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lang-mma
NonCommutativeGroebnerBasisfor a set of relations, and you canNonCommutativePolynomialReducerelative to these relations. I think this means that you can implement the quotient by working with the remainders.... $\endgroup$NonCommutativePolynomialReduce. But other operations might need to be implemented by hand. See the last example in the documentation forNonCommutativeAlgebraon implementing a Weyl algebra: they compute relative to a set of relations on a set of generators, but they also implement some added functionality, like differential operators, by hand. $\endgroup$