Add PreImagesRepresentativeNC method for SHBI

gap/attributes/homomorph.gi

@@ -328,7 +328,8 @@ InstallMethod(AsSemigroupIsomorphismByFunction,
 hom -> SemigroupIsomorphismByFunctionNC(Source(hom),
                                         Range(hom),
                                         x -> ImageElm(hom, x),
-                                        y -> PreImages(hom, y)));
+                                        y ->
+                                        PreImagesRepresentativeNC(hom, y)));
 
 # Methods for SHBI/SIBI/SHBF
 InstallMethod(IsSurjective, "for a semigroup homomorphism",
@@ -364,6 +365,17 @@ InstallMethod(ImagesSource, "for SHBI",
 [IsSemigroupHomomorphismByImages],
 hom -> Semigroup(MappingGeneratorsImages(hom)[2]));
 
+# <x> must lie in ImagesSource(hom).
+SEMIGROUPS.PreImagesRepresentativeSHBI := function(hom, x)
+  # Use MinimalFactorization rather than Factorization because
+  # MinimalFactorization is guaranteed to return a list of positive integers,
+  # but Factorization is not (i.e. if S is an inverse acting semigroup.
+  # Also since we require an IsomorphismFpSemigroup, there's no additional
+  # cost to using MinimalFactorization instead of Factorization.
+  return EvaluateWord(MappingGeneratorsImages(hom)[1],
+                      MinimalFactorization(ImagesSource(hom), x));
+end;
+
 InstallMethod(PreImagesRepresentative,
 "for a semigroup homom. by images and an element in the range",
 [IsSemigroupHomomorphismByImages, IsMultiplicativeElement],
@@ -374,15 +386,18 @@ function(hom, x)
   elif not x in ImagesSource(hom) then
     return fail;
   fi;
-  # Use MinimalFactorization rather than Factorization because
-  # MinimalFactorization is guaranteed to return a list of positive integers,
-  # but Factorization is not (i.e. if S is an inverse acting semigroup.
-  # Also since we require an IsomorphismFpSemigroup, there's no additional
-  # cost to using MinimalFactorization instead of Factorization.
-  return EvaluateWord(MappingGeneratorsImages(hom)[1],
-                      MinimalFactorization(ImagesSource(hom), x));
+  return SEMIGROUPS.PreImagesRepresentativeSHBI(hom, x);
 end);
 
+# GAP >= 4.17 calls PreImagesRepresentativeNC internally; in older versions it
+# is the same operation as PreImagesRepresentative, see init.g.
+if not IsIdenticalObj(PreImagesRepresentative, PreImagesRepresentativeNC) then
+  InstallMethod(PreImagesRepresentativeNC,
+  "for a semigroup homom. by images and an element in the image",
+  [IsSemigroupHomomorphismByImages, IsMultiplicativeElement],
+  SEMIGROUPS.PreImagesRepresentativeSHBI);
+fi;
+
 InstallMethod(ImagesRepresentative,
 "for a semigroup homom. by images and an element in the source",
 [IsSemigroupHomomorphismByImages, IsMultiplicativeElement],

gap/attributes/isorms.gi

@@ -324,7 +324,7 @@ function(R)
 
   tester := function(x)
     local y, found, g, i, tmp, map;
-    y := PreImagesRepresentative(hom, x ^ Projection(V, 2));
+    y := PreImagesRepresentativeNC(hom, x ^ Projection(V, 2));
     x := x ^ Projection(V, 1);
     tmp := [];
     found := false;
@@ -514,7 +514,7 @@ function(R)
 
   tester := function(x)
     local y, map, g;
-    y := PreImagesRepresentative(hom, x ^ Projection(V, 2));
+    y := PreImagesRepresentativeNC(hom, x ^ Projection(V, 2));
     x := x ^ Projection(V, 1);
     for g in T do
       map := RMSInducedFunction(R, R, x, y, g);

tst/standard/attributes/homomorph.tst

@@ -385,6 +385,11 @@ gap> x := ConstantTransformation(2, 1);
 Transformation( [ 1, 1 ] )
 gap> x ^ map;
 Transformation( [ 1, 1 ] )
+gap> iso := AsSemigroupIsomorphismByFunction(hom2);;
+gap> x ^ InverseGeneralMapping(iso);
+Transformation( [ 1, 1 ] )
+gap> PreImagesRepresentativeNC(hom2, x);
+Transformation( [ 1, 1 ] )
 gap> imgs2 := [gens[2], gens[2], gens[1], gens[3]];;
 gap> hom3 := SemigroupHomomorphismByImages(S, S, gens, imgs2);
 fail