Skip to content

NC versions of PreImages, PreImagesSet, PreImagesElm and PreImagesRepresentative - version 2 #6409

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
cdwensley wants to merge 7 commits into
base: master
Choose a base branch
from
+1,315 −495
Open

NC versions of PreImages, PreImagesSet, PreImagesElm and PreImagesRepresentative - version 2 #6409

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
7 commits
Select commit Hold shift + click to select a range
ed4c9a8
re-edited library files, adding NC
cdwensley May 20, 2026
1f6bbaf
added non-NC methods so that tests pass
cdwensley May 20, 2026
5b98560
adjust documentation in mapping.gd
cdwensley May 20, 2026
9fd6948
replace items deleted in error in alghom.gi
cdwensley May 21, 2026
8481a39
applied fix from stertooy
cdwensley May 21, 2026
a8e5012
minor correction
cdwensley May 21, 2026
168d917
another adjustment to bugfix test
cdwensley May 21, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion lib/algebra.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -3647,7 +3647,7 @@ InstallMethod( CentralIdempotentsOfAlgebra,

until k>Length(ideals);

id:= List( ids, e -> PreImagesRepresentative( hom, e ) );
id:= List( ids, e -> PreImagesRepresentativeNC( hom, e ) );

# Now we lift the idempotents to the big algebra `A'. The
# first idempotent is lifted as follows:
Expand Down
2 changes: 1 addition & 1 deletion lib/algfp.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -705,7 +705,7 @@ InstallHandlingByNiceBasis( "IsFpAlgebraElementsSpace", rec(
if hom = fail then
TryNextMethod();
fi;
return PreImagesRepresentative( hom, r );
return PreImagesRepresentativeNC( hom, r );
end ) );


Expand Down
43 changes: 39 additions & 4 deletions lib/alghom.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -576,16 +576,29 @@ InstallMethod( ImagesRepresentative,

#############################################################################
##
#M PreImagesRepresentativeNC( <map>, <elm> ) . . . . . for algebra g.m.b.i.
#M PreImagesRepresentative( <map>, <elm> ) . . . . . . for algebra g.m.b.i.
##
InstallMethod( PreImagesRepresentativeNC,
"for algebra g.m.b.i., and element",
FamRangeEqFamElm,
[ IsGeneralMapping and IsAlgebraGeneralMappingByImagesDefaultRep,
IsObject ],
function( map, elm )
return PreImagesRepresentativeNC(
AsLeftModuleGeneralMappingByImages(map), elm );
end );

InstallMethod( PreImagesRepresentative,
"for algebra g.m.b.i., and element",
FamRangeEqFamElm,
[ IsGeneralMapping and IsAlgebraGeneralMappingByImagesDefaultRep,
IsObject ],
function( map, elm )
return PreImagesRepresentative( AsLeftModuleGeneralMappingByImages(map),
elm );
if not ( elm in Range( map ) ) then
return fail;
fi;
return PreImagesRepresentativeNC( map, elm );
end );


Expand Down Expand Up @@ -902,6 +915,7 @@ InstallMethod( ImagesRepresentative,

#############################################################################
##
#M PreImagesRepresentativeNC( <ophom>, <mat> )
#M PreImagesRepresentative( <ophom>, <mat> )
##
BindGlobal( "PreImagesRepresentativeOperationAlgebraHomomorphism", function( ophom, mat )
Expand All @@ -915,12 +929,22 @@ BindGlobal( "PreImagesRepresentativeOperationAlgebraHomomorphism", function( oph
return mat;
end );

InstallMethod( PreImagesRepresentative,
InstallMethod( PreImagesRepresentativeNC,
"for an operation algebra homomorphism, and an element",
FamRangeEqFamElm,
[ IsOperationAlgebraHomomorphismDefaultRep, IsMatrix ],
PreImagesRepresentativeOperationAlgebraHomomorphism );

InstallMethod( PreImagesRepresentative,
"for an operation algebra homomorphism, and an element",
FamRangeEqFamElm,
[ IsOperationAlgebraHomomorphismDefaultRep, IsMatrix ],
function( ophom, mat )
if not ( mat in Range( ophom ) ) then
return fail;
fi;
return PreImagesRepresentativeOperationAlgebraHomomorphism( ophom, mat );
end );

