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ;
l:=FundamentalElement(Br);
w eq l^2; 

 f := BurauRepresentation(B);
f(w);






Output: Magma V2.10-6     Wed Jan 14 2004 10:02:05 on modular  [Seed = 3263683404]
   -------------------------------------

false

>>  f := BurauRepresentation(B);
                            ^
Runtime error in 'BurauRepresentation': Bad argument types
Argument types given: GrpBrdElt

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

Total time: 2.939 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:02:33 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D

*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*

D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d

*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c

*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ;
l:=FundamentalElement(Br);
w eq l^2; 

 f := BurauRepresentation(Br);
f(w);






Output: Magma V2.10-6     Wed Jan 14 2004 10:02:30 on modular  [Seed = 2917709768]
   -------------------------------------

false
[$.1^6 - $.1 + 1   -$.1^2 + $.1   -$.1^3 + $.1^2   -$.1^4 + $.1^3   -$.1^5 + 
    $.1^4   -$.1^6 + $.1^5]
[-$.1 + 1   ($.1^7 - 2*$.1^6 + $.1^5 + $.1^3 - $.1 + 1)/$.1^4   ($.1^12 - 
    2*$.1^11 + 2*$.1^10 - $.1^9 - $.1^5 + 3*$.1^4 - 2*$.1^3 - $.1^2 + 2*$.1 - 
    1)/$.1^4   ($.1^14 - 2*$.1^13 + 3*$.1^12 - 4*$.1^11 + 3*$.1^10 - $.1^9 - 
    $.1^5 + 3*$.1^4 - 2*$.1^3 - $.1^2 + 2*$.1 - 1)/$.1^3   (-$.1^13 + 2*$.1^12 -
    3*$.1^11 + 3*$.1^10 - $.1^9 - $.1^5 + 3*$.1^4 - 2*$.1^3 - $.1^2 + 2*$.1 - 
    1)/$.1^2   -$.1^6 + $.1^5]
[-$.1 + 1   ($.1^8 - 3*$.1^7 + 4*$.1^6 - 4*$.1^5 + 5*$.1^4 - 3*$.1^3 - $.1^2 + 
    2*$.1 - 1)/$.1^5   (-$.1^17 + 4*$.1^16 - 8*$.1^15 + 8*$.1^14 - 2*$.1^13 - 
    7*$.1^12 + 11*$.1^11 - 6*$.1^10 - 3*$.1^9 + 8*$.1^8 - 5*$.1^7 - 4*$.1^6 + 
    12*$.1^5 - 11*$.1^4 + 3*$.1^3 + 3*$.1^2 - 3*$.1 + 1)/$.1^5   (-$.1^19 + 
    4*$.1^18 - 8*$.1^17 + 12*$.1^16 - 13*$.1^15 + 9*$.1^14 + $.1^13 - 11*$.1^12 
    + 14*$.1^11 - 7*$.1^10 - 3*$.1^9 + 8*$.1^8 - 5*$.1^7 - 4*$.1^6 + 12*$.1^5 - 
    11*$.1^4 + 3*$.1^3 + 3*$.1^2 - 3*$.1 + 1)/$.1^4   ($.1^18 - 4*$.1^17 + 
    8*$.1^16 - 11*$.1^15 + 9*$.1^14 - $.1^13 - 9*$.1^12 + 13*$.1^11 - 7*$.1^10 -
    3*$.1^9 + 8*$.1^8 - 5*$.1^7 - 4*$.1^6 + 12*$.1^5 - 11*$.1^4 + 3*$.1^3 + 
    3*$.1^2 - 3*$.1 + 1)/$.1^3   -$.1^6 + $.1^5]
[-$.1 + 1   (2*$.1^8 - 5*$.1^7 + 7*$.1^6 - 8*$.1^5 + 8*$.1^4 - 5*$.1^3 + 2*$.1 -
    1)/$.1^5   ($.1^18 - 4*$.1^17 + 10*$.1^16 - 14*$.1^15 + 12*$.1^14 - 2*$.1^13
    - 10*$.1^12 + 14*$.1^11 - 6*$.1^10 - 6*$.1^9 + 11*$.1^8 - 5*$.1^7 - 8*$.1^6 
    + 18*$.1^5 - 16*$.1^4 + 6*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^5   ($.1^20 - 
    4*$.1^19 + 10*$.1^18 - 18*$.1^17 + 24*$.1^16 - 24*$.1^15 + 15*$.1^14 - 
    14*$.1^12 + 17*$.1^11 - 7*$.1^10 - 6*$.1^9 + 11*$.1^8 - 5*$.1^7 - 8*$.1^6 + 
    18*$.1^5 - 16*$.1^4 + 6*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^4   (-$.1^19 + 
    4*$.1^18 - 10*$.1^17 + 17*$.1^16 - 20*$.1^15 + 14*$.1^14 - $.1^13 - 
    12*$.1^12 + 16*$.1^11 - 7*$.1^10 - 6*$.1^9 + 11*$.1^8 - 5*$.1^7 - 8*$.1^6 + 
    18*$.1^5 - 16*$.1^4 + 6*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^3   -$.1^6 + $.1^5]
[-$.1 + 1   ($.1^8 - 3*$.1^7 + 4*$.1^6 - 5*$.1^5 + 6*$.1^4 - 4*$.1^3 + 2*$.1 - 
    1)/$.1^5   (-$.1^17 + 4*$.1^16 - 9*$.1^15 + 10*$.1^14 - 4*$.1^13 - 6*$.1^12 
    + 12*$.1^11 - 8*$.1^10 - 2*$.1^9 + 9*$.1^8 - 7*$.1^7 - 3*$.1^6 + 13*$.1^5 - 
    13*$.1^4 + 5*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^5   (-$.1^19 + 4*$.1^18 - 
    9*$.1^17 + 14*$.1^16 - 16*$.1^15 + 12*$.1^14 - 2*$.1^13 - 10*$.1^12 + 
    15*$.1^11 - 9*$.1^10 - 2*$.1^9 + 9*$.1^8 - 7*$.1^7 - 3*$.1^6 + 13*$.1^5 - 
    13*$.1^4 + 5*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^4   ($.1^18 - 4*$.1^17 + 
    9*$.1^16 - 13*$.1^15 + 12*$.1^14 - 3*$.1^13 - 8*$.1^12 + 14*$.1^11 - 
    9*$.1^10 - 2*$.1^9 + 9*$.1^8 - 7*$.1^7 - 3*$.1^6 + 13*$.1^5 - 13*$.1^4 + 
    5*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^3   -$.1^6 + $.1^5]
[-$.1 + 1   -$.1^2 + $.1   -$.1^3 + $.1^2   -$.1^4 + $.1^3   -$.1^5 + $.1^4   
    $.1^5]

