Valuation on power series and Laurent series

[xcaruso]

We implement the method valuation on the rings of power series and Laurent series.

📝 Checklist

• The title is concise and informative.
• 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 and checked the documentation preview.

[xcaruso]

I still have a problem with categories that I do not understand. Please tell me if you have some insight.

[saraedum]

Have you considered making this a UniqueRepresentation? Then you can throw out _eq_ and __reduce__ from your implementation.

[xcaruso]

Yes, I tried it (not so hard). But got an error that I did not really understand (something with metaclasses).

[saraedum]

Ah, that's annoying. Then you need to add a silly little factory.

Let me know if you need any support here (I can add it if you want me to.)

[mantepse]

could you add this simultaneously to the lazy power / Laurent series?

or should this be actually a method in a category?

[saraedum]

You want to do valuation_space.__make_element_class__(SeriesValuation)(valuation_space) to get the category right.

[xcaruso]

Thanks!

[xcaruso]

could you add this simultaneously to the lazy power / Laurent series?

Sure, I will do it.

[saraedum]

Suggested change

	return "%s-adic valuation" % self.domain().uniformizer()
	return "%s-adic valuation" % self.uniformizer()

I think it would be good to implement uniformizer() on the level of valuation.

[saraedum]

Actually, once the "category" test above passes, more tests coming from the category of discrete valuations are going to fail, namely that you are missing a bunch of methods: uniformizer, reduce, lift, residue_field.

[github-actions]

Documentation preview for this PR (built with commit 92a950d; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[xcaruso]

Thanks for your help. I think that everything is working correctly now.

[saraedum]

Actually this creates the object. That's the docstring for the other method I guess.

[saraedum]

Maybe _generic since there's nobody inheriting from this. Base sounds like abstract base to me (just a suggestion. Keep it if you want.)

[saraedum]

doctests fail with:

File "src/sage/rings/series_valuation.py", line 30, in sage.rings.series_valuation.SeriesValuationFactory
Failed example:
    v = R.valuation()
Exception raised:
    Traceback (most recent call last):
      File "/home/runner/miniconda3/envs/sage-dev/lib/python3.11/site-packages/sage/doctest/forker.py", line 728, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/runner/miniconda3/envs/sage-dev/lib/python3.11/site-packages/sage/doctest/forker.py", line 1152, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.rings.series_valuation.SeriesValuationFactory[1]>", line 1, in <module>
        v = R.valuation()
            ^^^^^^^^^^^^^
      File "/home/runner/miniconda3/envs/sage-dev/lib/python3.11/site-packages/sage/rings/power_series_ring.py", line 672, in valuation
        from sage.rings.series_valuation import SeriesValuation
    ModuleNotFoundError: No module named 'sage.rings.series_valuation'