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
Now let's consider the ring Q. Since Q is a field, 1 divides all elements. This implies that 1 is a greatest common divisor of any non-zero x and y. ( ad i) 1 is a divisor of both x and y ad ii) 1 is a divisor of e ) It is therefore not obvious that gcd should be extendend as you suggest. But maybe we can finde another name for the operation? /Jens Axel 2011/12/7 David Van Horn <dvanh...@ccs.neu.edu> > It would be nice if gcd and lcm were extended to rational numbers, which > seems in-line with Scheme's philosophy (but not standards) on numbers. > > (define (gcd-rational . rs) > (/ (apply gcd (map numerator rs)) > (apply lcm (map denominator rs)))) > > (define (lcm-rational . rs) > (/ (abs (apply * rs)) > (apply gcd-rational rs))) > > David > ______________________________**___________________ > For list-related administrative tasks: > > http://lists.racket-lang.org/**listinfo/dev<http://lists.racket-lang.org/listinfo/dev> > -- -- Jens Axel Søgaard
_________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev