Re: RE: notation help: f(x) = (sin x)^(1/3)

• To: mathgroup at smc.vnet.net
• Subject: [mg29995] Re: [mg29977] RE: [mg29947] notation help: f(x) = (sin x)^(1/3)
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Sat, 21 Jul 2001 00:49:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```No. For example, by default

In[9]:=
N[(-1)^(1/3)]
Out[9]=
0.5 + 0.866025 I

which is standard in most of mathematics beyond high school. Moreover, there
are very good reasons why a symbolic algebra program would by default assume
that all functions are complex. In general the algorithms needed to deal
with complex functions are much faster than corresponding real ones and
there are lots of problems, even those concerned exclusively with real
analysis which can't be solved at all without using complex numbers.

--
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/~andrzej/

> I have a follow-up to this.  Although I get a partial graph, I get a message
> about some domain values that return non-real machine size numbers, or
> something to that effect.  In fact, I defined f[x_]=(Sin[x])^(1/3) and when
> I found f[values in error message] mathematica returned one of the imaginary
> solutions, as opposed to the real solution.  I understand that I can 'force'
> mathematica to return the real solution, but shouldn't it do that by
> default?
>
> -----Original Message-----
> From: Tim 9-23 [mailto:bendoftimeb at stny.rr.com]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg29995] [mg29977] [mg29947] notation help: f(x) = (sin x)^(1/3)
>
>
> How do I plot this.  I must not be entering it correctly.  It's the
> plot of the cube root of the Sine function.
>
> Plot[[Sin[x]]^(1/3), {x, -10, 10}] isn't working.  Thanks.
>
> My email address is anti-spammed.  Remove the 2 B's after hitting email