Something that perhaps could be added is that leaving 0 `gcd` 0 undefined has two obvious annoying consequences: gcd is no longer idempotent (i.e. we don't have a `gcd` a = a, for all a), and it is no longer associative ((a `gcd` 0) `gcd` 0 is well-defined whilst a `gcd` (0 `gcd` 0) is not).
(We actually wrote something about this on a recent paper. If you're interested, see http://www.joaoff.com/publications/2009/euclid-alg ) Regards, Joao 2009/5/3 Nathan Bloomfield <nblo...@gmail.com> > > This, to defend myself, was not how it was explained in high school. > > No worries. I didn't realize this myself until college; most nonspecialist > teachers just don't know any better. Nor did, it appears, the original > authors of the Haskell Prelude. :) > > BTW, this definition of gcd makes it possible to consider gcds in rings > that otherwise have no natural order- such as rings of polynomials in > several variables, group rings, et cetera. > > Nathan Bloomfield > > > On Sun, May 3, 2009 at 11:16 AM, Achim Schneider <bars...@web.de> wrote: > >> Nathan Bloomfield <nblo...@gmail.com> wrote: >> >> > The "greatest" in gcd is not w.r.t. the canonical ordering on the >> > naturals; rather w.r.t. the partial order given by the divides >> > relation. >> > >> This, to defend myself, was not how it was explained in high school. >> >> -- >> (c) this sig last receiving data processing entity. Inspect headers >> for copyright history. All rights reserved. Copying, hiring, renting, >> performance and/or quoting of this signature prohibited. >> >> >> _______________________________________________ >> Haskell-Cafe mailing list >> Haskell-Cafe@haskell.org >> http://www.haskell.org/mailman/listinfo/haskell-cafe >> > > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe > >
_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
