From 2f6bf51db6999a7bb02cbaf1303b9479c6e2cc91 Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Fri, 23 Oct 2026 22:22:33 +0200
Subject: [PATCH] Fix `Embedding` of a family into its `LieFamily`

`Embedding( Fam, LieFamily( Fam ) )` failed for every family: it built
the mapping's type with `TypeOfDefaultGeneralMapping`, which expects
domains, not families. Build the type from `GeneralMappingsFamily`
instead. The preimage methods then failed on `Range`, which such a
mapping has no domain for; since the embedding is a bijection of
families, they now return the preimage directly.

Assisted-by: Generative AI
---
 lib/liefam.gi                                 | 20 ++++++++++++-------
 .../2026-10-23-LieFamily-Embedding.tst        | 15 ++++++++++++++
 2 files changed, 28 insertions(+), 7 deletions(-)
 create mode 100644 tst/testbugfix/2026-10-23-LieFamily-Embedding.tst

diff --git a/lib/liefam.gi b/lib/liefam.gi
index 848e616068..a81f72efd4 100644
--- a/lib/liefam.gi
+++ b/lib/liefam.gi
@@ -422,7 +422,7 @@ InstallOtherMethod( Embedding,
     fi;
 
     # Make the mapping object.
-    emb := Objectify( TypeOfDefaultGeneralMapping( Fam, LieFam,
+    emb := Objectify( NewType( GeneralMappingsFamily( Fam, LieFam ),
                               IsLieEmbeddingRep
                           and IsNonSPGeneralMapping
                           and IsMapping
@@ -455,18 +455,24 @@ InstallMethod( PreImagesElmNC,
     return [ elm![1] ];
     end );
 
+# The embedding is a bijection of families, so every element of the
+# range family has a preimage, and there is no range domain to test.
 InstallMethod( PreImagesElm,
     "for Lie embedding and Lie object in default representation",
     FamRangeEqFamElm,
     [ IsGeneralMapping and IsLieEmbeddingRep,
       IsLieObject and IsPackedElementDefaultRep ], 0,
     function( emb, elm )
-    if not ( elm in Range(emb) ) then
-        Error( "<elm> is not in the range of mapping <emb>" );
-    elif not ( elm in Image(emb) ) then
-        return [];
-    fi;
-    return PreImagesElmNC( emb, elm );
+    return [ elm![1] ];
+    end );
+
+InstallMethod( PreImagesRepresentative,
+    "for Lie embedding and Lie object in default representation",
+    FamRangeEqFamElm,
+    [ IsGeneralMapping and IsLieEmbeddingRep,
+      IsLieObject and IsPackedElementDefaultRep ], 0,
+    function( emb, elm )
+    return elm![1];
     end );
 
 #############################################################################
diff --git a/tst/testbugfix/2026-10-23-LieFamily-Embedding.tst b/tst/testbugfix/2026-10-23-LieFamily-Embedding.tst
new file mode 100644
index 0000000000..97d847e4db
--- /dev/null
+++ b/tst/testbugfix/2026-10-23-LieFamily-Embedding.tst
@@ -0,0 +1,15 @@
+# Embedding( Fam, LieFamily( Fam ) ) used to fail with a no method error
+gap> F := FamilyObj( 1 );; L := LieFamily( F );;
+gap> emb := Embedding( F, L );;
+gap> 3 ^ emb = LieObject( 3 );
+true
+gap> PreImagesRepresentative( emb, LieObject( 3 ) );
+3
+gap> PreImagesElm( emb, LieObject( 3 ) );
+[ 3 ]
+gap> m := [ [ 1, 2 ], [ 3, 4 ] ];;
+gap> F := FamilyObj( m );; emb := Embedding( F, LieFamily( F ) );;
+gap> m ^ emb = LieObject( m );
+true
+gap> PreImagesRepresentative( emb, LieObject( m ) ) = m;
+true