divided_difference in SchubertPolynomialRing should not throw errors on unused variables

[darij]

sage: X = SchubertPolynomialRing(ZZ)
sage: a = X([1,2,3,4,5])
sage: a.divided_difference(4)

This should yield 0, not an error. Elements of X are polynomials in infinitely many variables; when they don't use a variable, it doesn't mean that this variable cannot be divided-differenced over.

Followup to #23403.

[darij]

Now solved in #23403.

[tscrim]

It is an orthogonal issue from #23403, and this would be a great place to discuss this as there could be a good use case for considering having a finite number of variables and having this throw an error. I agree with the change, but it is better documented by having a separate ticket for it.

[darij]

As discussed with Travis, this ticket is now the place for branch public/combinat/improve_schubert_divided_difference , which builds on top of #23403. Will need rebasing, though, once #23403 is p_r'd.

[tscrim]

Okay, I did some more investigating. The biggest time sink in the symmetrica version is not symmetrica, but instead most of the time is spent on checking the input via reduced_word. Even with removing that check, enough time is spent on the overhead that even the non-optimized native algorithm beats going to/from symmetrica unless maybe I really spent some time optimizing the interface, which, IMO, is time not well spent.

[darij]

Turns out no rebase is needed.

[tscrim]

We should change newm to algorithm, which takes 'sage' or 'symmetrica'. I also think a better check is if i in ZZ: too, but that isn't something I will quibble over. Once that is done (with corresponding documentation updates), this will be a positive review.

[darij]

Is that something I should do, or you want to do?

I'm fine with if i in ZZ instead of if isinstance(i, (Integer, int)), if this is what you mean.

[tscrim]

Replying to darij:

Is that something I should do, or you want to do?

I can do it, but it might take me a little longer to push right now. However, it was somewhat a question of seeing if you agree; granted, I didn't phrase it like I should have.

I'm fine with if i in ZZ instead of if isinstance(i, (Integer, int)), if this is what you mean.

Yes, it is. The rationale: if by chance a user is doing 2/2, it will still work. Granted, this is not likely to happen, but I've had it happen to me enough that I'm paranoid about it now.

[git]

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

​a5b2cff	Merge branch 'public/combinat/improve_schubert_divided_difference' of git://trac.sagemath.org/sage into schub
​37b4648	changes suggested by Travis

[darij]

Done those changes. But be warned that I haven't tested the correct behavior of the 'symmetrica' algorithm on polynomials with too few variables.

[tscrim]

Thank you.