ENHANCE: Better treatment of solvable case when computing compatible …

…pairs.
gap-system · Dec 1, 2016 · a32d466 · a32d466
1 parent 9990986
commit a32d466
Showing 1 changed file with 65 additions and 43 deletions.
diff --git a/lib/grppcext.gi b/lib/grppcext.gi
@@ -517,7 +517,8 @@ IsCocycle := function( coc, cohom )
 end;
 
 InstallGlobalFunction(EXPermutationActionPairs,function(D)
-local ag, p1iso, agp, p2iso, DP, p1, p2, gens, genimgs, triso,s,i,u,opt;
+local ag, p1iso, agp, p2iso, DP, p1, p2, gens, genimgs, triso,s,i,u,opt,
+ gp2,pc1,pc2;
  if HasDirectProductInfo(D) then
  ag:=DirectProductInfo(D).groups[1];
  s:=Size(ag);
@@ -530,55 +531,76 @@ local ag, p1iso, agp, p2iso, DP, p1, p2, gens, genimgs, triso,s,i,u,opt;
  IsGroupOfAutomorphismsFiniteGroup(ag);
  p1iso:=IsomorphismPermGroup(ag);
  agp:=Image(p1iso);
- opt:=rec(limit:=s,random:=1);
- if HasBaseOfGroup(agp) then
- opt.knownBase:=BaseOfGroup(agp);
- fi;
- #p1iso:=p1iso*SmallerDegreePermutationRepresentation(agp);
- EraseNaturalHomomorphismsPool(agp);
- if s>1 then
- repeat
- u:=Group(());
- gens:=[];
- for i in GeneratorsOfGroup(agp) do
- if Size(u)<s and not i in u then
- Add(gens,i);
- u:=DoClosurePrmGp(u,[i],opt);
- fi;
- od;
- if HasBaseOfGroup(agp) then
- SetBaseOfGroup(u,BaseOfGroup(agp));
- fi;
- #Print("rep ",Size(u)," ",s,"\n");
- until Size(u)=s;
- agp:=u;
- else
- gens:=GeneratorsOfGroup(agp);
- fi;
- Info( InfoMatOrb, 1, "found ",Length(gens)," generators");
 
+ # are both groups solvable?
  p2iso:=IsomorphismPermGroup(DirectProductInfo(D).groups[2]);
- DP:=DirectProduct(agp,ImagesSource(p2iso));
- SetIsSolvableGroup(DP,IsSolvableGroup(agp)
- and IsSolvableGroup(ImagesSource(p2iso)));
- p1:=Projection(DP,1);
- p2:=Projection(DP,2);
- if IsSolvableGroup(DP) then
+ gp2:=ImagesSource(p2iso);
+ if IsSolvableGroup(gp2) and IsSolvableGroup(agp) then
+ # both groups are solvable -- go solvable
+ pc1:=IsomorphismPcGroup(agp);
+ pc2:=IsomorphismPcGroup(gp2);
+ DP:=DirectProduct(ImagesSource(pc1),ImagesSource(pc2));
+ p1:=Projection(DP,1);
+ p2:=Projection(DP,2);
  gens:=Pcgs(DP);
- else
- gens:=GeneratorsOfGroup(DP);
- fi;
- Unbind(ag);Unbind(agp);
 
- genimgs:=List(gens,
- i->ImagesRepresentative(Embedding(D,1),
- PreImagesRepresentative(p1iso,ImagesRepresentative(p1,i)))
- *ImagesRepresentative(Embedding(D,2),
- PreImagesRepresentative(p2iso,ImagesRepresentative(p2,i))) );
+ genimgs:=List(gens,
+ i->ImagesRepresentative(Embedding(D,1),
+ PreImagesRepresentative(p1iso,
+ PreImagesRepresentative(pc1,ImagesRepresentative(p1,i))))
+ *ImagesRepresentative(Embedding(D,2),
+ PreImagesRepresentative(p2iso,
+ PreImagesRepresentative(pc2,ImagesRepresentative(p2,i)))) );
 
+ else
+ opt:=rec(limit:=s,random:=1);
+ if HasBaseOfGroup(agp) then
+ opt.knownBase:=BaseOfGroup(agp);
+ fi;
+ #p1iso:=p1iso*SmallerDegreePermutationRepresentation(agp);
+ EraseNaturalHomomorphismsPool(agp);
+ if s>1 then
+ repeat
+ u:=Group(());
+ gens:=[];
+ for i in GeneratorsOfGroup(agp) do
+ if Size(u)<s and not i in u then
+ Add(gens,i);
+ u:=DoClosurePrmGp(u,[i],opt);
+ fi;
+ od;
+ if HasBaseOfGroup(agp) then
+ SetBaseOfGroup(u,BaseOfGroup(agp));
+ fi;
+ #Print("rep ",Size(u)," ",s,"\n");
+ until Size(u)=s;
+ agp:=u;
+ else
+ gens:=GeneratorsOfGroup(agp);
+ fi;
+ Info( InfoMatOrb, 1, "found ",Length(gens)," generators");
+
+ DP:=DirectProduct(agp,gp2);
+# SetIsSolvableGroup(DP,IsSolvableGroup(agp)
+# and IsSolvableGroup(ImagesSource(p2iso)));
+ p1:=Projection(DP,1);
+ p2:=Projection(DP,2);
+# if IsSolvableGroup(DP) then
+# gens:=Pcgs(DP);
+# else
+ gens:=GeneratorsOfGroup(DP);
+# fi;
+ Unbind(ag);Unbind(agp);
+
+ genimgs:=List(gens,
+ i->ImagesRepresentative(Embedding(D,1),
+ PreImagesRepresentative(p1iso,ImagesRepresentative(p1,i)))
+ *ImagesRepresentative(Embedding(D,2),
+ PreImagesRepresentative(p2iso,ImagesRepresentative(p2,i))) );
+
+ fi;
  triso:=GroupHomomorphismByImagesNC(DP,D,gens,genimgs);
  SetIsBijective(triso,true);
- D:=DP;
  return rec(pairgens:=genimgs,
  permgens:=gens,
  isomorphism:=triso,