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**Subject**: **Re: Modulo (for complex)**
**From**: Gavin Wraith <gavin@...>
**Date**: Thu, 04 Oct 2007 12:38:11 +0100

In message <500E9E7B-B73A-4C87-9E24-6A238371BDEF@dnainternet.net> you wrote:
> How should the % operator be defined for complex numbers, then? :)
There is no point in having % for reals or complexes; nor for any field.
It is useful for principal ideal domains whose nontrivial quotients
are finite, e.g. the integers, or the Gaussian integers (if you want
some complex numbers). Call a Gaussian integer x+iy "first quadrant"
if x>0 and y>=0. Then one can define quotient q and remainder r of two
Gaussian integers a and b, with b nonzero, such that a = b*q+r,
where r belongs to the first quadrant or is zero and has absolute value (distance from 0) less than that of b. This r is the right definition
of a%b and it has the property that a1%b == a2%b only when a1-a2
is a multiple of b.
--
Gavin Wraith (gavin@wra1th.plus.com)
Home page: http://www.wra1th.plus.com/