help-octave
[Top][All Lists]

## Re: plotting even function

 From: Thomas Shores Subject: Re: plotting even function Date: Sat, 19 Mar 2005 20:48:06 +0000 User-agent: KMail/1.7.1

```Umm... make that
y = 3/4*((2*x)^2)^(1/3) + 1/2

So add to my last plotting suggestions

octave:5> y = 3/4*((2*x).^2).^(1/3)+1/2;
octave:6> plot(x,y)

Tom Shores

On Saturday 19 March 2005 08:36 pm, Thomas Shores wrote:
> Hmmm...
> Well, actually the function really *is* even if you think of
> it this way:
>
> y  = 3/4*((2*x)^2)^3 + 1/2
>
> Here's the problem: how do you know that the exponent is a
> rational fraction, so that you can reinterpret it?  Octave
> rightfully doesn't.  It evidently uses complex analysis to
> find non-integral powers.  Try this
>
> octave:16> x = (-1)^(1/3)
> x = 0.50000 + 0.86603i
> octave:17> x^3
> ans = -1.0000e+00 + 3.6370e-16i
>
> So octave calculates a complex third root of unity, rather
> than the real root x = -1 that might spring to mind.  Makes
> sense, since you can generate the other roots from the
> complex primitive root of unity.
>
> Tom Shores
>
> On Sunday 20 March 2005 01:20 am, Geraint Paul Bevan wrote:
> > -----BEGIN PGP SIGNED MESSAGE-----
> > Hash: SHA1
> >
> > John B. Thoo wrote:
> > | Hi.  I hope that I'm not embarrassing myself by asking
> > | the following.
> > |
> > | I believe that
> > |
> > |        3       2/3    1
> > |   y = --- (2 x)    + ---
> > |        4              2
> > |
> > | is an even function, yet
> > |
> > | x = -1:0.04:1;
> > | plot (x, 0.75 * (2 .* x).^(2 / 3) + 0.5)
> > |
> > | is not symmetrical about the y-axis.  What is wrong with
> > | my thinking?
> > |
> > | TIA.
> > | ---John.
> >
> > x^(2/3) is not an even function,
> >
> > octave:1> [ (+8)^(2/3) ; (-8)^(2/3) ]
> > ans =
> >
> > ~    4.0000 + 0.0000i
> > ~   -2.0000 + 3.4641i
> >
> > so nor is the function which you are plotting.
> >
> > - --
> > Geraint Bevan
> > http://homepage.ntlworld.com/geraint.bevan
> >
> > -----BEGIN PGP SIGNATURE-----
> > Version: GnuPG v1.2.4 (GNU/Linux)
> >
> > iEYEARECAAYFAkI8z/sACgkQcXV3N50QmNOi1QCdEvZ44CO0bbl0h+TQvgF
> >pD 9uy YQgAn2a4A1x4m7ZdST8vG9IBRgBu1lCW
> > =7F+W
> > -----END PGP SIGNATURE-----
> >
> >
> >
> > -----------------------------------------------------------
> >-- 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
> > -----------------------------------------------------------
> >--
>
> -------------------------------------------------------------
> 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
> -------------------------------------------------------------

-------------------------------------------------------------
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
-------------------------------------------------------------

```