# [racket-dev] feature request: gcd, lcm for rationals

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
On 09-12-11 20:04, Jens Axel Søgaard wrote:
>* One definition of greatest common divisor in a ring R is: d is a
*>* greatest common divisor of x and y when: i) d divides both x and
*>* y ii) If e is a divisor of both x and y, then d divides e
*
I think you mixed up ii) here since to get the _greatest_ common
divisor it makes more sense if any other common divisor divides the
greatest instead of the other way around.
>* Now let's consider the ring Q. Since Q is a field, 1 divides all
*>* elements.
*
Since Q is a field any non-zero element a divides any element b: a *
b/a = b. And all such non-zero divisors divide each other by the same
token.
>* It is therefore not obvious that gcd should be extendend as you
*>* suggest.
*
Indeed. The definition seems plausible at a first glance:
>* (gcd-rational 2/3 2/3)
*2/3
>* (lcm-rational 2/3 2/3)
*2/3
but what about:
>* (gcd-rational 2/3 2/3 2/3)
*2/3
>* (lcm-rational 2/3 2/3 2/3)
*4/9
is that 4/9 the intended result?
Marijn
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v2.0.18 (GNU/Linux)
Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/
iEYEARECAAYFAk7odlMACgkQp/VmCx0OL2xJXgCfRhnUR/GXHs4PoMhVWGGkqdC2
95UAoKGN3/SigQDq5mPX+NO9dzj5Ox+S
=n0HH
-----END PGP SIGNATURE-----