MPolynomial_libsingular reports the wrong degree

[saraedum]

On sage-4.7: In the following example, the degree with respect to p should be 1 and the degree with respect to q should be 2.

sage: R.<p,q,t> = ZZ[]
sage: poly = p+q^2+t^3
sage: poly = poly.polynomial(t)[0]
sage: poly
q^2 + p
sage: poly.degree(p)
1
sage: poly.degree(q)
1

The issue can be easily worked around:

sage: poly.degree(poly.parent(q))
2

(originally reported on sage-support, see ​http://groups.google.com/group/sage-support/browse_thread/thread/608bc46e92da2f49/feb54d2384cef583?lnk=gst&q=polynomial#feb54d2384cef583)

---

Apply

1. trac_11652-rewrite.patch​
2. trac_11652_review.patch​

to the sage repository.

[saraedum]

In sage-4.8.alpha3 both calls produce degree 1.

[saraedum]

fixes detection of generators

[was]

apply this instead of trac_11652.patch -- it's a rewrite

[was]

I was going to referee this, but instead ended up improving the documentation (a lot) and rewriting the logic a bit. saraedum can you referee the new patch?

[zimmerma]

all doctests pass on top of sage-4.8.alpha6 on x64, however:

sage: R.<p,q,t> = ZZ[]
sage: poly = p+q^2+t^3
sage: poly = poly.polynomial(t)[0]
sage: poly.degree(p)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
TypeError: argument must canonically coerce to parent

I don't understand since the documentation says:

sage: poly.degree?
...
Definition:     poly.degree(self, x=None, std_grading=False)
...
       Return the maximal degree of this polynomial in "x", where "x" must
       be one of the generators for the parent of this polynomial.

Indeed p is one of those generators:

sage: p in poly.parent().gens()
True

Thus either the code or the documentation has to be fixed.

Paul

[saraedum]

The output for the example in the ticket description has changed. However, it's still wrong.

sage: poly
q^2 + p
sage: poly.degree(p)
1
sage: poly.degree(q)
1

[saraedum]

Apply trac_11652-rewrite.patch trac_11652_review.patch

[saraedum]

Replying to zimmerma:

I don't understand since the documentation says:

       Return the maximal degree of this polynomial in "x", where "x" must
       be one of the generators for the parent of this polynomial.

Indeed p is one of those generators:

sage: p in poly.parent().gens()
True

I tried to make the INPUT section a little more precise. But I believe that writing that x 'is' a generator and not only that x '==' a generator would be overdoing it.

Is it acceptable for you this way?

[roed]

This looks fine to me.

[jdemeyer]

Are the "work issues" still relevant? If not, please remove them.

[zimmerma]

Are the "work issues" still relevant? If not, please remove them.

I don't know. However the following in the description seems wrong:

sage: poly.degree(poly.parent(q))
1

since I get 2 with Sage 5.1.

Paul

[roed]

I've removed the work issues, changed the ticket description and marked it as positive review again. However, Paul originally objected to the documentation, so if he wants to request additional changes he should feel free to return the ticket to needs work. I just marked it as positive review since I thought that his concerns had been addressed and there hadn't been any comments for a few months.

[zimmerma]

I tried the patch on top of Sage 5.3 and got:

sage: R.<p,q,t> = ZZ[]
sage: poly = p+q^2+t^3
sage: poly = poly.polynomial(t)[0]
sage: poly
q^2 + p
sage: poly.degree(p)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/tmp/<ipython console> in <module>()

/usr/local/sage-5.3/sage/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_libsingular.so in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.degree (sage/rings/polynomial/multi_polynomial_libsingular.cpp:17832)()

TypeError: argument must canonically coerce to parent

Is that normal?

Paul

[roed]

Yes, that's correct. p is in Z[p,q,t], poly is in Z[p,q] and there's no coercion from Z[p,q,t] to Z[p,q].

[zimmerma]

David, for the variables p and q, there is a trivial conversion...

Anyway the issue raised in comment 5 is still there:

sage: poly.degree?
...
       Return the maximal degree of this polynomial in "x", where "x" must
       be one of the generators for the parent of this polynomial.
sage: poly.parent().gens()
(p, q)
sage: poly.degree(p)
...
TypeError: argument must canonically coerce to parent

According to the documentation, this should work.

[saraedum]

Replying to zimmerma:

David, for the variables p and q, there is a trivial conversion...

Anyway the issue raised in comment 5 is still there:

sage: poly.degree?
...
       Return the maximal degree of this polynomial in "x", where "x" must
       be one of the generators for the parent of this polynomial.
sage: poly.parent().gens()
(p, q)
sage: poly.degree(p)
...
TypeError: argument must canonically coerce to parent

According to the documentation, this should work.

Probably you did not have the latest patch applied. With the latest patch I get:

   * "x" - (default: "None") a multivariate polynomial which is (or
     coerces to) a generator of the parent of self. If "x" is "None",
     return the total degree, which is the maximum degree of any
     monomial. Note that a matrix term ordering alters the grading of
     the generators of the ring; see the tests below.  To avoid this
     behavior, use either "exponents()" for the exponents themselves,
     or the optional argument "std_grading=False".

[saraedum]

Sorry, you were referring to the summary and not to the parameter description. I believe it is acceptable that the summary is slightly imprecise; that's what the parameters' description is for.

---

New commits:

​7e35305	Trac 11652: fixes degree for multivariate libsingular polynomials
​54604e4	Trac 11652: Review patch for the docstring of degree() for multivariate polynomials

[zimmerma]

all tests pass on top of Sage 6.0 (except one which seems unrelated). Thus a positive review for me.

Paul