renaming PreImagesRepresentative as NC version

gap/cryst.gi

@@ -502,7 +502,7 @@ function( m, S )
         return false;
     fi;
 
-    mm := PreImagesRepresentative( PointHomomorphism( S ), mm );
+    mm := PreImagesRepresentativeNC( PointHomomorphism( S ), mm );
     if IsAffineCrystGroupOnRight( S ) then
         if not IsAffineMatrixOnRight( m ) then
             return false;

gap/cryst2.gi

@@ -303,7 +303,7 @@ function( S, rep )
     T := ReducedLatticeBasis( TranslationBasis( S )*m );
 
     mm  := CanonicalRightCosetElement( P, m );
-    res := PreImagesRepresentative( PointHomomorphism( S ), mm*m^-1 ) * rep;
+    res := PreImagesRepresentativeNC( PointHomomorphism( S ), mm*m^-1 ) * rep;
     res := MutableCopyMat( res );
     res[d+1]{[1..d]} := VectorModL( res[d+1]{[1..d]}, T );
     return res;
@@ -322,7 +322,7 @@ function( S, rep )
     T := ReducedLatticeBasis( TranslationBasis( S )*m );
 
     mm  := CanonicalRightCosetElement( P, m );
-    res := PreImagesRepresentative( PointHomomorphism( S ), mm*m^-1 ) * rep;
+    res := PreImagesRepresentativeNC( PointHomomorphism( S ), mm*m^-1 ) * rep;
     res := MutableCopyMat( res );
     res{[1..d]}[d+1] := VectorModL( res{[1..d]}[d+1], T );
     return res;
@@ -352,9 +352,9 @@ function( G1, G2 )
     L  := UnionModule( T1, T2 );
 
     gen  := GeneratorsOfGroup( P );
-    gen1 := List( gen, x -> PreImagesRepresentative( 
+    gen1 := List( gen, x -> PreImagesRepresentativeNC( 
                                    PointHomomorphism( G1 ), x) );
-    gen2 := List( gen, x -> PreImagesRepresentative( 
+    gen2 := List( gen, x -> PreImagesRepresentativeNC( 
                                    PointHomomorphism( G2 ), x)^-1 );
 
     orb := [ MutableMatrix( One( G1 ) ) ];
@@ -384,10 +384,10 @@ function( G1, G2 )
     # determine the lift of stb
     new := [];
     for g in GeneratorsOfGroup( stb ) do
-        g1 := PreImagesRepresentative( PointHomomorphism( G1 ), g );
+        g1 := PreImagesRepresentativeNC( PointHomomorphism( G1 ), g );
         g1 := AffMatMutableTrans( g1 );
         if Length(T1) > 0 then
-            g2 := PreImagesRepresentative( PointHomomorphism( G2 ), g );
+            g2 := PreImagesRepresentativeNC( PointHomomorphism( G2 ), g );
             t1 := g1[d+1]{[1..d]};
             t2 := g2[d+1]{[1..d]};
             s  := IntSolutionMat( Concatenation( T1, -T2 ), t2-t1 ); 
@@ -538,7 +538,7 @@ CentralizerAffineCrystGroup := function ( G, obj )
     fi; 
 
     gen := List( GeneratorsOfGroup( P ), 
-                 x -> PreImagesRepresentative( PointHomomorphism( G ), x ) );
+                 x -> PreImagesRepresentativeNC( PointHomomorphism( G ), x ) );
 
     # if G is finite
     if e = 0 then
@@ -782,7 +782,7 @@ function( S )
     T := TranslationBasis( S );
     N := NormalizerPointGroupInGLnZ( P ); 
     Pgens := GeneratorsOfGroup( P );
-    Sgens := List( Pgens, x -> PreImagesRepresentative( H, x ) );
+    Sgens := List( Pgens, x -> PreImagesRepresentativeNC( H, x ) );
 
