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arithmetic_remains.g
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arithmetic_remains.g
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# Hermite NF code, factorize in SLNZ
TryWord:=function(hom,mat)
local m,p,red,mr,g,h2,w,a;
m:=MappingGeneratorsImages(hom);
p:=ValueOption("start");
if p=fail then
p:=2;
fi;
repeat
p:=NextPrimeInt(p);
red:=List(m[2],x->x*Z(p)^0);
mr:=mat*Z(p)^0;
g:=Group(red);
h2:=GroupHomomorphismByImages(Source(hom),g,m[1],red);
w:=PreImagesRepresentative(h2,mr);
a:=Image(hom,w);
Print(p,":",a-mat," ",w,"\n");
until a=mat;
return w;
end;
TryWord0:=function(hom,mat)
local m,p,red,mr,g,h2,w,a;
m:=MappingGeneratorsImages(hom);
p:=ValueOption("start");
if p=fail then
p:=2;
fi;
repeat
p:=NextPrimeInt(p);
red:=List(m[2],x->x*Z(p)^0);
mr:=mat*Z(p)^0;
g:=Group(red);
h2:=GroupHomomorphismByImages(Source(hom),g,m[1],red);
SetEpimorphismFromFreeGroup(g,h2);
w:=Factorization(g,mr);
a:=Image(hom,w);
Print(p,":",a-mat," ",w,"\n");
until a=mat;
return w;
end;
TryWord1:=function(hom,mat,q)
local m,ring,red,mr,g,h2,w,a,n,piso,orb,p;
p:=Factors(q)[1];
m:=MappingGeneratorsImages(hom);
n:=LogInt(q,p)-1;
repeat
n:=n+1;
ring:=Integers mod p^n;
red:=List(m[2],x->x*One(ring));
mr:=mat*One(ring);
g:=Group(red);
orb:=Orbit(g,One(g)[1],OnRight);
piso:=ActionHomomorphism(g,orb,OnRight,"surjective");
h2:=GroupHomomorphismByImages(Source(hom),Image(piso),m[1],
List(red,x->ImagesRepresentative(piso,x)));
w:=PreImagesRepresentative(h2,ImagesRepresentative(piso,mr));
a:=Image(hom,w);
Print(n,":",a-mat,"\n");
until a=mat;
return w;
end;
TryWord2:=function(hom,mat)
local prime,onp,op,gens,o,l,prd,start,ende,j,k,a,i,m,one,dim,
istransvec,dict,new,dups,ap,mgi,let,prw,mf,non,sel,maxmem,nrm;
maxmem:=10^10;
if ValueOption("maxmem")<>fail then
maxmem:=ValueOption("maxmem");
fi;
nrm:=ValueOption("norm");
non:=ValueOption("nonhom");
mgi:=MappingGeneratorsImages(hom);
# find a boring prime
let:=ShallowCopy(mgi[1]);
gens:=ShallowCopy(mgi[2]);
prime:=23;
op:=Z(prime)^0;
# generators, inverse closed
for i in [1..Length(gens)] do
if not gens[i]^-1 in gens then
Add(gens,gens[i]^-1);
Add(let,let[i]^-1);
fi;
od;
sel:=[];
for i in [1..Length(gens)] do
if not ForAny([1..i-1],j->gens[i]=gens[j]) then
Add(sel,i);
fi;
od;
# first form all products of length up to l. There are technically |gens|^l
# products, so
l:=LogInt(Int(maxmem/Length(gens[1])^2),Length(gens));
one:=One(gens[1]);
dim:=Length(one);
onp:=one*op;
prd:=[one];
prw:=[One(let[1])];
dups:=[];
dict:=NewDictionary(onp,GL(Length(onp),prime),true);
AddDictionary(dict,onp,1);
start:=1;
for m in [1..l] do
Print(m,":",Length(prd),"\n");
ende:=Length(prd);
for j in [start..ende] do
for k in sel do
a:=prd[j]*gens[k];
ap:=a*op;
i:=LookupDictionary(dict,ap);
if i=fail then
new:=true;
elif a=prd[i] then
new:=false;
else
if not IsBound(dups[i]) then
# first duplication
new:=a<>prd[i];
if new then dups[i]:=[i];fi;
else
new:=ForAll(dups[i],x->prd[x]<>a);
fi;
# will duplicate also new one
if new then Add(dups[i],Length(prd)+1);fi;
fi;
if new then
#if nrm<>fail and not IsOne(a) and nrm(a)<nrm(prd[j]) then
# Error("normsmall");
#fi;
Add(prd,a);
Add(prw,prw[j]*let[k]);
if i=fail then
AddDictionary(dict,ap,Length(prd));
fi;
if a=mat and
(non=fail or not
IsOne(ImagesRepresentative(non,prw[Length(prw)]))) then
return prw[Length(prw)];
fi;
fi;
od;
od;
start:=ende+1;
od;
# prd also will be inverse-closed
Print("Stage2new :",Length(prd),"\n");
for i in [1..Length(prd)] do
Print("Stage2 ",i,"\n");
for j in [start..Length(prd)] do
if Sum([1..dim],k->prd[i][1][k]*prd[j][k][1])=mat[1][1]
and prd[i]*prd[j]=mat and
(non=fail or not
