Basically I have the same question as here, but in the non-commutative case: Given non-commutative multi-variate polynomials $f_1,\dotsc,f_s$, how can I test (with sage, or any other program which can do this) that $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal) and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?
There is a patch which somehow contains the necessary functions, but unfortunately I don't know how to use/install this patch. Also the help pages only confuse me. Can someone explain this in easy steps? Sorry for this stupid question ...