ENHANCE: Use better series, projective action on vectors.

Also ensure that automorphism group is automorphismgroup and fix comment. Two small fixes in ordering if there is trivial orbit on lines
gap-system · Sep 11, 2016 · 8358e70 · 8358e70
1 parent 9577f7e
commit 8358e70
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Showing 2 changed files with 41 additions and 13 deletions.
diff --git a/lib/autsr.gi b/lib/autsr.gi
@@ -1,6 +1,6 @@
 #############################################################################
 ##
-#W  auttf.gi                GAP library                      Alexander Hulpke
+#W  autsr.gi                GAP library                      Alexander Hulpke
 #W                                                           Soley Jonsdottir
 ##
 ##

diff --git a/lib/grppcaut.gi b/lib/grppcaut.gi
@@ -52,7 +52,10 @@ InducedActionFactor := function( mats, fac, low )
 end;
 
 VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
-  local PrunedBasis, f, lim, mo, dim, bas, newbas, dims, q, bp, ind, affine, acts, nv, stb, idx, idxh, incstb, incperm, notinc, free, freegens, stabp, stabm, dict, orb, tp, tm, p, img, sch, incpermstop, sz, sel, nbas, offset, i;
+  local PrunedBasis, f, lim, mo, dim, bas, newbas, dims, q, bp, ind, affine,
+  acts, nv, stb, idx, idxh, incstb, incperm, notinc, free, freegens, stabp,
+  stabm, dict, orb, tp, tm, p, img, sch, incpermstop, sz, sel, nbas, offset,
+  i,action,lineflag;
 
   PrunedBasis:=function(p)
   local b,q,i;
@@ -73,7 +76,7 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
   lim:=2;
   mo:=GModuleByMats(mats,f);
   dim:=mo.dimension;
-  bas:=PrunedBasis(MTX.BasesCompositionSeries(mo));
+  bas:=PrunedBasis(MTX.BasesCSSmallDimDown(mo));
 
   # form new basis of space
   newbas:=ShallowCopy(bas[2]);
@@ -92,6 +95,8 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
   vec:=vec*q;
 
   bp:=Length(dims)-1;
+  action:=false;
+  lineflag:=true;
   while bp>=1 do
     ind:=[dims[bp]+1..dims[bp+1]];
     q:=[dims[bp+1]+1..dim];
@@ -100,11 +105,25 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
       ind:=[dims[bp]+1..dim];
     else
       affine:=List(mats,i->vec{q}*(i{q}{ind}));
+      if ForAll(affine,IsZero) then
+	affine:=false;
+      fi;
     fi;
     Info(InfoMatOrb,2,"Acting dimension ",ind);
     acts:=List(mats,x->ImmutableMatrix(f,x{ind}{ind}));
     nv:=vec{ind};
-
+
+    if affine=false then
+      if lineflag and Size(mo.field)>2 then
+	action:=OnLines;
+	nv:=NormedRowVector(nv);
+      else
+	action:=OnRight;
+      fi;
+    else
+      action:=false;
+    fi;
+
     if (affine=false and ForAny([1..Length(acts)],i->nv*acts[i]<>nv))
     or (affine<>false and ForAny([1..Length(acts)],i->nv*acts[i]+affine[i]<>nv))
       then
@@ -120,15 +139,18 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
       stabp:=[];
       stabm:=[];
       dict:=NewDictionary(nv,true,f^Length(nv));
+
+      MakeImmutable(nv);
       orb:=[nv];
       AddDictionary(dict,nv,1);
       tp:=[One(group)];
       tm:=[One(free)];
       p:=1;
+
       while incstb and p<=Length(orb) do
 	for i in [1..Length(gens)] do
-	  if affine=false then
-	    img:=orb[p]*acts[i];
+	  if action<>false then
+	    img:=action(orb[p],acts[i]);
 	  else
 	    img:=orb[p]*acts[i]+affine[i];
 	  fi;
@@ -192,14 +214,14 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
 	p:=p+1;
       od;
       #sz:=Maximum(Difference(DivisorsInt(sz),[sz]));
-      if Length(orb)<=idxh then
+      if Length(orb)<=idxh and Length(orb)<idx then
 	Info(InfoWarning,1,"too small stabilizer");
 	p:=incpermstop;
 	sz:=Size(group)/Length(orb);
 	while Size(stb)<sz do
 	  for i in [1..Length(gens)] do
-	    if affine=false then
-	      img:=orb[p]*acts[i];
+	    if action<>false then
+	      img:=action(orb[p],acts[i]);
 	    else
 	      img:=orb[p]*acts[i]+affine[i];
 	    fi;
@@ -248,7 +270,7 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
       gens:=stabp;
       mats:=List(stabm,i->MappedWord(i,freegens,mats));
       shadows:=List(stabm,i->MappedWord(i,freegens,shadows));
-      if AssertionLevel()>0 then
+      if AssertionLevel()>0 and action=false or action=OnRight then
 	    ind:=[dims[bp]+1..dim];
 	    acts:=List(mats,x->ImmutableMatrix(f,x{ind}{ind}));
 	    nv:=vec{ind};
@@ -262,7 +284,7 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
 	acts:=List(mats,x->ImmutableMatrix(f,x{ind}{ind}));
 	mo:=GModuleByMats(acts,f);
 	#if not MTX.IsIrreducible(mo) then
-	nbas:=PrunedBasis(MTX.BasesCompositionSeries(mo));
+	nbas:=PrunedBasis(MTX.BasesCSSmallDimDown(mo));
 	offset:=Length(nbas)-bp;
         if offset>0 then
 	  #nbas:=nbas{[2..Length(nbas)]};
@@ -297,7 +319,12 @@ VectorStabilizerByFactors:=function(group,gens,mats,shadows,vec)
 
       fi;
     fi;
-    bp:=bp-1;
+    if action<>OnLines then
+      bp:=bp-1;
+      lineflag:=true;
+    else
+      lineflag:=false;
+    fi;
   od;
   Assert(1,ForAll(mats,i->vec*i=vec));
   return rec(stabilizer:=group,
@@ -873,7 +900,7 @@ InstallGlobalFunction(AutomorphismGroupSolvableGroup,function( G )
     local spec, weights, first, m, pcgsU, F, pcgsF, A, i, s, n, p, H, 
           pcgsH, pcgsN, N, epi, mats, M, autos, ocr, elms, e, list, imgs,
           auto, tmp, hom, gens, P, C, B, D, pcsA, rels, iso, xset,
-          gensA, new,as,somechar,someorb,asAutom,autactbase;
+          gensA, new,as,somechar,scharorb,asAutom,autactbase;
 
     asAutom:=function(sub,hom) return Image(hom,sub);end;
 
@@ -1054,6 +1081,7 @@ InstallGlobalFunction(AutomorphismGroupSolvableGroup,function( G )
 	B:=Filtered(B,x->ForAny(GeneratorsOfGroup(A),y->x<>asAutom(x,y)));
 	if Length(B)>0 then
 	  SortBy(B,Size);
+	  SetIsGroupOfAutomorphismsFiniteGroup(A,true);
 	  tmp:=Size(A);
 	  if autactbase<>fail then
 	    e:=List(autactbase,x->SubgroupNC(H,List(GeneratorsOfGroup(x),x->PcElementByExponents(pcgsH,ExponentsOfPcElement(spec,x){[1..Length(pcgsH)]}))));