[Jprogramming] jwiki/Essays/FFT

[Linda Alvord]

Or maybe imaginary roots:

   Iroots=: 13 :',._1^+:(i.y)%y'
   iroots
[: ,. _1 ^ [: +: i. % ]
   
   iroots 3
             1
 _0.5j0.866025
_0.5j_0.866025
   

Linda

-----Original Message-----
From: programming-bounces at forums.jsoftware.com
[mailto:programming-bounces at forums.jsoftware.com] On Behalf Of Bo Jacoby
Sent: Wednesday, July 18, 2012 1:09 AM
To: programming at jsoftware.com
Subject: Re: [Jprogramming] jwiki/Essays/FFT

<henryhrich at nc.rr.com> wrote: "My roots-of-unity verb was designed to get
higher accuracy than simpler approaches."

The verb
   PoU=:_1^+: NB. Power of Unity

is not contaminated by transcendental numbers such as (2p1) or
transcendental functions such as monadic (^). If (y) is rational then (PoU
y) is algebraic, so transcendence is not needed. The precision seems OK,
even without the use of ((**|)&.+.) 

   n,.PoU(n=.i.8)%8
0                   1
1   0.707107j0.707107
2                 0j1
3  _0.707107j0.707107
4                  _1
5 _0.707107j_0.707107
6                0j_1
7  0.707107j_0.707107
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