FIX: Cleanup (Isomorphism)SimplifiedFpGroup

- Avoid code duplication between isomorphism and group method. - Resolve issue with calling MappedWord on empty generator set. - Added tests for simplification This fixes #2911
gap-system · Oct 25, 2018 · 10b7b42 · 10b7b42
1 parent d4d604a
commit 10b7b42
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Showing 3 changed files with 56 additions and 68 deletions.
diff --git a/lib/ghomfp.gi b/lib/ghomfp.gi
@@ -915,36 +915,48 @@ local H, pres,map,mapi,opt;
 
   # perform Tietze transformations.
   opt:=TzOptions(pres);
-  if ValueOption("expandLimit")<>fail then
-    opt.expandLimit:=ValueOption("expandLimit");
-  else
-    opt.expandLimit:=120; # do not grow too much.
-  fi;
-  if ValueOption("eliminationsLimit")<>fail then
-    opt.eliminationsLimit:=ValueOption("eliminationsLimit");
-  else
-    opt.eliminationsLimit:=20; # do not be too greedy
-  fi;
-  if ValueOption("lengthLimit")<>fail then
-    opt.lengthLimit:=ValueOption("lengthLimit");
-  else
-    opt.lengthLimit:=Int(3*pres!.tietze[TZ_TOTAL]); # not too big.
-  fi;
 
   if ValueOption("protected")<>fail then
     opt.expandLimit:=ValueOption("protected");
   fi;
 
   opt.printLevel:=InfoLevel(InfoFpGroup); 
   TzInitGeneratorImages(pres);
-  TzGoGo( pres );
+  if ValueOption("easy")=true then
+    # case of old `SimplifiedFpGroup`, use default strategy parameters
+    TzGo( pres );
+  else
+    # Somewhat tuned strategy parameters
+    if ValueOption("expandLimit")<>fail then
+      opt.expandLimit:=ValueOption("expandLimit");
+    else
+      opt.expandLimit:=120; # do not grow too much.
+    fi;
+    if ValueOption("eliminationsLimit")<>fail then
+      opt.eliminationsLimit:=ValueOption("eliminationsLimit");
+    else
+      opt.eliminationsLimit:=20; # do not be too greedy
+    fi;
+    if ValueOption("lengthLimit")<>fail then
+      opt.lengthLimit:=ValueOption("lengthLimit");
+    else
+      opt.lengthLimit:=Int(3*pres!.tietze[TZ_TOTAL]); # not too big.
+    fi;
+    TzGoGo( pres );
+  fi;
 
   # reconvert the Tietze presentation to a group presentation.
   H := FpGroupPresentation( pres );
-  map:=GroupHomomorphismByImagesNC(G,H,GeneratorsOfGroup(G),
-         List(TzImagesOldGens(pres),
-           i->MappedWord(i,GeneratorsOfPresentation(pres),
-                           GeneratorsOfGroup(H))));
+
+  if Length(GeneratorsOfGroup(H))>0 then
+    map:=List(TzImagesOldGens(pres),
+          i->MappedWord(i,GeneratorsOfPresentation(pres),
+                          GeneratorsOfGroup(H)));
+  else
+    map:=List(TzImagesOldGens(pres),y->One(H));
+  fi;
+
+  map:=GroupHomomorphismByImagesNC(G,H,GeneratorsOfGroup(G),map);
 
   mapi:=GroupHomomorphismByImagesNC(H,G,GeneratorsOfGroup(H),
          List(TzPreImagesNewGens(pres),
@@ -958,6 +970,18 @@ local H, pres,map,mapi,opt;
   return map;
 end );
 
+#############################################################################
+##
+#M  SimplifiedFpGroup( <FpGroup> ) . . . . . . . . .  simplify the FpGroup by
+#M                                                     Tietze transformations
+##
+##  `SimplifiedFpGroup'  returns a group  isomorphic to the given one  with a
+##  presentation which has been tried to simplify via Tietze transformations.
+##
+InstallGlobalFunction( SimplifiedFpGroup, function ( G )
+  return Range(IsomorphismSimplifiedFpGroup(G:easy));
+end);
+
 #############################################################################
 ##
 #M  NaturalHomomorphismByNormalSubgroup(<G>,<N>)

diff --git a/lib/tietze.gi b/lib/tietze.gi
@@ -1180,54 +1180,6 @@ InstallGlobalFunction( RemoveRelator, function ( T, n )
 end );
 
 
-#############################################################################
-##
-#M  SimplifiedFpGroup( <FpGroup> ) . . . . . . . . .  sinplify the FpGroup by
-#M                                                     Tietze transformations
-##
-##  `SimplifiedFpGroup'  returns a group  isomorphic to the given one  with a
-##  presentation which has been tried to simplify via Tietze transformations.
-##
-InstallGlobalFunction( SimplifiedFpGroup, function ( G )
-
-    local H, T,map,mapi;
-
-    # check the given argument to be a finitely presented group.
-    if not ( IsSubgroupFpGroup( G ) and IsGroupOfFamily( G ) ) then
-        Error( "argument must be a finitely presented group" );
-    fi;
-
-    # convert the given group presentation to a Tietze presentation.
-    T := PresentationFpGroup( G, 0 );
-
-    # perform Tietze transformations.
-    TzInitGeneratorImages(T);
-    TzGo( T );
-
-  # reconvert the Tietze presentation to a group presentation.
-  H := FpGroupPresentation( T );
-
-  # translate info
-  map:=GroupHomomorphismByImagesNC(G,H,GeneratorsOfGroup(G),
-        List(TzImagesOldGens(T),
-          i->MappedWord(i,GeneratorsOfPresentation(T),
-                          GeneratorsOfGroup(H))));
-
-  mapi:=GroupHomomorphismByImagesNC(H,G,GeneratorsOfGroup(H),
-        List(TzPreImagesNewGens(T),
-          i->MappedWord(i,OldGeneratorsOfPresentation(T),
-                          GeneratorsOfGroup(G))));
-
-  SetIsBijective(map,true);
-  SetInverseGeneralMapping(map,mapi);
-  SetInverseGeneralMapping(mapi,map);
-  ProcessEpimorphismToNewFpGroup(map);
-
-  # return the resulting group.
-  return H;
-end );
-
-
 #############################################################################
 ##
 #M  AbstractWordTietzeWord( <word>, <fgens> )  . . . .  convert a Tietze word

diff --git a/tst/testinstall/grpfp.tst b/tst/testinstall/grpfp.tst
@@ -101,6 +101,18 @@ gap> Print( Collected( List( l, x -> Index( c2, x ) ) ), "\n" );
 gap> Print( Collected( List( LowIndexSubgroupsFpGroup( g, s, 5 ),
 >                            x -> Index( c2, x ) ) ), "\n" );
 [ [ 12, 1 ], [ 24, 1 ], [ 48, 1 ] ]
+
+# Tietze simplifications
+gap> F:=FreeGroup("a");;
+gap> SimplifiedFpGroup(F/[GeneratorsOfGroup(F)[1]]);
+<fp group on the generators [  ]>
+gap> F:=FreeGroup("a","b","c");;
+gap> rels:=ParseRelators(F,"a2,b3,c4,abC");
+[ a^2, b^3, c^4, a*b*c^-1 ]
+gap> IsomorphismSimplifiedFpGroup(F/rels);
+[ a, b, c ] -> [ c*b^-1, b, c ]
+
+#
 gap> STOP_TEST( "grpfp.tst", 1);
 
 #############################################################################