Add PreImagesSet method for semigroup homs by images

GAP 4.17 changes PreImagesSet: a generic method now checks that the
argument is a subset of the range and returns the preimage of its
intersection with the image. With that method, PreImagesSet no longer
signals an error for elements without preimages, which the tests
expect, and the error for elements outside the range changes.

Install a method for semigroup homomorphisms by images that performs
the range check with the package's own error message and otherwise
delegates to PreImagesElm, so behaviour is the same with all supported
GAP versions.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Author: 2 people

gap/attributes/homomorph.gi

@@ -425,6 +425,20 @@ function(hom, x)
   return preim;
 end);
 
+# GAP >= 4.17 has a library method for PreImagesSet that returns the preimage
+# of the intersection with the image; this method keeps erroring for elements
+# without preimages, consistent with the PreImagesElm method above.
+InstallMethod(PreImagesSet,
+"for a semigroup homom. by images and a list of elements in the range",
+[IsSemigroupHomomorphismByImages, IsList],
+function(hom, elms)
+  if not IsSubset(Range(hom), elms) then
+    ErrorNoReturn("the 2nd argument is not a subset of the range of the ",
+                  "1st argument (semigroup homom. by images)");
+  fi;
+  return Union(List(elms, x -> PreImagesElm(hom, x)));
+end);
+
 InstallMethod(KernelOfSemigroupHomomorphism, "for a semigroup homomorphism",
 [IsSemigroupHomomorphismByImagesOrFunction],
 function(hom)

tst/standard/attributes/homomorph.tst

@@ -126,8 +126,8 @@ gap> PreImagesElm(hom, 2);
 Error, the 2nd argument is not an element of the range of the 1st argument (se\
 migroup homom. by images)
 gap> PreImagesSet(hom, [2]);
-Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 1st choice method found for `PreImagesSet' on 2 arguments
+Error, the 2nd argument is not a subset of the range of the 1st argument (semi\
+group homom. by images)
 gap> IsSurjective(hom);
 true
 gap> IsInjective(hom);