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Code Snippets / [DBP] - The first few algebraic numbers

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Neuro Fuzzy
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Posted: 26th Dec 2011 00:31 Edited at: 26th Dec 2011 00:32
An algebraic number is a number that can be expressed as the root of a polynomial with integer coefficients. For example, 2 and -2 are roots of the polynomial x^2-4, so they are algebraic. The complex constant i is also algebraic, since it is a root of x^2
+1. So the algebraic numbers are a subset of the complex numbers. A number like sqrt(3)/3 is algebraic, while pi or e are not. This program creates a bunch of polynomials (that's what that ugly bunch of for statements is, creating polynomials like "-1+x^2-3x^4"), finds their roots (using newton's method), then returns them and plots them based on the polynomial's degree and the size of its coefficients.




Inspired by this:
http://en.wikipedia.org/wiki/File:Algebraicszoom.png
[edit]
I'll also add: it plots about 16,000 points, each of those the result of a root finding operation, so it takes about 30 seconds to calculate it all. The picture I linked to has about 163,000 points, so that's one of the reasons my version looks worse

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