improve conversions between Macaulay2 and Sage

[mwageringel]

This ticket implements and improves conversions between Macaulay2 and Sage:

• vectors/free module elements

• matrices: The function InterfaceElement._matrix_() is implemented to allow for this syntax:

sage: A = macaulay2('matrix {{1,2},{3,4}}')
sage: matrix(QQ, A)
[1 2]
[3 4]

This ticket also fixes an issue where the elements are not promoted to the correct ring:

sage: R.<x,y> = QQ[]
sage: m = macaulay2(matrix(R, [[1, 2], [3, 4]]))
sage: m.ring()  # should be R
ZZ

• finite fields: An issue is fixed where the generator names are not preserved:

sage: K = GF(49, 'b')
sage: K.gens(), macaulay2(K).gens()  # should be the same
((b,), {a})

CC: @saliola @dimpase @antonleykin

Component: interfaces: optional

Keywords: macaulay2, IMA Coding Sprint

Author: Markus Wageringel

Branch/Commit: 21025bd

Reviewer: Franco Saliola

Issue created by migration from https://trac.sagemath.org/ticket/28566

[mwageringel]

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

[mwageringel]

Author: Markus Wageringel

[mwageringel]

Commit: 602f6eb

[mwageringel]

Branch: public/interfaces/m2/28566

[mwageringel]

Changed keywords from macaulay2 to macaulay2, IMA Coding Sprint

[sagetrac-git]

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

ce24186

simplify some doctests

[sagetrac-git]

Changed commit from 602f6eb to ce24186

[saliola]

comment:4

I reviewed all the changes up to this point (​602f6eb) and have only a couple of minor suggestions for the presentation of doctests (see ce24186).

After discussions, it seems that instead of using promote in M2, one should use the matrix(R,v) constructor in M2; see matrix(R,v) documentation for M2.

This also applies to constructing vectors: first construct a matrix in M2 over the correct base ring and then apply the vector command vector(Matrix).

[sagetrac-git]

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

21025bd

28566: use ring-preserving constructor for Macaulay2 matrix/vector

[sagetrac-git]

Changed commit from ce24186 to 21025bd

[mwageringel]

comment:6

Replying to @saliola:

After discussions, it seems that instead of using promote in M2, one should use the matrix(R,v) constructor in M2; see matrix(R,v) documentation for M2.

This also applies to constructing vectors: first construct a matrix in M2 over the correct base ring and then apply the vector command vector(Matrix).

Thanks, I have changed it.

[saliola]

Reviewer: Franco Saliola

[vbraun]

Changed branch from public/interfaces/m2/28566 to 21025bd