I have searched the mathworld.wolfram.com and here is what I found:

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc.

And here is a definition of congruerence which is what should applicable here. It defines the modulus as a set of numbers, so that -3 and 1 are both the modulus for your example. To define the operation well you need to take not the modulus but the common residue which is unique and is nonnegative. And this is what does Perl.

In reply to Re: Modulus Inconsistencies (Or Calling all Mathematicians) by zby
in thread Modulus Inconsistencies (Or Calling all Mathematicians) by RollyGuy

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