Quelle tensor19.tex Sprache: Latech

randomsubproduct:=function(list)
local len, product, i, eps;

len:=Length(list);
product:=One(list[1]);
for i in [1..len] do
    eps:=Random([0,1]);
    product:=product*(list[i]^eps);
od;
return product;
end;

olustur:=function(q)
local g,gens,gensg,mat,c1,c2,i,x,tensorgens,g1,g2,y;
g:=GL(2,q);
gensg:=GeneratorsOfGroup(g);
gens:=[ ];
for i in [1..5] do
     for x in gensg do
          mat:=IdentityMat(10,GF(q));
                   mat[2*i-1][2*i-1]:=x[1][1];
                   mat[2*i-1][2*i]:=x[1][2];
                   mat[2*i][2*i-1]:=x[2][1];
                   mat[2*i][2*i]:=x[2][2];
          Add(gens,mat);
      od;
od;
c1:=IdentityMat(10,GF(q));
c1[1][1]:=0*Z(q);
c1[2][2]:=0*Z(q);
c1[3][3]:=0*Z(q);
c1[4][4]:=0*Z(q);
c1[1][3]:=Z(q)^0;
c1[2][4]:=Z(q)^0;
c1[3][1]:=Z(q)^0;
c1[4][2]:=Z(q)^0;
c2:=NullMat(10,10,GF(q));
for i in [1..8] do
     c2[i][i+2]:=Z(q)^0;
od;
c2[9][1]:=Z(q)^0;
c2[10][2]:=Z(q)^0;
tensorgens:=[];
for x in gens do
     Add(tensorgens,KroneckerProduct(x,IdentityMat(3,GF(q))));
od;
Add(tensorgens,KroneckerProduct(c1,IdentityMat(3,GF(q))));
Add(tensorgens,KroneckerProduct(c2,IdentityMat(3,GF(q))));
g2:=SL(3,q);
for y in GeneratorsOfGroup(g2) do
     Add(tensorgens,KroneckerProduct(IdentityMat(10,GF(q)),y));
od;
g1:=Group(tensorgens);
return g1;
end;

create:=function(q)
local g,gens,gensg,mat,c1,c2,i,x,tensorgens,G;
g:=GL(2,q);
gensg:=GeneratorsOfGroup(g);
gens:=[ ];
for i in [1..5] do
     for x in gensg do
          mat:=IdentityMat(10,GF(q));
                   mat[2*i-1][2*i-1]:=x[1][1];
                   mat[2*i-1][2*i]:=x[1][2];
                   mat[2*i][2*i-1]:=x[2][1];
                   mat[2*i][2*i]:=x[2][2];
          Add(gens,mat);
      od;
od;
c1:=IdentityMat(10,GF(q));
c1[1][1]:=0*Z(q);
c1[2][2]:=0*Z(q);
c1[3][3]:=0*Z(q);
c1[4][4]:=0*Z(q);
c1[1][3]:=Z(q)^0;
c1[2][4]:=Z(q)^0;
c1[3][1]:=Z(q)^0;
c1[4][2]:=Z(q)^0;
c2:=NullMat(10,10,GF(q));
for i in [1..8] do
     c2[i][i+2]:=Z(q)^0;
od;
c2[9][1]:=Z(q)^0;
c2[10][2]:=Z(q)^0;
tensorgens:=[];
for x in gens do
     Add(tensorgens,KroneckerProduct(x,IdentityMat(10,GF(q))));
     Add(tensorgens,KroneckerProduct(IdentityMat(10,GF(q)),x));
od;
#Add(tensorgens,KroneckerProduct(c1,c1));
Add(tensorgens,KroneckerProduct(c2,IdentityMat(10,GF(q))));
Add(tensorgens,KroneckerProduct(IdentityMat(10,GF(q)),c2));
G:=Group(tensorgens);
return G;
end;

