(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.
Waddayathink?
--
Lou Pecora
- My views are my own.
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