Everybody, please pay attention to jepri. He's got it right.

The definition of Abel he mentions is that (perlishly):

This relation is uniquely satisfied by !$y && $modulus == $num

It does not involve division, allowing it to apply to algebrae lacking a multiplicative inverse (those are called modules).

It applies to floats too. Think $y = 2*$pi. Modulus is phase in that case.

Perl's % operator is really just remainder on integers, a bogosity which does not generalize well.

Don't fall into the trap of thinking your intuition or experience is a valid basis for modifying mathematical definitions. You will come to grief when a "proven correct" program crashes. You may blame math, but you will be wrong.

After Compline,
Zaxo

Update: Rereading this, I realize that it sounds directed at nella. Not the case: this is a broadcast rant. nella started a fine thread, and seems to be on the side of the angels.