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just a quick question: are you referring to mod or modulo or some combination of the two?

yup, the simplification seemingly doesn't even hold for the -1.6 example...

the sum-free formula returns 0.4, so it seems correct, the simplified formula some complex number and the log and exp free one actually even totally simplifys to -z, which makes it totally useless, of course...



if that formula indeed is the correct one, the cool thing about it would be, that a complex a also is defined that way.

EDIT!
Since LaTex apparently is (or at some point was) broken, all the results are lost...
Here is the final Complex Mod Function with z and a being complex numbers:

z mod a = CMod(z,a)=π+ i (e^{2 i π z/a} Log(1-e^{-2 i π z/a})-e^{-2 i π z/a} Log(1-e^{2 i π z/a}))
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the simplified formula was meant to be the one where I converted log()-log() to log(/).
That one somehow does not return correct results.

but if we stick to log()-log(), everything seems to work nicely.
Now I'd like to see an Mset with that formula rather than the symmetric approach.
Reading about mod, I found out that both variants are kind of valid. One, however, is called "mathematical" and the other one "symmetrical"

The symmetrical one is mod(|z|,a)*sign(z) and doesn't really allow for a complex a.
The mathematical one is the more complicated one...
, which has the big advantage to even work in case of a complex a. No idea if that would make any sense, though