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ENHANCE: Split cohomology stabilizer over factor modules first to red…
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…uce orbit length.
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@hulpke
hulpke committed Oct 16, 2018
1 parent 1170fb9 commit 9b12e62
Showing 1 changed file with 164 additions and 136 deletions.
300 changes: 164 additions & 136 deletions lib/norad.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -380,7 +380,7 @@ local sus,ser,len,factorhom,uf,n,d,up,mran,nran,mpcgs,pcgs,pcisom,nf,ng,np,sub,
famo2,ufr,dims,vecs,ovecs,vecsz,l,prop,properties,clusters,clusterspaces,
fs,i,v1,o1,p1,
orblens,stabilizespaceandupdate,dual,myact,bound,boundbas,ranges,j,module,sumos,
minimalsubs,localinduce,lmpcgs,tst,nonzero,sel,myact2,tailnum;
minimalsubs,localinduce,lmpcgs,tst,nonzero,sel,myact2,tailnum,lfamo;

#timer:=List([1..15],x->0);
localinduce:=function(seq)
Expand Down Expand Up @@ -796,10 +796,11 @@ local sus,ser,len,factorhom,uf,n,d,up,mran,nran,mpcgs,pcgs,pcisom,nf,ng,np,sub,
l:=List([1..Length(part)],
x->part[x]*PcElementByExponentsNC(famo,l{ranges[x]}));
l:=List([1..Length(part)],x->l[x]^gen);

l:=CanonicalPcgs(InducedPcgsByGeneratorsNC(pcgs,l));

l:=List([1..Length(part)],
x->ExponentsOfPcElement(famo,
LeftQuotient(part[x],l[x]))*One(f));
x->ExponentsOfPcElement(famo, LeftQuotient(part[x],l[x]))*One(f));
l:=Concatenation(l);
l:=SiftedVector(bound,l);
ConvertToVectorRep(l,Size(f));
Expand Down Expand Up @@ -877,142 +878,169 @@ local sus,ser,len,factorhom,uf,n,d,up,mran,nran,mpcgs,pcgs,pcisom,nf,ng,np,sub,

if Length(part)>0 and Length(famo)>0 then

ranges:=List([1..Length(part)],
x->[(x-1)*Length(famo)+1..x*Length(famo)]);

sub:=Concatenation(List(part,a->List(famo,x->Zero(f))));

# coboundaries
boundbas:=List(famo,x->Concatenation(List(part,
y->ExponentsOfPcElement(famo,Comm(y,x))*One(f))));
bound:=List(boundbas,ShallowCopy);
TriangulizeMat(bound);
bound:=List(bound,Zero);
bound:=Basis(VectorSpace(f,bound));

Info(InfoFitFree,2,"up 0:",
" on ",
Product(RelativeOrders(famo))," cobounds:",Size(f)^Length(bound)
);

myact:=function(l,gen)
local pos,map,l0;

# make l the conjugated generator list
l:=List([1..Length(part)],
x->part[x]*PcElementByExponentsNC(famo,l{ranges[x]}));
l:=List([1..Length(part)],x->l[x]^gen);

# when acting with radical elements, it centralizes in the factor
pos:=Position(np,gen);
if pos=fail then
# not in the radical. There might be an induced automorphism of
# the factor which we'll have to undo

# find out what the images in the factor are by conjugating in the
# factor. This is intended to avoid image calculations
pos:=Position(ng,gen);
if pos=fail then

# must use image instead
map:=ImagesRepresentative(ser.factorhom,gen);
map:=List(uff,x->x^map);
else
map:=List(uff,x->x^nf[pos]);
fi;

# construct the map reps->preimages and map the gens we want (to work
# in the right coordinates)
map:=GroupGeneralMappingByImagesNC(uf,G,map,l);
l:=List(uff,x->ImagesRepresentative(map,x));
fi;

l:=List([1..Length(part)],x->LeftQuotient(part[x],l[x]));
l:=List(l,x->ExponentsOfPcElement(famo,x)*One(f));
l:=Concatenation(l);
l:=SiftedVector(bound,l);
ConvertToVectorRep(l,Size(f));
MakeImmutable(l);
return l;
end;
sub:=myact(sub,One(np[1])); # standardize -- force compression

if false then
stb:=TwoLevelStabilizer(ng,nf,ng,np,np,factorhom,sub,f^Length(sub),myact);
else
if Length(bound)>0 then
sel:=Filtered([1..Length(sub)],x->bound!.heads[x]=0);
else
sel:=[1..Length(sub)];
fi;
myact2:=RealizeAffineAction(Concatenation(ng,np),sub,sel,f,myact);

