Use S ::= QQ[x,y];
M := Module([x,y^2,2+x^2y],[x,0,y]); -- define the submodule of S^3
-- generated by (x,y^2,2+x^2y) and (x,0,y)
GBasis(M);
[Vector(x, 0, y), Vector(x, y^2, x^2y + 2)]
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Describe M;
Record[Type = MODULE, Value = Record[Gens = [[x, y^2, x^2y + 2], [x,
0, y]], MRC = 1, GBasis = [[x, 0, y], [x, y^2, x^2y + 2]]]]
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M.GBasis;
[Vector(x, 0, y), Vector(x, y^2, x^2y + 2)]
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M.Gens[1];
Vector(x, y^2, x^2y + 2)
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M.NumComps; -- M is a submodule of a free module of rank 3
3
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