Improper integral

[Wes Loewer]

(06-12-2014 06:49 AM)parisse Wrote:  Most CAS are using the standard definition for fractional powers, i.e. complex value for negative argument, giac does the same, that's why you get a complex result, since argument is negative in 0..1.

Since this seems to be the source of a significant amount of confusion for the experienced users of this forum, I can only imagine the confusion for students.

from CAS:
5 NTHROOT -1 = -1
(-1)^(1/5) = 0.809016994375+0.587785252292*i
These are consistent with the stated CAS definitions of NTHROOT (real) and fractional powers (complex).

from Home:
5 NTHROOT -1 = -1
(-1)^(1/5) = 0.809016994375+0.587785252292*i (in complex mode)
(-1)^(1/5) = error (in real mode)
I'm guessing this error is the result of using exp(y*ln(x)) to evaluate x^y.

I understand why each of these answers is given, but I can't help but think that the average user is going to be confused.

I realize that the Prime CAS is consistent with other CAS's, but it's quite different from other calculators. Both TI and Casio treat NTHROOT and fractional powers the same and use the Mode Complex settings to determine whether to use the real root or the complex root.

At least in American schools, students are taught that n NTHROOT x is the same as x^(1/n). The Prime's target consumer is going to expect this same behavior on their calculators.

Also, all the other graphing calculators that I'm aware of give (-1)^(1/5) = -1 in real mode. The Prime is the only one I know that gives an error. The error message alone (Error: (X<0)^(∉Z)) is enough to scare away new users.

-wes