# stabilize in cohomology group
stb:=TwoLevelStabilizer(ng,nf,ng,np,np,factorhom,sub{sel},
f^Length(sel),myact2:
actrange:=[1..Length(np)-tailnum]);
fi;

ng:=stb.gens;
nf:=stb.imgs;
np:=localinduce(stb.pcgs);
#old: lfamo:=famo;

if Length(bound)>0 then
#nontrivial blocks -- now correct

myact:=function(l,gen)
local pos,map;

# make l the conjugated generator list
l:=List([1..Length(part)],
x->part[x]*PcElementByExponentsNC(famo,l{ranges[x]}));
l:=List([1..Length(part)],x->l[x]^gen);

# when acting with radical elements, it centralizes in the factor
pos:=Position(np,gen);
if pos=fail then
# not in the radical. There might be an induced automorphism of
# the factor which we'll have to undo

# find out what the images in the factor are by conjugating in the
# factor. This is intended to avoid image calculations
pos:=Position(ng,gen);
if pos=fail then

# must use image instead
map:=ImagesRepresentative(ser.factorhom,gen);
map:=List(uff,x->x^map);
else
map:=List(uff,x->x^nf[pos]);
fi;

# construct the map reps->preimages and map the gens we want (to work
# in the right coordinates)
map:=GroupGeneralMappingByImages(uf,G,map,l);
l:=List(uff,x->ImagesRepresentative(map,x));
fi;

l:=List([1..Length(part)],x->LeftQuotient(part[x],l[x]));
l:=List(l,x->ExponentsOfPcElement(famo,x)*One(f));
l:=Concatenation(l);
return l;
end;

# as corrections involve only pcgs parts, the inages inthe
# radical factor are not affected.
ng:=List(ng,x->x/PcElementByExponents(famo,
SolutionMat(boundbas,myact(sub,x))));
np:=InducedPcgsByGeneratorsNC(pcgs,
Concatenation(
List(np{[1..Length(np)-tailnum]},x->x/PcElementByExponents(famo,
SolutionMat(boundbas,myact(sub,x)))),
np{[Length(np)-tailnum+1..Length(np)]}));
Assert(1,ForAll(ng,x->myact(sub,x)=sub));
Assert(1,ForAll(np,x->myact(sub,x)=sub));
# calculate cohomology for quotient modules first to reduce orbit lengths
module:=GModuleByMats(LinearActionLayer(Concatenation(ng,np),famo),f);
sumos:=Reversed(MTX.BasesCompositionSeries(module));
sumos:=sumos{[2..Length(sumos)]};
Info(InfoFitFree,2,"Module layers ",List(sumos,Length));

p1:=0;
o1:=1;
repeat
p1:=p1+1;
while p1<Length(sumos) and Length(sumos[o1])-Length(sumos[p1+1])<10 do
p1:=p1+1;
od;

sub:=List(sumos[p1],x->PcElementByExponents(famo,x));
sub:=InducedPcgsByGeneratorsNC(NumeratorOfModuloPcgs(famo),Concatenation(DenominatorOfModuloPcgs(famo),sub));
lfamo:=NumeratorOfModuloPcgs(famo) mod sub;

Info(InfoFitFree,3,"Factor ",p1," Module ",Length(lfamo));

ranges:=List([1..Length(part)],
x->[(x-1)*Length(lfamo)+1..x*Length(lfamo)]);

sub:=Concatenation(List(part,a->List(lfamo,x->Zero(f))));

# coboundaries
boundbas:=List(lfamo,x->Concatenation(List(part,
y->ExponentsOfPcElement(lfamo,Comm(y,x))*One(f))));
boundbas:=ImmutableMatrix(f,boundbas);
bound:=List(boundbas,ShallowCopy);
TriangulizeMat(bound);
bound:=List(bound,Zero);
bound:=Basis(VectorSpace(f,bound));

#if
Info(InfoFitFree,2,"up 0:", " on ",
Product(RelativeOrders(lfamo))," cobounds:",Size(f)^Length(bound));

myact:=function(l,gen)
local pos,map,l0;

