Subject: Re : how to handle roots of unity symbolically ?
From: Richard Fateman
Date: Sat, 24 Nov 2012 10:18:48 -0800
On 11/24/2012 10:05 AM, Robert Dodier wrote:
> On 2012-11-24, Richard Fateman <fateman at eecs.berkeley.edu> wrote:
>
>> The description of tellrat should probably say that you should use a
>> minimal polynomial:
> What is the effect of tellrat(p) when p is not a minimal polynomial?
> Should tellrat attempt to find a minimal polynomial, or reject an
> argument which is not a minimal polynomial?
Costly perhaps. Needs to prove irreducibility, possibly over other
previous algebraic extensions.
Assuming minimal polynomial, all that is needed is the occasional
polynomial remainder calculation
when the degree is too great.
Probably it would be good to find an algebraic number theorist who might
care about this.
PS. regarding denesting and radcan.
1. significant denesting algorithms came later.
2. my impression is that they are somewhat expensive and perhaps not
effective. I don't recall
exactly the results, but see for example
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.5512
which might describe the algorithm in Maxima.
I think that even if an expression cannot be de-nested, it can still be
simplified or not.
It depends on how you express elements of (some, related) algebraic
extensions.
Also, introducing abs() is, so far as I can tell, death to any algebraic
simplification, where
algebra means formal fields etc. If you are doing "physics" style
calculations, then anything
goes, resulting in proofs of -1=1, etc.
RJF