#############################################################################
##
Expand Down Expand Up @@ -1076,14 +1100,25 @@ InstallMethod( ImagesRepresentative,

#############################################################################
##
#M PreImagesRepresentativeNC( <ophom>, <mat> )
#M PreImagesRepresentative( <ophom>, <mat> )
##
InstallMethod( PreImagesRepresentative,
InstallMethod( PreImagesRepresentativeNC,
"for an alg. hom. from f. p. algebra, and an element",
FamRangeEqFamElm,
[ IsAlgebraHomomorphismFromFpRep, IsMatrix ],
PreImagesRepresentativeOperationAlgebraHomomorphism );

InstallMethod( PreImagesRepresentative,
"for an alg. hom. from f. p. algebra, and an element",
FamRangeEqFamElm,
[ IsAlgebraHomomorphismFromFpRep, IsMatrix ],
function( ophom, mat );
if not ( mat in Range( ophom ) ) then
return fail;
fi;
return PreImagesRepresentativeOperationAlgebraHomomorphism( ophom, mat );
end );

#############################################################################
##
Expand Down
38 changes: 26 additions & 12 deletions lib/alglie.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -34,7 +34,7 @@ InstallMethod( LieUpperCentralSeries,
# under the natural homomorphism.
Add( S, C );
hom:= NaturalHomomorphismByIdeal( L, C );
C:= PreImages( hom, LieCentre( Range( hom ) ) );
C:= PreImagesNC( hom, LieCentre( Range( hom ) ) );
#T we would like to get ideals!
#T is it possible to teach the hom. that the preimage of an ideal is an ideal?

Expand Down Expand Up @@ -1706,7 +1706,7 @@ InstallMethod( LieSolvableRadical,
quo:= ImagesSource( hom );
r1:= LieSolvableRadical( quo );
B:= BasisVectors( Basis( r1 ) );
B:= List( B, x -> PreImagesRepresentative( hom, x ) );
B:= List( B, x -> PreImagesRepresentativeNC( hom, x ) );
Append( B, BasisVectors( Basis( n ) ) );

fi;
Expand Down Expand Up @@ -2092,7 +2092,7 @@ InstallMethod( DirectSumDecomposition,
SetRadicalOfAlgebra( Q, Subalgebra( Q, [ Zero( Q ) ] ) );

id:= List( CentralIdempotentsOfAlgebra( Q ),
x->PreImagesRepresentative(hom,x));
x->PreImagesRepresentativeNC(hom,x));

# Now we lift the idempotents to the big algebra `A'. The
# first idempotent is lifted as follows:
Expand Down Expand Up @@ -4017,9 +4017,10 @@ InstallMethod( ImagesRepresentative,

###########################################################################
##
#M PreImagesRepresentativeNC( f, x )
#M PreImagesRepresentative( f, x )
##
InstallMethod( PreImagesRepresentative,
InstallMethod( PreImagesRepresentativeNC,
"for Fp to SCA mapping, and element",
FamRangeEqFamElm,
[ IsFptoSCAMorphism, IsSCAlgebraObj ], 0,
Expand Down Expand Up @@ -4095,6 +4096,19 @@ InstallMethod( PreImagesRepresentative,

end);

InstallMethod( PreImagesRepresentative,
"for Fp to SCA mapping, and element",
FamRangeEqFamElm,
[ IsFptoSCAMorphism, IsSCAlgebraObj ], 0,

function( f, x )
if not ( x in Range( f ) ) then
return fail;
fi;
return PreImagesRepresentative( f, x );

end );

#############################################################################
##
#M Dimension( <FpL> )
Expand Down Expand Up @@ -5592,8 +5606,8 @@ InstallMethod( JenningsLieAlgebra,
T:= EmptySCTable( dim , Zero(F) , "antisymmetric" );
pimgs := [];
for i in [1..dim] do
a:= PreImagesRepresentative( Homs[pos[i]] ,
PreImagesRepresentative( hom_pcg[pos[i]], gens[i] ) );
a:= PreImagesRepresentativeNC( Homs[pos[i]] ,
PreImagesRepresentativeNC( hom_pcg[pos[i]], gens[i] ) );

