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.Sun, 27 Jan 2013 20:23:38 +0100Ideals of non-commutative polynomialshttps://ask.sagemath.org/question/9748/ideals-of-non-commutative-polynomials/Basically I have the same question as [here](http://ask.sagemath.org/question/1267/find-specific-linear-combination-in-multivariate), but in the non-commutative case: Given non-commutative polynomials $f_1,\dotsc,f_s \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$, how can I test (with sage, or any other program which can do this) that some $g \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$ satisfies $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal), and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?
In trac ticket [#11068](http://trac.sagemath.org/sage_trac/ticket/11068) non-commutative quotient rings were implemented. However, according to the reference manual on [quotient rings](http://www.sagemath.org/doc/reference/sage/rings/quotient_ring.html), this assumes that one defines a reduce method by hand. But in my example , it is not clear how to do this.Martin BrandenburgSun, 27 Jan 2013 20:23:38 +0100https://ask.sagemath.org/question/9748/