(very) Minor improvements to the multivariate polynomials documentation

[89f39f15-88e8-4e79-9bc0-0739a7fc497c]

Mostly typo fixing, adding references to trac tickets, adding quotes, fixing a few spelling mistakes, ...

Component: commutative algebra

Author: Charles Bouillaguet

Issue created by migration from https://trac.sagemath.org/ticket/13716

[89f39f15-88e8-4e79-9bc0-0739a7fc497c]

comment:1

Attachment: 13716_improve_multipolynomial_doc.patch.gz

[ppurka]

comment:2

Some comments:

1. Line 1308 is missing a backtick on closing.

Returns the leading term of ``self`` i.e., ``self.lc()*self.lm()`. The

2. Lines 1577 and 1578 should have the latex variables enclosed in single backticks not double (like `I = (f_1,...,f_r)`:

       given an ideal ``I = (f_1,...,f_r)`` and some ``g (== self)`` in ``I``, find 
        ``s_1,...,s_r`` such that ``g = s_1*f_1 + ... + s_r*f_r``. 

3. Shouldn't line 1975 also have \ne in the latter expression?

        - `LT(g_i) \neq LT(g_j)` for all `i != j` 

4. Should we refer to the derivative() function in line 342 instead as :meth:`sage.calculus.functional.derivative` ? This will create a hyperlink to the derivative documentation in the notebook help.
5. I am not very happy to see lots of "self" throughout the docs, but converting all of them would be a lot of work. So, I guess we can just let it pass and hope it gets fixed little by little over time.
6. Most importantly, this patch touches a huge number of lines in several files. I am ok with this change (in fact, ok with any change which improves docs), but ultimately its up to Jeroen whether this gets merged, since he doesn't usually like massive minor changes. :)

[DaveWitteMorris]

comment:8

Removing the "beginner" tag from old tickets. Some could be returned to beginner-friendly status by adding a comment about what needs to be done. Some others might be easy for an experienced developer to finish.