On Tue, Dec 17, 2024 at 07:57:40AM -0800, Sid Andal wrote:
> I'm trying to construct polynomials in non-commuting variables in x, y, and
> z
> over the integers: Z<x, y, z>, or over some other commutative ring.
>
> The XPolynomial domain constructor allows to define such polynomials.
>
> However, additionally, I'd like to be able to construction the quotient,
> (Z<x, y, z>/I), where I is the ideal generated, say, by the following three
> commutators:
>
> [x, y] = x + 2y - z + 1
> [x, z] = 3x - y + 5z - 7
> [y, z] = - 4x + 8 y - 2 z + 9
>
> Are there any suitable constructors to help with this?
AFAICS what you have above is a multivariate version of Ore algebra,
we have SparseMultivariateSkewPolynomial which implements them.
We have nothing ready to use for general ideals. If your ideal
have a known finite Groebner basis, then it would be reasonably
easy to write a new constructor for quotient (in terms of
Groebner basis of the ideal).
--
Waldek Hebisch
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