54.2 Submodules

is the left module generated by the collection gens, with parent module M. The second form generates the submodule of M for that the list gens is known to be a list of basis vectors; in this case, it is not checked whether gens really are linearly independent and whether all in gens lie in M.

gap> coll:= [ [Z(2),0*Z(2)], [0*Z(2),Z(2)], [Z(2),Z(2)] ];;
gap> V:= LeftModuleByGenerators( GF(16), coll );; 
gap> W:= Submodule( V, [ coll[1], coll[2] ] );
<vector space over GF(2^4), with 2 generators>
gap> Parent( W ) = V;
true

SubmoduleNC does the same as Submodule, except that it does not check whether all in gens lie in M.

is the left module generated by the left module generators of M and the element m.

gap> V:= LeftModuleByGenerators( Rationals, [ [ 1, 0, 0 ], [ 0, 1, 0 ] ] );
<vector space over Rationals, with 2 generators>
gap> ClosureLeftModule( V, [ 1, 1, 1 ] );
<vector space over Rationals, with 3 generators>

returns the zero submodule of M.

gap> V:= LeftModuleByGenerators( Rationals, [ [ 1, 0, 0 ], [ 0, 1, 0 ] ] );;
gap> TrivialSubmodule( V );
<vector space over Rationals, with 0 generators>

[Top] [Previous] [Up] [Next] [Index]