euclidean algorithm for complex numbers

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Anonymous

euclidean algorithm for complex numbers 2016-01-14 11:17:06 Post No. 7782907

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euclidean algorithm for complex numbers 2016-01-14 11:17:06 Post No. 7782907

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Hi /sci/,

Does anyone know if an algorithm exists for reducing complex numbers.

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>>7782907

reducing to reach what form?

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>>7782915

[math]a\,=\,b\,q\,+\,r[/math] where [math]q[/math] is the greatest complex number smaller than [math]\lfloor \frac{a}{b} \rfloor[/math] and [math]0\,\leqslant r \,\leqslant b\,-\,1[/math].

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>>7782925

ok, what definition of inequalities in C do you choose?

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For complex numbers in general, you can just divide a/b. I'm assuming you're referring to complex numbers where the real and imaginary parts are integers, those are called Gaussian Integers and you can indeed use a kind of euclidean algorithm. Any system with this property is called an Euclidean domain, see this link for an example using the Gaussian Integers

http://mathforum.org/library/drmath/view/67068.html

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