Hi, I have a symbolic polynomial system that I would like to characterize the roots of. Although I know that if there are any roots they are real and positive, the polynomials involve square roots (of positive quantities) and sage does not seem to like that and nor does it like ^(1/2). The following is sufficient to illustrate my problem:
---------------------------------------------------------------------- | Sage Version 4.3.3, Release Date: 2010-02-21 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- sage: R.<x,y,z> = QQ[] sage: ideal(sqrt(x) - 2, y - 2*x, x - z**2).groebner_basis() --------------------------------------------------------------------------- ... AttributeError: 'Ideal_generic' object has no attribute 'groebner_basis' due to the sqrt(x). I would like the output to be [z^2 - 4, x - 4, y - 8] Is it possible to persuade sage to coerce sqrt(x) - 2 to x - 4 if we assume that x is non-negative? Also, this error message does not seem to be specific to QQ. Of course, I could rewrite sqrt(x) - 2 myself so that sage yields the correct answer. But in my actual situation, there are many polynomials and they involve square roots in complicated ways (nested fractions and so forth), so rewriting it all by hand (correctly) is not an attractive prospect. Or does anyone know of an open-source (or closed in a pinch) that will solve for the roots of a complicated polynomial system when there are square roots? I do not need support for arbitrary exponents, just square roots and multiples of 2. Thank you very much, Ben -- 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
