I want to take, for example, x^2 + 1 mod a*x and get quotient (1/a)*x and remainder 1. It doesn't work if I work in PolynomialRing because then you can't have 1/a. It doesn't work in the quotient field because then you always get remainder 0. To have f.quo_rem(g) work, I must anticipate all denominators that might occur in the coefficients and multiply f by them to begin with, as shown in the following example. But I'd rather have sage treat x as a polynomial variable and the others, like a, as rational variables. Can that be done?
---------------------------------------------------------------------- | Sage Version 4.8, Release Date: 2012-01-20 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- sage: R.<a,x> = PolynomialRing(QQ,2) sage: f = x^2 + 1 sage: g = a*x sage: f.quo_rem(g) (0, x^2 + 1) sage: f.parent() Multivariate Polynomial Ring in a, x over Rational Field sage: f = a*(x^2+1) sage: f.quo_rem(g) (x, a) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
