On Fri, May 21, 2010 at 5:03 PM, Anne Schilling <a...@math.ucdavis.edu> wrote: > Hi Simon! > > Thank you very much for your answer. > >> On May 18, 7:47 am, Anne Schilling <nicolas.thi...@u-psud.fr> wrote: >>> >>> sage: LD.<d>=LaurentPolynomialRing(QQ) >>> sage: P=PolynomialRing(LD,'z',2) >> >> Sage tries to use Singular to factor your polynomial. Hence, it needs >> to convert both your polynomial and its ring to Singular. >> >> The problem is that your coefficients are Laurent Polynomials, but >> Singular can only do the fraction field of the Laurent polynomial >> ring. >> >> So, you can do: >> >> sage: LD.<d>=LaurentPolynomialRing(QQ) >> sage: P=PolynomialRing(Frac(LD),'z',2) >> sage: z = P.gens() >> sage: f = z[0]**2-d**2*z[1]**2 >> sage: f.factor() >> (-z0 + (-d)*z1) * (-z0 + d*z1) > > There still seems to be a problem though, since Sage does not > recognize that the answer is in P. See: > > ---------------------------------------------------------------------- > | Sage Version 4.4.1, Release Date: 2010-05-02 | > | Type notebook() for the GUI, and license() for information. | > ---------------------------------------------------------------------- > Loading Sage library. Current Mercurial branch is: combinat > sage: LD.<d>=LaurentPolynomialRing(QQ) > sage: P=PolynomialRing(Frac(LD),'z',2) > sage: z=P.gens() > sage: f=z[0]**2-d**2*z[1]**2 > sage: f in P > True > sage: g=f.factor() > sage: g > (-z0 + (-d)*z1) * (-z0 + d*z1) > sage: g in P > False
This is for the same reason that: sage: factor(6) in ZZ False sage: factor(6) 2 * 3 sage: type(factor(6)) <class 'sage.structure.factorization.Factorization'> A factorization is not an element, but a formal product -- it is its own class. You can use .prod(), though: sage: F = factor(6) sage: F.prod() 6 sage: F.prod() in ZZ True -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
