Fix for computing quotients of certain algebra modules

The issue was originally reported by Rudolf Tange on the GAP
support mailing list.

lib/algrep.gd

@@ -1135,6 +1135,11 @@ DeclareCategoryFamily( "IsSparseRowSpaceElement" );
 #T TB, January 12th, 2000.
 
 
+#
+DeclareHandlingByNiceBasis( "IsSparseVectorSpace",
+    "for free left modules of sparse vectors");
+
+
 ##############################################################################
 ##
 #O  FullSparseRowSpace( <R>, <n> )

lib/algrep.gi

@@ -3177,6 +3177,26 @@ InstallMethod( Coefficients,
 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.
+##
+InstallHandlingByNiceBasis( "IsSparseVectorSpace", rec(
+    detect:= function( R, gens, V, zero )
+        if IsSparseRowSpaceElementCollection(V) then
+            return fail;
+        else
+            return false;
+        fi;
+    end,
+    NiceFreeLeftModuleInfo := function( C ) end,
+    NiceVector := function( C, c ) end,
+    UglyVector := function( C, vec ) end,
+) );
+
+
 #############################################################################
 ##
 #M  FullSparseRowSpace( <F>, <n> )  . . . . . . for a ring and an integer

tst/testinstall/algrep.tst

@@ -0,0 +1,34 @@
+gap> START_TEST("algrep.tst");
+
+#
+gap> L:=FullMatrixLieAlgebra(GF(5),2);
+<Lie algebra over GF(5), with 3 generators>
+gap> V:=AdjointModule(L);
+<left-module over <Lie algebra over GF(5), with 3 generators>>
+gap> s:=List([0..3],r->SymmetricPowerOfAlgebraModule(V,r));;
+gap> V:=DirectSumOfAlgebraModules(s);
+<35-dimensional left-module over <Lie algebra over GF(5), with 3 generators>>
+gap> BV:=Basis(V);;
+gap> lst:=[BV[5]];;
+gap> W:=SubAlgebraModule(V,lst,"basis");
+<1-dimensional left-module over <Lie algebra over GF(5), with 3 generators>>
+gap> V/W;
+<34-dimensional left-module over <Lie algebra over GF(5), with 3 generators>>
+
+#
+gap> A:=FullSparseRowSpace(GF(5), 35);
+<vector space of dimension 35 over GF(5)>
+gap> AV:=Basis(A);;
+gap> CanonicalBasis(A);  # not currently supported for sparse row spaces
+fail
+gap> IsCanonicalBasis(AV);
+false
+gap> v:=AV[12];
+(Z(5)^0)*e.12
+gap> ForAll(AV, v -> v in A);
+true
+gap> ForAll([1..10], i -> Random(A) in A);
+true
+
+#
+gap> STOP_TEST( "algrep.tst", 1);