# How to define polynomial ring over noncommutative rings?

I want to study the algebra
$$U_q^+(\mathfrak{g})[x_1,\ldots,x_n]$$
where $U_q(\mathfrak{g})$ is the upper half quantum group of a simple lie algebra, and $x_1,\ldots,x_n$ are commutative variables.
In Sagemath, it seems to me that the only way to construct $U_q(\mathfrak{g})$ is by using “**Quantum Groups Using GAP’s QuaGroup Package**”. But it does not support change ring or tensor product. Moreover, polynomial rings in SageMath have to be constructed over a commutative ring. How can I construct this algebra in SageMath?

This tutorial may help: https://sheaves.github.io/Noncommutat...