     # we work in a standard representation
     if not IsStandardAffineCrystGroup( S ) then
@@ -805,7 +805,7 @@ function( S )
         if m = mm then
             res := [ data[1], List( data[2]*g, FractionModOne ) ];
         else
-           m := AffMatMutableTrans( PreImagesRepresentative( hom, mm ) );
+           m := AffMatMutableTrans( PreImagesRepresentativeNC( hom, mm ) );
            m[d+1]{[1..d]} := List( m[d+1]{[1..d]}, FractionModOne );
            res := [ m, List( data[2]*g, FractionModOne ) ];
         fi;

gap/equiv.gi

@@ -33,11 +33,11 @@ ConjugatorSpaceGroupsStdSamePG := function( S1, S2 )
     od;
 
     gen1 := List( GeneratorsOfGroup( P ), 
-            x -> PreImagesRepresentative( PointHomomorphism( S1 ), x ) );
+            x -> PreImagesRepresentativeNC( PointHomomorphism( S1 ), x ) );
     t1   := Concatenation( List( gen1, x -> x[d+1]{[1..d]} ) );
 
     gen2 := List( GeneratorsOfGroup( P ), 
-             x -> PreImagesRepresentative( PointHomomorphism( S2 ), x ) );
+             x -> PreImagesRepresentativeNC( PointHomomorphism( S2 ), x ) );
     t2   := Concatenation( List( gen2, x -> x[d+1]{[1..d]} ) );
 
     sol  := SolveInhomEquationsModZ( M, t1-t2, true )[1];
@@ -59,7 +59,7 @@ ConjugatorSpaceGroupsStdSamePG := function( S1, S2 )
                 Add( orb, img );
                 Add( rep, nn  );
                 gen1 := List( GeneratorsOfGroup( P ),
-                  x -> PreImagesRepresentative( PointHomomorphism( img ), x ) );
+                  x -> PreImagesRepresentativeNC( PointHomomorphism( img ), x ) );
                 n1 := nn{[1..d]}{[1..d]};
                 t1 := Concatenation( List( gen1, x -> x[d+1]{[1..d]}));
                 sol  := SolveInhomEquationsModZ( M, t1-t2, true )[1];

gap/fpgrp.gi

@@ -30,7 +30,7 @@ function ( P )
         F    := Image( IsomorphismFpGroupByGenerators( N, gens ) );
     fi;
 
-    gensP := List( gens, x -> PreImagesRepresentative( mono, x ) );
+    gensP := List( gens, x -> PreImagesRepresentativeNC( mono, x ) );
     gensS := List( gens, x -> ImagesRepresentative( NiceToCryst( P ), x ) );
     gensF := GeneratorsOfGroup( F );
 

gap/hom.gi

@@ -22,9 +22,9 @@ end );
 
 #############################################################################
 ##
-#M  PreImagesRepresentative( <hom>, <elm> ) . . . . . . for PointHomomorphism
+#M  PreImagesRepresentativeNC( <hom>, <elm> ) . . . . . for PointHomomorphism
 ##
-InstallMethod( PreImagesRepresentative, FamRangeEqFamElm,
+InstallMethod( PreImagesRepresentativeNC, FamRangeEqFamElm,
         [ IsGroupGeneralMappingByImages and IsPointHomomorphism,
           IsMultiplicativeElementWithInverse ], 0,
     function( hom, elm )

gap/orbstab.gi

@@ -164,7 +164,7 @@ function( G, d, e, opr )
       local dim, gen, t1, sol;
       dim := DimensionOfMatrixGroup( P );
       gen := List( GeneratorsOfGroup( P ), 
-                   x -> PreImagesRepresentative( PointHomomorphism( U ), x ) );
+                 x -> PreImagesRepresentativeNC( PointHomomorphism( U ), x ) );
       t1  := Concatenation( List( gen, x -> x[dim+1]{[1..dim]} ) ) - t2;
       sol := IntSolutionMat( tr1, -t1 );
       if sol = fail then
@@ -203,7 +203,7 @@ function( G, d, e, opr )
         return fail;
     fi;
     r := r*r2;
-    R := PreImagesRepresentative( PointHomomorphism( G ), r );
+    R := PreImagesRepresentativeNC( PointHomomorphism( G ), r );
 
     dim := DimensionOfMatrixGroup( PG );
     gP := GeneratorsOfGroup( Pe );
@@ -218,7 +218,7 @@ function( G, d, e, opr )
     tr1 := List( TG, t -> Concatenation( List( gP, x -> t * ( One(Pe)-x ) ) ) );
     tr1 := Concatenation( tr1, M );
     tr2 := ReducedLatticeBasis( tr1 );
-    tt  := List( gP, x -> PreImagesRepresentative( PointHomomorphism(e), x ));
+    tt  := List( gP, x -> PreImagesRepresentativeNC( PointHomomorphism(e), x ));
     tt  := Concatenation( List( tt, x -> x[dim+1]{[1..dim]} ) );
 
