Adding `DegNegLex` to TermOrder

[AlexanderDreyer]

The attached patch adds the Degree Negative Lexicographical term order (DegNegLex) to Sage 5.1.

It is defined as follows: x^a < x^b if and only if deg(x^a) < deg(x^b) or deg(x^a) = deg(x^b) and there exists 1 <= i <= n such that a₁ = b ₁ , ... , a _i-1 = b _i-1, ..., a_i > b_i.

It is a native term ordering of PolyBoRi ("dp_asc") which Sage does not support yet. But Sage uses it internally to implement DegRevLex-ordered BooleanPolynomialRings by reverting .gens(). It is useful for Sage to distinguish between the original dp_asc and DegRevLex. It will help to fix some design issues discovered when fixing #13202.

Singular supports this as (a(1:n),ls(n)). The patch also includes the patches for the interfaces libSingular and Singular-pexpect.

• Apply: degneglex.patch

[AlexanderDreyer]

Replaced the patch, there was a wrong Singular ordering in the back.

[malb]

The patch looks good, i.e., reading it revealed no issues. So if doctests pass I say it's good to go.

[malb]

Patchbot reports:

sage -t  -force_lib devel/sage-13229/sage/rings/polynomial/multi_polynomial_libsingular.pyx
**********************************************************************
File "/mnt/storage2TB/patchbot/Sage/sage-5.1.rc1/devel/sage-13229/sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1261:
    sage: singular(R)
Expected:
    //   characteristic : 0
    //   number of vars : 2
    //        block   1 : ordering a
    //                  : names    x0 x1
    //                  : weights   1  1
    //        block   2 : ordering rp
    //                  : names    x0 x1
    //        block   3 : ordering C
Got:
    //   characteristic : 0
    //   number of vars : 2
    //        block   1 : ordering a
    //                  : names    x0 x1
    //                  : weights   1  1
    //        block   2 : ordering ls
    //                  : names    x0 x1
    //        block   3 : ordering C
**********************************************************************

[AlexanderDreyer]

Please reload the patch. (There was an intermediate patch, was this was wrong.)

[malb]

Alright, let's see what the patchbot has to say about the current one then :)

[AlexanderDreyer]

Patch for the sage library (devel/sage)

[AlexanderDreyer]

Fixing that trailing whitespace issue (understanding how patch-bot works).

[AlexanderDreyer]

The patchbot green-lighted, so we have positive review here?