conversion of nested polynomial rings to Macaulay2

[mwageringel]

This ticket implements conversion to and from Macaulay2 of polynomial rings over arbitrary base rings – nested polynomial rings in particular – as well as their elements.

This ticket also implements _macaulay2_() for polydicts. This is used in elements of nested polynomial rings, for example.

It also fixes an issue where constant polynomials are accidentally converted to elements of the base ring in Macaulay2, not to elements of the polynomial ring.

We add a special case in the conversion of Galois fields, since in Macaulay2 it is more natural to define finite fields as ZZ/p rather than GF p. This has a positive effect on performance, and simplifies the construction of Macaulay2 polynomial rings.

Depends on #28566
Depends on #28571
Depends on #28572
Depends on #28074

CC: @saliola @dimpase @antonleykin

Component: interfaces: optional

Keywords: macaulay2, IMA Coding Sprint

Author: Markus Wageringel

Branch/Commit: ac2ff35

Reviewer: Franco Saliola, Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/28574

[mwageringel]

Branch: u/gh-mwageringel/28574

[mwageringel]

Commit: 49d5c0b

[mwageringel]

Dependencies: #28571, #28074

[mwageringel]

New commits:

5709e61	28074: refactor caching of Macaulay2 polynomial rings
c2d89a0	Merge tag '9.0.beta0'
2823dc0	pass macaulay2 as argument to _macaulay2_init_()
af595de	28574: construct Macaulay2 polynomial rings over arbitrary base rings
e854720	28574: fix conversion of polynomials to M2
49d5c0b	28574: convert elements of nested polynomial rings from M2 to sage

[mwageringel]

Author: Markus Wageringel

[saliola]

Changed branch from u/gh-mwageringel/28574 to public/interfaces/m2/28574

[saliola]

Changed commit from 49d5c0b to 23b2bf4

[fchapoton]

comment:4

reviewer name missing

[mwageringel]

Reviewer: Franco Saliola

[mwageringel]

comment:5

Thanks.

[saliola]

Work Issues: Fix merge conflicts with #28566

[saliola]

Changed dependencies from #28571, #28074 to #28566, #28571, #28074

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

03d1460	28566: implement _matrix_() in Macaulay2 interface
5308c90	28566: implement conversion of vectors in Macaulay2 interface
602f6eb	28566: preserve variable name in Macaulay2 Galois fields
ce24186	simplify some doctests
21025bd	28566: use ring-preserving constructor for Macaulay2 matrix/vector
0c1e001	Merge remote-tracking branch 'origin/public/interfaces/m2/28566' into public/interfaces/m2/28574
72abe24	finish merging

[sagetrac-git]

Changed commit from 23b2bf4 to 72abe24

[sagetrac-git]

Changed commit from 72abe24 to a312b15

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

ec1773e	disable caching of M2 conversion of polynomials in quotient rings (change _macaulay2_init_ to _macaulay2_)
25afa2f	simplify doctest
19d9995	28572: remove unnecessary doctests
0d90888	f4 and mgb opts for M2 gb computations
59b3215	add documentation and minor fixes
1ad24c3	pass F4 and MGB to M2 as strings
7038ba2	28567: run Macaulay2 f4 and mgb doctests over a finite field
00c028f	28567: add missing optional doctest flag
15d35e3	Merge remote-tracking branch 'origin/public/interfaces/m2/f4etc' into public/interfaces/m2/m2_quotient_rings
a312b15	Merge branch 'public/interfaces/m2/m2_quotient_rings' into public/interfaces/m2/28574

[saliola]

Changed dependencies from #28566, #28571, #28074 to #28566, #28571, #28572, #28074

[saliola]

Changed work issues from Fix merge conflicts with #28566 to none

[saliola]

comment:10

In order to make this ticket merge cleanly with some of the other M2 tickets summarized at #28573, I set dependencies and merged the appropriate branches. Provided the dependencies are respected, everything should merge cleanly now.

[saliola]

comment:11

I am happy with this ticket. Markus, if you accept the proposed merging, then you can set this to positive review.

[mwageringel]

Work Issues: rebase on #28572

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

61ca2db	conversion of quotient rings to macaulay2 & improvements to conversion of ideals
84702b4	28572: fix conversion of quotient rings from Macaulay2 to Sage
4db4a3c	mark m2 doctests as optional
80b99b9	add _macaulay2_init_ method to QuotientRingElement
c185cff	correct inaccuracy in doctest description
ca619b8	properly handle conversion of quotient ring elements & inherit variable names when converting from M2 quotient rings
3a0e906	disable caching of M2 conversion of polynomials in quotient rings (change _macaulay2_init_ to _macaulay2_)
117ab9f	simplify doctest
3f4f6f5	28572: remove unnecessary doctests
ac2ff35	28574: Merge #28572 into 'public/interfaces/m2/28574'

[sagetrac-git]

Changed commit from a312b15 to ac2ff35

[mwageringel]

comment:14

I have replaced the last merge commit by a new merge with #28572 and still all tests pass on my end.

Franco, please review the merging, though maybe wait for the next beta to see if it merges cleanly.

[mwageringel]

Changed work issues from rebase on #28572 to none

[dimpase]

Changed reviewer from Franco Saliola to Franco Saliola, Dima Pasechnik

[dimpase]

comment:15

seems to be merging just fine (with 9.0.beta4)

[vbraun]

Changed branch from public/interfaces/m2/28574 to ac2ff35