Ideals of non-commutative polynomials
Basically I have the same question as here, but in the non-commutative case: Given non-commutative polynomials f1,…,fs∈Q⟨x1,…,xn⟩, how can I test (with sage, or any other program which can do this) that some g∈Q⟨x1,…,xn⟩ satisfies g∈⟨f1,…,fs⟩ (two-sided ideal), and find an explicit linear combination g=∑iaifibi which demonstrates this?
In trac ticket #11068 non-commutative quotient rings were implemented. However, according to the reference manual on quotient rings, this assumes that one defines a reduce method by hand. But in my example , it is not clear how to do this.