Make rank return an Integer object

[kryzar]

📚 Description

The following raises an error:

Fq = GF(3)
A = Fq['T']
K.<T> = Frac(A)
phi = DrinfeldModule(A, [T, 0, 1])
rank = phi.rank()
cat = phi.category()
psi = cat.random_object(rank)

...
TypeError: rank must be a positive integer

There are at least two possible fixes:

1. Make rank return an Integer object.
2. Make cat.random_object accept both Integers and ints.

I suggest the former, and provide an implementation.

📝 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

[DavidAyotte]

This seems like a good fix, but I think a better fix would be to make the degree method of an Ore polynomial return an Integer object:

sage: P.<t> = OrePolynomialRing(GF(5)['T'], GF(5)['T'].frobenius_endomorphism())
sage: type(t.degree())
<class 'int'>

[kryzar]

This seems like a good fix, but I think a better fix would be to make the degree method of an Ore polynomial return an Integer object:

sage: P.<t> = OrePolynomialRing(GF(5)['T'], GF(5)['T'].frobenius_endomorphism())
sage: type(t.degree())
<class 'int'>

Agreed.

[mkoeppe]

The docstring linter complains:

./sage/rings/function_field/drinfeld_modules/drinfeld_module.py:1178:1: RST218 Literal block expected; none found.

[xcaruso]

This seems like a good fix, but I think a better fix would be to make the degree method of an Ore polynomial return an Integer object:

sage: P.<t> = OrePolynomialRing(GF(5)['T'], GF(5)['T'].frobenius_endomorphism())
sage: type(t.degree())
<class 'int'>

I also agree. Antoine, are you going to implement this?

[kryzar]

This seems like a good fix, but I think a better fix would be to make the degree method of an Ore polynomial return an Integer object:

sage: P.<t> = OrePolynomialRing(GF(5)['T'], GF(5)['T'].frobenius_endomorphism())
sage: type(t.degree())
<class 'int'>

I also agree. Antoine, are you going to implement this?

I can!

[kryzar]

The degree of an Ore polynomial should now be an Integer. I hope I did everything that needed to be done!

You'll notice that some tests fail: they are related to multi polynomials, and are also present on the develop branch. I therefore ignored them.

[DavidAyotte]

Thanks Antoine! It all looks good to me. I'll approve once the linter is fixed and the actions are done.

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: 798045e

[DavidAyotte]

Looks good to me! Thanks!

[xcaruso]

Looks good to me as well.

[kryzar]

Thank you Volker.