#10844: Implemented discriminant for multivariate polynomials
----------------------------+-----------------------------------------------
Reporter: mmarco | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: algebra | Keywords: Polynomials Discriminant
Author: Miguel Marco | Upstream: N/A
Reviewer: Simon Spicer | Merged:
Work_issues: |
----------------------------+-----------------------------------------------
Changes (by spice):
* status: new => needs_work
* reviewer: => Simon Spicer
* milestone: => sage-4.7
Comment:
I tried testing this patch (and its addendum) on sage 4.6.2, and this
doctest failed:
{{{
sage: R.<x,y>=QQ[]
sage: f=x^5*y+3*x^2*y^2-2*x+y-1
sage: f.discriminant(y)
x^10 + 2*x^5 + 24*x^3 + 12*x^2 + 1
sage: sage: f.polynomial(y).discriminant()
---------------------------------------------------------------------------
PariError Traceback (most recent call
last)
/Users/simonspicer/sage/devel/sage-Kimberly/<ipython console> in
<module>()
/Users/simonspicer/sage/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.discriminant
(sage/rings/polynomial/polynomial_element.c:28533)()
/Users/simonspicer/sage/local/lib/python2.6/site-
packages/sage/structure/element.so in
sage.structure.element.NamedBinopMethod.__call__
(sage/structure/element.c:19623)()
/Users/simonspicer/sage/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.resultant
(sage/rings/polynomial/polynomial_element.c:28214)()
/Users/simonspicer/sage/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial._pari_
(sage/rings/polynomial/polynomial_element.c:27630)()
/Users/simonspicer/sage/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial._pari_with_name
(sage/rings/polynomial/polynomial_element.c:27755)()
/Users/simonspicer/sage/local/lib/python2.6/site-
packages/sage/libs/pari/gen.so in sage.libs.pari.gen._pari_trap
(sage/libs/pari/gen.c:46023)()
PariError: (5)
}}}
However, after applying patch #10799, which fixes `.resultant()` and
`.discriminant()` for univariate polynomials over polynomial rings, the
doctest passes. So I think that is more the PARI polynomial issue
addressed in #10799.
I therefore suggest mentioning that #10844 is dependent on #10799. Also,
you might need to recenter the patch, since both affect
sage/polynomial/polynomial_element.pyx.
Contingent on applying the above patch first, the code checks out and
passes all tests I threw at it. Once you've recentered it I can give it a
positive review.
Simon
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10844#comment:3>
Sage <http://www.sagemath.org>
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