[with patch, positive review] MPolynomial_libsingular over ZZ

[malb]

There it is.

[malb]

the attached patch depends on #686

[malb]

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  http://trac.sagemath.org/sage_trac/attachment/ticket/4021/mpolynomial_libsingular_zz.patch looks fine.

[malb]

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
http://trac.sagemath.org/sage_trac/attachment/ticket/4021/mpolynomial_libsingular_zz.patch
looks fine.

[AlexGhitza]

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.

[mabshoff]

Merged all three patches in Sage 3.1.3.alpha2

[mabshoff]

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