Dear support: sage: z = (-1)^(1/3) sage: z (-1)^(1/3) sage: z.n() 0.500000000000000 + 0.866025403784439*I
So far, so good - known behavior, take "primitive" root. But: sage: z^2 1 sage: (z.n())^2 -0.500000000000000 + 0.866025403784439*I This seems problematic, and is because ((-1)^(1/3))^2 == (-1)^(2/3) is true (not True), even though it's not, really, in Sage. I checked and this is independent of the Pynac switch. I could see it leading to rather different results depending on when one deciding to finally take the numerical value of a long symbolic computation. On the other hand, maybe it's another case of "be really careful when using complex numbers" - but a much more subtle one than (-1)^(1/3) not being -1. Just asking. - kcrisman --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