IsOne(ImagesRepresentative(non,prw[i]*prw[j]))) then
return prw[i]*prw[j];
Error("found2");
fi;
od;
od;
# older stage 2 -- divide off
Print("Stage2\n");
for i in [1..Length(prd)] do
mf:=LeftQuotient(prd[i],mat);
ap:=LookupDictionary(dict,mf*op);
if ap<>fail then
if IsBound(dups[ap]) then
ap:=dups[ap];
else
ap:=[ap];
fi;
for j in ap do
if prd[j]=mf then
Error("found2");
fi;
od;
fi;
od;
for i in [1..Length(prd)] do
Print("Stage3 ",i,"\n");
for j in [1..Length(prd)] do
mf:=Comm(prd[i],prd[j]);
if mf=mat then
Error("found4");
fi;
od;
od;
for i in [1..Length(prd)] do
Print("Stage4 ",i,"\n");
for j in [1..Length(prd)] do
mf:=LeftQuotient(prd[i]*prd[j],mat);
ap:=LookupDictionary(dict,mf*op);
if ap<>fail then
if IsBound(dups[ap]) then
ap:=dups[ap];
else
ap:=[ap];
fi;
for k in ap do
if prd[k]=mat then
Error("found3");
fi;
od;
fi;
od;
od;
Error("notfound");
end;
#rho1.1=t12*t13^-3*t32*t23^-3;
#rho1.2=t12^2*t13^-2*t21^-3*t31^-1*t13^-1*t12;
#rho1.3=t13*t12^-1*t21*t13^-1*t32*t23^-3;
#u:=Subgroup(f,[f.1*f.2^-3*f.6*f.4^-3,
# f.1^2*f.2^-2*f.3^-3*f.5^-1*f.2^-1*f.1,
# f.2*f.1^-1*f.3*f.2^-1*f.6*f.4^-3]);
FindForm:=function(g)
local n,f,m,at,ai,i,j,k,v,p,a;
n:=DimensionOfMatrixGroup(g);
f:=DefaultFieldOfMatrixGroup(g);
m:=[];
for a in GeneratorsOfGroup(g) do
at:=TransposedMat(a);
ai:=Inverse(a);
# equation at*J=J*ai:
for i in [1..n] do
for j in [1..n] do
v:=ListWithIdenticalEntries(n^2,0);
for k in [1..n] do
#T_ak*J_kb - J_akI_kb
p:=(k-1)*n+j;
v[p]:=v[p]+at[i][k];
p:=(i-1)*n+k;
v[p]:=v[p]-ai[k][j];
od;
v:=v*One(f);
Add(m,v);
od;
od;
od;
return NullspaceMat(TransposedMat(m));
end;
HumphriesGrp:=Group([[1,1,0],[0,-1,0],[0,0,-1]],[[-1,0,0],[0,1,1],[0,0,-1]],[[-1,0,0],[0,-1,0],[1,5,1]],[[-1,0,0],[0,-1,0],[1,4,1]]);
OLDMonodromyExample:=function(n)
local x,f,g;
x:=X(Rationals,"x");
f:=(x-1)^4;
if n=1 then
g:=x^4-2*x^3+3*x^2-2*x+1;
elif n=2 then
g:=x^4-x^3+2*x^2-x+1;
elif n=3 then
g:=x^4-x^3+x^2-x+1;
elif n=4 then
g:=x^4+2*x^3+3*x^2+2*x+1;
elif n=5 then
g:=x^4+2*x^2+1;
elif n=6 then
g:=x^4+x^3+2*x^2+x+1;
elif n=7 then
g:=x^4+x^2+1;
else
Error("wrong n");
fi;
f:=CompanionMat(f);
g:=CompanionMat(g);
return Group(f,g);
end;
ASIndexGamma:=function(H,m)
local ring,mats,G,ind;
ring:=Integers mod m;
mats:=List(GeneratorsOfGroup(H),x->x*One(ring));
G:=Group(mats);
FittingFreeLiftSetup(G);
ind:=Size(SL(Length(One(G)),ring))/Size(G);
Print("Index is ",ind,"=",Collected(Factors(ind)),"\n");
return ind;
end;
ConstructOnePolrep:=function(mats,ii)
local f,n,r,v,sn,l,j,homo,a,homoe,fct,hom;
f:=FieldOfMatrixList(mats);
n:=Length(mats[1]);
r:=PolynomialRing(f,n);
v:=IndeterminatesOfPolynomialRing(r);
sn:=SymmetricGroup(n);
# homogeneous polynomials
homo:=[];
for j in Partitions(ii) do
a:=Product([1..Length(j)],x->v[x]^j[x]);
Append(homo,Orbit(sn,a,OnIndeterminates));
od;
Sort(homo);
homoe:=List(homo,x->ExtRepPolynomialRatFun(x)[1]);
fct:=function(x)
local a,zz,i,m;
a:=List(homo,y->Value(y,v,v*x));
m:=[];
for i in [1..Length(homo)] do;
m[i]:=ListWithIdenticalEntries(Length(homo),Zero(f));
zz:=ExtRepPolynomialRatFun(a[i]);
m[i]{List([1,3..Length(zz)-1],x->Position(homoe,zz[x]))}
:=zz{[2,4..Length(zz)]};
od;
return m;
end;
return rec(gens:=List(mats,x->TransposedMat(fct(x))),
kind:="polrep",
name:=Concatenation("Pol",String(ii)));
end;
ConstructAllPolreps:=function(mats)
local n,i,l;
l:=[];
n:=Length(mats[1]);
for i in [1..n] do
Add(l,ConstructOnePolrep(mats,i));
od;
return l;
end;
# 15-dim rep for n=3, from homogeneous 2, symmetric square, span (1,0,...)
rep15:=x->[ [ x[1][1]^4, x[1][1]^3*x[1][2], x[1][1]^3*x[1][3], x[1][1]^2*x[1][2]^2,
x[1][1]^2*x[1][2]*x[1][3], x[1][1]^2*x[1][3]^2, x[1][1]*x[1][2]^3,
x[1][1]*x[1][2]^2*x[1][3], x[1][1]*x[1][2]*x[1][3]^2, x[1][1]*x[1][3]^3,
