Add keyword prec for exponential and logarithm of Drinfeld modules

[xcaruso]

Currently, the methods exponential and logarithm for Drinfeld modules return a LazyPowerSeriesRing for which not all methods are available.
We add a keyword prec. When it is Infinity (which is the default), the behavior is unchanged. However, when we pass in a finite number, a classical power series (up to the given precision) is returned.

📝 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.
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[github-actions]

Documentation preview for this PR (built with commit 1fa959b; changes) is ready! 🎉
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[mantepse]

Off topic: Which methods are missing in LazyPowerSeries?

[xcaruso]

e.g. sqrt (it is implemented only for series congruent to 1 modulo x), nth_root, continued_fraction...
Also printing more terms is a little bit tricky; we need to set the parameter parent.options.display_length (which moreover is global, we cannot easily change this for just one shot).

[mantepse]

e.g. sqrt (it is implemented only for series congruent to 1 modulo x), nth_root,

Oh, I missed the possibility of taking out x^n!

continued_fraction...

I actually have code for that, but was too lazy to get it in.

Also printing more terms is a little bit tricky; we need to set the parameter parent.options.display_length (which moreover is global, we cannot easily change this for just one shot).

I agree. Maybe we can discuss this at sd128?

[xcaruso]

Also printing more terms is a little bit tricky; we need to set the parameter parent.options.display_length (which moreover is global, we cannot easily change this for just one shot).

I agree. Maybe we can discuss this at sd128?

Sure!
I implemented a few years ago exact $p$-adics using relaxed artihemtics. The precision model there is able to handle both infinite and finite precision in the same parent. Maybe, it's also a good option to follow this.

[kryzar]

Once again, it seems that the failed tests are independent to that PR:

• First failed test
• Second failed test, first failed subtest
• Second test, second failed subtest
• Third failed test, first failed subtest
• Third failed test, second failed subtest

@xcaruso, could you merge from develop and push here? I have hope this will fix the issue. (I don't believe I have authorizations on your fork (which I am not asking for), as I tried to do that but failed.)

[kryzar]

I did my review. I only request that you add the latest changes from develop. My comments in the review are only suggestions, and you can freely choose to accept them or not. I'll approve the review either way. The only thing truly missing are the valid automatic tests (which unfortunately do not seem to be your fault's...).

Thank you very much for this lovely and useful PR 💙

[kryzar]

Once again, these failing doctests seem unrelated to our work. Therefore, I approve the PR.

Many thanks to Xavier.

[kryzar]

🍷