Hi! On 4 Sep., 22:52, tvn <[email protected]> wrote: > HI Jason, I tried what you posted and get some errors , I am using > the latest Sage version 4.5.2 > > ---------------------------------------------------------------------- > | Sage Version 4.5.2, Release Date: 2010-08-05 | > | Type notebook() for the GUI, and license() for information. | > ---------------------------------------------------------------------- > sage: R.<x,y>=CC['x','y'] > sage: f = x-y > sage: g = x^2 -y^2 > sage: I = R.ide > R.ideal R.ideal_monoid > sage: I = R.ideal([f]).radical() > <BOOM>
If you want to handle solutions in CC, it is not necessarily the case that the Gröbner basis computations have to be over CC. The problem is that elements of CC are not "exact". But when computing a Gröbner basis, rounding errors are fatal. However, if all your polynomials have rational coefficients, the radical can be computed over the rationals, too. So, you may do sage: R.<x,y>=QQ[] # a convenient way to define a ring sage: f = x-y sage: g = x^2-y^2 sage: I = R*[f] # a convenient way to define an ideal sage: G = I.radical().groebner_basis() sage: G [x - y] sage: g.reduce(G) # test that g belongs to the radical of I 0 You can consult the documentation by sage: I.radical? and of course it might be a good idea to look into a textbook in order to see if the radical really does what you need. Cheers, Simon -- 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-support URL: http://www.sagemath.org
