What? The greatest common divisor would definitely not divide 1, unless it truly were 1. -Ian ----- Original Message ----- From: "Jens Axel Søgaard" <jensa...@soegaard.net> To: "David Van Horn" <dvanh...@ccs.neu.edu> Cc: "Racket Dev List" <dev@racket-lang.org> Sent: Friday, December 9, 2011 2:04:46 PM GMT -05:00 US/Canada Eastern Subject: Re: [racket-dev] feature request: gcd, lcm for rationals
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 -- -- Jens Axel Søgaard _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
