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SubmoduleOfMinGens

submodule generated by minimal generators

Syntax
SubmoduleOfMinGens(M: MODULE): MODULE

Description
It works only in the homogeneous case: for the inhomogeneous case see MinSubsetOfGens .

This function returns the ideal generated by a minimal set of generators (i.e. with minimal cardinality) of M . The minimal set of generators is not necessarily a subset of the given generators.

Similar to IdealOfMinGens .

Example
/**/  use R ::= QQ[x,y,z];
/**/  R3 := NewFreeModule(R, 3);
/**/  MGens := matrix(R, [[x,y,z], [x^2,0,z^2], [2*x^2,x*y,z^2+x*z]]);
/**/  M := SubmoduleRows(R3, MGens);
/**/  MGM := SubmoduleOfMinGens(M);  indent(MGM);
SubmoduleRows(F, matrix([
  [x, y, z],
  [0, x*y, x*z -z^2]
]))

See Also