implement action of DifferentialWeylAlgebra on polynomials

[mwageringel]

This ticket implements the action of differential operators (from the Weyl algebra) on polynomials:

sage: W.<x,y> = DifferentialWeylAlgebra(QQ)
sage: dx, dy = W.differentials()
sage: dx.diff(x^3)
3*x^2
sage: (x*dx + dy + 1).diff(x^4*y^4 + 1)
5*x^4*y^4 + 4*x^4*y^3 + 1

Component: algebra

Author: Markus Wageringel

Branch/Commit: 7cdc6b0

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29928

[mwageringel]

Branch: u/gh-mwageringel/29928

[mwageringel]

Commit: 7cdc6b0

[mwageringel]

New commits:

7cdc6b0

implement action of weyl algebra on polynomials

[mwageringel]

Author: Markus Wageringel

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:2

This is good to have. Although I don't see why this needs the full Action framework. I guess there is a bit of an issue with overloading * between the action and the natural coercion. Perhaps we could have the action use the @ operator to distinguish the two. That being said, let's get this in as-is and do more based on this ticket later.

[mwageringel]

comment:3

Thanks for the review. Mainly, I assumed using the action framework was the preferred way to implement this, but you are probably right that it is not entirely necessary.

Using the @ operator here sounds like a good option to me. Though, given the recent discussion on devel, it might be difficult to reach a consensus about this.

[tscrim]

comment:4

Well, I don't think we have to worry too much about multiplying matrices, but I see your point (and I might want to push to use @ for tensor products). However, it would be nice to overload some operator so we don't have to write f.diff(g). Maybe a shift operator >> or << would be good? Or the & operator?

[vbraun]

Changed branch from u/gh-mwageringel/29928 to 7cdc6b0