x[1][2]^4, x[1][2]^3*x[1][3], x[1][2]^2*x[1][3]^2, x[1][2]*x[1][3]^3,
x[1][3]^4 ],
[ 4*x[1][1]^3*x[2][1], x[1][1]^3*x[2][2]+3*x[1][1]^2*x[1][2]*x[2][1],
x[1][1]^3*x[2][3]+3*x[1][1]^2*x[1][3]*x[2][1],
2*x[1][1]^2*x[1][2]*x[2][2]+2*x[1][1]*x[1][2]^2*x[2][1],
x[1][1]^2*x[1][2]*x[2][3]+x[1][1]^2*x[1][3]*x[2][2]+2*x[1][1]*x[1][2]*x[\
1][3]*x[2][1], 2*x[1][1]^2*x[1][3]*x[2][3]+2*x[1][1]*x[1][3]^2*x[2][1],
3*x[1][1]*x[1][2]^2*x[2][2]+x[1][2]^3*x[2][1],
x[1][1]*x[1][2]^2*x[2][3]+2*x[1][1]*x[1][2]*x[1][3]*x[2][2]+x[1][2]^2*x[\
1][3]*x[2][1],
2*x[1][1]*x[1][2]*x[1][3]*x[2][3]+x[1][1]*x[1][3]^2*x[2][2]+x[1][2]*x[1]\
[3]^2*x[2][1], 3*x[1][1]*x[1][3]^2*x[2][3]+x[1][3]^3*x[2][1],
4*x[1][2]^3*x[2][2], x[1][2]^3*x[2][3]+3*x[1][2]^2*x[1][3]*x[2][2],
2*x[1][2]^2*x[1][3]*x[2][3]+2*x[1][2]*x[1][3]^2*x[2][2],
3*x[1][2]*x[1][3]^2*x[2][3]+x[1][3]^3*x[2][2], 4*x[1][3]^3*x[2][3] ],
[ 4*x[1][1]^3*x[3][1], x[1][1]^3*x[3][2]+3*x[1][1]^2*x[1][2]*x[3][1],
x[1][1]^3*x[3][3]+3*x[1][1]^2*x[1][3]*x[3][1],
2*x[1][1]^2*x[1][2]*x[3][2]+2*x[1][1]*x[1][2]^2*x[3][1],
x[1][1]^2*x[1][2]*x[3][3]+x[1][1]^2*x[1][3]*x[3][2]+2*x[1][1]*x[1][2]*x[\
1][3]*x[3][1], 2*x[1][1]^2*x[1][3]*x[3][3]+2*x[1][1]*x[1][3]^2*x[3][1],
3*x[1][1]*x[1][2]^2*x[3][2]+x[1][2]^3*x[3][1],
x[1][1]*x[1][2]^2*x[3][3]+2*x[1][1]*x[1][2]*x[1][3]*x[3][2]+x[1][2]^2*x[\
1][3]*x[3][1],
2*x[1][1]*x[1][2]*x[1][3]*x[3][3]+x[1][1]*x[1][3]^2*x[3][2]+x[1][2]*x[1]\
[3]^2*x[3][1], 3*x[1][1]*x[1][3]^2*x[3][3]+x[1][3]^3*x[3][1],
4*x[1][2]^3*x[3][2], x[1][2]^3*x[3][3]+3*x[1][2]^2*x[1][3]*x[3][2],
2*x[1][2]^2*x[1][3]*x[3][3]+2*x[1][2]*x[1][3]^2*x[3][2],
3*x[1][2]*x[1][3]^2*x[3][3]+x[1][3]^3*x[3][2], 4*x[1][3]^3*x[3][3] ],
[ 6*x[1][1]^2*x[2][1]^2,
3*x[1][1]^2*x[2][1]*x[2][2]+3*x[1][1]*x[1][2]*x[2][1]^2,
3*x[1][1]^2*x[2][1]*x[2][3]+3*x[1][1]*x[1][3]*x[2][1]^2,
x[1][1]^2*x[2][2]^2+4*x[1][1]*x[1][2]*x[2][1]*x[2][2]+x[1][2]^2*x[2][1]^\
2, x[1][1]^2*x[2][2]*x[2][3]+2*x[1][1]*x[1][2]*x[2][1]*x[2][3]+2*x[1][1]*x[1][\
3]*x[2][1]*x[2][2]+x[1][2]*x[1][3]*x[2][1]^2,
x[1][1]^2*x[2][3]^2+4*x[1][1]*x[1][3]*x[2][1]*x[2][3]+x[1][3]^2*x[2][1]^\
2, 3*x[1][1]*x[1][2]*x[2][2]^2+3*x[1][2]^2*x[2][1]*x[2][2],
2*x[1][1]*x[1][2]*x[2][2]*x[2][3]+x[1][1]*x[1][3]*x[2][2]^2+x[1][2]^2*x[\
2][1]*x[2][3]+2*x[1][2]*x[1][3]*x[2][1]*x[2][2],
x[1][1]*x[1][2]*x[2][3]^2+2*x[1][1]*x[1][3]*x[2][2]*x[2][3]+2*x[1][2]*x[\
1][3]*x[2][1]*x[2][3]+x[1][3]^2*x[2][1]*x[2][2],
3*x[1][1]*x[1][3]*x[2][3]^2+3*x[1][3]^2*x[2][1]*x[2][3],
6*x[1][2]^2*x[2][2]^2,
3*x[1][2]^2*x[2][2]*x[2][3]+3*x[1][2]*x[1][3]*x[2][2]^2,
x[1][2]^2*x[2][3]^2+4*x[1][2]*x[1][3]*x[2][2]*x[2][3]+x[1][3]^2*x[2][2]^\
2, 3*x[1][2]*x[1][3]*x[2][3]^2+3*x[1][3]^2*x[2][2]*x[2][3],
6*x[1][3]^2*x[2][3]^2 ],
[ 12*x[1][1]^2*x[2][1]*x[3][1],
3*x[1][1]^2*x[2][1]*x[3][2]+3*x[1][1]^2*x[2][2]*x[3][1]+6*x[1][1]*x[1][2\
]*x[2][1]*x[3][1],
3*x[1][1]^2*x[2][1]*x[3][3]+3*x[1][1]^2*x[2][3]*x[3][1]+6*x[1][1]*x[1][3\
]*x[2][1]*x[3][1],
2*x[1][1]^2*x[2][2]*x[3][2]+4*x[1][1]*x[1][2]*x[2][1]*x[3][2]+4*x[1][1]*\
x[1][2]*x[2][2]*x[3][1]+2*x[1][2]^2*x[2][1]*x[3][1],
x[1][1]^2*x[2][2]*x[3][3]+x[1][1]^2*x[2][3]*x[3][2]+2*x[1][1]*x[1][2]*x[\
2][1]*x[3][3]+2*x[1][1]*x[1][2]*x[2][3]*x[3][1]+2*x[1][1]*x[1][3]*x[2][1]*x[3]\
[2]+2*x[1][1]*x[1][3]*x[2][2]*x[3][1]+2*x[1][2]*x[1][3]*x[2][1]*x[3][1],
2*x[1][1]^2*x[2][3]*x[3][3]+4*x[1][1]*x[1][3]*x[2][1]*x[3][3]+4*x[1][1]*\
x[1][3]*x[2][3]*x[3][1]+2*x[1][3]^2*x[2][1]*x[3][1],
6*x[1][1]*x[1][2]*x[2][2]*x[3][2]+3*x[1][2]^2*x[2][1]*x[3][2]+3*x[1][2]^\
2*x[2][2]*x[3][1],
2*x[1][1]*x[1][2]*x[2][2]*x[3][3]+2*x[1][1]*x[1][2]*x[2][3]*x[3][2]+2*x[\
1][1]*x[1][3]*x[2][2]*x[3][2]+x[1][2]^2*x[2][1]*x[3][3]+x[1][2]^2*x[2][3]*x[3]\
[1]+2*x[1][2]*x[1][3]*x[2][1]*x[3][2]+2*x[1][2]*x[1][3]*x[2][2]*x[3][1],
