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MinGens

list of minimal generators

Syntax
MinGens(M: IDEAL|MODULE): LIST

Description
If M is a homogeneous ideal or module, this function returns a list of minimal generators for M (not necessarily a subset of gens(M) ).

For non-homogeneous input use MinSubsetOfGens .

NOTE: the coefficient ring must be a field.

Example
/**/  use R ::= QQ[x,y,z];
/**/  I := ideal(x-y, (x-y)^4, z+y, (z+y)^2);
/**/  MinGens(I);
[y + z, x + 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);
/**/  gens(M);
[[x, y, z], [x^2, 0, z^2], [2*x^2, x*y, x*z +z^2]]
/**/  MinGens(M);
[[x, y, z], [0, x*y, x*z -z^2]]

See Also