I am working in the area of non-symmetric Macdonald polynomials, specifically, I am trying to write a function that implements formula 7 of "A Combinatorial formula for nonsymmetric Macdonald Polynomials" by Haglund, Haiman, and Loehr. Currently, I am having difficulty factoring polynomials in sage. Here are some examples of what works and what doesn't work:
Factoring in a polynomial ring over a polynomial ring fails in sage: sage: S.<q>=QQ[];S Univariate Polynomial Ring in q over Rational Field sage: R.<x0,x1>=S[];R Multivariate Polynomial Ring in x0, x1 over Univariate Polynomial Ring in q over Rational Field sage: f=(x0*x1+x1^2)/(x0+x1);f (x0*x1 + x1^2)/(x0 + x1) sage: f.factor() TypeError: no conversion of this ring to a Singular ring defined Factoring in a polynomial ring over a fraction field works with positive coefficients in sage: sage: S.<q> = QQ[]; S Univariate Polynomial Ring in q over Rational Field sage: S = FractionField(S); S Fraction Field of Univariate Polynomial Ring in q over Rational Field sage: R.<x0,x1> = S[]; R Multivariate Polynomial Ring in x0, x1 over Fraction Field of Univariate Polynomial Ring in q over Rational Field sage: f=(x0*x1+x1^2)/(x0+x1);f (x0*x1 + x1^2)/(x0 + x1) sage: f.factor() x1 But when negative coefficients are used, sage doesn't want to factor: sage: S.<q>=QQ[];S Univariate Polynomial Ring in q over Rational Field sage: S=FractionField(S);S Fraction Field of Univariate Polynomial Ring in q over Rational Field sage: R.<x0,x1>=S[];R Multivariate Polynomial Ring in x0, x1 over Fraction Field of Univariate Polynomial Ring in q over Rational Field sage: f=(-x0*x1+x1^2)/(-x0+x1);f (-x0*x1 + x1^2)/(-x0 + x1) sage: f.factor() TypeError: Cannot multiply (-1) * x1 * (x0 - x1) and (1/(-1)) * (x0 - x1)^-1 because they cannot be coerced into a common universe My desired result: I would like to be able to factor in polynomial rings over polynomial rings, like in example one above, regardless of coefficients. My question: Does anyone know of a quick and easy (I'm a newbie at sage) fix for these problems? And does anyone know if sage will have support for such factoring in a later version? Thanks for your help. Jeff --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
