POV-Ray : Newsgroups : povray.off-topic : DFT and FFT : Re: ax^2 + bx + c = 0 Server Time
6 Sep 2024 17:17:54 EDT (-0400)
  Re: ax^2 + bx + c = 0  
From: Invisible
Date: 19 Jan 2009 08:04:24
Message: <49747a58$1@news.povray.org>
Invisible wrote:
> Invisible wrote:
> 
>> http://planetmath.org/?op=getobj&from=objects&id=1407
>>
>> Does it make your eyes bleed?
> 
> Actually... if you gather up some of those subexpressions and represent 
> them as single letters, it's not that complicated.

Unless my eyes deceive me, this is equivilent:

J = 2a^3 - 9ab + 26c
K = Sqrt(J^2 + 4(-a^2 + 3b)^3)
M = (1 + i Sqrt(3))/2
N = (-1 + i Sqrt(3))/2

r1 = -(a/3) +   Cbrt((-J + K)/54) +   Cbrt((-J - K)/54)
r2 = -(a/3) + M Cbrt((-J + K)/54) + N Cbrt((-J - K)/54)
r3 = -(a/3) + N Cbrt((-J + K)/54) + M Cbrt((-J - K)/54)

While hardly on the same level as the quadratic, it's not "that" hard.


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