Re: Unexpected Output When Plotting...

*To*: mathgroup at smc.vnet.net*Subject*: [mg125500] Re: Unexpected Output When Plotting...*From*: Peter Breitfeld <phbrf at t-online.de>*Date*: Thu, 15 Mar 2012 00:37:15 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jjpb6t$p8g$1@smc.vnet.net>

James Kochanski wrote: > Can anyone explain to me why Graphs #5 and #6 (please see below) do not include any output for x < 0 and x < -1, respectively? > > Thanks! > > Jim Kochanski > > Following graphs are plotted from x = -10 to x = 10 > Graph #1 : Plot[Cos[x], {x, -10, 10}] > Graph #2 : Plot[Cos[x + 1], {x, -10, 10}] > Graph #3 : Plot[Cos[x^3], {x, -10, 10}] > Graph #4 : Plot[Cos[x^3 + 1], {x, -10, 10}] > > Following graph is only plotted from x = 0 to x = 10 > Graph #5 : Plot[Cos[(x^3)^(1/3)], {x, -10, 10}] > > Following graph is only plotted from x = -1 to x = 10 > Graph #6 : Plot[Cos[(x^3 + 1)^(1/3)], {x, -10, 10}] > This is because Mathematica always uses the principal root, eg.: (-8)^(1/3)//ComplexExpand yields 1+I Sqrt[3] and Complex Values aren't displayed with Plot. You may use the following little Funktion: Attributes[realPower] = {Listable, NumericFunction, OneIdentity} realPower[b_?Negative, Rational[m_, n_?OddQ]] := (-(-b)^(1/n))^m realPower[x_, y_] := Power[x, y] Then Plot[Cos[realPower[x^3+1,1/3]],{x,-10,10}] will plot the whole range. -- _________________________________________________________________ Peter Breitfeld | Bad Saulgau, Germany | http://www.pBreitfeld.de