Merge pull request #843 from hulpke/newmtc

New Implementation of MTC

lib/ghomfp.gi

@@ -197,30 +197,29 @@ end);
 InstallMethod(CosetTableFpHom,"for fp homomorphisms",true,
   [ IsFromFpGroupGeneralMappingByImages and IsGroupGeneralMappingByImages],0,
 function(hom)
-local u,aug,hgu,mapi;
+local u,aug,hgu,mapi,w;
   # source group with suitable generators
   u:=Source(hom);
   aug:=false;
   mapi:=MappingGeneratorsImages(hom);
   hgu:=List(mapi[1],UnderlyingElement);
-  # try to re-use an existing augmented coset table:
-  aug:=AugmentedCosetTableInWholeGroup(u,mapi[1]);
-  if not IsSubset(hgu,aug.primaryGeneratorWords) then
-    # we don't know what to do with the extra primary words, so enforce MTC
-    # version
-    aug:=AugmentedCosetTableMtcInWholeGroup(
-           SubgroupNC(FamilyObj(u)!.wholeGroup,mapi[1]));
-  fi;
-  # as we add homomorphism specific entries, lets be safe and copy.
-  aug:=CopiedAugmentedCosetTable(aug);
+
+  # construct augmented coset table
+  w:=FamilyObj(mapi[1])!.wholeGroup;
+  aug:=NEWTC_CosetEnumerator(FreeGeneratorsOfFpGroup(w),
+	RelatorsOfFpGroup(w),
+	hgu,
+	true);
 
   aug.homgens:=mapi[1];
   aug.homgenims:=mapi[2];
 
   # assign the primary generator images
-  aug.primaryImages:=List(aug.primaryGeneratorWords,
+  aug.primaryImages:=List(aug.subgens,
                           i->aug.homgenims[Position(hgu,i)]);
 
+  # TODO: possibly re-use an existing augmented table stored already
+
   TrySecondaryImages(aug);
 
   return aug;
@@ -235,7 +234,7 @@ InstallMethod( ImagesRepresentative, "map from (sub)fp group, rewrite",
   [ IsFromFpGroupGeneralMappingByImages and IsGroupGeneralMappingByImages,
     IsMultiplicativeElementWithInverse ], 0,
 function( hom, word )
-local aug,si,r,i,j,tt,ct,cft,c,f,g,ind,e;
+local aug,si,r,i,j,tt,ct,cft,c,f,g,ind,e,eval;
   # get a coset table
   aug:=CosetTableFpHom(hom);
   r:=One(Range(hom));
@@ -247,6 +246,36 @@ local aug,si,r,i,j,tt,ct,cft,c,f,g,ind,e;
   else
     Error("no decoding possible");
   fi;
+  word:=UnderlyingElement(word);
+
+  if IsBound(aug.isNewAugmentedTable) then
+
+    eval:=function(i)
+    local w,j;
+      w:=One(si[1]);
+      if not IsBound(si[i]) then
+	for j in aug.secondary[i] do
+	  if j<0 then
+	    w:=w/eval(-j);
+	  else
+	    w:=w*eval(j);
+	  fi;
+	od;
+	si[i]:=w;
+      fi;
+      return si[i];
+    end;
+
+    for i in NEWTC_Rewrite(aug,1,LetterRepAssocWord(word)) do
+      if i<0 then r:=r/eval(-i);
+      else r:=r*eval(i);
+      fi;
+    od;
+    return r;
+
+  fi;
+
+  # old version
 
   # instead of calling `RewriteWord', we rewrite locally in the images.
   # this ought to be a bit faster and better on memory.
@@ -260,7 +289,6 @@ local aug,si,r,i,j,tt,ct,cft,c,f,g,ind,e;
   fi;
   tt:=aug.transtab;
 
-  word:=UnderlyingElement(word);
   c:=1; # current coset
 
   if not IsLetterAssocWordRep(word) then
@@ -818,41 +846,38 @@ InstallMethod(IsomorphismFpGroupByGeneratorsNC,"subgroups of fp group",
   [IsSubgroupFpGroup,IsList and IsMultiplicativeElementWithInverseCollection,
    IsString],0,
 function(u,gens,nam)
-local aug,w,p,pres,f,fam;
+local aug,w,p,pres,f,fam,G;
   if HasIsWholeFamily(u) and IsWholeFamily(u) and
     IsIdenticalObj(gens,GeneratorsOfGroup(u)) then
       return IdentityMapping(u);
   fi;
   # get an augmented coset table from the group. It must be compatible with
   # `gens', so we must always use MTC.
-  if HasGeneratorsOfGroup(u) and IsIdenticalObj(GeneratorsOfGroup(u),gens) then
-    aug:=AugmentedCosetTableMtcInWholeGroup(u);
-  else
-    w:=FamilyObj(u)!.wholeGroup;
-    aug:=AugmentedCosetTableMtc(w,SubgroupNC(w,gens),2,"%");
-    # do not store the generators for the subgroup (the user could do this
-    # himself if he wanted), the danger of consequential errors due to a
-    # wrong <gens> list is too high.
-  fi;
-
-  # force computation of words for the secondary generators
-  SecondaryGeneratorWordsAugmentedCosetTable(aug);
-
-  # create a tietze object to reduce the presentation a bit
-  if not IsBound(aug.subgroupRelators) then
-    aug.subgroupRelators := RewriteSubgroupRelators( aug, aug.groupRelators);
+
+  # use new MTC
+  w:=FamilyObj(u)!.wholeGroup;
+  aug:=NEWTC_CosetEnumerator(FreeGeneratorsOfFpGroup(w),
+	RelatorsOfFpGroup(w),
+	List(GeneratorsOfGroup(u),UnderlyingElement),
+	true);
+
+  pres:=NEWTC_PresentationMTC(aug,1,"%");
+  if Length(GeneratorsOfPresentation(pres))>Length(gens) then
+    aug:=NEWTC_CosetEnumerator(FreeGeneratorsOfFpGroup(w),
+	  RelatorsOfFpGroup(w),
+	  List(GeneratorsOfGroup(u),UnderlyingElement),
+	  true,false);
+
+    pres:=NEWTC_PresentationMTC(aug,0,"%");
   fi;
-  aug:=CopiedAugmentedCosetTable(aug);
-  pres := PresentationAugmentedCosetTable( aug,nam,0,true );
-  TzOptions(pres).printLevel:=InfoLevel(InfoFpGroup);
-  DecodeTree(pres);
+  Assert(0,Length(GeneratorsOfPresentation(pres))=Length(gens));
 
