-----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----- _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev