From 6629021f4569e22ab3af0fb4560fe44321392c1a Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Wed, 5 Aug 2020 12:33:41 +0200
Subject: [PATCH] Fix PreImagesSet for input sets not contained in image

---
 CHANGES.md           |  5 +++++
 gap/basic/grphoms.gi |  9 +++------
 tst/bugfix.tst       | 13 +++++++++++++
 3 files changed, 21 insertions(+), 6 deletions(-)

diff --git a/CHANGES.md b/CHANGES.md
index 777ce45..cd54a0f 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -1,5 +1,10 @@
 This file describes changes in the GAP package 'polycyclic'.
 
+X.YY (YYYY-MM-DD)
+  - Fix a bug in `PreImagesSet` which lead to a "method not found" error
+    if the given input set was not contained in the image of the given
+    homomorphism.
+
 2.16 (2020-07-25)
   - Fix a bug in `NormalIntersection` which could lead to wrong results;
     this also affected other operations, such `Core`, `Intersection`
diff --git a/gap/basic/grphoms.gi b/gap/basic/grphoms.gi
index c908280..ab97e11 100644
--- a/gap/basic/grphoms.gi
+++ b/gap/basic/grphoms.gi
@@ -296,14 +296,11 @@ InstallMethod( PreImagesSet,
                CollFamRangeEqFamElms,
                [ IsFromPcpGHBI and IsToPcpGHBI, IsPcpGroup ],
 function( hom, U )
-    local prei, kern;
+    local prei, gens, kern;
     prei := List( Igs(U), x -> PreImagesRepresentative(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 -> PreImagesRepresentative(hom,x) );
     fi;
     kern := Igs( KernelOfMultiplicativeGeneralMapping( hom ) );
     return SubgroupByIgs( Source(hom), kern, prei );
diff --git a/tst/bugfix.tst b/tst/bugfix.tst
index 393390e..12f353f 100644
--- a/tst/bugfix.tst
+++ b/tst/bugfix.tst
@@ -479,5 +479,18 @@ true
 gap> HirschLength( Ker );
 5
 
+#
+# PreImages resp. PreImagesSet used to run into a "method not found"
+# error when the input set is not contained in the image of the map.
+#
+gap> G := AbelianPcpGroup([0]);
+Pcp-group with orders [ 0 ]
+gap> phi := GroupHomomorphismByImages(G,G,[G.1],[One(G)]);
+[ g1 ] -> [ id ]
+gap> H := PreImagesSet(phi, G);
+Pcp-group with orders [ 0 ]
+gap> G = H;
+true
+
 #
 gap> STOP_TEST( "bugfix.tst", 10000000);