SICP問題2.95

非整数演算を含んだGCDの動作

(define p1 (make-polynomial 'x '((2 1) (1 -2) (0 1))))
; p1
p1
; (polynomial x (2 1) (1 -2) (0 1))
(define p2 (make-polynomial 'x '((2 11) (0 7))))
; p2
p2
; (polynomial x (2 11) (0 7))
(define p3 (make-polynomial 'x '((1 13) (0 5))))
; p3
p3
; (polynomial x (1 13) (0 5))
(define q1 (mul p1 p2))
; q1
q1
; (polynomial x (4 11) (3 -22) (2 18) (1 -14) (0 7))
(define q2 (mul p1 p3))
; q2
q2
; (polynomial x (3 13) (2 -21) (1 3) (0 5))
(greatest-common-divisor q1 q2)
; (polynomial x (2 1458/169) (1 -2916/169) (0 1458/169))

gcd-termsをトレースするように修正

(define (install-polynomial-package)
  (define (make-poly variable termlist)
    (cons variable termlist))
  (define (variable p) (car p))
  (define (term-list p) (cdr p))
  (define (variable? x) (symbol? x))
  (define (same-variable? v1 v2)
    (and (variable? v1) (variable? v2) (eq? v1 v2)))
  (define (add-terms L1 L2)
    (cond ((empty-termlist? L1) L2)
          ((empty-termlist? L2) L1)
          (else
           (let ((t1 (first-term L1))
                 (t2 (first-term L2)))
             (cond ((> (order t1) (order t2))
                    (adjoin-term 
                     t1 (add-terms (rest-terms L1) L2)))
                   ((< (order t1) (order t2))
                    (adjoin-term
                     t2 (add-terms L1 (rest-terms L2))))
                   (else
                    (adjoin-term
                     (make-term (order t1)
                                (add (coeff t1) (coeff t2)))
                     (add-terms (rest-terms L1) (rest-terms L2)))))))))
  (define (mul-terms L1 L2)
    (if (empty-termlist? L1)
        (the-empty-termlist)
        (add-terms (mul-term-by-all-terms (first-term L1) L2)
                   (mul-terms (rest-terms L1) L2))))
  (define (mul-term-by-all-terms t1 L)
    (if (empty-termlist? L)
        (the-empty-termlist)
        (let ((t2 (first-term L)))
          (adjoin-term
            (make-term (add (order t1) (order t2))
                       (mul (coeff t1) (coeff t2)))
            (mul-term-by-all-terms t1 (rest-terms L))))))
  (define (adjoin-term term termlist)
    (if (=zero? (coeff term))
        termlist
        (cons term termlist)))
  (define (the-empty-termlist) '())
  (define (first-term termlist) (car termlist))
  (define (rest-terms termlist) (cdr termlist))
  (define (empty-termlist? termlist) (null? termlist))
  (define (make-term order coeff) (list order coeff))
  (define (order term) (car term))
  (define (coeff term) (cadr term))
  (define (div-terms L1 L2)
    (if (empty-termlist? L1)
        (list (the-empty-termlist) (the-empty-termlist))
        (let ((t1 (first-term L1))
              (t2 (first-term L2)))
          (if (> (order t2) (order t1))
              (list (the-empty-termlist) L1)
              (let ((new-c (div (coeff t1) (coeff t2)))
                    (new-o (- (order t1) (order t2))))
                (let ((rest-of-result
                       (div-terms 
                        (add-terms L1 
                                   (negate-termlist (mul-terms (list (make-term new-o new-c)) L2)))
                        L2)
                       ))
                  (list (add-terms (list (make-term new-o new-c))
                                   (car rest-of-result))
                        (cadr rest-of-result))
                  ))))))
  (define (gcd-terms a b)
    ; トレースするために以下を追加
    (display (list 'parameters a b))
    (newline)
    (if (empty-termlist? b)
        a
        (gcd-terms b (remainder-terms a b))))
  (define (remainder-terms a b)
    (cadr (div-terms a b)))
  (define (add-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
        (make-poly (variable p1)
                   (add-terms (term-list p1)
                              (term-list p2)))
        (error "Polys not in same var -- ADD-POLY"
               (list p1 p2))))
  (define (mul-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
        (make-poly (variable p1)
                   (mul-terms (term-list p1)
                              (term-list p2)))
        (error "Polys not in same var -- MUL-POLY"
               (list p1 p2))))
  (define (div-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
        (make-poly (variable p1)
                   (div-terms (term-list p1)
                              (term-list p2)))
        (error "Polys not in same var -- DIV-POLY"
               (list p1 p2))))
  (define (gcd-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
        (make-poly (variable p1)
                   (gcd-terms (term-list p1)
                              (term-list p2)))
        (error "Polys not in same var -- GCD-POLY"
               (list p1 p2))))
  (define (=zero-poly? L)
    (define (=zero-term? x)
      (or (empty-termlist? x)
          (if (=zero? (coeff (first-term x)))
              (=zero-term? (rest-terms x))
              #f)))
    (=zero-term? (term-list L)))
  (define (negate-termlist L)
    (if (empty-termlist? L)
        L
        (let ((f (first-term L))
              (r (rest-terms L)))
          (adjoin-term
           (make-term (order f)
                      (negate (coeff f)))
           (negate-termlist r)))))
  (define (sub-poly x y)
    (add-poly x 
              (make-poly (variable y)
                         (negate-termlist (term-list y)))))
  ;; システムの他の部分とのインタフェース
  (define (tag p) (attach-tag 'polynomial p))
  (put 'add '(polynomial polynomial)
       (lambda (p1 p2) (tag (add-poly p1 p2))))
  (put 'mul '(polynomial polynomial)
       (lambda (p1 p2) (tag (mul-poly p1 p2))))
  (put 'make 'polynomial
       (lambda (var terms) (tag (make-poly var terms))))
  (put '=zero? '(polynomial)
       (lambda (x) (=zero-poly? x)))
  (put 'negate '(polynomial)
       (lambda (x) (tag (make-poly (variable x)
                                   (negate-termlist (term-list x))))))
  (put 'sub '(polynomial polynomial)
       (lambda (p1 p2) (tag (sub-poly p1 p2))))
  (put 'div '(polynomial polynomial)
       (lambda (p1 p2) (tag (div-poly p1 p2))))
  (put 'greatest-common-divisor '(polynomial polynomial)
       (lambda (x y) (tag (gcd-poly x y))))
  'done)
(install-polynomial-package)
(define (make-polynomial var terms)
  ((get 'make 'polynomial) var terms))

テスト

(greatest-common-divisor q1 q2)
; (parameters ((4 11) (3 -22) (2 18) (1 -14) (0 7)) ((3 13) (2 -21) (1 3) (0 5)))
; (parameters ((3 13) (2 -21) (1 3) (0 5)) ((2 1458/169) (1 -2916/169) (0 1458/169)))
; (parameters ((2 1458/169) (1 -2916/169) (0 1458/169)) ())
; (polynomial x (2 1458/169) (1 -2916/169) (0 1458/169))