Allow multiplication of a left and right noncommutative ideal

[tscrim]

Their product has a simple generating set, but right now Sage does not allow this:

sage: MS = MatrixSpace(QQ,2,2)
sage: IL = MS * [2*MS.0,3*MS.1]
sage: IR = MS.3 * MS
sage: IL * IR
...
NotImplementedError: Cannot multiply non-commutative ideals.

We fix this.

Component: algebra

Keywords: ideals

Author: Travis Scrimshaw

Branch/Commit: c41575e

Reviewer: Dave Morris

Issue created by migration from https://trac.sagemath.org/ticket/34261

[tscrim]

Commit: 20dd21c

[tscrim]

New commits:

20dd21c

Allowing L * R nc ideals.

[tscrim]

Branch: public/algebras/ideal_multiplication-34261

[DaveWitteMorris]

comment:3

I don't think you should allow two-sided ideals as input, because the generating set of a product of two-sided ideals is not just the product of the generating sets: (RaR)(RbR) may be much larger than RabR when R is not commutative. Therefore, I think you need to delete the line or self.side() == other.side() == "twosided".

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

66c079b	Merge branch 'public/algebras/ideal_multiplication-34261' of https://github.com/sagemath/sagetrac-mirror into public/algebras/ideal_multiplication-34261
c41575e	Cannot specify a generating set when multiplying two-sided ideals.

[sagetrac-git]

Changed commit from 20dd21c to c41575e

[tscrim]

comment:6

Indeed, you're correct. I have updated the code.

[DaveWitteMorris]

comment:7

LGTM. The patchbot timeouts do not seem to be related, and the build-and-test was successful.

[DaveWitteMorris]

Reviewer: Dave Morris

[tscrim]

comment:8

Thank you.

[vbraun]

Changed branch from public/algebras/ideal_multiplication-34261 to c41575e