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SICPゼミ第38回

練習問題2.91

(define (install-polynomial-package)
  ;; 内部手続き
  ;; poly の表現
  (define (make-poly variable term-list) (cons variable term-list ))
  (define (variable p) (car p))
  (define (term-list p) (cdr p))
  (define same-variable? eq?)
  (define variable? symbol?)
  ;; 項と項リストの表現
  (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 (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 (inversion termList)
    (if (empty-termlist? termList)
        termList
        (let ((term (first-term termList)))
          (if (eq? (type-tag term) 'polynomial)
              (adjoin-term
               (make-term (order term)
                          (inversion (coeff term)))
               (inversion (rest-terms termList)))
              (adjoin-term
               (make-term (order term)
                          (mul (make-scheme-number -1) (coeff term)))
               (inversion (rest-terms termList)))))))
  (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 (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 (+ (order t1) (order t2))
                      (mul (coeff t1) (coeff t2)))
           (mul-term-by-all-terms t1 (rest-terms L))))))
  (define (adjoin-term term term-list)
    (if (=zero? (coeff term ))
        term-list
        (cons term term-list )))
  (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
                       (let ((rest (add-terms L1
                                              (inversion
                                               (mul-terms L2 (list (make-term new-o new-c)))))))
                         (div-terms rest L2))))
                  (cons (adjoin-term (make-term new-o new-c)
                                     (car rest-of-result))
                        (cdr rest-of-result))
                  ))))))
  (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: ADD-POLY" (list p1 p2))))
(define (the-empty-termlist) '())
(define (first-term term-list) (car term-list ))
(define (rest-terms term-list) (cdr term-list ))
(define (empty-termlist? term-list) (null? term-list ))
(define (make-term order coeff) (list order coeff ))
(define (order term) (car term ))
(define (coeff term) (cadr term ))
  ;; システムのほかの部分とのインターフェイス
  (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 'div '(polynomial polynomial)
       (lambda (p1 p2) (tag (div-poly p1 p2))))
  'done)

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