Hi Laurent, On 1 Mai, 16:33, Laurent <[email protected]> wrote: > Or, alternatively, how do I get the radical form of a in the following ? > sage: sageMatrix = matrix(QQ,[[1,4],[4,2]]) > sage: eig=sageMatrix.eigenvalues() > sage: eig[0] > sage: a=eig[0]
Kind of a solution is provided by the method as_number_field_element: sage: M = matrix(QQ,[[1,4],[4,2]]) sage: ev1,ev2 = M.eigenvalues() sage: ev1.as_number_field_element() (Number Field in a with defining polynomial y^2 - y - 16, -a + 2, Ring morphism: From: Number Field in a with defining polynomial y^2 - y - 16 To: Algebraic Real Field Defn: a |--> 4.531128874149275?) So, ev1 (and ev2 as well) are obtained from minus the roots of x^2- x-16 plus two. And the polynomial can be solved for: sage: solve(x^2-x-16,x) [x == -1/2*sqrt(65) + 1/2, x == 1/2*sqrt(65) + 1/2] Confirming the result: sage: RR(-(-1/2*sqrt(65) + 1/2)+2) == RR(ev2) True sage: RR(-(1/2*sqrt(65) + 1/2)+2) == RR(ev1) True Certainly the above can somehow be automated. 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
