SICP問題2.88

多項式システムを減算ができるように拡張する。(汎用符号反転演算を定義して行う)

符号を反転する汎用演算子を追加

(define (negate x) (apply-generic 'negate x))

scheme-number-packageの修正

(define (install-scheme-number-pacakge)
  (define (tag x)
    (attach-tag 'scheme-number x))
  (put 'add '(scheme-number scheme-number)
       (lambda (x y) (tag (+ x y))))
  (put 'sub '(scheme-number scheme-number)
       (lambda (x y) (tag (- x y))))
  (put 'mul '(scheme-number scheme-number)
       (lambda (x y) (tag (* x y))))
  (put 'div '(scheme-number scheme-number)
       (lambda (x y) (tag (/ x y)))) ; 2009/11/16 +になっていたので/に修正
  (put 'make 'scheme-number
       (lambda (x) (tag x)))
  (put '=zero? '(scheme-number) 
       (lambda (x) (= x 0)))
  ; 追加
  (put 'negate '(scheme-number)
       (lambda (x) (tag (- x))))
  'done)
(define (make-scheme-number n)
  ((get 'make 'scheme-number) n))
(install-scheme-number-pacakge)

polynomial-packageの修正

(define (install-polynomial-package)
  ;; 内部手続き
  ;; 多項式の表現
  (define (make-poly variable term-list)
    (cons variable term-list))
  (define (variable p) (car p))
  (define (term-list p) (cdr p))
  (define (variable? x) (symbol? x))
  (define (same-variable? v1 v2)
    (and (variable? v1) (variable? v2) (eq? v1 v2)))
  ;; 項とリストの表現
  ; 多項式の輪のリストを構成する手続き
  (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)))))))))
  
  ; 二つの多項式の乗の項リスト
  (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 term-list)
    (if (=zero? (coeff term))
        termlist
        (cons term term-list)))
  (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))
  (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 (=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)))
  ;; 追加
  (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)))
  ;; 追加
  (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))))
  'done)
(install-polynomial-package)
(define (make-polynomial var terms)
  ((get 'make 'polynomial) var terms))

テスト

(negate (make-scheme-number 5))
; -5
(negate (make-polynomial 'X '((5 3) (4 2) (3 2))))
; (polynomial X (5 -3) (4 -2) (3 -2))
(sub (make-polynomial 'X '((5 3) (4 2) (3 2)))
     (make-polynomial 'X '((6 4) (4 3) (2 2))))
; (polynomial X (6 -4) (5 3) (4 -1) (3 2) (2 -2))

OK