2*x[1][1]*x[1][2]*x[2][3]*x[3][3]+2*x[1][1]*x[1][3]*x[2][2]*x[3][3]+2*x[\
1][1]*x[1][3]*x[2][3]*x[3][2]+2*x[1][2]*x[1][3]*x[2][1]*x[3][3]+2*x[1][2]*x[1]\
[3]*x[2][3]*x[3][1]+x[1][3]^2*x[2][1]*x[3][2]+x[1][3]^2*x[2][2]*x[3][1],
6*x[1][1]*x[1][3]*x[2][3]*x[3][3]+3*x[1][3]^2*x[2][1]*x[3][3]+3*x[1][3]^\
2*x[2][3]*x[3][1], 12*x[1][2]^2*x[2][2]*x[3][2],
3*x[1][2]^2*x[2][2]*x[3][3]+3*x[1][2]^2*x[2][3]*x[3][2]+6*x[1][2]*x[1][3\
]*x[2][2]*x[3][2],
2*x[1][2]^2*x[2][3]*x[3][3]+4*x[1][2]*x[1][3]*x[2][2]*x[3][3]+4*x[1][2]*\
x[1][3]*x[2][3]*x[3][2]+2*x[1][3]^2*x[2][2]*x[3][2],
6*x[1][2]*x[1][3]*x[2][3]*x[3][3]+3*x[1][3]^2*x[2][2]*x[3][3]+3*x[1][3]^\
2*x[2][3]*x[3][2], 12*x[1][3]^2*x[2][3]*x[3][3] ],
[ 6*x[1][1]^2*x[3][1]^2,
3*x[1][1]^2*x[3][1]*x[3][2]+3*x[1][1]*x[1][2]*x[3][1]^2,
3*x[1][1]^2*x[3][1]*x[3][3]+3*x[1][1]*x[1][3]*x[3][1]^2,
x[1][1]^2*x[3][2]^2+4*x[1][1]*x[1][2]*x[3][1]*x[3][2]+x[1][2]^2*x[3][1]^\
2, x[1][1]^2*x[3][2]*x[3][3]+2*x[1][1]*x[1][2]*x[3][1]*x[3][3]+2*x[1][1]*x[1][\
3]*x[3][1]*x[3][2]+x[1][2]*x[1][3]*x[3][1]^2,
x[1][1]^2*x[3][3]^2+4*x[1][1]*x[1][3]*x[3][1]*x[3][3]+x[1][3]^2*x[3][1]^\
2, 3*x[1][1]*x[1][2]*x[3][2]^2+3*x[1][2]^2*x[3][1]*x[3][2],
2*x[1][1]*x[1][2]*x[3][2]*x[3][3]+x[1][1]*x[1][3]*x[3][2]^2+x[1][2]^2*x[\
3][1]*x[3][3]+2*x[1][2]*x[1][3]*x[3][1]*x[3][2],
x[1][1]*x[1][2]*x[3][3]^2+2*x[1][1]*x[1][3]*x[3][2]*x[3][3]+2*x[1][2]*x[\
1][3]*x[3][1]*x[3][3]+x[1][3]^2*x[3][1]*x[3][2],
3*x[1][1]*x[1][3]*x[3][3]^2+3*x[1][3]^2*x[3][1]*x[3][3],
6*x[1][2]^2*x[3][2]^2,
3*x[1][2]^2*x[3][2]*x[3][3]+3*x[1][2]*x[1][3]*x[3][2]^2,
x[1][2]^2*x[3][3]^2+4*x[1][2]*x[1][3]*x[3][2]*x[3][3]+x[1][3]^2*x[3][2]^\
2, 3*x[1][2]*x[1][3]*x[3][3]^2+3*x[1][3]^2*x[3][2]*x[3][3],
6*x[1][3]^2*x[3][3]^2 ],
[ 4*x[1][1]*x[2][1]^3, 3*x[1][1]*x[2][1]^2*x[2][2]+x[1][2]*x[2][1]^3,
3*x[1][1]*x[2][1]^2*x[2][3]+x[1][3]*x[2][1]^3,
2*x[1][1]*x[2][1]*x[2][2]^2+2*x[1][2]*x[2][1]^2*x[2][2],
2*x[1][1]*x[2][1]*x[2][2]*x[2][3]+x[1][2]*x[2][1]^2*x[2][3]+x[1][3]*x[2]\
[1]^2*x[2][2], 2*x[1][1]*x[2][1]*x[2][3]^2+2*x[1][3]*x[2][1]^2*x[2][3],
x[1][1]*x[2][2]^3+3*x[1][2]*x[2][1]*x[2][2]^2,
x[1][1]*x[2][2]^2*x[2][3]+2*x[1][2]*x[2][1]*x[2][2]*x[2][3]+x[1][3]*x[2]\
[1]*x[2][2]^2,
x[1][1]*x[2][2]*x[2][3]^2+x[1][2]*x[2][1]*x[2][3]^2+2*x[1][3]*x[2][1]*x[\
2][2]*x[2][3], x[1][1]*x[2][3]^3+3*x[1][3]*x[2][1]*x[2][3]^2,
4*x[1][2]*x[2][2]^3, 3*x[1][2]*x[2][2]^2*x[2][3]+x[1][3]*x[2][2]^3,
2*x[1][2]*x[2][2]*x[2][3]^2+2*x[1][3]*x[2][2]^2*x[2][3],
x[1][2]*x[2][3]^3+3*x[1][3]*x[2][2]*x[2][3]^2, 4*x[1][3]*x[2][3]^3 ],
[ 12*x[1][1]*x[2][1]^2*x[3][1],
3*x[1][1]*x[2][1]^2*x[3][2]+6*x[1][1]*x[2][1]*x[2][2]*x[3][1]+3*x[1][2]*\
x[2][1]^2*x[3][1],
3*x[1][1]*x[2][1]^2*x[3][3]+6*x[1][1]*x[2][1]*x[2][3]*x[3][1]+3*x[1][3]*\
x[2][1]^2*x[3][1],
4*x[1][1]*x[2][1]*x[2][2]*x[3][2]+2*x[1][1]*x[2][2]^2*x[3][1]+2*x[1][2]*\
x[2][1]^2*x[3][2]+4*x[1][2]*x[2][1]*x[2][2]*x[3][1],
2*x[1][1]*x[2][1]*x[2][2]*x[3][3]+2*x[1][1]*x[2][1]*x[2][3]*x[3][2]+2*x[\
1][1]*x[2][2]*x[2][3]*x[3][1]+x[1][2]*x[2][1]^2*x[3][3]+2*x[1][2]*x[2][1]*x[2]\
[3]*x[3][1]+x[1][3]*x[2][1]^2*x[3][2]+2*x[1][3]*x[2][1]*x[2][2]*x[3][1],
4*x[1][1]*x[2][1]*x[2][3]*x[3][3]+2*x[1][1]*x[2][3]^2*x[3][1]+2*x[1][3]*\
x[2][1]^2*x[3][3]+4*x[1][3]*x[2][1]*x[2][3]*x[3][1],
3*x[1][1]*x[2][2]^2*x[3][2]+6*x[1][2]*x[2][1]*x[2][2]*x[3][2]+3*x[1][2]*\
x[2][2]^2*x[3][1],
x[1][1]*x[2][2]^2*x[3][3]+2*x[1][1]*x[2][2]*x[2][3]*x[3][2]+2*x[1][2]*x[\
2][1]*x[2][2]*x[3][3]+2*x[1][2]*x[2][1]*x[2][3]*x[3][2]+2*x[1][2]*x[2][2]*x[2]\
[3]*x[3][1]+2*x[1][3]*x[2][1]*x[2][2]*x[3][2]+x[1][3]*x[2][2]^2*x[3][1],
2*x[1][1]*x[2][2]*x[2][3]*x[3][3]+x[1][1]*x[2][3]^2*x[3][2]+2*x[1][2]*x[\
2][1]*x[2][3]*x[3][3]+x[1][2]*x[2][3]^2*x[3][1]+2*x[1][3]*x[2][1]*x[2][2]*x[3]\
