Fix caching of Macaulay2 polynomial rings

[gh-mwageringel]

This ticket:

• adds caching of univariate Macaulay2 polynomial rings;

• fixes an issue where, upon conversion of an ideal from Sage to Macaulay2, the Macaulay2 ring that is already cached does not get re-used, but is reconstructed instead;

sage: R.<x,y> = QQ[]
sage: R1 = macaulay2(R)
sage: I = R.ideal(y^2 - x)
sage: R2 = macaulay2(I).ring()
sage: R1._operator('===', R2)   # should be true
false

• moves is_exact() from MPolynomialRing_macaulay2_repr to MPolynomialRing_base where it seems to belong.

[gh-mwageringel]

This is accomplished by refactoring and deduplicating some code related to the conversion. In some places, I replaced _macaulay2_() methods by implementations of _macaulay2_init_() which returns a string to be used as input for the Macaulay2 interpreter. This has the advantage that the generic interface mechanism in sage.structure.sage_object then takes care of the caching. The methods _macaulay2_set_ring() and _macaulay2_base_str() are removed.

(For the future – not in this ticket – it would also be nice to have caching when converting in the other direction, from Macaulay2 to Sage, so that the new Sage object remembers the Macaulay2 element it was constructed from. However, none of the interfaces seem to be doing this currently, as far as I can tell, so this could be more complicated to deal with.)

This branch is based on #27979 to avoid merge conflicts. Only the last commit is new. I tested this with Macaulay2 version 1.12 and Python 2 and 3.

---

New commits:

​a4036cd	Fixed further Macaulay2-related doctests
​c0321d3	fix ascii art for matrices in Macaulay2 1.13+
​7fe0483	deprecate Macaulay2Element.to_sage
​68b5715	deprecate Macaulay2Element.structure_sheaf
​e0ead46	py3 fixes
​2eba33c	trac 27979 several enhancements to M2 interface
​c1464de	28074: refactor caching of Macaulay2 polynomial rings

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​ef43417

28074: refactor caching of Macaulay2 polynomial rings

[gh-mwageringel]

I have just fixed 2 pyflakes warnings. The remaining one is about long which is dealt with in #27826.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​46da1b6	28074: refactor caching of Macaulay2 polynomial rings
​5e606b6	use cpdef for is_exact as in super class CommutativeRing

[gh-mwageringel]

I rebased on 8.9.beta4 and changed the signature of is_exact to resolve a Cython warning.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​2cbfbb3

28074: refactor caching of Macaulay2 polynomial rings

[gh-mwageringel]

Rebased.

[chapoton]

red branch

[dimpase]

New commits:

​5709e61

28074: refactor caching of Macaulay2 polynomial rings

[dimpase]

looks good to me. Sorry for sitting on it for so long.

[chapoton]

moving milestone to 9.0 (after release of 8.9)