Incorrect results and quirks

[B1nary0]

(03-31-2015 04:24 AM)Tim Wessman Wrote:  Hello,

I would invite you to consider what wolfram alpha spits out here:
http://www.wolframalpha.com/input/?i=X^%281%2F3%29

You'll notice that your X^1/3 does not return a nice, real number like you want. This is because the principal root - the one that makes the most sense mathematically - *is* complex for X < 0. You must click "change to real valued root" on that site to change it. This is equivalent to using ^ vs NTHROOT on the calculator. NTHROOT will give the real root while ^ returns the principle root. I would say that matching what is considered generally to be considered the best math software in the world (mathematica) would normally be considered a good thing!

As for the (-) confusion, please remember that the negative operator is not the same as the minus operator in algebraic evaluation on calculators. Take a look at this output from the nspire. :-)



On algebraic systems, the negative operator has a lower precedence then ^. So you are really evaluating -(1^1/3) not (-1)^1/3 as you might be thinking. Uh-oh! there is also that "non real root" error I mentioned in my first post.

When you have a stored variable such as in your program, the value is used directly and so it is like surrounding your variable with a set of parenthesis. When you pass a list, it applies the arguments to each element of the list. If you hit an error, the error will be returned for the whole evaluation.

The difference is,... on the TI-nSpire and every other calculator I have ever used,.... (-1)^(1/3) returns -1,.... of course (-1)^(1/2) returns a non-real result, or an error.... is there some setting I can change to get the simple, straight forward -1 answer out of the program?,.... by the way,... if I then cube the exact version of the answer,... it returns another imaginary number rather than returning to -1