[3]+2*x[1][3]*x[2][1]*x[2][3]*x[3][2]+2*x[1][3]*x[2][2]*x[2][3]*x[3][1],
3*x[1][1]*x[2][3]^2*x[3][3]+6*x[1][3]*x[2][1]*x[2][3]*x[3][3]+3*x[1][3]*\
x[2][3]^2*x[3][1], 12*x[1][2]*x[2][2]^2*x[3][2],
3*x[1][2]*x[2][2]^2*x[3][3]+6*x[1][2]*x[2][2]*x[2][3]*x[3][2]+3*x[1][3]*\
x[2][2]^2*x[3][2],
4*x[1][2]*x[2][2]*x[2][3]*x[3][3]+2*x[1][2]*x[2][3]^2*x[3][2]+2*x[1][3]*\
x[2][2]^2*x[3][3]+4*x[1][3]*x[2][2]*x[2][3]*x[3][2],
3*x[1][2]*x[2][3]^2*x[3][3]+6*x[1][3]*x[2][2]*x[2][3]*x[3][3]+3*x[1][3]*\
x[2][3]^2*x[3][2], 12*x[1][3]*x[2][3]^2*x[3][3] ],
[ 12*x[1][1]*x[2][1]*x[3][1]^2,
6*x[1][1]*x[2][1]*x[3][1]*x[3][2]+3*x[1][1]*x[2][2]*x[3][1]^2+3*x[1][2]*\
x[2][1]*x[3][1]^2,
6*x[1][1]*x[2][1]*x[3][1]*x[3][3]+3*x[1][1]*x[2][3]*x[3][1]^2+3*x[1][3]*\
x[2][1]*x[3][1]^2,
2*x[1][1]*x[2][1]*x[3][2]^2+4*x[1][1]*x[2][2]*x[3][1]*x[3][2]+4*x[1][2]*\
x[2][1]*x[3][1]*x[3][2]+2*x[1][2]*x[2][2]*x[3][1]^2,
2*x[1][1]*x[2][1]*x[3][2]*x[3][3]+2*x[1][1]*x[2][2]*x[3][1]*x[3][3]+2*x[\
1][1]*x[2][3]*x[3][1]*x[3][2]+2*x[1][2]*x[2][1]*x[3][1]*x[3][3]+x[1][2]*x[2][3\
]*x[3][1]^2+2*x[1][3]*x[2][1]*x[3][1]*x[3][2]+x[1][3]*x[2][2]*x[3][1]^2,
2*x[1][1]*x[2][1]*x[3][3]^2+4*x[1][1]*x[2][3]*x[3][1]*x[3][3]+4*x[1][3]*\
x[2][1]*x[3][1]*x[3][3]+2*x[1][3]*x[2][3]*x[3][1]^2,
3*x[1][1]*x[2][2]*x[3][2]^2+3*x[1][2]*x[2][1]*x[3][2]^2+6*x[1][2]*x[2][2\
]*x[3][1]*x[3][2],
2*x[1][1]*x[2][2]*x[3][2]*x[3][3]+x[1][1]*x[2][3]*x[3][2]^2+2*x[1][2]*x[\
2][1]*x[3][2]*x[3][3]+2*x[1][2]*x[2][2]*x[3][1]*x[3][3]+2*x[1][2]*x[2][3]*x[3]\
[1]*x[3][2]+x[1][3]*x[2][1]*x[3][2]^2+2*x[1][3]*x[2][2]*x[3][1]*x[3][2],
x[1][1]*x[2][2]*x[3][3]^2+2*x[1][1]*x[2][3]*x[3][2]*x[3][3]+x[1][2]*x[2]\
[1]*x[3][3]^2+2*x[1][2]*x[2][3]*x[3][1]*x[3][3]+2*x[1][3]*x[2][1]*x[3][2]*x[3]\
[3]+2*x[1][3]*x[2][2]*x[3][1]*x[3][3]+2*x[1][3]*x[2][3]*x[3][1]*x[3][2],
3*x[1][1]*x[2][3]*x[3][3]^2+3*x[1][3]*x[2][1]*x[3][3]^2+6*x[1][3]*x[2][3\
]*x[3][1]*x[3][3], 12*x[1][2]*x[2][2]*x[3][2]^2,
6*x[1][2]*x[2][2]*x[3][2]*x[3][3]+3*x[1][2]*x[2][3]*x[3][2]^2+3*x[1][3]*\
x[2][2]*x[3][2]^2,
2*x[1][2]*x[2][2]*x[3][3]^2+4*x[1][2]*x[2][3]*x[3][2]*x[3][3]+4*x[1][3]*\
x[2][2]*x[3][2]*x[3][3]+2*x[1][3]*x[2][3]*x[3][2]^2,
3*x[1][2]*x[2][3]*x[3][3]^2+3*x[1][3]*x[2][2]*x[3][3]^2+6*x[1][3]*x[2][3\
]*x[3][2]*x[3][3], 12*x[1][3]*x[2][3]*x[3][3]^2 ],
[ 4*x[1][1]*x[3][1]^3, 3*x[1][1]*x[3][1]^2*x[3][2]+x[1][2]*x[3][1]^3,
3*x[1][1]*x[3][1]^2*x[3][3]+x[1][3]*x[3][1]^3,
2*x[1][1]*x[3][1]*x[3][2]^2+2*x[1][2]*x[3][1]^2*x[3][2],
2*x[1][1]*x[3][1]*x[3][2]*x[3][3]+x[1][2]*x[3][1]^2*x[3][3]+x[1][3]*x[3]\
[1]^2*x[3][2], 2*x[1][1]*x[3][1]*x[3][3]^2+2*x[1][3]*x[3][1]^2*x[3][3],
x[1][1]*x[3][2]^3+3*x[1][2]*x[3][1]*x[3][2]^2,
x[1][1]*x[3][2]^2*x[3][3]+2*x[1][2]*x[3][1]*x[3][2]*x[3][3]+x[1][3]*x[3]\
[1]*x[3][2]^2,
x[1][1]*x[3][2]*x[3][3]^2+x[1][2]*x[3][1]*x[3][3]^2+2*x[1][3]*x[3][1]*x[\
3][2]*x[3][3], x[1][1]*x[3][3]^3+3*x[1][3]*x[3][1]*x[3][3]^2,
4*x[1][2]*x[3][2]^3, 3*x[1][2]*x[3][2]^2*x[3][3]+x[1][3]*x[3][2]^3,
2*x[1][2]*x[3][2]*x[3][3]^2+2*x[1][3]*x[3][2]^2*x[3][3],
x[1][2]*x[3][3]^3+3*x[1][3]*x[3][2]*x[3][3]^2, 4*x[1][3]*x[3][3]^3 ],
[ x[2][1]^4, x[2][1]^3*x[2][2], x[2][1]^3*x[2][3], x[2][1]^2*x[2][2]^2,
x[2][1]^2*x[2][2]*x[2][3], x[2][1]^2*x[2][3]^2, x[2][1]*x[2][2]^3,
x[2][1]*x[2][2]^2*x[2][3], x[2][1]*x[2][2]*x[2][3]^2, x[2][1]*x[2][3]^3,
x[2][2]^4, x[2][2]^3*x[2][3], x[2][2]^2*x[2][3]^2, x[2][2]*x[2][3]^3,
x[2][3]^4 ],
[ 4*x[2][1]^3*x[3][1], x[2][1]^3*x[3][2]+3*x[2][1]^2*x[2][2]*x[3][1],
x[2][1]^3*x[3][3]+3*x[2][1]^2*x[2][3]*x[3][1],
2*x[2][1]^2*x[2][2]*x[3][2]+2*x[2][1]*x[2][2]^2*x[3][1],
x[2][1]^2*x[2][2]*x[3][3]+x[2][1]^2*x[2][3]*x[3][2]+2*x[2][1]*x[2][2]*x[\
2][3]*x[3][1], 2*x[2][1]^2*x[2][3]*x[3][3]+2*x[2][1]*x[2][3]^2*x[3][1],
