polynomial decomposition
Assume i have some multivariate polynomials P1,...,Pn
and a polynomial P
. Sage is able to tell whether P
is in the ideal generated by P1,...,Pn
by writing P in R.ideal([P1,...,Pn])
, where R
is the polynomial ring containing the Pi
. When the answer is True
, i would like to obtain a certificate, that is a list of polynomials Q1,...,Qn
such that P = P1*Q1 + ... + Pn*Qn
. Is there an easy way to get this ? If possible i would like the Qi
to have small coefficients.