# (Numeric) should -7 % 5 = -2 ?

Louis M. Pecora pecora at anvil.nrl.navy.mil
Tue Jul 1 17:19:59 CEST 2003

```In article <3g32gvcolis4485956egtc35akm6lh3uq5 at 4ax.com>, Tim Roberts
<timr at probo.com> wrote:

> >Hmmm...  "remainder" makes sense.  But "%" is mod, right.  IIRC from my
> >abstract algebra days (only 30 yrs ago :-) ) The "X mod n" function
> >maps onto the postive integers from 0 to n-1.  So sounds like numeric
> >contradicts the math texts.  Not good since it's a math module.
>
> That's a bit harsh.

You may be right.  I got to work and checked my old Abstract Algebra
book.  The defintion is,

We write  a=b mod m if m divides (a-b) (i.e. no remeinder).

The defintion does not say how to compute the mod, rather it is an
expression of a relationship between a and b.  Hence, writing -2=-7 mod
5 appears to be OK.

The "uniqueness" comes in when we recogize that mod m defines an
equivalence relation on the integers and so for a given m every integer
falls into a unique class (or subset of integers).  The set of m
subsets is equivalent to the positive integers  0 to m-1.

So it appears that the translation between math and computer science is
not as clear as I thought.  In math (well, number theory) mod is a
relation, not an operation.  In computer science it is an operation.