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 <[email protected]>
> 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
