Singular Manual: linear_relations

| #### D.3.1.24 linear_relations Procedure from library `matrix.lib` (see matrix_lib). Usage: linear_relations(M); M: a module Assume: All non-zero entries of M are homogeneous polynomials of the same positive degree. The base field must be an exact field (not real or complex). It is not checked whether these assumptions hold. Return: a maximal module R such that M*R is formed by zero vectors. Example:
    LIB "matrix.lib";
    ring r = (3,w), (a,b,c,d),dp;
    minpoly = w2-w-1;
    module M = [a2,b2],[wab,w2c2+2b2],[(w-2)*a2+wab,wb2+w2c2];
    module REL = linear_relations(M);
    pmat(REL);
    ==> (-w-1),
    ==> -1,
    ==> 1
    pmat(matrix(M)*matrix(REL));
    ==> 0,
    ==> 0

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