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

On Thu, Jun 12, 2008 at 12:53 PM, Richard Fateman
<fateman at cs.berkeley.edu> wrote:
> Seems to me that realpart should operate only on constants that look like
> <realnumber> + <realnumber>*%i.
> rectform is another functionality, trying to obtain  <evaluable-to-a-real>
> +<evaluable-to-a-real>*%i

Currently, rectform(expr) is precisely equal to
realpart(expr)+%i*imagpart(expr) and polarform(expr) should be (see
below) precisely equal to cabs(expr)*%e^(%i*carg(expr)).  These seem
like reasonable definitions to me.

As it happens, there is a bug in cabs: cabs(exp(%i)) => sqrt(sin(1)^2+cos(1)^2)

This can be corrected by redefining $cabs:

    (defun $cabs (xx) (cabs xx))

I do not know who introduced the current strange definition of $cabs;
I'm pretty sure it was not in the original.

           -s