[Maxima] solve remembers too much, asks odd questions.

[Richard Fateman]

On 11/7/2010 4:22 AM, Barton Willis wrote:
>
> Isn't something terribly wrong? For b = 1 + %i and y = 9/10, my condition gives
>
>    b * ceiling(((1/b + conjugate(1/b))*carg(y) - 2 * %pi)/(4*%pi)) = (1 + %i) * ceiling((0 - 2 * %pi)/(4 * %pi)) =
>      (1 + %i) * ceiling(-1/2) = 0.
>
> So I claim that ((9/10)^(1/(1+%i))^(1+%i) = 9/10.


>   The option variables
> domain, m1pbranch, and numer_pbranch alter the way Maxima evaluates / simplifies
> powers. Might these option variables to be the problem? Further (maybe this is weak evidence)
>
> Welcome to Clozure Common Lisp Version 1.6-dev  (WindowsX8632)!
> ? (setf b (complex 1 1))
> #C(1 1)
> ? (expt (expt (/ 9 10) (/ b)) b)
> #C(0.8999999 -7.376074E-8)
> ?
> How how quaint: The result is a binary32 float.
>
GCL gives
#C(0.90000000000000002 -6.2450045135165055E-17)
confirming the result.  so Maxima seems to be terribly wrong.
(I suspect that my paper and your result coincide,  but I'm not paid 
enough to check :)
  Frankly, I thought the area around 1.0 would confirm the identity, and 
some other places
identified in my paper would show the examples where the identity fails)

RJF