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