On Jan 23, 11:41 pm, Paul Zimmermann <[EMAIL PROTECTED]> wrote: > Thus you have constructed a nice expression for 1: > > sage: sol[2].subs(a=1).right() > (2/(3*sqrt(3)) + 10/27)^(1/3) - 2/(9*(2/(3*sqrt(3)) + 10/27)^(1/3)) + 1/3 > > Quiz: how to simplify that expression to 1 within SAGE? I've tried simplify, > and radical_simplify, but neither succeeds...
The Sage rings AA and QQbar can decide equalities between radical expressions (over the reals and complex numbers respectively): sage: a = AA((2/(3*sqrt(3)) + 10/27)^(1/3) - 2/(9*(2/(3*sqrt(3)) + 10/27)^(1/3)) + 1/3) sage: a [0.99999999999999988 .. 1.0000000000000003] sage: a == 1 True By the way, when I implemented AA/QQbar, I decided on the following behavior for exponentiation: sage: AA(-1)^(1/3) -1 sage: QQbar(-1)^(1/3) [0.49999999999999994 .. 0.50000000000000012] + [0.86602540378443859 .. 0.86602540378443871]*I So when taking roots, for AA we prefer real roots if they exist, but for QQbar we take the principal root. Carl Witty --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com 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 -~----------~----~----~----~------~----~------~--~---
