The solution of a cubic or quartic may require the use of complex numbers. (Indeed that's how the complex numbers were first discovered.) Below I exhibit a long expression for such a number that solve() found for me. It evaluates using n(t) to a real (decimal) number, and it passes " t in RR" although that takes five minutes and turns the fan of my laptop on (a sign of serious CPU use). Then I enter this number in range(0,t), which should be OK if t is real, but it causes the same crash that range(0,I) causes, complaining that t is complex. Below is the code (Sage version is 8.0--I plan to update Real Soon Now). Well, so you may wonder "what is the actual question"? It is, how can I get my hands on this number in a form that I can actually put into range? I want to bound a search by the size of the solution of a quartic and could not manage it because of this problem.
def test(): t = -2/3*((sqrt(3)*sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 45*sqrt(-(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) - 704/225*sqrt(3)/sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 364/675/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 368/225) + 6)^2 - 90*sqrt(3)*sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) + 4050*sqrt(-(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) - 704/225*sqrt(3)/sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 364/675/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 368/225) - 4590)/((sqrt(3)*sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 45*sqrt(-(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) - 704/225*sqrt(3)/sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 364/675/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 368/225) + 6)*(sqrt(1/3)*sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 15*sqrt(-(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) - 704/75*sqrt(1/3)/sqrt((675*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(2/3) + 552*(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 364)/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3)) - 364/675/(88/30375*I*sqrt(79)*sqrt(3) + 1328/3375)^(1/3) + 368/225) + 2)) + 0.0100000000000000 print(n(t)) print(t in RR) print(range(0,t)) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
