On Feb 8, 12:52 pm, William Stein <[email protected]> wrote: > Since you're lucky and all conjugates are expressible in terms of > radicals, the following > easily gives all 8: > > sage: t = sqrt(2-sqrt(2)) + i*sqrt(sqrt(2)-1) > sage: f = t.minpoly(); f > x^8 - 12*x^6 + 6*x^4 - 12*x^2 + 1
Do you really need radicals, or do you just want exact results rather than floating-point approximations? If the latter, you can use: sage: t = sqrt(2-sqrt(2)) + i*sqrt(sqrt(2)-1) sage: f = t.minpoly(); f x^8 - 12*x^6 + 6*x^4 - 12*x^2 + 1 sage: f.roots(ring=QQbar, multiplicities=False) [-0.2939850909925362?, 0.2939850909925362?, 3.401533039052611?, -3.401533039052611?, 0.7653668647301795? + 0.6435942529055826?*I, 0.7653668647301795? - 0.6435942529055826?*I, -0.7653668647301795? + 0.6435942529055826?*I, -0.7653668647301795? - 0.6435942529055826?*I] While elements of QQbar usually print as floating-point approximations, operations with them are actually exact. Carl --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
