Height function for projective subvarieties

[MatheMagicianPi]

Introduces three new methods related to height of projective subvarieties.

Direct transfer from #34559. Methods implemented: local_height, local_height_arch, global_height.

Fixes #34559

📝 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.
• Someone else has created tests covering the changes.
• Someone else has updated the documentation accordingly.

⌛ Dependencies

[kwankyu]

Is @guojing0 the author of the code, but you @MatheMagicianPi created this PR in behalf of him?

If so, then did you notice him personally about this?

I am asking these because I wonder how credits problem should be handled.

[EnderWannabe]

Hi @kwankyu, you are right that @guojing0 is the author of the code. These functions began as part of his GSoC 2022 project on height functions which I helped supervise. I prompted Dang (@MatheMagicianPi) to create this pull request on his behalf to try and close this issue, as Jing is currently working on other issues. I'm happy to defer to your judgement on how code should be credited.

[kwankyu]

Some people use "Assignees" to give credits to all those involved in a PR resolving an issue. It is unfortunate that it is not "Contributors" or "Authors", but it seem the best we can do in the GitHub system. So I assigned both of them to "Assignees".

By the way, I think it is all right that you review this PR unless you prefer others.

[kwankyu]

There are no spaces separating parts of the docstring here and below.

[kwankyu]

The standard in

https://doc.sagemath.org/html/en/developer/coding_basics.html#template

(also many examples in the file being modified) suggests blank lines just below INPUT: and OUTPUT:.

[kwankyu]

Thanks.

On more thing: as RealField is a piece of code, we write

``RealField``

Otherwise, it looks good to me.

[github-actions]

Documentation preview for this PR (built with commit bf3b9a1; changes) is ready! 🎉

[kwankyu]

Thanks. LGTM.