# [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 <dvanhorn at 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
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--
--
Jens Axel Søgaard
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