     # is there a conjugating translation?
@@ -229,7 +229,7 @@ function( G, d, e, opr )
 
     # now we have to try the normalizer
     gN := Filtered( GeneratorsOfGroup( Normalizer(n, Pe) ), x -> not x in Pe );
-    gN := List( gN, x -> PreImagesRepresentative( PointHomomorphism(G), x ) );
+    gN := List( gN, x -> PreImagesRepresentativeNC( PointHomomorphism(G), x ) );
 
     orb := [ res ];
     rep := [ R ];
@@ -289,7 +289,7 @@ ConjugatingTranslation := function( G, gen, T )
         if not g in PointGroup( G ) then
             return fail;
         fi;
-        m := PreImagesRepresentative( PointHomomorphism( G ), g );
+        m := PreImagesRepresentativeNC( PointHomomorphism( G ), g );
         Append( b, -gen[i][d+1]{[1..d]} +  m[d+1]{[1..d]} );
         M{[1..lt]}{[1..d]+(i-1)*d} := T * (I - g);
         if lg > 0 then
@@ -335,7 +335,7 @@ function( G, H )
     d := DimensionOfMatrixGroup( P );
     I := IdentityMat( d );
     gens := List( GeneratorsOfGroup( P ), 
-                  x -> PreImagesRepresentative( PointHomomorphism( G ), x ) );
+                  x -> PreImagesRepresentativeNC( PointHomomorphism( G ), x ) );
 
     # stabilizer of translation conjugacy class of H
     TG  := TranslationBasis( G );

gap/pcpgrp.gi

@@ -26,8 +26,8 @@ function ( P )
     repr := IsomorphismPcpGroup( N );
     F    := Image( repr );
     gens := Igs( F );
-    prei := List( gens, x -> PreImagesRepresentative( repr, x ) );
-    prei := List( prei, x -> PreImagesRepresentative( mono, x ) );
+    prei := List( gens, x -> PreImagesRepresentativeNC( repr, x ) );
+    prei := List( prei, x -> PreImagesRepresentativeNC( mono, x ) );
 
     iso := GroupHomomorphismByImagesNC( P, F, prei, gens );
     SetMappingGeneratorsImages( iso, [ prei, gens ] );
@@ -56,7 +56,7 @@ function( S )
     # determine preimages
     F := Image( iso );
     gensF := Cgs(F);
-    gensN := List( gensF, x -> PreImagesRepresentative( iso, x ) );
+    gensN := List( gensF, x -> PreImagesRepresentativeNC( iso, x ) );
     matsP := List( gensN, x -> ImagesRepresentative( NiceToCryst( P ), x ) );
 
     # set up some variables
@@ -168,7 +168,7 @@ function(iso, elm)
     # get preimages
     F := Image(w);
     gensF := Cgs(F);
-    gensN := List(gensF, x -> PreImagesRepresentative(w, x));
+    gensN := List(gensF, x -> PreImagesRepresentativeNC(w, x));
     matsP := List(gensN, x -> ImagesRepresentative(l, x));
 
     # point group part
@@ -195,7 +195,7 @@ function(iso, elm)
     h := Cgs(H);
 
     # do some check
-    p := List(h, x -> PreImagesRepresentative(iso,x));
+    p := List(h, x -> PreImagesRepresentativeNC(iso,x));
     if MappedVector(exp, p) <> elm then Error("hier"); fi;
 
     return MappedVector(exp, h);

gap/zass.gi

@@ -240,7 +240,7 @@ CollectEquivExtensions := function( ll, nn, norm, grp )
             h :=GroupHomomorphismByImagesNC( sg, grp, sgens, gens );
             y :=[];
             for i in [1..Length(gens)] do
-               m := PreImagesRepresentative( h, n*gens[i]*n^-1 );
+               m := PreImagesRepresentativeNC( h, n*gens[i]*n^-1 );
                Append( y, m[d+1]{[1..d]}*n );
             od;
             y := StandardTranslation( y, nn );

init.g

@@ -11,6 +11,11 @@
 ##                            GAP 4 Version
 ##
 
+##  introducing globally the NC version of PreImagesRepresentative 
+if not IsBound( PreImagesRepresentativeNC ) then 
+    BindGlobal( "PreImagesRepresentativeNC", PreImagesRepresentative ); 
+fi; 
+
 #############################################################################
 ##
 #R  read the declaration files