Re: [math-fun] Complex modulo function?

I believe that the APL language folks are the first to attempt coming up with a standard for complex modulo. I discuss these issues in a paper I wrote in 1993: http://home.pipeline.com/~hbaker1/Gaussian.html At 12:11 AM 5/16/2020, Tom Karzes wrote:

Wolfram defines mod as:

a mod b = a - b * floor(a/b)

for real or complex a and b.

I think they define complex floor as:

floor(a) = floor(re(a)) + i * floor(im(a))

for complex a.

Tom

Kerry Mitchell writes:

...

Hi all,

Is there a standard, or at least, reasonable, definition of the modulo function for complex numbers? What I've come up with is:

a mod b = r means a = qb + r,

where q is the Gaussian integer that minimizes |r|, with |qb| <= |a|.

Thanks for any guidance, Kerry