Re : Re: how to handle roots of unity symbolically ?
Subject: Re : Re: how to handle roots of unity symbolically ?
From: Roberto Fernandez
Date: Fri, 23 Nov 2012 18:01:25 +0100 (CET)
----- harald at lefant.net a ?crit?:
>
> > this simplifies some expressions, but fails with others, for example:
> > when w^6=1 , w^2-w+1 is not simplified, when 0 was expected...
>
> I believe your test case is wrong:
> Consider w=1 is a solution of w^6=1, but 1^2-1+1 = 1 not 0 as you
> seem to expect...
>
sorry, I've not been clear enough.
"w" can't be instantiated to every root of unity, only to the ones which generate the group.
for w^n = 1, "w" can only be instantiated to the solutions for which [w^0, w^1, w^2, ... w^(n-1)] is the set of ALL the roots.
as an example, it can always be instantiated to %e^(2*%i*%pi/n)