enhancements in infinite polynomial rings

[fchapoton]

This make a few little changes, nothing serious.

This catches more precise exceptions, not Exception.

[mantepse]

Thank you! It appears to me that the all_gens method is completely new (in Sage), do you have any plans with it?

[fchapoton]

well, not really. The problem is that the usual semantic of gen and gens is not respected in this file. They do not return some elements of the ring. I am not sure what to do. I can remove all_gens or call it otherwise or make it hidden..

[mantepse]

Do you know whether there is any good reason for not respecting the usual semantics?

[fchapoton]

it's because there are infinitely many generators, in a finite number of families

[mantepse]

I don't see how that's a good reason. Is this the only infinite dimensional ring in sage which has gen and gens?

[fchapoton]

It is also a matter of offering a simple and practical access to the variables.

[mantepse]

Can we have both, in case it makes sense? I find

sage: P.<a, b> = InfinitePolynomialRing(QQ)

practical, and I do not see why we couldn't have, at the same time

sage: [P.gen(i) for i in range(5)]
[a[0], b[0], a[1], b[1], a[2]]

I looked at the code: on the plus side, ParentWithGens is deprecated, on the minus side, there is no method returning a family of generators.

I think that there are quite a few things that would work better with gen returning a proper generator of the ring, for examples substitution and defining homomorphisms.

[mantepse]

Old discussion: https://groups.google.com/g/sage-devel/c/-CVdz6H7dTc/m/_x1px4bHAgAJ

[fchapoton]

See also #34120

[fchapoton]

I do not want to do big things and changes here. So maybe we can keep only the changes that enlarge the possible input of the gen method of infinite polynomial rings ? Would you approve that ?

[mantepse]

I would rather not modify the semantics before agreeing on the desirable semantics, especially since we seem to agree that the current semantics breaks stuff quite badly. Do you have any concrete plans with your proposed improvement?

[fchapoton]

I dot not have any specific plan about gen and gens. I may try to get rid of ParentWithGens when I have time.

So we can close the present poule-requete, vielleicht ?

[fchapoton]

Ok, I have replaced the branch by a new one only making very simple changes, and not touching anything about gens

[github-actions]

Documentation preview for this PR (built with commit 96d8a84; changes) is ready! 🎉

[mantepse]

Can I assume that the failure in singular is unrelated?

File "src/sage/interfaces/singular.py", line 530, in sage.interfaces.singular.Singular._send_interrupt
Failed example:
    2*a
Expected:
    2
Got:
    <BLANKLINE>

If so, positive review from my side.

[fchapoton]

Well, it's only on conda+mac, and not on the main Build and Test or in other conda builds. So, yes, unrelated.
Please approve and set to positive. Thanks for your review !

[mantepse]

Thank you!