# calculate the p-th power image of `a':

Expand All @@ -5610,8 +5624,8 @@ InstallMethod( JenningsLieAlgebra,
# Calculate the commutator [a,b], and map the result into
# the correct homogeneous component.

b:= PreImagesRepresentative( Homs[pos[j]],
PreImagesRepresentative( hom_pcg[pos[j]], gens[j] ));
b:= PreImagesRepresentativeNC( Homs[pos[j]],
PreImagesRepresentativeNC( hom_pcg[pos[j]], gens[j] ));
c:= Image( hom_pcg[pos[i] + pos[j]],
Image(Homs[pos[i] + pos[j]], a^-1*b^-1*a*b) );
e:= ExtRepOfObj(c);
Expand Down Expand Up @@ -5788,8 +5802,8 @@ InstallMethod( PCentralLieAlgebra,
T:= EmptySCTable( dim , Zero(F) , "antisymmetric" );
pimgs := [];
for i in [1..dim] do
a:= PreImagesRepresentative( Homs[pos[i]] ,
PreImagesRepresentative( hom_pcg[pos[i]], gens[i] ) );
a:= PreImagesRepresentativeNC( Homs[pos[i]] ,
PreImagesRepresentativeNC( hom_pcg[pos[i]], gens[i] ) );


# calculate the p-th power image of `a':
Expand All @@ -5807,8 +5821,8 @@ InstallMethod( PCentralLieAlgebra,
# Calculate the commutator [a,b], and map the result into
# the correct homogeneous component.

b:= PreImagesRepresentative( Homs[pos[j]],
PreImagesRepresentative( hom_pcg[pos[j]], gens[j] ));
b:= PreImagesRepresentativeNC( Homs[pos[j]],
PreImagesRepresentativeNC( hom_pcg[pos[j]], gens[j] ));
c:= Image( hom_pcg[pos[i] + pos[j]],
Image(Homs[pos[i] + pos[j]], a^-1*b^-1*a*b) );
e:= ExtRepOfObj(c);
Expand Down
8 changes: 4 additions & 4 deletions lib/algrep.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1212,24 +1212,24 @@ InstallMethod( NaturalHomomorphismBySubAlgebraModule,
if IsLeftAlgebraModuleElementCollection( V ) then
if IsRightAlgebraModuleElementCollection( V ) then
left_op:= function( x, v )
return ImagesRepresentative( f, x^PreImagesRepresentative( f, v ) );
return ImagesRepresentative( f, x^PreImagesRepresentativeNC( f, v ) );
end;
right_op:= function( v, x )
return ImagesRepresentative( f, PreImagesRepresentative( f, v )^x );
return ImagesRepresentative( f, PreImagesRepresentativeNC( f, v )^x );
end;
qmod:= BiAlgebraModule( LeftActingAlgebra( V ),
RightActingAlgebra( V ),
left_op, right_op, quot );
else
left_op:= function( x, v )
return ImagesRepresentative( f, x^PreImagesRepresentative( f, v ) );
return ImagesRepresentative( f, x^PreImagesRepresentativeNC( f, v ) );
end;
qmod:= LeftAlgebraModule( LeftActingAlgebra( V ),
left_op, quot);
fi;
else
right_op:= function( v, x )
return ImagesRepresentative( f, PreImagesRepresentative( f, v )^x );
return ImagesRepresentative( f, PreImagesRepresentativeNC( f, v )^x );
end;
qmod:= RightAlgebraModule( RightActingAlgebra( V ),
right_op, quot );
Expand Down
42 changes: 21 additions & 21 deletions lib/autsr.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -118,7 +118,7 @@ local C,M,p,all,gens,sub,q,hom,fp,rels,new,pre,i,free,cnt;
rels:=Filtered(RelatorsOfFpGroup(fp),x->ForAll(ExponentSums(x),x->x mod p=0));
rels:=List(rels,x->ElementOfFpGroup(FamilyObj(One(fp)),x));
new:=RestrictedMapping(nat,C)*hom;
pre:=List(rels,x->PreImagesRepresentative(new,x));
pre:=List(rels,x->PreImagesRepresentativeNC(new,x));
for i in [1..Length(rels)] do
if not pre[i] in sub then
Add(all,MappedWord(rels[i],
Expand All @@ -141,7 +141,7 @@ local ocr,fphom,fpg,free,len,dim,tmp,L0,R,rels,mat,r,RS,i,g,v,cnt;
fpg:=FreeGeneratorsOfFpGroup(Range(fphom));
ocr.factorpres:=[fpg,RelatorsOfFpGroup(Range(fphom))];
ocr.generators:=List(GeneratorsOfGroup(Range(fphom)),
i->PreImagesRepresentative(fphom,i));
i->PreImagesRepresentativeNC(fphom,i));
OCAddMatrices(ocr,ocr.generators);
OCAddRelations(ocr,ocr.generators);
OCAddSumMatrices(ocr,ocr.generators);
Expand Down Expand Up @@ -274,8 +274,8 @@ BindGlobal("AGSRAutomLift",function(ocr,nat,fhom,miso)
# allow to deduce corresponding module aut.
t:=ocr.trickrels;
phom:=IdentityMapping(ocr.moduleauts);
s:=List(t.gens,x->PreImagesRepresentative(nat,x));
l:=List(t.gens,x->PreImagesRepresentative(nat,ImagesRepresentative(fhom,x)));
s:=List(t.gens,x->PreImagesRepresentativeNC(nat,x));
l:=List(t.gens,x->PreImagesRepresentativeNC(nat,ImagesRepresentative(fhom,x)));
s:=List(t.rels,x->MappedWord(x,GeneratorsOfGroup(t.free),s));
l:=List(t.rels,x->MappedWord(x,GeneratorsOfGroup(t.free),l));