Total time: 3.079 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:23:01 2004

Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd ";
#s;

Output: Magma V2.10-6     Wed Jan 14 2004 10:22:58 on modular  [Seed = 2799941648]
   -------------------------------------

131

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:31:03 2004

Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd ";
#s;

Output: Magma V2.10-6     Wed Jan 14 2004 10:31:00 on modular  [Seed = 3204161134]
   -------------------------------------

131

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:31:41 2004

Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd";
#s;

Output: Magma V2.10-6     Wed Jan 14 2004 10:31:38 on modular  [Seed = 2160435262]
   -------------------------------------

130

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:32:50 2004

Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd";
#s;

Output: Magma V2.10-6     Wed Jan 14 2004 10:32:47 on modular  [Seed = 2496771567]
   -------------------------------------

130

Total time: 3.049 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:37:29 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E**E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d";
#s;

Output: Magma V2.10-6     Wed Jan 14 2004 10:37:26 on modular  [Seed = 1696614198]
   -------------------------------------


>> *b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E**E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d
                                         ^
User error: bad syntax

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

Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:38:51 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d";


Output: Magma V2.10-6     Wed Jan 14 2004 10:38:47 on modular  [Seed = 1865043341]
   -------------------------------------


>> quit;
        ^
User error: Unterminated string

Total time: 2.919 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:39:12 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d";


Output: Magma V2.10-6     Wed Jan 14 2004 10:39:09 on modular  [Seed = 1983075470]
   -------------------------------------


>> quit;
        ^
User error: Unterminated string

Total time: 3.019 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:39:28 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d;


Output: Magma V2.10-6     Wed Jan 14 2004 10:39:25 on modular  [Seed = 2033998769]
   -------------------------------------


>> w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C
                                        ^
User error: Identifier 'cD' has not been declared or assigned

Total time: 3.059 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:39:47 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d;


Output: Magma V2.10-6     Wed Jan 14 2004 10:39:44 on modular  [Seed = 1074094821]
   -------------------------------------


Total time: 3.029 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:41:00 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d;
w;


