gcd

[eddier]

There is an error in the documentation in the code snippets section under Tips and Tricks.

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(gcd a b c ...)

gives the greatest common divisor of two or more integers. A common denominator is the

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(lcm a b c ...)

or least common multiple of two or more integers. The (lcm a b c ...) function could be defined as

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(define-macro (lcm)
  (/ (apply * (args) 2) (apply (gcd_ (args) 2)))


given the (gcd_ auxilary function.



Maybe I should have used the alternative name "gcf," greatest common factor instead of gcd.



Eddie

[Lutz]

I don't get it, can you write down the whole thing? Adding 'lcm' did not work.



Lutz

[eddier]

The documentation says gcd is a "denominator." This is not true. The gcd is the "greatest common divisor" not the "greatest common denominator." There is  no greatest common denominator. For example



A common denominator for 1/4 and 1/3 could be 12. But, someone else could pick 24, and another 48, and so on.



If we want a least common denominator, it is the lcm  or "least common multiple" of the two denominators.



Sorry about the error in the lcm code. The two functions should be coded as follows

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(define (gcd_ a b)
  # gcd auxilary function
  (let (r (% b a))
    (if (= r 0) a (gcd_ r a))))

(define-macro (gcd)
  # return the greatest common divisor of its integer arguments
  (apply gcd_ (args) 2))

(define (lcm_ a b)
  # lcm auxilary function
  (/ (* a b) (gcd_ a b)))

(define-macro (lcm)
  # return the least common multiple of its integer arguments
  (apply lcm_ (args) 2))


[eddier]

Even better, leave out the lcm_ auxilary function and use a lambda.

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(define-macro (lcm)
  (apply (fn (x y) (/ (* x y) (gcd_ x y))) (args) 2))


[Lutz]

Thanks I will add this. At the moment I only cghanged the wording in the title.



Lutz