Expand All @@ -294,7 +294,7 @@ BindGlobal("AGSRAutomLift",function(ocr,nat,fhom,miso)
Size(Image(phom)));
fi;
for ep in enum do
e:=PreImagesRepresentative(phom,ep);
e:=PreImagesRepresentativeNC(phom,ep);
psim:=e*miso;
psim:=psim^-1;
w:=-List(v,i->i*psim);
Expand Down Expand Up @@ -486,7 +486,7 @@ local S,c,hom,q,a,b,i,t,have,ups,new,u,good,abort,clim,worked,pp,

cnt:=0;
for b in t do
new:=PreImagesRepresentative(hom,b);
new:=PreImagesRepresentativeNC(hom,b);
if (pp=false or new^pp in S) and locond(new) then
S:=ClosureGroup(S,new);
have:=true;
Expand Down Expand Up @@ -1028,7 +1028,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
b:=MTX.BasisRadical(mo);
fratsim:=Length(b)=0;
if not fratsim then
b:=List(b,x->PreImagesRepresentative(hom,PcElementByExponents(MPcgs,x)));
b:=List(b,x->PreImagesRepresentativeNC(hom,PcElementByExponents(MPcgs,x)));
for j in b do
N:=ClosureSubgroup(N,b);
od;
Expand Down Expand Up @@ -1129,8 +1129,8 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
if perm in Aperm then
return true;
fi;
aut:=PreImagesRepresentative(AQiso,perm);
newgens:=List(gens,x->PreImagesRepresentative(comiso,
aut:=PreImagesRepresentativeNC(AQiso,perm);
newgens:=List(gens,x->PreImagesRepresentativeNC(comiso,
ImagesRepresentative(aut,ImagesRepresentative(comiso,x))));

