realpart strangeness, was: besselarray bug, was: Bessel plotting problem

I have been finding a goldmine of neet relations here between trigonometry and the bessel_j function.  I am attaching my wxm file.  Note that all the angles are exact integers when expressed in degrees!  You can view it in wxMaxima which is your creation I think.  I even took the determinant of the matrix because I am just insane enough to try it.  It's zero.

Rich



 ------------Original Message------------
From: "Andrej Vodopivec" <andrej.vodopivec at gmail.com>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Maxima - list" <maxima at math.utexas.edu>
Date: Fri, Jun-13-2008 1:24 PM
Subject: Re: [Maxima] realpart strangeness, was: besselarray bug, was: Bessel plotting problem

Some more examples:

(%i1) create_list(bessel_j(1/3, -x), x, 1, 10), numer$
(%i2) map(x->realpart(x)/imagpart(x), %)$
(%i3) identify(%);
(%o3) [1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3),1/sqrt(3)]

(%i4) create_list(bessel_j(1/5, -x), x, 1, 10), numer$
(%i5) map(x->realpart(x)/imagpart(x), %)$
(%i6) identify(%);
(%o6) [sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5),
sqrt(2*sqrt(5)+5)/sqrt(5),sqrt(2*sqrt(5)+5)/sqrt(5)]

(%i7) create_list(bessel_j(1/6, -x), x, 1, 10), numer$
(%i8) map(x->realpart(x)/imagpart(x), %)$
(%i9) identify(%);
(%o9) [sqrt(3),sqrt(3),sqrt(3),sqrt(3),sqrt(3),sqrt(3),sqrt(3),sqrt(3),sqrt(3),sqrt(3)]

(%i10) create_list(bessel_j(1/8, -x), x, 1, 10), numer$
(%i11) map(x->realpart(x)/imagpart(x), %)$
(%i12) identify(%);
(%o12) [sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1,sqrt(2)+1]

The code for identify is here:
http://wxmaxima.sf.net/identify.zip

HTH,

Andrej
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Neet.wxm
Type: application/wxm
Size: 3221 bytes
Desc: not available
Url : http://www.math.utexas.edu/pipermail/maxima/attachments/20080613/57e903de/attachment.bin