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euclidean algorithm for complex numbers
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You are currently reading a thread in /sci/ - Science & Math

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