math.lsp

#|

Portions of this file are:

Copyright (c) 1989-94 Massachusetts Institute of Technology

This material was developed by the Scheme project at the Massachusetts
Institute of Technology, Department of Electrical Engineering and
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to inform MIT of noteworthy uses of this software.

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(define (gcd . integers)
  (fold-left gcd2 0 integers))

(define (lcm . integers)
  (fold-left lcm2 1 integers))

(define (gcd2 n m)
  (let loop ((n n) (m m))
    (cond ((not (zero? m)) (loop m (remainder n m)))
	  ((negative? n) (- n))
	  (else n))))

(define (lcm2 n m)
  (if (or (zero? n) (zero? m))
    0
    (quotient (let ((n (* n m)))
		(if (negative? n)
		  (- n)
		  n))
	      (gcd2 n m))))

(define (fold-left procedure initial olist)
  (let fold ((initial initial)
	     (list olist))
    (if (pair? list)
	(fold (procedure initial (car list))
	      (cdr list))
	(begin
	  (if (not (null? list))
	      (error "wrong-type-argument ~S" olist))
	  initial))))