3*x[2][1]*x[2][2]^2*x[3][2]+x[2][2]^3*x[3][1],
x[2][1]*x[2][2]^2*x[3][3]+2*x[2][1]*x[2][2]*x[2][3]*x[3][2]+x[2][2]^2*x[\
2][3]*x[3][1],
2*x[2][1]*x[2][2]*x[2][3]*x[3][3]+x[2][1]*x[2][3]^2*x[3][2]+x[2][2]*x[2]\
[3]^2*x[3][1], 3*x[2][1]*x[2][3]^2*x[3][3]+x[2][3]^3*x[3][1],
4*x[2][2]^3*x[3][2], x[2][2]^3*x[3][3]+3*x[2][2]^2*x[2][3]*x[3][2],
2*x[2][2]^2*x[2][3]*x[3][3]+2*x[2][2]*x[2][3]^2*x[3][2],
3*x[2][2]*x[2][3]^2*x[3][3]+x[2][3]^3*x[3][2], 4*x[2][3]^3*x[3][3] ],
[ 6*x[2][1]^2*x[3][1]^2,
3*x[2][1]^2*x[3][1]*x[3][2]+3*x[2][1]*x[2][2]*x[3][1]^2,
3*x[2][1]^2*x[3][1]*x[3][3]+3*x[2][1]*x[2][3]*x[3][1]^2,
x[2][1]^2*x[3][2]^2+4*x[2][1]*x[2][2]*x[3][1]*x[3][2]+x[2][2]^2*x[3][1]^\
2, x[2][1]^2*x[3][2]*x[3][3]+2*x[2][1]*x[2][2]*x[3][1]*x[3][3]+2*x[2][1]*x[2][\
3]*x[3][1]*x[3][2]+x[2][2]*x[2][3]*x[3][1]^2,
x[2][1]^2*x[3][3]^2+4*x[2][1]*x[2][3]*x[3][1]*x[3][3]+x[2][3]^2*x[3][1]^\
2, 3*x[2][1]*x[2][2]*x[3][2]^2+3*x[2][2]^2*x[3][1]*x[3][2],
2*x[2][1]*x[2][2]*x[3][2]*x[3][3]+x[2][1]*x[2][3]*x[3][2]^2+x[2][2]^2*x[\
3][1]*x[3][3]+2*x[2][2]*x[2][3]*x[3][1]*x[3][2],
x[2][1]*x[2][2]*x[3][3]^2+2*x[2][1]*x[2][3]*x[3][2]*x[3][3]+2*x[2][2]*x[\
2][3]*x[3][1]*x[3][3]+x[2][3]^2*x[3][1]*x[3][2],
3*x[2][1]*x[2][3]*x[3][3]^2+3*x[2][3]^2*x[3][1]*x[3][3],
6*x[2][2]^2*x[3][2]^2,
3*x[2][2]^2*x[3][2]*x[3][3]+3*x[2][2]*x[2][3]*x[3][2]^2,
x[2][2]^2*x[3][3]^2+4*x[2][2]*x[2][3]*x[3][2]*x[3][3]+x[2][3]^2*x[3][2]^\
2, 3*x[2][2]*x[2][3]*x[3][3]^2+3*x[2][3]^2*x[3][2]*x[3][3],
6*x[2][3]^2*x[3][3]^2 ],
[ 4*x[2][1]*x[3][1]^3, 3*x[2][1]*x[3][1]^2*x[3][2]+x[2][2]*x[3][1]^3,
3*x[2][1]*x[3][1]^2*x[3][3]+x[2][3]*x[3][1]^3,
2*x[2][1]*x[3][1]*x[3][2]^2+2*x[2][2]*x[3][1]^2*x[3][2],
2*x[2][1]*x[3][1]*x[3][2]*x[3][3]+x[2][2]*x[3][1]^2*x[3][3]+x[2][3]*x[3]\
[1]^2*x[3][2], 2*x[2][1]*x[3][1]*x[3][3]^2+2*x[2][3]*x[3][1]^2*x[3][3],
x[2][1]*x[3][2]^3+3*x[2][2]*x[3][1]*x[3][2]^2,
x[2][1]*x[3][2]^2*x[3][3]+2*x[2][2]*x[3][1]*x[3][2]*x[3][3]+x[2][3]*x[3]\
[1]*x[3][2]^2,
x[2][1]*x[3][2]*x[3][3]^2+x[2][2]*x[3][1]*x[3][3]^2+2*x[2][3]*x[3][1]*x[\
3][2]*x[3][3], x[2][1]*x[3][3]^3+3*x[2][3]*x[3][1]*x[3][3]^2,
4*x[2][2]*x[3][2]^3, 3*x[2][2]*x[3][2]^2*x[3][3]+x[2][3]*x[3][2]^3,
2*x[2][2]*x[3][2]*x[3][3]^2+2*x[2][3]*x[3][2]^2*x[3][3],
x[2][2]*x[3][3]^3+3*x[2][3]*x[3][2]*x[3][3]^2, 4*x[2][3]*x[3][3]^3 ],
[ x[3][1]^4, x[3][1]^3*x[3][2], x[3][1]^3*x[3][3], x[3][1]^2*x[3][2]^2,
x[3][1]^2*x[3][2]*x[3][3], x[3][1]^2*x[3][3]^2, x[3][1]*x[3][2]^3,
x[3][1]*x[3][2]^2*x[3][3], x[3][1]*x[3][2]*x[3][3]^2, x[3][1]*x[3][3]^3,
x[3][2]^4, x[3][2]^3*x[3][3], x[3][2]^2*x[3][3]^2, x[3][2]*x[3][3]^3,
x[3][3]^4 ] ];
ConstructTensors:=function(seeds)
local f,all,pat,allmo,i,j,np,t,mo,k,cf,lim;
lim:=ValueOption("limit");
if lim=fail then lim:=infinity;fi;
f:=FieldOfMatrixList(seeds[1]);
all:=ShallowCopy(seeds);
pat:=List([1..Length(seeds)],x->[x]);
allmo:=List(seeds,x->GModuleByMats(x,f));
i:=1;
while i<=Length(all) do
for j in [1..Length(seeds)] do
np:=Concatenation(pat[i],[j]);
Sort(np);
# if np in pat then
# Print("duplicate ",np,"\n");
# else
Add(pat,np);
t:=List([1..Length(seeds[j])],
x->KroneckerProduct(all[i][x],seeds[j][x]));
mo:=GModuleByMats(t,f);
cf:=List(MTX.CollectedFactors(mo),x->x[1]);
Sort(cf,function(a,b) return a.dimension<b.dimension;end);
for mo in cf do
k:=PositionProperty([1..Length(allmo)],x->
allmo[x].dimension=mo.dimension and MTX.Isomorphism(allmo[x],mo)<>fail);
if k=fail then
Print("new irred ",np," ",mo.dimension,"\n");
Add(pat,np);
Add(all,mo.generators);
Add(allmo,mo);
if Length(all)=lim then return all;fi;
#else
# Print("isom ",np," ",mo.dimension," ",k,"\n");
fi;
od;
# fi;
od;
i:=i+1;
od;
return all;
end;
Constructsymmreps:=function(mats)
local i,l;
l:=[ShallowCopy(mats)];
for i in [2..4] do
