Nathan Bloomfield wrote:
Hello haskell-cafe;
I'm fiddling with this http://cdsmith.wordpress.com/2009/07/20/calculating-multiplicative-inverses-... blog post about inverting elements of Z/(p), trying to write the inversion function in pointfree style. This led me to try executing statements like
n `mod` 0
which in the ring theoretic sense should be n, at least for integers*. (MathWorld agrees. http://mathworld.wolfram.com/Congruence.html)
I agree that (n `mod` 0) ought to be n. Specifically divMod n 0 = (0,n) and quotRem n 0 = (0,n) In (divMod n m) the sign of the remainder is always the same as the sign of m, unless n or m is zero. In (quotRem n m) the sign of the quotient is the product of the signs of n and m, unless n or m is zero. -- Chris