Fix + extend msolve interface

[mezzarobba]

Since #33734, msolve developers have changed (stabilized?) the output format and documented the computation of varieties over finite fields and Gröbner bases.

We update the existing interface accordingly, and add (basic) interfaces to the new features.

(See also #31664.)

Component: commutative algebra

Author: Marc Mezzarobba

Branch/Commit: 17ea8dd

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/34519

[mkoeppe]

Dependencies: #31664

[mezzarobba]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 Since #33734, msolve developers have changed (stabilized?) the output format and documented the computation of varieties over finite fields and Gröbner bases.
+
+We update the existing interface accordingly, and add (basic) interfaces to the new features.

[mezzarobba]

Branch: u/mmezzarobba/34519-msolve

[mezzarobba]

Commit: bc01223

[mezzarobba]

New commits:

367b862	#34519 fix msolve interface
ea64d4a	#34519 msolve: real solving with ℓ > 1
9055d30	#34519 msolve: varieties over finite fields
1d70b04	#34519 msolve._variety() -> msolve.variety()
14fc8e7	#34519 _run_msolve()
bc01223	#34519 Gröbner bases using msolve

[mezzarobba]

Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
 Since #33734, msolve developers have changed (stabilized?) the output format and documented the computation of varieties over finite fields and Gröbner bases.
 
 We update the existing interface accordingly, and add (basic) interfaces to the new features.
+
+(See also #31664.)

[mezzarobba]

comment:3

I don't think #31664 should be a dependency: the interface works as soon as msolve is available in $PATH, so the two tickets are independent.

[mezzarobba]

Changed dependencies from #31664 to none

[mkoeppe]

Reviewer: Matthias Koeppe

[mkoeppe]

comment:4

I've tested it with the msolve built using #31664, working well.
Thanks a lot for your work!