changed PreImages... calls to PreImages...NC

gap/basic/convert.gi

@@ -167,7 +167,7 @@ function( G )
     iso  := IsomorphismPcGroup( G );
     F    := Image( iso );
     H    := PcGroupToPcpGroup( F );
-    gens := List( Pcgs(F), x -> PreImagesRepresentative( iso, x ) );
+    gens := List( Pcgs(F), x -> PreImagesRepresentativeNC( iso, x ) );
     hom  := GroupHomomorphismByImagesNC( G, H, gens, AsList(Pcp(H)) );
     SetIsBijective( hom, true );
     return hom;

gap/basic/grphoms.gi

@@ -287,7 +287,7 @@ end );
 ##
 #M  PreImages
 ##
-InstallMethod( PreImagesRepresentative,
+InstallMethod( PreImagesRepresentativeNC,
                "for ToPcpGHBI",
                FamRangeEqFamElm,
                [ IsToPcpGHBI, IsPcpElement ],
@@ -299,19 +299,16 @@ function( hom, elm )
     return MappedVector(e, hom!.igs_imgs_to_gens[2]);
 end );
 
-InstallMethod( PreImagesSet,
+InstallMethod( PreImagesSetNC,
                "for PcpGHBI",
                CollFamRangeEqFamElms,
                [ IsFromPcpGHBI and IsToPcpGHBI, IsPcpGroup ],
 function( hom, U )
-    local prei, kern;
-    prei := List( Igs(U), x -> PreImagesRepresentative(hom,x) );
+    local prei, gens, kern;
+    prei := List( Igs(U), x -> PreImagesRepresentativeNC(hom,x) );
     if fail in prei then
-    	TryNextMethod();
-		# Potential solution: Intersect U with ImagesSource(hom)
-		# and then compute the preimage of that.
-		#gens := GeneratorsOfGroup( Intersection( ImagesSource(hom), U ) );
-        #prei := List( gens, x -> PreImagesRepresentative(hom,x) );
+        gens := GeneratorsOfGroup( Intersection( ImagesSource(hom), U ) );
+        prei := List( gens, x -> PreImagesRepresentativeNC(hom,x) );
     fi;
     kern := Igs( KernelOfMultiplicativeGeneralMapping( hom ) );
     return SubgroupByIgs( Source(hom), kern, prei );

gap/cover/const/aut.gi

@@ -24,7 +24,7 @@ end );
 BindGlobal( "ReduceAuto", function( auto, C, isom, gens, imgs )
     local news;
     news := List(imgs, x -> Image(auto, x));
-    news := List(news, x -> PreImagesRepresentative(isom, x));
+    news := List(news, x -> PreImagesRepresentativeNC(isom, x));
     news := GroupHomomorphismByImagesNC( C, C, gens, news );
     SetIsBijective( news, true );
     return news;

gap/exam/generic.gi

@@ -183,7 +183,7 @@ InstallGlobalFunction( MaximalOrderByUnitsPcpGroup, function(f)
     G := Image(i);
 
     # get action of U on O
-    u := List( Pcp(G), x -> PreImagesRepresentative(i,x) );
+    u := List( Pcp(G), x -> PreImagesRepresentativeNC(i,x) );
     a := List( u, x -> List( O, y -> Coefficients(O, y*x)));
 
     # return split extension

gap/pcpgrp/centcon.gi

@@ -304,7 +304,7 @@ BindGlobal( "ConjugacyElementsBySeries", function( G, g, h, pcps )
             # extract results
             if IsBool(stb) then return false; fi;
             C := PreImage( nat, stb.stab );
-            k := k * PreImagesRepresentative( nat, stb.prei );
+            k := k * PreImagesRepresentativeNC( nat, stb.prei );
         fi;
     od;
 

gap/pcpgrp/general.gi

@@ -144,7 +144,7 @@ function( G )
     F := FrattiniSubgroup(K);
     f := List( GeneratorsOfGroup(F), x ->
          MappedVector( ExponentsOfPcElement(Pcgs(K), x), Igs(H) ) );
-    h := List( f, x -> PreImagesRepresentative(H!.bijection,x));
+    h := List( f, x -> PreImagesRepresentativeNC(H!.bijection,x));
     return Subgroup( G, h );
 end );
 

gap/pcpgrp/pcpattr.gi

@@ -56,6 +56,6 @@ function( G, p )
     fi;
     # HACK: Until we write a proper native method, use that for pc groups
     iso := IsomorphismPcGroup(G);
-    return PreImagesSet(iso, SylowSubgroup(Image(iso),p));
+    return PreImagesSetNC(iso, SylowSubgroup(Image(iso),p));
 end );
 

gap/pcpgrp/schur.gi

@@ -192,8 +192,8 @@ BindGlobal( "NonAbelianExteriorSquareEpimorphism", function( G )
     SetIsSurjective( epi, true );
 
     lambda := function( g, h )
-        return Comm( PreImagesRepresentative( lift, g ),
-                     PreImagesRepresentative( lift, h ) );
+        return Comm( PreImagesRepresentativeNC( lift, g ),
+                     PreImagesRepresentativeNC( lift, h ) );
     end;
 
     D!.epimorphism := epi;

gap/pcpgrp/tensor.gi

@@ -522,7 +522,7 @@ BindGlobal( "NonAbelianTensorSquareEpimorphism", function( G )
     GoG := Subgroup(U, c);
     gens := GeneratorsOfGroup( GoG );
     embed := Image( epi )!.embedding;
-    imgs := List( gens, g->PreImagesRepresentative( embed, Image( epi, g ) ) );
+    imgs := List( gens, g->PreImagesRepresentativeNC( embed, Image( epi, g ) ) );
 
     alpha := GroupHomomorphismByImagesNC( GoG, Source( embed ), gens, imgs );
     SetIsSurjective( alpha, true );

init.g

@@ -5,6 +5,17 @@
 #W                                                                   Max Horn
 ##
 
+#############################################################################
+##I introduce the NC versions of PreImages...
+if not IsBound( PreImagesNC ) then
+    BindGlobal( "PreImagesNC", PreImages );
+fi;
+if not IsBound( PreImagesSetNC ) then
+    BindGlobal( "PreImagesSetNC", PreImagesSet );
+fi;
+if not IsBound( PreImagesRepresentativeNC ) then
+    BindGlobal( "PreImagesRepresentativeNC", PreImagesRepresentative );
+fi;
 
 #############################################################################
 ##