ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 08 Jan 2011 21:54:12 +0100Quotient decomposition by Groebner basishttps://ask.sagemath.org/question/7853/quotient-decomposition-by-groebner-basis/I can accomplish the following task in awkward ways using syzygy modules, but I am wondering if there is a better way somehow. It would be nice to have a single command for it.
Suppose we have a polynomial $P$ and a set of polynomials $Q_1,...,Q_n$, and it is possible to calculate the Groebner basis $G$ of the ideal generated by all the $Q_i$. Let $R$ be the remainder of $P$ after reducing by $G$. In Sage, how can we find polynomials $S_1,...,S_n$ such that $P = R + \sum S_i Q_i$?mhamptonSat, 08 Jan 2011 21:54:12 +0100https://ask.sagemath.org/question/7853/