Re: Graphing Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg22539] Re: [mg22476] Graphing Functions
- From: Otto Linsuain <linsuain+ at andrew.cmu.edu>
- Date: Thu, 9 Mar 2000 03:24:25 -0500 (EST)
- References: <200003080722.CAA13186@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Julian. I am not sure that the problem here is Mathematica, but
mathematics. There are several branches to the function x^(1/3), here is
a table of what is going on:
Branch Phase of x Phase of x^(1/3)
1. 0 for x>0 0 for x>0 Real positive
Pi for x<0 Pi/3 for x<0 Not real
_________________________________________________________________
2. 2Pi for x>0 2Pi/3 for x>0 Not Real
3Pi for x<0 Pi for x<0 Real negative
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3. 4Pi for x>0 4Pi/3 for x>0 Not real
5Pi for x<0 5Pi/3 for x<0 Not real
___________________________________________________________________
So Mathematica cannot choose ONE branch that would yield a real number
for x^(1/3) for all x, both positive and negative. Or, in other words,
the real function that is equal to x^(1/3) for positive x and to
-(|x|^(1/3)) for negative x is not a continuous function of the phase of
x in the complex plane. Perhaps you can force Mathematica to plot the
function for positive x, then to plot another branch for negative x and
then Show both graphs together, or define the function by parts.
You may want to look at this graph:
Plot[{Re[x^(1/3)],Im[x^(1/3)]},{x,-10,10}] it will plot both the real
and imaginary parts in one graph. Otto Linsuain.
Excerpts from mail: 8-Mar-100 [mg22476] Graphing Functions by "Julian P.
Charko"@telus
> The function in question is:
>
> x^(1/3) -
> x^(2/3).
>
> The plotting function Plot[f, xmin, xmax] seems unable to deal with cube
> roots of negative fractional real numbers.
>
> Please let me know how I can obtain a plot of the above function over
> the real number line from say, from x = -10 to x = 10.
>
- References:
- Graphing Functions
- From: "Julian P. Charko" <jcharko@telusplanet.net>
- Graphing Functions