Guys, please keep in mind that exponentials of negative bases are not really functions. They give a mix of real and multivalued complex results. You cannot treat x^(1/3) as a synonym for cuberoot (x) if x,0. The latter is a well defined function and the former is not. Perhaps this might be a good reason to introduce a new function cuberoot(x) and evaluate it (using for example Newton''s Formula). Cheers, MathBear
P.S. If you let the independent variable be the exponent and have a negative base, then for any interval of x however short, the function will flip flop infinitely often between real and multivalued complex results. The output is completely discontinuous and very messy. Just try graphing it! There is a good reason why exponential finctions of a real variable are restricted to positive bases. On Thursday, June 19, 2014 11:39 AM, David Smith <[email protected]> wrote: I could live with nthroot -- but is cuberoot (or curt or cbrt) so different from sqrt? Anyway, it would be nice to have functions that resemble ones students see routinely without generating error messages. I'm very much aware of the difficulties involved in reaching that goal, and I'll be patient. Still waiting for a solution on arcsec, as well. There the issue is primarily plotting, although "integral" fails, even with a proper domain. numerical_integral works as it should. In the great scheme of things, these are certainly peripheral issues -- and they wouldn't be issues at all if textbook authors didn't feel obliged to drag in every function they know about. As author, I'll guilty of that too (fear of the adoption committee), but in my defense, we only do these things in exercises. On Wednesday, June 18, 2014 8:48:36 PM UTC-4, kcrisman wrote: Just to chime in, as someone who has dealt with this question a lot (though, perhaps ironically, never in a classroom situation): > > >I would be very against a "cuberoot" function, but an "nthroot" function where >it was really clear what input was allowed could fly. I appreciate Greg's >rationale. Note however - what is the 0.1 power? Is that the same as the 1/10 >power? This is a tricky floating point question to interpret. > > >I don't think that the slowdown would be too bad since it would primarily be >for pedagogical purposes for plotting. > > >David, I don't know how this would work with integrals, though - we'd have to >see if Maxima had something equivalent. Perhaps it could do a temporary set >of the Maxima domain to real somehow, if that is what allows Maxima to do the >"right thing" in this context, I don't know. > > >Thanks for fighting the good fight on trying to resolve this once and for all! >- kcrisman -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-edu. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-edu. For more options, visit https://groups.google.com/d/optout.
