Add warning in LazyPowerSeriesRing.taylor() documentation

[AdityaK1729]

part 1 of #39838
As the title says, adds another warning in the LazyPowerSeriesRing.taylor() documentation

📝 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.

⌛ Dependencies

[AdityaK1729]

Can someone review changes, thanks

[AdityaK1729]

Can someone review changes, thanks

@user202729

[EigenVector22]

hello, i think that you have only implemented the second part of the proposed solution and that is adding the warning which is definitely helpful, but you didn't implement the main fix, that is checking coefficients up to the halting precision during construction which would involve computing coefficients up to the default halting precision at initializing time and then verifying whether they can be expressed in the base ring or not, also by doing this we won't be disturbing the lazy evaluation behavior for higher precision terms.

This is what i suspect is the case here, as the issue label also pointed out it's an enhancement issue.

Of course, the final implementation details could be confirmed by the maintainers,
Thanks,

[github-actions]

Documentation preview for this PR (built with commit ebaa8e7; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[AdityaK1729]

@user202729 @DaveWitteMorris can you please review the PR, thanks :)

[user202729]

Suggested change

	:issue:`39838` For inputs with precision greater than the default,
	this does not check that the function is well-defined in the base ring::
	For inputs with precision greater than the default,
	this does not check that the function is well-defined in the base ring (:issue:`39838`)::

As is, the capitalization is incorrect since For is not at the start of a sentence.

Also the explanation is misleading, first, the input always have infinite precision, and second this never check the function is well-defined even if a coefficient less than halting_precision does not belong to the base ring.

And this doesn't completely fix the issue, consider change the initial message to avoid https://docs.github.com/en/get-started/writing-on-github/working-with-advanced-formatting/using-keywords-in-issues-and-pull-requests

[mantepse]

This is very misleading - the default precision is infinity.