Subject: solve remembers too much, asks odd questions.
From: Barton Willis
Date: Sun, 7 Nov 2010 06:22:57 -0600
-----maxima-bounces at math.utexas.edu wrote: -----
>What,?then,?is?the?minimal?constraint?on?y?and?b?such?that?...
>
>????y?=?(y^1/b)^b???
>
>Let's?pick?a?simple?example,?b=1+i.
My answer to this is in http://www.math.utexas.edu/pipermail/maxima/2010/023053.html. Specializing
my condition to (y^1/b)^b gives
b * ceiling(((1/b + conjugate(1/b))*carg(y) - 2 * %pi)/(4*%pi)) is an integer.
>define??t(y)?=??y?-?y^(1/b)^b.
>
>If?Maxima?(for?example)?is?doing?the?computation?"correctly"?can?we
>expect?that?t(y)==0??
>
>define?tt(y):rectform(ev(t(y),numer))??to?make?the?results?easier?on?the?
>eye.
>
>tt(1.0)?is?indeed?0.0??hurrah.
>
>but?tt(1.1)?is?not?zero.??tt(0.9)?is?not?zero.?not?even?close.
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.
--Barton