separate:=function(g,N)
local r, ready, s, t, order, factor, f1, f2, len, cl, cl2, i, count, divisors, x;
ready:=false;
count:=0;
repeat
   r:=PseudoRandom(g);
   order:=ProjectiveOrder(r)[1];
   factor:=Collected(Factors(order));
   len:=Length(factor);
   if len >1 then
      f1:=(factor[len][1])^(factor[len][2]);
      f2:=(factor[len-1][1])^(factor[len-1][2]);
      s:=r^(order/f1);
      t:=r^(order/f2);
      cl:=[s];
      for i in [1..10] do
        Add(cl,s^PseudoRandom(g));
      od;
      if ForAll (cl,x->Comm(x,t)=One(x)) then
         cl2:=[t];
         for i in [1..10] do
            Add(cl2,t^PseudoRandom(g));
         od;
         for i in [1..10] do
           Add(cl,randomsubproduct(cl)^PseudoRandom(g));
           Add(cl2,randomsubproduct(cl2)^PseudoRandom(g));
         od;
         if ForAll (cl,x->ForAll(cl2,y->Comm(x,y)=One(x))) then
            ready:=true;
         fi;
       fi;
   fi;
   count:=count+1;
until ready or count>N;
if ready then
   for i in [1..2] do
       r:=PseudoRandom(g);
       divisors:=DivisorsInt(ProjectiveOrder(r)[1]);
       for x in divisors do
           if CheckAnswer(r^x,cl) then
              Add(cl2,r^x);
           elif CheckAnswer(r^x,cl2) then
              Add(cl,r^x);
           fi;
       od;
   od;
   for i in [1..10] do
       Add(cl,randomsubproduct(cl)^PseudoRandom(g));
       Add(cl2,randomsubproduct(cl2)^PseudoRandom(g));
   od;
   return [Group(cl),Group(cl2)];
else
   return fail;
fi;
end;

NextStep := function ( g, a )

  local b, c,g1;

  b := ProjectiveOrder(g)[1]/a;
         if b=1 then return fail; fi;

  if Gcd( b, a ) = 1 then
     c := b^-1 mod a;
Print("b=",b," c=",c,"\n");
            return g^(b*c);

         fi;

  return fail;

end;

CheckAnswer := function( x, Bgens )

     local y;

     if x = fail then return false; fi;
     if Length(Bgens) = 0 then return true; fi;
     for y in Bgens do
      if Comm( x, y ) <> Bgens[1]^0 then
     return false;
                fi;
     od;

     return true;

end;

TensorDecompose := function( G, g, Agens, Bgens, N)

local  h, a, b, i, B, hs, ans, order;

B := Group( Bgens );
a := ProjectiveOrder(g)[1];
        Print( "aoriginal=",a,"\n");
        hs := [];
for i in [ 1 .. N ] do
     h := PseudoRandom( B );
            order:=ProjectiveOrder(g*h)[1];
            Add( hs, [h, order ] );
     a := Gcd( a, order);
od;
        Print( " a = ", a, "\n" );
i := 1;
        repeat
              h := PseudoRandom(B);
       a := Gcd( a, ProjectiveOrder( g*h )[1] );
       ans := NextStep ( g * h, a);
#             if ans<>fail then Error(); fi;
       if CheckAnswer( ans, Bgens ) then
     Print( "i = ", i, "\n" );
                   if CheckAnswer( g*ans^(-1), Agens) then
                       return [ans, g*ans^(-1)];
                   fi;
       fi;
       i := i + 1;
        until  i > 1000 * N;

#  h :=  First( hs, i -> Gcd( a, i[2]/a) = 1);

end;

writeeuclid:=function(g,r,Agens,Bgens)
local order,factor,euclid,i,a,parts,b,c,x;
order:=ProjectiveOrder(r)[1];
factor:=Collected(Factors(order));
euclid:=[];
parts:=[];
     for i in [1..Length(factor)] do
           euclid[i]:=order/(factor[i][1])^(factor[i][2]);
           x:=r^euclid[i];
           if CheckAnswer(x,Bgens) then
                       parts[i]:=[x,x^0];
           elif CheckAnswer(x,Agens) then
                       parts[i]:=[x^0,x];
           else
                       parts[i]:=TensorDecompose(g,x,Agens,Bgens,100);
           fi;
     od;
a:=GcdRepresentation(euclid);
b:=1;
c:=1;
      for i in [1..Length(factor)] do
            b:=b*((parts[i][1])^a[i]);
            c:=c*((parts[i][2])^a[i]);
      od;
      if r=b*c then
            return [b,c];
      else
            return fail;
      fi;
end;

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