From afc698ad2c1b0ee28bfc3672c0175d9b544e6c88 Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Mon, 1 Jan 2018 23:43:17 +0100
Subject: [PATCH] Fix inefficiency when dealing with certain algebra modules

The issue was originally reported by Rudolf Tange on the GAP support
mailing list. The fix is virtually identical to a fix for a similar
issue, see 7aec45fa176be87c32afd53f3cbf88f7ee5c890f
---
 lib/algrep.gd              |  5 +++++
 lib/algrep.gi              | 18 ++++++++++++++++--
 tst/testinstall/algrep.tst | 16 ++++++++++++++++
 3 files changed, 37 insertions(+), 2 deletions(-)

diff --git a/lib/algrep.gd b/lib/algrep.gd
index 9faea8e5597..8cab5ff4177 100644
--- a/lib/algrep.gd
+++ b/lib/algrep.gd
@@ -790,6 +790,11 @@ DeclareCategory( "IsMonomialElement", IsVector );
 DeclareCategoryCollections( "IsMonomialElement" );
 DeclareCategoryFamily( "IsMonomialElement" );
 
+#
+DeclareHandlingByNiceBasis( "IsMonomialElementVectorSpace",
+    "for free left modules of monomial elements");
+
+
 #############################################################################
 ##
 #O  ConvertToNormalFormMonomialElement( <me> )
diff --git a/lib/algrep.gi b/lib/algrep.gi
index e480abe00b5..5fd6b7cc091 100644
--- a/lib/algrep.gi
+++ b/lib/algrep.gi
@@ -3180,8 +3180,9 @@ end );
 #############################################################################
 ##
 ##  Prevent nice basis handling to kick in for vector spaces over sparse
-##  elements, as that ends up trying to enumerate the vector space, which
-##  is not a good idea for non-trivial examples.
+##  elements (including monomial elements), as that ends up trying to
+##  enumerate the vector space, which is not a good idea for non-trivial
+##  examples.
 ##
 InstallHandlingByNiceBasis( "IsSparseVectorSpace", rec(
     detect:= function( R, gens, V, zero )
@@ -3196,6 +3197,19 @@ InstallHandlingByNiceBasis( "IsSparseVectorSpace", rec(
     UglyVector := function( C, vec ) end,
 ) );
 
+InstallHandlingByNiceBasis( "IsMonomialElementVectorSpace", rec(
+    detect:= function( R, gens, V, zero )
+        if IsMonomialElementCollection(V) then
+            return fail;
+        else
+            return false;
+        fi;
+    end,
+    NiceFreeLeftModuleInfo := function( C ) end,
+    NiceVector := function( C, c ) end,
+    UglyVector := function( C, vec ) end,
+) );
+
 
 #############################################################################
 ##
diff --git a/tst/testinstall/algrep.tst b/tst/testinstall/algrep.tst
index f8a971a73c7..444a047cd7b 100644
--- a/tst/testinstall/algrep.tst
+++ b/tst/testinstall/algrep.tst
@@ -30,5 +30,21 @@ true
 gap> ForAll([1..10], i -> Random(A) in A);
 true
 
+#
+# creating subalgebra
+#
+gap> L:=FullMatrixLieAlgebra(GF(3), 2);; Dimension(L);;
+gap> V:=AdjointModule(L);
+<left-module over <Lie algebra of dimension 4 over GF(3)>>
+gap> S:=SymmetricPowerOfAlgebraModule(V, 4);
+<35-dimensional left-module over <Lie algebra of dimension 4 over GF(3)>>
+gap> bas:=Basis(S){[ 1, 2, 4, 5, 6, 9, 13, 14, 15, 16, 19, 25, 32, 33, 34, 35 ]};;
+gap> S1:=SubAlgebraModule(S,bas);
+<left-module over <Lie algebra of dimension 4 over GF(3)>>
+gap> Dimension(S1);
+16
+gap> S1:=SubAlgebraModule(S,bas,"basis");
+<16-dimensional left-module over <Lie algebra of dimension 4 over GF(3)>>
+
 #
 gap> STOP_TEST( "algrep.tst", 1);