Add Pseudomorphism Implementation for Free Modules

[ymusleh]

The goal of this PR is to add a basic implementation of pseudomorphisms of free modules.

Let $M$ be a free module over a ring $R$. Let $\theta: R \to R$ be a ring homomorphism and $\delta: R \to R$ a ring $\theta$-derivation.

A pseudomorphism $f: M \to M$ is a map twisted by $(\theta, \delta)$ such that

$f(\lambda x) = \theta(\lambda)f(x) + \delta(\lambda)x$

$f$ can be specified by a matrix representing its action on a basis for $M$.

Currently this PR implements the following functionality:

• Constructors for pseudomorphisms and the space of pseudomorphisms with a fixed twist
• Call methods to apply pseudomorphisms to a fixed element of the module
• Call method for pseudohomspace to coerce matrix or module morphisms to a pseudomorphism

See the documentation for more details.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

None

[github-actions]

Documentation preview for this PR (built with commit 1134baa; changes) is ready! 🎉

[ymusleh]

@xcaruso What is your opinion on continuing with this since I see you closed the Anderson motive PR, which was a major motivation for implementing pseudomorphisms. Should we still go ahead and get this merged?

[xcaruso]

Yes.
I closed the PR on Anderson motive by mistake because I got a problem when trying to push. So I finally created a new branch on my github account: https://github.com/xcaruso/sage/tree/anderson-motives
I will re-create a PR (more probably, several PRs) when this will be ready.