Decomposition of a polynomial over generators of an ideal

Question

Let $f$ be a polynomial in six variables, say, over complex numbers, and $l_1$, $l_2$ are some linear forms in the same variables. If I know that polynomial $f$ belong to the ideal generated by $l_1$ and $l_2$ i.e. $$ f \in (l_1, l_2), $$ what computer algebra system can I use to find coefficients $f_1$ and $f_2$ of the decomposition $$ f=f_1l_1+f_2l_2? $$

Is there a name for $f_1$ and $f_2$?

Answer 1

This can be done with SAGE or Singular.

http://www.sagemath.org/doc/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_ideal.html

http://ask.sagemath.org/question/8827/find-specific-linear-combination-in-multivariate-polynomial-ring/