Output: Magma V2.10-6     Wed Jan 14 2004 10:40:57 on modular  [Seed = 1343583036]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d^3 * e * d * c * b * a 
* d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b 
* e * d * c * d * e * c * d * c^6 * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * 
e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * 
a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * 
c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b 
* e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * 
c * b^2 * c^2 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c 
* b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d 
* e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * 
c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * 
d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * 
e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * 
e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * 
d^2 * c * b^2 * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e 
* d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a 
* d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * 
e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * 
e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d 
* c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * 
e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * 
c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d 
* e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d 
* c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b * a * d * c * 
e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * 
a * e * d * c * b * e * d * c * d * e * d * c * e * d * c * b * a * d * c * b * 
e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * 
d * e * d^3
<Artin, -50, [
    (4, 5),
    (4, 5),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 2),
    (4, 5),
    (3, 4),
    (1, 6)(2, 4, 3, 5),
    (2, 3),
    (3
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:41:46 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d;
w;
NormalForm(w);


Output: Magma V2.10-6     Wed Jan 14 2004 10:41:43 on modular  [Seed = 1528723465]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * 
d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * 
d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * 
c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * 
e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * 
b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * 
c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * 
e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * 
d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * 
a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * 
c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d^3 * e * d * c * b * a 
* d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b 
* e * d * c * d * e * c * d * c^6 * e * d * c * b * a * e * d * c * b * d * c * 
e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * 
e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * 
a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * 
c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b 
* e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * 
c * b^2 * c^2 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c 
* b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * 
d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d 
* e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e 
* d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * 
d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * 
c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e 
* d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * 
d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * 
e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e 
* d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a 
* e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * 
e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * 
d^2 * c * b^2 * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 
* d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * 
c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e 
* d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c 
* b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a 
* d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * 
e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * 
e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d 
* c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * 
e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * 
c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d 
* e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d 
* c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b * a * d * c * 
e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * 
a * e * d * c * b * e * d * c * d * e * d * c * e * d * c * b * a * d * c * b * 
e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * 
d * e * d^3
<Artin, -50, [
    (4, 5),
    (4, 5),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (4, 5),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5),
    (2, 3),
    (3, 4),
    (3, 4),
    (3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (4, 5),
    (3, 4),
    (2, 3),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6)(2, 5),
    (1, 6)(2, 5, 3, 4),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 6, 2, 5)(3, 4),
    (1, 5, 2, 6)(3, 4),
    (1, 6)(2, 5, 3, 4),
    (1, 6)(2, 5),
    (1, 6)(2, 4, 3, 5),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (5, 6),
    (4, 5),
    (3, 4),
    (2, 3),
    (1, 2),
    (4, 5),
    (3, 4),
    (1, 6)(2, 4, 3, 5),
    (2, 3),
    (3
 ** WARNING: Output too long, hence truncated.

************** MAGMA *****************
Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167)
Time: Wed Jan 14 10:42:10 2004

Input: Br<a,b,c,d,e>:=BraidGroup(6);
A:=a^(-1);
B:=b^(-1);
C:=c^(-1);
D:=d^(-1);
E:=e^(-1);
w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d;

NormalForm(w);


Output: Magma V2.10-6     Wed Jan 14 2004 10:42:07 on modular  [Seed = 577175816]
   -------------------------------------

e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * 
b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * 
d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * 
e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * 
e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * 
e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * 
b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * 
a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d 
* c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2
<Artin, -4, [
    (1, 6)(3, 5),
    (1, 6)(2, 4, 5, 3),
    (1, 6)(2, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3)(4, 5),
    (1, 6)(2, 3, 5),
    (3, 5),
    (3, 5),
    (3, 5, 4),
    (3, 4, 5),
    (4, 5),
    (3, 5, 4),
    (3, 4),
    (3, 4, 5),
    (4, 5)
], 0>

Total time: 3.069 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 0x503fe304.odnxx1.adsl-dhcp.tele.dk. (80.63.227.4)
Time: Wed Jan 14 14:49:15 2004

Input: Factorization(21152923813644279445637889283551800700802491206174149213598656176159750053385842115946365356305306542786771153583613865570045471663739101218972164851995066805188927363175826739);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.10-6     Wed Jan 14 2004 14:48:52 on modular  [Seed = 2328844231]
   -------------------------------------


Errors: /home/mfd/gomagma: line 2: 10723 Alarm clock             /usr/local/bin/magma


************** MAGMA *****************
Host 0x503fe304.odnxx1.adsl-dhcp.tele.dk. (80.63.227.4)
Time: Wed Jan 14 14:49:40 2004

Input: Factorization(211529238136);

Output: Magma V2.10-6     Wed Jan 14 2004 14:49:37 on modular  [Seed = 2243975357]
   -------------------------------------

[ <2, 3>, <47, 1>, <67, 1>, <661, 1>, <12703, 1> ]

Total time: 3.009 seconds, Total memory usage: 1.80MB


************** MAGMA *****************
Host 0x503fe304.odnxx1.adsl-dhcp.tele.dk. (80.63.227.4)
Time: Wed Jan 14 14:50:00 2004

Input: