From help-request at octave dot org Tue Mar 22 06:31:38 2005 Subject: Re: plotting even function From: Gunnar To: help at octave dot org Date: Tue, 22 Mar 2005 11:59:57 +0100 On Sunday 20 March 2005 18.09, Geraint Paul Bevan wrote: > John B. Thoo wrote: > > Also, why is (x^(1/3))^2 not even? If f(x) = (x^(1/3))^2, then isn't > > f(-x) = ((-x)^(1/3))^2 = (- x^(1/3))^2 = (x^(1/3))^2 = f(x) > > It is not true to say that (-x)^(1/3) is the same as -(x^(1/3)). That > is one possibility but there are two more. If n is an integer, x^n has > a unique value but x^(1/n) has n possible values i.e. the square root > x^(1/2) has two possible values, the cube root x^(1/3) has three > possible values, etc. Isn't that just a matter of definition and our frames of references? What do we mean when we talk about a^(1/3) ? In simple real analysis it means the positive solution, x, to the equation x^3=a for a>0, and when a<0 it is then -x where x is the positive solution to x^3= -a. At this level x^(2/3) is even. It's not even when you have studied complex analysis, but of course, then you know how to make it an even function, and you can also make it a not-even, and not-odd function. I must say that I enjoyed reading this discussion. B.t.w. Maple does not plot anything for negative x-values for the function x^(2/3). It also does not simplify (-1)^(2/3) to -1. Cheers, Gunnar. ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web: http://www.octave.org How to fund new projects: http://www.octave.org/funding.html Subscription information: http://www.octave.org/archive.html -------------------------------------------------------------