linear algebra on polynomials
pasechnik ยท Tue Dec 19, 2006 7:09 pm
is there an obvious way to solve the following (easy) problem in Singular:
given a finite-dimensional subspace S of homogeneous polynomials over a field F, determine whether a given polynomial g is contained in S, and, if yes, to provide an expression in generators of S. (S is given by a list f_1,..,f_k of polynomials that generate it.)
Obviously, Singular can compute whether g is contained in the ideal (f_1,...f_k), but
here the problem is easier, and can be solved by building and solving a system of linear
equations.
So my question is how to avoid coding this myself (something that requires bookeeping of monomials present in f_i's, etc etc).
Thanks,
Dmitrii
given a finite-dimensional subspace S of homogeneous polynomials over a field F, determine whether a given polynomial g is contained in S, and, if yes, to provide an expression in generators of S. (S is given by a list f_1,..,f_k of polynomials that generate it.)
Obviously, Singular can compute whether g is contained in the ideal (f_1,...f_k), but
here the problem is easier, and can be solved by building and solving a system of linear
equations.
So my question is how to avoid coding this myself (something that requires bookeeping of monomials present in f_i's, etc etc).
Thanks,
Dmitrii