Add(l,List(mats,x->SymmetricPower(x,i)));
od;
return l;
end;
RepresKind:=function(mats,kind)
local n,r,f;
n:=Int(Filtered(kind,x->x in CHARS_DIGITS));
r:=fail;
if Length(kind)>3 and kind{[1..3]}="Pol" then
r:=ConstructOnePolrep(mats,n);
elif Length(kind)>1 and kind{[1]}="S" then
# symmetric
r:=rec(name:=Concatenation("S",String(n)),
kind:="sympow",level:=n,
gens:=List(mats,y->SymmetricPower(y,n)));
elif Length(kind)>1 and kind{[1]}="E" then
# exterior
r:=rec(name:=Concatenation("E",String(n)),
kind:="sympow",level:=n,
gens:=List(mats,y->ExteriorPower(y,n)));
elif kind="rep15" then
r:=rec(name:="Rep15", kind:="rep15",
gens:=List(mats,rep15));
fi;
if r=fail then
Error("Do not know repres ",kind);
else
f:=FieldOfMatrixList(r.gens);
if IsFinite(f) then
n:=GModuleByMats(r.gens,f);
r.absirr:=MTX.IsAbsolutelyIrreducible(n);
fi;
return r;
fi;
end;
# which kinds to try in which dimension
KindsForDim:=function(n)
local kinds,i;
kinds:=["Pol1","Pol2","Pol3"];
if n=3 then
Add(kinds,"rep15");
else
Append(kinds,["S2","E2"]);
fi;
for i in [4..n] do
Add(kinds,Concatenation("Pol",String(i)));
od;
return kinds;
end;
#3: [ "Pol1", "Pol2", "Pol3", "rep15" ]
#4: [ "E2", "Pol1", "Pol2", "Pol4" ]
#5: [ "Pol1", "Pol2", "Pol3" ]
#6: [ "E2", "Pol1", "Pol2", "Pol3", "Pol4" ]
#7: [ "Pol1", "Pol2", "Pol3" ]
#8: [ "E2", "Pol1", "Pol2", "Pol3", "Pol4" ]
#9: [ "Pol1", "Pol2", "Pol3" ]
#10: [ "E2", "Pol1", "Pol2", "Pol3", "Pol4" ]
#11: [ "Pol1", "Pol2", "Pol3" ]
TestReps:=function(g,l,subs)
local i,j,r,mo,hom,is;
is:=[1..Length(subs)];
for i in [1..Length(l)] do
hom:=GroupHomomorphismByImagesNC(g,Group(l[i]),GeneratorsOfGroup(g),l[i]);
#if hom=fail then Error("UGH");fi;
r:=[];
for j in [1..Length(subs)] do
mo:=List(GeneratorsOfGroup(subs[j]),x->Image(hom,x));
mo:=GModuleByMats(mo,DefaultFieldOfMatrixGroup(g));
if MTX.IsAbsolutelyIrreducible(mo) then
#if Size(Group(mo.generators))>Size(subs[j]) then Error("ZZZ");fi;
Add(r,j);
fi;
od;
Print(i,":",Length(One(Range(hom)))," ",r,"\n");
is:=Intersection(is,r);
if Length(is)=0 then return true;fi;
od;
return false;
end;
IntFacTrial:=function(n)
local f,i;
f:=[];
i:=1;
while n>1 and i<=Length(Primes) do
while n mod Primes[i]=0 do
n:=n/Primes[i];
AddSet(f,Primes[i]);
od;
i:=i+1;
od;
if n=1 then return f;
else
return fail;
fi;
end;
RegModZSpanOrig:=function(gens,seed,oneirr,bad)
local n,matsplit,b,cnt,HM,si,new,bc,i,j,d,process,stack,max,prime;
process:=function(new)
bc:=Concatenation(b,[new])*oneirr;
if Length(b)=Length(b[1]) or Length(b)+1>RankMat(bc) then
if HM=fail then
HM:=HermiteNormalFormIntegerMatTransform(b);
fi;
d:=SolutionMat(HM.normal,new);
if d<>fail and ForAll(d,IsInt) then
# same lattice
cnt:=cnt+1;
if Length(b)>=Length(b[1]) and cnt>=5 then
return b;
fi;
else
bc:=Concatenation(b,[new]);
if ForAll(bad,x->RankMat(bc*Z(x)^0)<=Length(b))
and (Length(bc)>Length(bc[1]) or RankMat(bc)<=Length(b)) then
# new lattice, same rank
cnt:=0;
b:=bc;
#Print(Maximum(Union(b)),"\n");
#b0:=b;
HM:=HermiteNormalFormIntegerMatTransform(b);
b:=Filtered(HM.normal,x->not IsZero(x));
#if Maximum(Union(b))>10^60 then Error("huge"); fi;
else
# add vector, prime was bad;
b:=bc;
#b:=LLLint(bc);
HM:=fail;
prime:=NextPrimeInt(prime);
oneirr:=Z(prime)^0;
Print("prime increased to:",prime,"\n");
fi;
fi;
else
# rank increases
cnt:=0;
Add(b,new);
HM:=fail;
fi;
end;
if oneirr=false then
oneirr:=Z(101);
fi;
prime:=Characteristic(oneirr);
n:=Length(gens[1]);
matsplit:=l->List([1..n],x->l{[n*(x-1)+1..n*x]});
b:=ShallowCopy(seed);
max:=Maximum(Concatenation(seed));
max:=Maximum(max,Maximum(Concatenation(Concatenation(gens))));
cnt:=0;
HM:=fail;
stack:=[];
for i in b do
si:=matsplit(i);
for j in gens do
new:=Concatenation(si*j);
