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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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