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Admit non-fields as left acting domains for free (associative or Lie) algebras, and fix the zero-dimensional case #4245

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Feb 9, 2021
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Admit non-fields as left acting domains for free (associative or Lie) algebras, and fix the zero-dimensional case #4245

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edbc52c
Fix zero-dimensional hom_component and non-field left acting ring
laurentbartholdi Feb 4, 2021
d5d0382
Added test case, changed indentation
laurentbartholdi Feb 5, 2021
45a834e
Now, really added file
laurentbartholdi Feb 5, 2021
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4 changes: 2 additions & 2 deletions lib/algebra.gi
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Expand Up @@ -3381,8 +3381,8 @@ BindGlobal( "FreeAlgebraConstructor", function( name, magma )
od;
x := Zero(R);
y := [One(R)];
return VectorSpace(R, List(B[degree+1],
p->ElementOfMagmaRing( F, x, y, [p] )));
return FreeLeftModule(R, List(B[degree+1],
p->ElementOfMagmaRing( F, x, y, [p] )), Zero(A));
end));

# Return the result.
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5 changes: 3 additions & 2 deletions lib/alglie.gi
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Expand Up @@ -3752,8 +3752,9 @@ InstallGlobalFunction( FreeLieAlgebra, function( arg )
od; od;
od;
od;
return VectorSpace( R, List( B[degree],
p->ElementOfMagmaRing( F, zero, [ one ], [ p[3] ] )));
if degree<1 then B := []; else B := B[degree]; fi;
return FreeLeftModule( R, List( B,
p->ElementOfMagmaRing( F, zero, [ one ], [ p[3] ] )), Zero(L));
end) );
# Return the ring.
return L;
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13 changes: 13 additions & 0 deletions tst/testbugfix/2021-02-04-zero-dim-hom_components.tst
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@@ -0,0 +1,13 @@
# zero-dimensional hom_components #4245
gap> l := FreeLieAlgebra(Integers,1);
<free left module over Integers, and ring, with 1 generators>
gap> List([0..2],Grading(l).hom_components);
[ <free left module over Integers, with 0 generators>,
<free left module over Integers, with 1 generators>,
<free left module over Integers, with 0 generators> ]
gap> a := FreeAssociativeAlgebra(Integers,2);
<free left module over Integers, and ring, with 2 generators>
gap> List([0..2],Grading(a).hom_components);
[ <free left module over Integers, with 0 generators>,
<free left module over Integers, with 2 generators>,
<free left module over Integers, with 4 generators> ]