Proper syntax for creating morphism

[simon-king-jena]

Currently (and even with #10668), there is a generic call method for homsets that is not really useful, as it does not make any use of element classes or other ingredients of the "usual" framework for making a parent callable. In particular, homsets typically override __call__, which means that we can not benefit from a generic coercion model.

This ticket aims at providing a generic call method for homsets (similarly to what we have for parents) and use it in all concrete implementations of homsets.

Depends on #10668

CC: @nthiery @jpflori

Component: coercion

Issue created by migration from https://trac.sagemath.org/ticket/17150

[simon-king-jena]

comment:1

A comment from #10668, what Nicolas would like to have:

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For A a parent, A.hom(on_basis = [data],...) would call
A.morphism_on_basis(data,...). This morphism_on_basis could
typically be implemented in A, or in C.ParentMethods for C the
category of A.

There are 5-6 explicit hom functions in Sage that would need to be
generalized to accept this syntax, while keeping backward
compatibility if no keyword is specified.

---

I am not totally sure whether I would like that change. The A.hom(data, B) method should, in my opinion, be a short-cut for A.Hom(B)(data), and it should be the responsibility of the homset to process the data (by means of _element_constructor_). I would like to have everything as close to what we have for parents as possible. So, _element_constructor_ and friends should be used.