if Maximum(new)>max*1000 then
Add(stack,new);
else
process(new);
max:=Maximum(max,Maximum(Concatenation(b)));
fi;
od;
od;
for i in stack do
process(i);
od;
return b;
end;
InterestingPrimes:=function(H)
local f,b,i,all,primes,d,cnt,fct,basch,n,r,v,sn,j,a,homo,homoe,dold,ii,
rad,new,irr,HM,p,cnt1,reduced,good,bad,gens,kinds,ngens;
n:=Length(One(H));
if n<>3 then Error("so far only dimension 3 done");fi;
# get an irrelevant prime, to allow matrix work modulo
# also immediately test small primes to be rid of them
good:=[];
bad:=[];
irr:=ValueOption("prime");
if irr=fail then
irr:=1;
repeat
irr:=NextPrimeInt(irr);
HM:=List(GeneratorsOfGroup(H),x->x*Z(irr)^0);
HM:=Group(HM);
if not IsNaturalSL(HM) then Add(good,irr);
elif irr=2 and n<=4 then
# special treatment of 2 -- need to use mod 4:
HM:=Integers mod 4;
HM:=List(GeneratorsOfGroup(H),x->x*One(HM));
HM:=Group(HM);
FittingFreeLiftSetup(HM);
if Size(HM)<Size(SL(n,Integers mod 4)) then
Add(good,2);
SetIsNaturalSL(HM,false);
else
SetIsNaturalSL(HM,true);
fi;
else Add(bad,irr);fi;
until IsNaturalSL(HM) and irr>7;
fi;
Print("irrelevant prime ",irr,"\n");
sn:=SymmetricGroup(n);
all:=[];
kinds:=KindsForDim(n);
for i in [1..Length(kinds)] do
Print("i=",i," ",kinds[i],"\n");
gens:=RepresKind(GeneratorsOfGroup(H),kinds[i]).gens;
f:=EpimorphismFromFreeGroup(Group(gens));
rad:=5;
primes:=[];
cnt:=0;
dold:=0;
reduced:=false;
b:=[Concatenation(gens[1])];
ngens:=ShallowCopy(gens);
repeat
b:=RegModZSpanOrig(gens,b,Z(irr)^0,Difference(bad,[irr]));
d:=DeterminantMat(List(b,x->List(b,y->x*y)));
# remove primes we know already about
for p in Union(good,bad) do
while d mod p=0 do
d:=d/p;
od;
od;
#Print("det=",d,"\n");
#if d>10^40 then Error("YYY");fi;
# if d=dold then cnt:=cnt+1;else cnt:=0;fi;
# dold:=d;
#
# # no new primes or stable for a while
rad:=rad+2;
until cnt>=10 or d<10^100;
if d>1 then
d:=Set(Factors(d));
Print("->",d,"\n");
for p in d do
HM:=List(GeneratorsOfGroup(H),x->x*Z(p)^0);
HM:=Group(HM);
if not IsNaturalSL(HM) then AddSet(good,p);
else AddSet(bad,p);fi;
od;
Print("good=",good," bad=",bad,"\n");
fi;
od;
return good;
end;
# old, obsolete code
AAAAAAASStabilizerGens:=function(gens,u,m)
local n,ring,one,u1,v1,gens1,orb,d,t,stabgens,stabsub,o,i,img,p,post,vo,s,gp,
ff,actfun;
n:=Length(u);
ring:=Integers mod m;
one:=One(ring);
u1:=u*one;
gens1:=List(gens,x->x*one);
#gens1:=GeneratorsWithMemory(gens1);
# do clever orbit algorithm using recognition
gp:=Group(gens1);
ff:=FittingFreeLiftSetup(gp);
d:=Enumerator(ring^n);
p:=MappingGeneratorsImages(ff.pcisom);
o:=MappingGeneratorsImages(ff.factorhom);
orb:=OrbitStabRepsMultistage(p[1],p[1],ff.pcisom,
Size(Image(ff.pcisom)),TrivialSubgroup(Image(ff.pcisom)),o[1],o[1],o[2],
ff.factorhom,Size(gp),OnRight,d,u1);
stabgens:=Concatenation(orb.stabradgens,orb.stabfacgens);
stabgens:=List(stabgens,x->ASBestPreImg(x,m,gens));
Assert(1,ForAll(stabgens,y->DeterminantMat(y)=1));
# function for action on Gamma_m orbits, represented by ``canonical'' reps
actfun:=function(v,a)
local i;
v:=v*a;
for i in d do
if ASOrbitGammaM(v,i,m)<>false then
return i;
fi;
od;
return v;
end;
orb:=OrbitStabRepsMultistage(orb.stabradgens,
stabgens{[1..Length(orb.stabradgens)]},ff.pcisom,
orb.stabrsubsz,TrivialSubgroup(Image(ff.pcisom)),
orb.stabfacgens,stabgens{[Length(orb.stabradgens)+1..Length(stabgens)]},
orb.stabfacimgs,
ff.factorhom,orb.subsz,actfun,false,u);
stabgens:=Concatenation(orb.stabradgens,orb.stabfacgens);
stabgens:=List(stabgens,x->ASBestPreImg(x,m,gens));
Assert(1,ForAll(stabgens,y->DeterminantMat(y)=1));
# correct stabilizing generators
for i in [1..Length(stabgens)] do
d:=ASOrbitGammaM(u*stabgens[i],u,m);
stabgens[i]:=stabgens[i]*d;
od;
Error("ZZZ");
end;