MPolynomial_libsingular over ZZ

[malb]

There it is.

CC: @williamstein

Component: commutative algebra

Keywords: libsingular, singular, ZZ, multivariate

Issue created by migration from https://trac.sagemath.org/ticket/4021

[malb]

comment:1

Attachment: mpolynomial_libsingular_zz.patch.gz

the attached patch depends on #686

[malb]

comment:2

On [sage-devel] Oliver Wienand (author of the upcoming Singular implementation for GBs over rings) wrote:

I have just glimpsed over the code. But maybe it is worth stating in
the comments, that the reduce impl. only returns unqiue answer against
strong Gröbner basis.

Gröbner basis G of I <=> the leading ideal of G generates all leading
terms of I
strong % of I <=> for every leading term t of I there exists an
element g of G, such that the leading term of g divides t.

(leading terms means coef * product of variables)

Otherwise the reduce code shown in
https://github.com/sagemath/sage-prod/files/10641888/mpolynomial_libsingular_zz.patch.gz
looks fine.

[malb]

comment:4

Attachment: mpolynomial_zz_reduce_doc.patch.gz

The second patch addresses the review of Oliver Wienand on [sage-devel]:

I have just glimpsed over the code. But maybe it is worth stating in
the comments, that the reduce impl. only returns unqiue answer against
strong Gröbner basis.

Gröbner basis G of I <=> the leading ideal of G generates all leading
terms of I
strong % of I <=> for every leading term t of I there exists an
element g of G, such that the leading term of g divides t.

(leading terms meaans coef * product of variables)

Otherwise the reduce code shown in
https://github.com/sagemath/sage-prod/files/10641888/mpolynomial_libsingular_zz.patch.gz
looks fine.

[aghitza]

comment:5

Attachment: trac4021-doctest-fix.patch.gz

Applies cleanly on 3.1.3.alpha1 + the patch at #686, except for a reject in rings/polynomial/multi_polynomial_libsingular.pyx, which can be ignored.

There is a tiny doctest failure in rings/polynomial/multi_polynomial_element.py which is fixed by the attached patch.

[sagetrac-mabshoff]

comment:6

Merged all three patches in Sage 3.1.3.alpha2

[sagetrac-mabshoff]

comment:7

Merged all three patches in Sage 3.1.3.alpha2 and this time I closed the ticket :)