   # new free group
   f:=FpGroupPresentation(pres);
   aug.homgens:=gens;
   aug.homgenims:=GeneratorsOfGroup(f);
   aug.primaryImages:=GeneratorsOfGroup(f);
-  SecondaryImagesAugmentedCosetTable(aug);
+  aug.secondaryImages:=ShallowCopy(GeneratorsOfGroup(f));
 
   f:=GroupHomomorphismByImagesNC(u,f,gens,GeneratorsOfGroup(f):noassert);
 

lib/grpfp.gi

@@ -1340,12 +1340,6 @@ function( H )
   return AugmentedCosetTableRrsInWholeGroup(H).cosetTable;
 end );
 
-InstallMethod( CosetTableInWholeGroup,"from augmented table Mtc",
-    true, [ IsSubgroupFpGroup and HasAugmentedCosetTableMtcInWholeGroup], 0,
-function( H )
-  return AugmentedCosetTableMtcInWholeGroup(H).cosetTable;
-end );
-
 InstallMethod(CosetTableInWholeGroup,"ByQuoSubRep",true,
   [IsSubgroupOfWholeGroupByQuotientRep],0,
 function(G)
@@ -3768,6 +3762,7 @@ local   fgens,      # generators of the free group
 	H,          # subgroup of <G>
 	gen,	    # generator of cyclic subgroup
 	max,        # maximal coset table length required
+	e,
 	T;          # coset table of <G> by <H>
 
   fgens := FreeGeneratorsOfFpGroup( G );
@@ -3793,11 +3788,14 @@ local   fgens,      # generators of the free group
     gen:=gen[1];
 
     H := Subgroup(G,[gen]);
-    T := AugmentedCosetTableMtc( G, H, -1, "_x":max:=max );
-    if T.exponent = infinity then
+    T := NEWTC_CosetEnumerator( FreeGeneratorsOfFpGroup(G),
+	  RelatorsOfFpGroup(G),GeneratorsOfGroup(H),true,false:
+	    cyclic:=true,limit:=1+max );
+    e:=NEWTC_CyclicSubgroupOrder(T);
+    if e=0 then
       return infinity;
     else
-      return T.index * T.exponent;
+      return T.index * e;
     fi;
   fi;
 
@@ -3839,7 +3837,8 @@ end);
 ##
 InstallGlobalFunction(IsomorphismPermGroupOrFailFpGroup, 
 function(arg)
-  local mappow, G, max, p, gens, rels, comb, i, l, m, H, t, gen, silent, sz, t1, bad, trial, b, bs, r, nl, o, u, rp, eo, rpo, e, e2, sc, j, z;
+local mappow, G, max, p, gens, rels, comb, i, l, m, H, t, gen, silent, sz,
+  t1, bad, trial, b, bs, r, nl, o, u, rp, eo, rpo, e, e2, sc, j, z;
 
   mappow:=function(n,g,e)
     while e>0 do
@@ -3904,23 +3903,25 @@ function(arg)
     if t<>fail then
       gen:=t[1];
       Unbind(t);
-      t:=AugmentedCosetTableMtc(G,Subgroup(G,[gen]),1,"@":
-          silent:=true,max:=max );
+      t := NEWTC_CosetEnumerator( FreeGeneratorsOfFpGroup(G),
+	    RelatorsOfFpGroup(G),[gen],true,false:
+	      cyclic:=true,limit:=1+max,quiet:=true );
     fi;
     if t=fail then
       # we cannot get the size within the permitted limits -- give up
       return fail;
     fi;
-    if t.exponent=infinity then
+    e:=NEWTC_CyclicSubgroupOrder(t);
+    if e=0 then
       SetSize(G,infinity);
       return fail;
     fi;
-    sz:=t.exponent*IndexCosetTab(t.cosetTable);
+    sz:=e*t.index;
     SetSize(G,sz);
     Info(InfoFpGroup,1,"found size ",sz);
-    if sz>200*IndexCosetTab(t.cosetTable) then
+    if sz>200*t.index then
       # try the corresponding perm rep
-      p:=t.cosetTable{[1,3..Length(t.cosetTable)-1]};
+      p:=t.ct{t.offset+[1..Length(FreeGeneratorsOfFpGroup(G))]};
       Unbind(t);
 
       for j in [1..Length(p)] do

lib/sgpres.gd

@@ -1040,6 +1040,10 @@ DeclareGlobalFunction("SecondaryGeneratorWordsAugmentedCosetTable");
 ##
 DeclareGlobalFunction("CopiedAugmentedCosetTable");
 
+# forward declaration of the new mtc worker and presentation builder fct.
+DeclareGlobalFunction("NEWTC_CosetEnumerator");
+DeclareGlobalFunction("NEWTC_PresentationMTC");
+DeclareGlobalFunction("NEWTC_CyclicSubgroupOrder");
 
 #############################################################################
 ##