# make l the conjugated generator list
l:=List([1..Length(part)],
x->part[x]*PcElementByExponentsNC(lfamo,l{ranges[x]}));
l:=List([1..Length(part)],x->l[x]^gen);

# when acting with radical elements, it centralizes in the factor
pos:=Position(np,gen);
if pos=fail then
# not in the radical. There might be an induced automorphism of
# the factor which we'll have to undo

# find out what the images in the factor are by conjugating in the
# factor. This is intended to avoid image calculations
# (because we do not have `CanonicalPcgs')
pos:=Position(ng,gen);
if pos=fail then
# nonstandard generator, must use image instead
map:=ImagesRepresentative(ser.factorhom,gen);
map:=List(uff,x->x^map);
else
map:=List(uff,x->x^nf[pos]);
fi;

# construct the map reps->preimages and map the gens we want (to work
# in the right coordinates)
map:=GroupGeneralMappingByImagesNC(uf,G,map,l);
l:=List(uff,x->ImagesRepresentative(map,x));
fi;

fi;
#l:=List([1..Length(part)],x->LeftQuotient(part[x],l[x]));
#l:=List(l,x->ExponentsOfPcElement(famo,x)*One(f));

l:=List([1..Length(part)],
x->ExponentsOfPcElement(lfamo, LeftQuotient(part[x],l[x]))*One(f));

l:=Concatenation(l);
l:=SiftedVector(bound,l);
ConvertToVectorRep(l,Size(f));
MakeImmutable(l);
return l;
end;
sub:=myact(sub,One(np[1])); # standardize -- force compression

if Length(bound)>0 then
sel:=Filtered([1..Length(sub)],x->bound!.heads[x]=0);
else
sel:=[1..Length(sub)];
fi;
myact2:=RealizeAffineAction(Concatenation(ng,np),sub,sel,f,myact);

# stabilize in cohomology group
stb:=TwoLevelStabilizer(ng,nf,ng,np,np,factorhom,sub{sel},
f^Length(sel),myact2:
actrange:=[1..Length(np)-tailnum]);

Info(InfoFitFree,2,"orblen=",stb.orblen);

ng:=stb.gens;
nf:=stb.imgs;
np:=localinduce(stb.pcgs);

if Length(bound)>0 then
#nontrivial blocks -- now correct

myact:=function(l,gen)
local pos,map;

# make l the conjugated generator list
l:=List([1..Length(part)],
x->part[x]*PcElementByExponentsNC(famo,l{ranges[x]}));
l:=List([1..Length(part)],x->l[x]^gen);

# when acting with radical elements, it centralizes in the factor
pos:=Position(np,gen);
if pos=fail then
# not in the radical. There might be an induced automorphism of
# the factor which we'll have to undo

# find out what the images in the factor are by conjugating in the
# factor. This is intended to avoid image calculations
pos:=Position(ng,gen);
if pos=fail then

# must use image instead
map:=ImagesRepresentative(ser.factorhom,gen);
map:=List(uff,x->x^map);
else
map:=List(uff,x->x^nf[pos]);
fi;

# construct the map reps->preimages and map the gens we want (to work
# in the right coordinates)
map:=GroupGeneralMappingByImages(uf,G,map,l);
l:=List(uff,x->ImagesRepresentative(map,x));
fi;

l:=List([1..Length(part)],x->LeftQuotient(part[x],l[x]));
l:=List(l,x->ExponentsOfPcElement(famo,x)*One(f));
l:=Concatenation(l);
return l;
end;

# as corrections involve only pcgs parts, the images inthe
# radical factor are not affected.
ng:=List(ng,x->x/PcElementByExponents(famo,
SolutionMat(boundbas,myact(sub,x))));
np:=InducedPcgsByGeneratorsNC(pcgs,
Concatenation(
List(np{[1..Length(np)-tailnum]},x->x/PcElementByExponents(famo,
SolutionMat(boundbas,myact(sub,x)))),
np{[Length(np)-tailnum+1..Length(np)]}));
Assert(1,ForAll(ng,x->myact(sub,x)=sub));
Assert(1,ForAll(np,x->myact(sub,x)=sub));

fi;

o1:=p1;
until p1=Length(sumos);

fi;

od;

return SubgroupByFittingFreeData(G,ng,nf,np);
Expand Down

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