mo2:=GModuleByMats(LinearActionLayer(newgens,MPcgs),mo.field);
Expand Down Expand Up @@ -1163,9 +1163,9 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
if perm in Aperm then
return true;
fi;
aut:=PreImagesRepresentative(AQiso,perm);
aut:=PreImagesRepresentativeNC(AQiso,perm);
newgens:=List(GeneratorsOfGroup(Q),
x->PreImagesRepresentative(q,Image(aut,ImagesRepresentative(q,x))));
x->PreImagesRepresentativeNC(q,Image(aut,ImagesRepresentative(q,x))));
mo2:=GModuleByMats(LinearActionLayer(newgens,MPcgs),mo.field);
return MTX.IsomorphismModules(mo,mo2)<>fail;
end;
Expand All @@ -1175,9 +1175,9 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
if perm in Aperm then
return true;
fi;
aut:=PreImagesRepresentative(AQiso,perm);
aut:=PreImagesRepresentativeNC(AQiso,perm);
newgens:=List(GeneratorsOfGroup(Q),
x->PreImagesRepresentative(q,Image(aut,ImagesRepresentative(q,x))));
x->PreImagesRepresentativeNC(q,Image(aut,ImagesRepresentative(q,x))));
mo2:=GModuleByMats(LinearActionLayer(newgens,MPcgs),mo.field);
iso:=MTX.IsomorphismModules(mo,mo2);
if iso=fail then
Expand Down Expand Up @@ -1234,12 +1234,12 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
# stabilize class
k:=SmallGeneratingSet(sub);
ac:=OrbitStabilizerAlgorithm(sub,false,false,
k,List(k,x->PreImagesRepresentative(AQiso,x)),
k,List(k,x->PreImagesRepresentativeNC(AQiso,x)),
rec(pnt:=j,
act:=
function(set,phi)
#local phi;
#phi:=PreImagesRepresentative(AQiso,perm);
#phi:=PreImagesRepresentativeNC(AQiso,perm);
return Set(List(set,x->Image(phi,x)));
end,
onlystab:=true));
Expand Down Expand Up @@ -1367,7 +1367,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
GeneratorsOfGroup(rf),
List(GeneratorsOfGroup(rf),
y->ImagesRepresentative(hom,ImagesRepresentative(j,
PreImagesRepresentative(hom,y)))));
PreImagesRepresentativeNC(hom,y)))));
Assert(2,IsBijective(k));
Add(ind,k);
od;
Expand All @@ -1390,7 +1390,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
proj:=GroupHomomorphismByImagesNC(AQP,Image(resperm),
B[2],List(GeneratorsOfGroup(res),x->ImagesRepresentative(resperm,x)));
C:=PreImage(proj,Image(resperm,ind));
C:=List(SmallGeneratingSet(C),x->PreImagesRepresentative(AQiso,x));
C:=List(SmallGeneratingSet(C),x->PreImagesRepresentativeNC(AQiso,x));
AQ:=Group(C);
SetIsFinite(AQ,true);
SetIsGroupOfAutomorphismsFiniteGroup(AQ,true);
Expand All @@ -1416,7 +1416,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
C:=MappingGeneratorsImages(AQiso);
if C[2]<>GeneratorsOfGroup(AQP) then
C:=[List(GeneratorsOfGroup(AQP),
x->PreImagesRepresentative(AQiso,x)),
x->PreImagesRepresentativeNC(AQiso,x)),
GeneratorsOfGroup(AQP)];
fi;
for j in u do
Expand Down Expand Up @@ -1450,7 +1450,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
substb:=SmallGeneratingSet(substb);
AQP:=Group(substb);
SetSize(AQP,B);
C:=[List(substb,x->PreImagesRepresentative(AQiso,x)),substb];
C:=[List(substb,x->PreImagesRepresentativeNC(AQiso,x)),substb];
fi;

od;
Expand Down Expand Up @@ -1883,7 +1883,7 @@ local d,a,map,cG,nG,nH,i,j,u,v,asAutomorphism,K,L,conj,e1,e2,
else
gens:=SmallGeneratingSet(api);
fi;
pre:=List(gens,x->PreImagesRepresentative(iso,x));
pre:=List(gens,x->PreImagesRepresentativeNC(iso,x));
map:=RepresentativeAction(SubgroupNC(a,pre),u,v,asAutomorphism);
if map=fail then
return fail;
Expand All @@ -1904,6 +1904,6 @@ local d,a,map,cG,nG,nH,i,j,u,v,asAutomorphism,K,L,conj,e1,e2,
fi;

return GroupHomomorphismByImagesNC(G,H,GeneratorsOfGroup(G),
List(GeneratorsOfGroup(G),x->PreImagesRepresentative(e2,
List(GeneratorsOfGroup(G),x->PreImagesRepresentativeNC(e2,
Image(conj,Image(e1,x)))));
end);
Loading
Loading