Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>To:?maxima at math.utexas.edu
>From:?Joan?Pau?<joanpau at gmail.com>
>Sent?by:?maxima-bounces at math.utexas.edu
>Date:?06/10/2009?06:56AM
>Subject:?[Maxima]?doubt?about?conjugate
>
>I?don't?know?if?this?is?the?right?place?for?this?mail,?so?first?off
>all?excuse?me?if?it?isn't.?When?computing?the?unit?eigenvectors?for
>the?matrix?(depending?on?the?real?non-negative?parameter?c)
>
>declare(c,?real);?assume?(c>=0);
>Ap?:?matrix(
>???????????[0,1,0],
>???????????[0,0,1],
>???????????[-c,-1,0]);
>
>appears?the?conjugate?of?the?expresion
>
>exp?:?(?sqrt(3)*sqrt(27*c^2+4)-9*c?)^1/3;
>
>conjugate(exp);?/*?-->?conjugate(?(?sqrt(3)*sqrt(27*c^2+4)-9*c?)^1/3?)
>
>I?would?like?to?know?if?the?conjugate?is?not?computed?because?of?the
>three?possible?third?roots?(1?real?and?2?complex)?of?the?expression.
>It?is?possible?to?get?Maxima?or?the?conjugate?function?to?take?into
>account?only?the?real?solutions?of?a?root,?to?make?conjugate(exp)?to
>return?the?expression?unchanged?
>
>I?would?be?interested?in?how?the?conjugate?function?is?implemented,?to
>examine?it,?learn?and?maybe?do?some?suggestions.?I?found?the
>conjugate.lisp?file?under?/src,?but?the?function?definition?is?not
>there?(or?probably?I?didn't?understand?how?the?function?works).
The conjugate function is in conjugate.lisp--look for the function
simp-conjugagte.
As for why Maxima is unable to determine that ( sqrt(3)*sqrt(27*c^2
+4)-9*c )^1/3 is
real when c >=0, I don't know right now. Assuming that it is real, I think
the problem
is that Maxima is unable to determine the sign of the argument of the cube
root. As
the author of conjugate.lisp, at least I would like to blame the sign code,
not
conjugagte.lisp :) But I'll take a look at this soon.
Barton