---------- Forwarded message ---------- From: Bobby Moretti <[EMAIL PROTECTED]> Date: Jan 21, 2007 3:59 PM Subject: Re: [sage-devel] factor(n) reducing some polynomials over the rationals To: [EMAIL PROTECTED]
The indeterminate 'x', predefined as a polynomial ring element, gets imported automatically: ---------------------------------------------------------------------- | SAGE Version 1.7.1, Release Date: 2007-01-18 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- Loading SAGE library. Current Mercurial branch is: calc sage: type(x) <class 'sage.rings.polynomial_element.Polynomial_rational_dense'> So if you define any polynomials in terms of arithmetic with x, it will assume that your polynomial is over the rationals. If you want a polynomial over the integers, you have to specify this ring manually. If you do g.<x> = PolynomialRing(ZZ) Then it overloads x, and x becomes an indeterminate for polynomials over the integers. sage: g.<x> = PolynomialRing(ZZ) sage: type(x) <class 'sage.rings.polynomial_element.Polynomial_integer_dense'> sage: factor(2*x^2+1) 2*x^2 + 1 On 1/21/07, Timothy Clemans <[EMAIL PROTECTED]> wrote: > > "sage: factor(n)" should only reduce input over the integers. > > sage: factor(2*x^2 + x + 1) > (2) * (x^2 + 1/2*x + 1/2) > sage: factor(2*x^2 + x + 2) > (2) * (x^2 + 1/2*x + 1) > sage: factor(2*x^2 + x + 3) > (2) * (x^2 + 1/2*x + 3/2) > sage: factor(2*x^2 + x + 4) > (2) * (x^2 + 1/2*x + 2) > > Is there a function in SAGE or one of the components that reduces > polynomials only over the integers? > > > > > -- Bobby Moretti [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
