taken from: http://dedanoe.googlepages.com/tabular_solution_bjanevski.html
Tabular Solution To Polynomials Out Of Exact Coefficients
I bet you never heard of this: How would you solve an polynomial out
of exact coefficients
using simple tabular calculus. One Great Armageddonian Dedanoe's
friend,
the sch.math.i.char Borce Janevski came up with it and it's quite
funny and functional.
Here it is:
Say we have the polynomial P(x)=a[n]x^n+a[n-1]x^(n-1)+...+a[2]x^2+a[1]x
+a[0]=0 and
we are looking to find the first x that reduces the power of P(x).
First things first:
Let's consider the array with power=2:
....01, 04, 09, 16, 25, 36...
....03, 05, 07, 09, 11...
....02, 02, 02, 02...
where red-blue=pink.
The array ends with 2!
Let's consider now the array with power=3:
....001, 008, 027, 064, 125, 216...
....007, 019, 037, 061, 091...
....012, 018, 024, 030...
....006, 006, 006...
where red-blue=pink.
The array ends with 3! and so on...
if the power=N then the array ends with N!
I cannot complete this page. I don't recall exactly how he did it, i
must consult
him again (perhaps this week) and i also need his approval to make
this devine article
published via usenet or on my google domain
Unleash death and TrueAAOO chaos,
Excellency Dedanoe Unlishnidaos.
http://dedanoe.googlepages.com
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