conversion of quotient rings to macaulay2

[saliola]

Currently, conversion of quotient rings to M2 is not supported; we add this functionality:

sage: R.<x,y> = PolynomialRing(QQ)
sage: I = R.ideal([x^2 - y])
sage: macaulay2(R.quotient_ring(I))

This also improves the conversion of ideals by moving the MPolynomialIdeal_macaulay2_repr._macaulay2_ to Ideal_generic._macaulay2_init_; for example, the following now work but didn't before (see the doctests for examples):

• ideals in univariate polynomial rings

sage: R.<x> = PolynomialRing(ZZ)
sage: macaulay2(R.ideal(x^2))

• ideals in PIDs

sage: macaulay2(ideal(5))

Note that quotient rings in M2 inherit variable names from the ambient ring, so we mimic this behaviour in Sage::

sage: R = macaulay2("ZZ/7[x,y]")
sage: I = macaulay2("ideal (x^3 - y^2)")
sage: (R/I).gens()
{x, y}
sage: (R/I).sage().gens()
(x, y)

We also implement conversion of polynomials from quotient rings from/to M2:

sage: x, y = (R/I).gens()
sage: f = (x^3 + 2*y^2*x)^7; f
    18    14
2x*y   + y
sage: f.sage()
2*x*y^18 + y^14
sage: _.parent()
Quotient of Multivariate Polynomial Ring in x, y over Finite Field of size 7 by the ideal (x^3 - y^2)
sage: macaulay2(f.sage())
    18    14
2x*y   + y

Depends on #28567 Depends on #28571 Depends on #28074 Depends on #28591

CC: @dimpase @mwageringel @antonleykin

Component: interfaces: optional

Keywords: IMA Coding Sprint, macaulay2, interfaces

Author: Franco Saliola

Branch/Commit: 3f4f6f5

Reviewer: Markus Wageringel, Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/28572

[saliola]

Commit: 6e734c6

[saliola]

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

[saliola]

Branch: public/interfaces/m2/m2_quotient_rings

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 6e734c6 to 6a537c8

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

6a537c8

28572: fix conversion of quotient rings from Macaulay2 to Sage

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

5ddbe5c	mark m2 doctests as optional
4b256a1	add _macaulay2_init_ method to QuotientRingElement

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 6a537c8 to 4b256a1

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 4b256a1 to d1566e5

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

d1566e5

correct inaccuracy in doctest description

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from d1566e5 to bd06a80

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

bd06a80

properly handle conversion of quotient ring elements & inherit variable names when converting from M2 quotient rings

[saliola]

Description changed:

--- 
+++ 
@@ -19,3 +19,32 @@
 sage: macaulay2(ideal(5))

+ +Note that quotient rings in M2 inherit variable names from the ambient ring, so we mimic this behaviour in Sage:: + + +sage: R = macaulay2("ZZ/7[x,y]") +sage: I = macaulay2("ideal (x^3 - y^2)") +sage: (R/I).gens() +{x, y} +sage: (R/I).sage().gens() +(x, y) + + +We also implement conversion of polynomials from quotient rings from/to M2: + +``` +sage: x, y = (R/I).gens() +sage: f = (x^3 + 2y^2x)^7; f

• 18 14 +2xy + y +sage: f.sage() +2x*y^18 + y^14 +sage: _.parent() +Quotient of Multivariate Polynomial Ring in x, y over Finite Field of size 7 by the ideal (x^3 - y^2) +sage: macaulay2(f.sage())
• 18 14 +2x*y + y +```

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from bd06a80 to ec1773e

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

ec1773e

disable caching of M2 conversion of polynomials in quotient rings (change _macaulay2_init_ to _macaulay2_)

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

25afa2f

simplify doctest

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from ec1773e to 25afa2f

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 25afa2f to 19d9995

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

19d9995

28572: remove unnecessary doctests

[mwageringel]

comment:10

The following does not work yet (not even with #28574):

sage: R = QQ['x,y'].quotient('x^2-y')['z,t']
sage: f = R.base_ring()('x')^2 - R('z^2')
sage: macaulay2(f)  # fails

This fails because the variable names in the quotient ring are named xbar,ybar in Sage, but x,y in Macaulay2. The conversion routine for polynomials does not currently take this into account when the base ring is a quotient ring.

Other than that, everything looks good to me up until here.

[saliola]

Changed dependencies from #28571, #28074 to #28567, #28571, #28074

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 19d9995 to 15d35e3

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

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

[saliola]

comment:13

I added a dependency to #28567 because this did not merge cleanly on top of it (and I merged it into this branch).

[mwageringel]

comment:14

Ok.

[mwageringel]

Reviewer: Markus Wageringel

[vbraun]

comment:15

Merge conflict (please merge in next beta)

[dimpase]

Changed dependencies from #28567, #28571, #28074 to #28567, #28571, #28074, #28591

[dimpase]

comment:17

rebased on top of the branch of #28591

---

Last 10 new commits:

e40eb60	make tests more foolproof.
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

[dimpase]

Changed branch from public/interfaces/m2/m2_quotient_rings to u/dimpase/interfaces/m2/m2_quotient_rings

[dimpase]

Changed commit from 15d35e3 to 3f4f6f5

[dimpase]

Changed reviewer from Markus Wageringel to Markus Wageringel, Dima Pasechnik

[vbraun]

Changed branch from u/dimpase/interfaces/m2/m2_quotient_rings to 3f4f6f5