move multivariate polynomials over RR to libsingular

[malb]

Singular supports real numbers as 'base field', we only need to implement the conversion routines.

CC: @burcin @nathanncohen

Component: commutative algebra

Author: Martin Albrecht

Issue created by migration from https://trac.sagemath.org/ticket/7577

[malb]

comment:1

Attachment: mpolynomial_rr_libsingular.patch.gz

I am CCing burcin because he knows libSingular and I am CCing ncohen because I wrote this patch in order to speed up the linear programming interface.

[mwhansen]

comment:2

I get the following failures with this patch:

        sage -t  devel/sage-main/sage/matrix/matrix_sparse.pyx # 1 doctests failed
        sage -t  devel/sage-main/sage/calculus/desolvers.py # Segfault
        sage -t  devel/sage-main/sage/rings/polynomial/multi_polynomial.pyx # 2 doctests failed
        sage -t  devel/sage-main/sage/matrix/matrix_mpolynomial_dense.pyx # 2 doctests failed

[malb]

comment:3

On what kind of machine?

[mwhansen]

comment:4

On sage.math. This is with the new Singular spkg from 7194.

[malb]

comment:5

I can reproduce

sage -t  devel/sage-main/sage/matrix/matrix_sparse.pyx # 1 doctests failed
sage -t  devel/sage-main/sage/calculus/desolvers.py # Segfault
sage -t  devel/sage-main/sage/matrix/matrix_mpolynomial_dense.pyx # 2 doctests failed

but not

sage -t  devel/sage-main/sage/rings/polynomial/multi_polynomial.pyx # 2 doctests failed

I am attaching a fix for the failures I can reproduce.

[malb]

comment:6

There is another issue: Singular uses MPF instead of MPFR to implement floating point numbers. Thus, we get less assurance about the precision with this new patch.

[jdemeyer]

comment:7

Attachment: mpolynomial_rr_libsingular_fixes.patch.gz