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 7aec45f

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> )

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,
+) );
+
 
 #############################################################################
 ##

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);